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Charging behavior of polyamines in solution and on

1. Figure 1 5 The degassing apparatus Figure 1 6 photo of the Jonction titration setup 14 1 4 Materials The burette solutions are HCl 0 25 M prepared form 1 M solution Merck Titrisol KOH 0 25 M prepared from 1 M solution J T Baker KCl 3 M prepared from pure salt p a Acros Organics and pure decarbonated water The concentrations of the burette solutions can be varied according to the pH range of interest ionic strengths range burette precision or some other preference The reported concentrations were found to be the most convenient for all the titrations performed during this work For all the solutions the Millipore water from the Millipore A 10 deionization and purification system was used from which the CO was removed through boiling This procedure consists of boiling the water for 5 10 min and then cooling it under pure nitrogen atmosphere 1 5 Experimental procedure The typical experiment is performed in the following manner First the analyte is added to the titration cell which is then closed The electrodes and all the tubings were flushed with Millipore water rinsed with soft paper and mounted to the cell Then the titration software is launched The experiment is fully controlled by the software and from this point the manual control over the burettes is disabled First the initial solution is automatically dosed to the titration cell
2. Nmin Q m 1 6 Nmax Nmin where n denotes the charge number of a dissociation species Nmin and Nmar are the minimum and maximum charge numbers respectively for acids n is negative and for bases it is positive The total concentration is given by X So Xa 1 7 To be able to compare the concentrations of species in different solutions the relative concentrations X X o have to be used The pH scale and the ionic product of water K are defined as pH log a and 1 8 Kw ap Aon 1 9 The electroneutrality condition is one of the most important concepts for resolving the speciation in water solutions 8 It states that the net charge of the solution as a whole equals zero X n X H OH 0 1 10 where X is the analytical concentration of a species X For example if the solution contains HCl KOH and KCl the electroneutrality condition reads H Kt OH7 C17 0 1 11 H Acidity and OH Alkalinity are two quantities which will be useful for the calculation of the proton binding isotherms The H Acidity H Acy is the excess concentration of the protons with respect to their concentration in a neutral solution For example in a solution of acetic acid KOH and HCl the H Acidity is H Acy H OH CH3 COO7 C17 K 1 12 Conversely the OH Alkalinity OH AlIk is the negative H Acidity for example OH Al
3. A 2 f dt T A2 The input global parameters for this subroutine are the drift criterion drift crit drift monitoring interval T first and second data acquisition in terval A and A2 and the maximum waiting time TO drift Dynamic mode addition calculation SV Dynamic Disp_d vi The dose of a titrant is calculated from the two recent points in the titration curve by using the formula Catt ApH Vo sn Vi pH pH addititon A 3 where V2 Vi pH and pH are the volumes and the pH values of the two most recent data points respectively see figure A 13 The attenuation constant catt was introduced to decrease the overshootings that cause a lower data density before the equivalence point Conversely undershooting and consequent accu mulation of data points appear after the equivalence point Therefore cai has to be assigned the highest possible value but which still sufficiently attenuates the overshooting usually 0 7 0 8 is a good choice but this depends on the concen trations of the solutions in the burettes The method is depicted in figure A 14 Input global parameters The aimed pH increment Dyn_delta_E attenuation factor C_slope Calculation of the dosages for the initial solution In this subroutine the initial volumes of the acid Va base Vb salt Vs and water Vw are cal 172 overshooting aimed ApH 0 28 0 32 0 36 0 40 V KOH ml Figure A 14 Dy
4. surface charge Cm c surface charge Cm D electrophoretic mobility a N S 10m D o 1 A 6 Q electrophoretic mobility 1 s N aval m 10 b j gt Figure 4 9 Proton binding isotherms a d and pH dependence of the elec trophoretic mobility e h of carboxylated latex suspension in the presence of pPDADAMAC pDADMAC loadings 0 15mg m a e 0 40mg m b f 0 65mg m c g 0 84mg m d h Ionic strengths o 0 01M O 0 05M A 0 10M V 0 25M 1 00M The lines in the figures e d represent the the modified Stern model predictions parameters listed in table 4 5 The lines in figures e h represent the O Brien and White model prediction shear plane distance listed in table 4 5 106 Table 4 4 The shear plane distances obtained by fitting the experimental elec trophoretic mobilities according to the O Brien and White theory 81 pDADMAC loading mgm 0 15 0 40 0 65 0 84 shear plane distance nm 0 20 0 30 0 32 0 40 4 6 Discussion The adsorption isotherms from the batch experiments figure 4 6 at pH 10 are showing a high affinity equilibrium adsorption behavior of pDADMAC at the carboxylate latex surface Small deviations from this behavior are possibly due to a fact that the equilibrium was not reached High affinity adsorption is a regime where the adsorption is qu
5. 200 kDa was purchased from Aldrich Cat No 26062 79 3 The car bon and nitrogen content and the mass percentage of the purchased solution have been verified by the total carbon and nitrogen analysis and were found to agree with the formula The solution was used without any further purification and was diluted to give the necessary concentration 90 The sample of carboxyl sulfate latex particles was kindly supplied by the BASF company The diameter of the particles and the polydispersity measured with atomic force microscopy AFM are 190 nm and 25 3 respectively Static and dynamic light scattering measurements of the particle diameter resulted in a value of 250 nm The difference between the values measured with AFM and light scattering is due to the fact that the diameter measured by light scattering is intensity weighted 80 The surface area of the pure particles calculated from the AFM measurement and taking the polydispersity into account is 27 3m gt Prior to the experiments the particles were dialyzed against the Milli Q water which was daily exchanged until the conductivity of the outer batch water was below 1 1uScm For this dialysis membranes Spectra pore pore size of 500 kDa have been used The water from which the CO was removed by boiling was used for the preparation of all the solutions The burette solutions for the potentiometric titrations were prepared from CO 2 free KOH Baker Dilut it
6. controls The input of concentrations of 162 the strong acid strong base and salt solutions that were added to the cell prior to the titration experiment 3 V sample control Input of the total volume of all the components added to the cell prior to the titration experiment including water and weak electrolytes 4 Added solid salt The control for input of the moles of solid 1 1 salt added to the cell prior to the experiment 5 message If a value smaller than 0 has been entered in the above controls an error message will be indicated 6 Sample led indicator Flashes if an entry was made in the above controls 7 OK button Triggers quitting from the subroutine Burette assignment prod_assign vi In this subroutine acid base salt or water can be assigned to each burette The burette numbers are defined by their VISA addresses in LabView every external device has to be assigned a logical address which are in turn related to the ports where they are connected It is logical that one keeps the order of the burettes at the bench in the sequence of their visa addresses such that burettel is the one on the left and burette4 the one on the right side However it does not matter which solution is contained in which burette as long as all of them are different This was done in order to provide the freedom for the user to exchange the upper units of the burettes without having to inte
7. o U Le titrateur Jonction r alis e avec et sans la substance analys e L valuation de la charge se base sur une soustraction de l acidit de solution blanc l acidit de solution contenant la mol cule analys e Une normalisation de la charge par la charge maximale donne le degr de protonation et la d pendence de ce dernier avec le pH est nomm e l isotherme de liaison des protons L interpr tation des courbes de titration du blanc est effectu e avec une fonction analytique dont les param tres sont obtenus par r gression non lin aire Cette proc dure nous permet de v rifier les conditions d exp rience En outre la pr cision exp rimentale est verifi e en analysant les substances standards dont les valeurs de pK apparaissent dans la litt rature en particulier l acide ac tique et l thyl ne diamine De tr s satisfaisants r sultats exp rimentaux ont mis en vidence une grande pr cision de mesure avec des valeurs de pK tr s proches des valeurs th oriques Dans le deuxi me chapitre la m thode pot ntiom trique est mise en uvre pour analyser le comportement lectrostatique du dendrim re poly amidoamine La structure chimique de cette mol cule est represent e sur la figure la page il suivante Un m canisme de protonation est propos il se base sur un traitement statistique de toutes les esp ces provenant de la protonation Ceci inclut une distinction des esp ces macroscopique
8. 88 Basic Stern model Modified Stern model p z N P ie Zz Z T K T CP T N ads N ToCCOO7 y z Z y z E gt gt ge a T wee a d om et a diffuse layer diffuse layer Yo Ya Yo Ya Figure 4 2 Basic Stern model left and the extension of that model for the specifically adsorbed ions right Presented are the charge density distributions top and the corresponding electrostatic potentials bottom with respect to the axis normal to the surface 89 hand the surface charge is governed by the surface protonation equilibria COOH Ht COO 4 4 The corresponding deprotonation constant is me 120007 K T COOH exp qWo kT 4 5 where Wo is the potential at the surface in the plane of the surface bound pro tons Adsorbed pDADMAC sites are considered as completely dissociated so that pDADMAC sites are carrying a pH independent positive charge In the Stern model a potential drop between the 0 plane and the d plane is allowed such that 00 bo Va where Cy is the Stern layer capacitance which can be related to the distance Cs 4 6 between the surface and the diffuse layer plane 0 r d 4 7 The surface potential and the surface charge can be found numerically by solving equations 4 1 4 6 4 3 Experimental Poly dimethyl diallylammonium chloride pDADMAC of molecular weight 100
9. Diaphragm resistance 0 4 0 9 kQ The performance of the electrode couple is measured by the stability of the reading expressed as the drift and the time needed for equilibration after an abrupt change in pH of the medium A satisfactory drift value is about 2 x 1074 pH units per minute ca 0 1 mV min This drift criterion should normally be achieved within no more than 5 minutes except in the region around pH 7 where the drifts are usually larger and the equilibration time longer While the above electrodes have shown good performance in solutions of simple acids or bases their lifetime is becoming considerably shorter if they are used in suspen sions The problem usually arises from the deposition of the particles or polymers at the glass electrode surface and at the ceramic diaphragm which is the electric 141 contact of the reference electrode with the outer solution This is very pronounced in the systems containing polyelectrolytes or colloidal particles and even more in their mixtures Generally the glass electrode is usually conditioned with HCl 100 However in the case when the electrodes were immersed into particle suspensions there is no common way of conditioning but it rather depends on the composition of the suspension As a rule of a thumb a good approach is to tune the pH of the con ditioning solution in order to achieve the conditions where the electrode charge is similar to the charge of the particle I
10. to display TI INA 116 amplifier Filter 50 Hz A D Converter Microcontroller Microchip TC 514 Microchip PIC Figure A 2 Scheme of the signal processing by the HighImp4 instrument Jonction titrator As a difference to the Wallingford titrator the Microlink 3200 interface was elimi nated from Jonction titrator setup Therefore a voltmeter that communicates di rectly with the PC through a RS232 connection was constructed by Mr Stephane Jeannerret The communication between the burettes and the PC is established directly by using the RS232 connections as well Except for the drivers and some simple supporting routines for the burettes which were found on the web page of National Instruments http www ni com support all the necessary software was originally developed in the Labview programming language By the time of this manuscript the PC control of the conductivity meter reading and the stirrer were not included in our setup A scheme of our new setup is presented in chapter 1 Hardware Highimp4 instrument HighImp4 is an instrument which embeds a high impedance voltmeter and an A D converter The instrument was developed by Mr Stephane Jeannerret at the Department of inorganic analytical and applied chemistry at the University of Geneva All the technical details about this device and the according low level Labview programs drivers can be found in 101 The signal processing by this instrument is depicted in figure A
11. HCl Merck Titrisol and KCl Merck p a For the pH measurements during the sample preparations a combined glass electrode purchased from Metrohm AG and a standard pH meter Metrohm 691 were used The potentiometric titration experiments were performed with pDADMAC latex mixtures at five different pDADMAC loadings see table 4 3 The final concentration of the latex was 10 g L in all experiments About 20 g of a 47 g L latex stock solution was first mixed with pDADMAC stock solution and the mixture was adjusted to pH 10 The total amount of titrated latex particles is determinant for the accuracy of the charge determination from the potentiometric titration see chapter 1 The total titratable charge calculated from the latex loading is 0 16 mmol which means that the error of the charge determination is lower than 2 The mixture was then shaken head over head for cca 2 minutes and the pH was adjusted again Samples prepared in this way were then subjected to potentiometric titration experiments Potentiometric titrations were performed with the Wallingford Titrator 16 91 Table 4 1 Sample preparation for the titration experiments Additions of the pDADMAC stock solution 750 mg L to 20 g of 47 g L latex suspension pDADMAC loading mgm 0 15 0 40 0 65 0 85 1 00 additions pDADMAC stock solution 8 5 0 13 9 21 5 29 0 344 for a description of the automated titrators see appendix The experimental set up consists
12. followed by the adjustment of the ionic strength to the pre defined initial value 92 After that the initial conditions are achieved pH 3 and J 10mM Then titration to pH 11 is performed with a pH step of 0 4 units which is kept constant see see fig A 5 in the appendix This is followed by a backward titration to pH 3 with constant dosages of 0 2mL of HCl In the dynamic titration mode the consecutive additions of acid or base are being calculated according to the pre defined step in pH The titrations of the mixture were performed in a rapid manner in order to avoid the slow processes that were observed through long equilibration times and high drifts up to 1mV min after three minutes of the electrode signal These processes could possibly be desorption or conformational changes of the adsorbed pDADMAC Rapid means that the maximum waiting time between the readings was 3 minutes in the case that the drift criterion of 0 1mV min was not achieved sooner Still for high pDADMAC loadings and in a narrow pH region the drifts after 3 minutes were observed to be in the order of 5mV min The pH region of such high drifts seems to be reproducible for a certain loading Each addition of acid or base is followed by the ionic strength adjustment through an addition of KCl buret solution or water After such a forth and back titration cycle the ionic strength is increased The above procedure has been repeated until all titra
13. isotherms An overall charge will be attributed to the protonation sites of silica thus the exact speciation will not be discussed 5 2 Experimental Stober silica particles were kindly supplied by the Nippon Shokubai company Japan The particles were obtained as powder which was pre treated by heating 117 500 nm Figure 5 1 The transmission electron micrograph of the heated silica particles which were used for the titrations at 800 C for 24 hours This procedure was reported as useful for elimination of the microporosity of Stober Silica particles 90 91 After the heating treatment the particles were suspended in MilliQ water to give a 10 by weight stock suspension The suspension was sonicated 4 x 15 min and shaken in between sonication Figure 5 1 is a transmission electron micrograph of the particles after the heating treatment The micrograph is showing that the particles are fairly spher ical and monodisperse From the TEM the particles have a radius of 64nm The hydrodynamic radius calculated from TEM is 66 5nm The hydrodynamic radius measured with dynamic light scattering equals 69nm The surface area calculated from the diameter measured with TEM equals 24 3 m g7 The BET surface area equals to 32 0m g7 The 0 2 by weight stock solutions of high molecular mass 400 500 kDa and low molecular mass 100 200kDa poly dimethyldiallylammonium chloride pDADMAC were prepared with MilliQ water
14. this process can be related to several factors The first is probably the natural abundance of silica which can act as a carrier of the natural organic substances and small molecules 8 Another example of application of silica particles is the preparation of microcapsules by layer by layer adsorption of oppositely charged polyelectrolytes 7 Silicon wafers with a surface oxide layer are suitable for measurements like reflection infrared spectroscopy total or attenuated or ellip sometry Adsorption studies have been carried out with various strong 67 97 or weak 83 polyelectrolytes or polyampholytes 98 Particularly interesting for the present chapter are the potentiometric titration studies carried out by Shubin 66 67 where the surface charge was related to the conformation of the adsorbed polyelectrolyte The proton binding isotherms obtained in the present study will be inter preted in the same way as was presented in the previous chapter The dissolved charge will be subtracted from the added amount of quaternary amine sites in order to obtain the adsorbed charge which has an influence on the electrostatic potential at the origin of the silica surface Wo where the protonation sites are situated According to the MUSIC the sites can be singly or doubly coordinated with oxygen 77 In this chapter the modified Stern model as presented in the previous chapter will be used in order to fit the experimental proton binding
15. 1 3 Fitting of the burette endings which prevents leakage or and contact with air embedded in one housing HighImp4 instrument The communication of the voltmeter unit with the PC is established by means of a Labview based software Jonction titrator can use any kind of standard Metrohm titration cells with double walls for thermostating These cells usually have a volume of ca 200 mL with a minimum solution volume for the electrodes to be immersed of ca 90 mL However a substantial increase in the solution volume may occur during the constant ionic strength titrations Moreover one might want to perform several successive titrations at different ionic strengths without changing the sample In that case salt additions between the titration runs are necessary and the total volume of the cell content may vary substantially depending on the investigated pH range and the ionic strengths At the same time the electrodes have to be immersed even into small volumes Therefore construction of a custom titration cell is recommended with a design that allows titrations of small samples and a big volume increase during the experiment without overflowing the cell We have designed a double wall plexiglas titration cell which allows a range in volume between 45 and 450 mL see figure 1 4 The newly designed titration cell is fitted with a standard Metrohm titration cell lid e g 6 1414 010 from which the clamp part has to be cut away Degas
16. 37 and capillary electrophoresis 38 The most abundant physico chemical studies are those of poly propylene imine PPI dendrimers 28 33 35 37 and poly amidoamine PAMAM dendrimers see Fig 2 1 26 27 29 31 41 In both cases these dendrimers can accumulate positive charge by protonation of the primary amines at the rim and the tertiary amines in the interior Their charge is thus pH dependent whereby they are 37 positively charged at low pH and neutral at high pH The charging mechanisms of poly amidoamine and poly propyleneimine dendrimers will be presented in chapter 3 In the present chapter the aim is to discuss experimental potentiometric titration data for poly amidoamine den drimers The interpretation of the proton binding isotherms will be presented in terms of a site binding model which can be used to infer both the macroscopic and microscopic protonation mechanisms After introducing the model the most important relations for the macroscopic interpretation will be put forward The overall proton binding isotherms and the protonation macroconstants calculated by means of the site binding model will be compared with the experimental pro ton binding isotherms and the macroscopic protonation constants obtained by direct fitting of the isotherms 2 2 Macroscopic protonation equilibria in poly electrolyte solutions The macroscopic protonation equilibria of polyelectrolytes is equivalent to the protonatio
17. Figure 1 8 Titration curves and charging curves of acetic acid o titration curves LJ charging curves Open symbols forward titration runs Closed sym bols backward titration runs 0 0 2 D O e 0 5 x nee ry a 1 0 06 s 1 5 a O A DA 5 aa oO 2 0 8 D 2 02 2 5x10 0 0 Figure 1 9 The charging curve of acetic acid multiplied with the total volume of the solution o forward titration run e backward titration run 19 titrant volume EMF V or Vp can be obtained from the electroneutrality condi tion for the blank solution 1 16 The right hand part can be expressed through the volumes of the added strong acid and base and the total volume of the system Va Vb Vi and the burette concentrations of these solutions ca cy AU PT 10PH PKvw H Acy plank Lure 1 17 V4 yH YOu Here the concentrations of the Ht and OH ions are expressed through pH Kw and the activity coefficients according to the definition of pH 1 8 and the ionic product of water 1 9 As an approximation we can use the common activity coefficient yy You 7 which accounts for the non ideal behavior of ions 18 and obtain ave T V 1 E C b _ 10 pH _ 10P4 PE 1 18 H Acy biank The pH of the solution can be expressed through the experimentally measured EMF assuming the linear relationship EMF E5 A pH 1 19 In the above expressions the experimentally
18. Figure 3 8 The microscopic mechanism of the first generation poly amidoamine dendrimer The most important microspecies are presented for several distin guished macrospecies denoted with m see figure 3 7 A probability is assigned to each microspecies and the micro pK values are assigned to the unprotonated sites 68 poly propyleneimine dendrimers are similar For example at m 9 there is the same most probable microspecies with the primary and one innermost ter tiary groups protonated Another similarity is that at m gt 9 neither of the two mechanisms does exert clearly predominant species As the number of the possible microstates grows as 2 the computation of the detailed microscopic mechanisms which requires calculation of the free energy for all the microstates is becoming increasingly consuming in terms of computation time with an increasing generation number In fact for generations higher than the second this computation was not possible with the 1 7 GHz CPU and 512 MB RAM PC However the proton binding isotherm can be predicted by using a recursive approach 43 The sites are divided into repeating blocks for which the model can be solved explicitly The protonation patterns for the blocks are assumed to be conserved when considering the whole molecule In spite of the fact that detailed mechanisms for the higher generations of dendrimers were not calculated the prediction of the most prominent species can be do
19. Les esp ces participant l change des protons avec l eau peuvent tre libres dans la solution pr sentes sous la forme d un poly lectrolyte ou encore se situer une interface Au cours de la th se un titrateur automatique compl tement command par ordinateur a t assembl dans l atelier d lectronique du d partement Les programmes pour effectuer les titarages potentiom triques forces ioniques con stantes ont t mis en uvre Le titrateur est compos de quatre burettes de haute pr cision d une cellulle permettant une grande augmentation du volume de la solution d un voltm tre de haute imp dance d un couple d lectrodes pour la mesure du pH lectrode de verre et une lectrode de r f rence Ag AgCl et d un syst me de d gazage par l azote Un convertisseur analogique digital a t incorpor avec le voltm tre Le nouveau titrateur Jonction est repr sent sur la figure la page suivante et d crit dans l annexe de la th se Dans le premier chapitre sont pr sent es la m thodologie exp rimentale ainsi que l analyse des donn es pour une valuation de la charge pr sente sur une mol cule subissant l change de protons avec l eau Pour obtenir les donn es de l acidit en fonction du pH un titrage est effectu e durant lequel les volumes des solutions ajout es HCl KOH KCl et le pH sont mesur s L exp rience est voltmeter A D converter LUN
20. Microscopic protonation mechanisms of dendrimers 3d Inbr dnelion s i sa sss 6s 2a SRI be ES we we oe ad 3 2 Microscopic protonation equilibria 3 3 Protonation behavior of hyperbranched polyamines 3 4 Poly amidoamine vs poly propyleneimine dendrimers 3 5 Poly propyleneimine dendrimer with ethylenediamine core 2 3 dendrimer e eis acu He Re Pee ea 3 6 Conclusion 4 pDADMAC carboxylated latex AT AOTOMONON oc 24 RUES ed Sedan eee 4 2 Extension of the Basic Stern model 4 3 Experimental 22425442284 e444 04444 6424 AA Data treatment e se c stes eo stes e he RES RES ES A5 Resuli ere Gare deck Be soia Ese wrk BG SO a a eee ee a AU Dino 5 2 26d 2 6 amp oo o 658 o 4 S986 so se re 4 7 Conclusion 5 pDADMAC silica Bel TRO RS ooh 8 a ooh oe oe oe EES 5 2 Experimental L 242 She a eee a ae da ee dE aa 5 3 Data treatment and results s 4 4e bo ee 4 8 de SS DA DISCUSSION oe dus gins to eee te a ee 4 5 5 Conclusion Conclusions A Automated potentiometric titrator Acknowledgements R sum La m thode des titrages potentiom triques est utilis e pour les tudes du com portement lectrostatique des poly lectrolytes ou des interfaces collo dales en milieu aqueux Le titrage potentiometrique nous permet de mesurer la charge provenant des reactions acide base
21. Pr tonation microst te lt s lt a ewo sa es sa 2a 6 eS Chemical structures of the poly propyleneimine and 2 3 den driers sasis AS e eae e dr a o a res D eaa G Sg Cluster parameter assignment for the poly propyleneimine den dre S e rea a eh oe Dei Rl eK OS Re BALE Re RG Proton binding isotherms of the first five generations of the poly amidoamine and poly propyleneimine dendrimers Macrospeciation diagram of the zeroth generation poly amidoamine dendrimer Macrospeciation diagram of the zeroth generation poly propyleneimine dendrimer The macrospeciation diagrams for the first generation poly amidoamine and poly propyleneimine dendrimers The microscopic mechanism of the first generation poly amidoamine dendrimer The microscopic mechanism of the first generation poly propyleneimine dendrimer The most important microspecies of the fourth generation poly amidoamine and poly propyleneimine dendriemrs The proton binding isotherms of the first five generations of 2 3 dendrimers wcs a aTe keke Ge kb be Mr be Ba BS 180 46 48 99 99 61 63 64 65 67 68 70 73 75 3 12 The macroscopic speciation diagrams of the zeroth generation 2 3 de drim t 4 4 siae a a oe ee eo ee A 2 im 76 3 13 The microscopic mechanism of the first generation 2 3 dendrimer 77 3 14 The most prominent microspeci
22. Science 277 1232 1237 1997 Stumm W and Morgan J J Aquatic Chemistry John Wiley and Sons New Vork 1996 Hill T L Statistical Thermodynamics Dover New York 1986 Atkins P W Physical Chemistry Oxford University Press Oxford 1994 185 11 12 13 14 15 16 17 18 19 22 i 23 24 Smith R M and Martell A E Critical Stability Constants volume 6 Plenum Press New York 1989 Contescu C Jagiello J and Schwarz J A Langmuir 9 1754 1756 1996 Miyake S Talanta 13 1253 1966 Avdeef A Analytical Chemistry 50 2137 2142 1978 Toren E C Jr Analytical Chemistry 40 402R 413R 1968 Kinniburgh D G and Milne C J Guide to the wallingford titrator Tech nical British Geological Survey 1992 Nag fortran library mark 18 1997 Baes C F Jr and Mesmer R E The Hydrolysis of Cations Krieger Malabar 1986 Press W H Teukolsky S A Vetterling W T and Flannery B P Nu merical Recipes in Fortran Cambrige University Press Cambridge 1986 Gans P and O Sullivan B Talanta 51 33 37 2000 Sun L and Crooks R M Journal of Physical Chemistry B 106 5864 5872 2002 V gtle F Gestermann S Hesse R Schwierz H and Windisch B Progress in Polymer Science 25 987 1041 2000 Ottaviani M F Monalti F Romanelli M Turro N J A and Tomalia D Journal of Physical Chemistry B 100 11033 11042 1996 Haensler J and Szoka F C Bi
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24. acetic acid The determined pK values are within 0 03 units from the values reported in literature The blank titration curve parame ters include the concentrations of the strong acid and base in the burettes the slope and offset of the electrode reading versus pH the common activity coef ficient of Ht and OH ions and the dissociation product of water A study of the correlations between these parameters has shown that the common activity coefficient one of the burette reagent concentrations and one of the electrode parameters are reasonable for fitting The fitted common activity coefficients have shown to be in agreement with the predictions of the Davies formula As 131 well the blank titration curves were used to verify the titration baselines which are showing the carbonate content in the titrated system The amount of the dissolved carbon dioxide was reduced to less than 1075 moldm by a careful preparation of reagents and degassing with purified nitrogen The potentiometric titration study of the protonation of poly amidoamine dendrimers is presented in chapter 2 The proton binding isotherms of the high generations are showing two steps at 7 5 lt pH lt 10 and 4 lt pH lt 7 and an intermediate plateau at 7 lt pH lt 8 with the degree of protonation of 1 2 It was shown that the proton binding isotherms can be very well interpreted with a site binding model which includes the microcopic protonation constants and the
25. adjustments In the constant ionic strength mode this sub routine is called after each acid or base addition It calculates and doses the salt Vs or water Vw additions needed to correct for the ionic strength changes The formulas for the calculation are I Vt cs Vst csin Vsin ns 10 sum Vs sq A 10 sum ca Va cain Vain cb Vb cb_in Vb_in abs A 11 abs ca Va ca in Va in cb Vb cb_in Vb in A 12 Vw snl Vt A 13 suml ca Va cain Vain cb Vb cbin Vbin abs 2 cs Vst 2 csin Vsin 2 ns 10 A 14 Input global parameters Ionic strength 176 Acknowledgements I dedicate this thesis to my parents Special thanks to prof Michal Borkovec for all his support As well I would in particular like to thank the following people whose help was invaluable Mr St phane Jeannerret Dr C cile G hin Delval Dr Jorg Kleimann Dr Claire Chassagne Dr Motoyoshi Kobayashi Mr Francois Bujard All the guys from the group for discussion support and friendship Last but not least 177 List of Figures igl 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 Acetic acid proton binding isotherm Scheme of the Jonction titrator 4 2 6 2s 68 6 be ee EE Ble Bry Fitting of the burette endings The tiation ll 2 3 24 V4 4 Re ER dae he da eae a ee The deg
26. and calculated from the site binding model at different ionic strengths The error of the presented values is lt 0 03 units 0 1M 0 5M 1 0M m fit model fit model fit model 1 9 70 9 59 9 83 9 78 9 98 9 87 2 9 26 9 17 9 47 9 36 9 55 9 45 3 8 74 8 82 8 99 9 01 9 10 9 10 4 8 31 8 39 8 61 8 59 8 73 8 68 5 6 68 6 67 7 13 7 03 7 34 7 32 6 3 15 3 21 3 65 3 57 3 91 B87 Figure 2 4 Cluster parameter assignment for the poly amidoamine dendrimer 48 Table 2 3 Comparison of macroscopic ionization constants pK of the PAMAM dendrimer G1 from direct fit of the titration curves and calculated from the site binding model at different ionic strengths The error of the presented values is lt 0 03 units 0 1M 0 5M 1 0M m fit model fit model fit model 1 9 95 9 85 10 02 10 78 10 16 10 15 2 9 70 9 50 9 87 9 72 9 76 9 79 3 9 25 9 25 9 47 9 47 9 76 9 54 4 9 19 9 05 9 34 9 27 9 28 9 34 5 8 78 8 86 9 08 9 08 9 21 9 15 6 8 68 8 65 8 92 8 88 9 07 8 95 7 8 30 8 41 8 57 8 64 8 60 8 72 8 7 96 8 07 8 29 8 30 8 47 8 39 9 7 10 7 06 7 43 7 44 7 50 7 68 10 6 36 6 35 6 91 6 81 7 21 7 00 11 5 95 5 96 6 33 6 43 6 39 6 61 12 5 55 6 61 6 17 6 08 6 56 6 27 13 5 10 5 18 5 52 5 66 5 59 5 84 14 3 07 3 20 3 51 3 57 3 66 3 86 49 be used While these parameters cannot be uniquely determined from a single titration curve they can be obtained by a simultaneous fit of GO and G1 data The interaction parameters are 0 15 and 2 85 At this poin
27. au pH On appelle ceci un m canisme de protonation macroscopique Pour les deux premi res g nerations pour lequelles le nombre de sites reste mod r il est m me possible d obtenir ces constantes directe ment par r gression non lin aire Les valeurs obtenues de cette fa on sont en tr s bon accord avec des valeurs calcul es partir des param tres cluster Un m canisme de protonation macroscopique pour la premi re g n ration de den drim re poly amidoamine est pr sent sur la figure ci dessus Les m canismes de protonation microscopique tiennent compte des proba bilit s de pr sence de toutes les micro esp ces en fonction du pH Aussi pour degree of protonation Isothermes de protonation de la quatri me g n ration des den drim res poly amidoamine poly propyl neimine et 2 3 les m canismes macroscopiques il est possible d tablir les m canismes micro scopiques en partant des param tres cluster cela en utilisant un traitement statis tique o l quation 1 donne les probabilit s de pr sence des micro esp ces Dans le troixi me chapitre les m canismes de protonation sont compar s pour trois types de dendrim res polyamine savoir les dendrim res poly amidoamine poly propyleneimine et un dendrim re qui ressemble ce dernier mais avec une unit centrale plus longue Au moment de la r daction de la pr sente th se ce dernier dendrim re n est pas pr sent dans la litt
28. au pH Par contre les isothermes de proto nation de la surface avec le PDADMAC adsorb donc dans le cas d un syst me mixte montrent une inversion de charge autour d une certaine valeur pH Cette valeur peut tre consid r e comme le point de charge nulle PCN auquel de le potentiel lectrostatique de surface est gal z ro Les isothermes des com posants purs ainsi que de syst me mixte sont pr sent s sur la figure la page suivante viii Le comportement lectrostatique de la surface du latex carboxyl en pr sence du pDADMAC ressemble au comportement d une surface d un oxyde m tallique par le fait de la pr sence du point de charge nulle La co ncidence existe entre celui ci et le point isoel ctrique trouv par des mesures de mobilit lectrophoretique du m me syst me De plus le point de charge nulle du syst me mixte peut tre r gi par la quantit de poly lectrolyte adsorb Cependant le point de charge nulle est pr sent dans les isothermes d adsorption mais unique ment dans les cas d adsorptions correspondant au rapport num rique entre les sites DADMAC et carboxylates lt 1 Le comportement lectrostatique de syst me mixte est bien en accord avec un mod le de Stern modifi pour la pr sence du poly lectrolyte adsorb Tout l exc s de charge dissout y compris les sites DADMAC dans la solution peut tre d tect comme un exc s de charge au point de charge nulle en observ
29. calibration data C gt il 4 Slope A 0 0000 Offset A 28250 04 15 Slope B 10 0000 Offset B 128250 0 Slope C 10 0000 Offset C 128250 0 Slope D 0 0000 Offset D 128250 0 Load Save Not used 4 View mY 3 Cc 4 Graph 5 6 on Raw Value Real Value A 0 0 0000 OFFS Al w 4 0 if Amplitude 3 9 1 1 1312 4 1312 6 1312 7 Time min 1 1312 5 1312 8 EAE Time min E 28 41 Communication with HighImp4 Units ampitude I 182 17 Send slope C Save for mY Mode Send offset Cc Save for User Mode Send Units C 2 Cc Figure A 10 The user interface for the electrode calibration 166 Controls and indicators 10 11 Channel selection lets the user choose the voltmeter channel that will be used for the electrode reading and calibration Average control the user can choose the number of points for block averaging View mV switch sets the value displayed in the graphic It can be in millivolts obtained by a rough internal calibration of the instrument or the calibrated signal obtained from the raw values by using the current values of the calibration parameters Graph controls the switch to the left is used to display the time depen dency of the reading value in the graph below and the one to the right to clear the graph Raw value indicator indicates the currently read raw value at the
30. constant charge in the whole experimental pH range The results of the adsorption measurements in the range of the loadings which were used for the titration experiments are presented in figure 4 6 It can be noted that at pH 10 all the added pDADMAC is adsorbed The adsorption data calculated from the proton binding isotherms are in a reasonably good agrement with the results obtained from the batch experiemnts Thus it is likely that N diss corresponds to the pDADMAC in the solution at least at the point of zero charge In the batch experiments the adsorption of PDADMAC to 98 Table 4 2 The parameters of the basic Stern model for the pure carboxylate latex lo sitesnm pKa Cs Fm 3 74 4 20 OO charge mCg Figure 4 5 Proton binding isotherms of pDADMAC at five different ionic strengths o 0 01 M O 0 05M A 0 10M v 0 0 50 M gt 1 00 M 99 the carboxylate latex particles was measured at pH 4 and pH 10 and at ionic strength 0 1 M and in the concentration range of PDADMAC as studied in the titration experiments The pDADMAC surface concentration of 1 0 mgm corresponds to 1 1 binding of pDADMAC sites to the latex surface sites Figure 4 6 is showing that the adsorption is higher at pH 10 than at pH 4 It has to be stressed that the sample preparation for the adsorption exper iments is somewhat different than for the titration experiments which may be a reason for the disc
31. distributions at solid surfaces with adsorbed polyelectrolytes can be gained indirectly by measuring the thickness and conformation of the adsorbed polyelectrolyte layers 64 65 Potentiometric titrations provide a direct measurement of the surface charge In this case the excess charge present in the solution compensated by the pro tons or OH ions is attributed to the surface which is acting as a conjugated acid or base 8 Several potentiometric titration studies of the systems consisting of strong 66 68 and weak 69 polyelectrolytes adsorbed on oppositely charged surfaces are available In these studies the measured amounts of adsorbed poly electrolytes and the net surface charge have been interpreted in terms of the self consistent mean field model 57 The same approach was found appropriate in interpretation of the layer thickness 70 the effects of the polyelectrolyte poly dispersity 64 and some other effects like the influence of the surface curvature on the adsorption 71 In the self consistent mean field approach the inter actions between the ionic species polylectrolyte segments the solvent and the surface sites are treated explicitly The relation between the surface charge and the potential within the adsorbed layer can be solved by applying a site binding model which is acting as a boundary condition for solving the Poisson Boltzmann equation 66 The minimum free energy and the corresponding spatial dis
32. excess charge at point of zero charge does not influence the surface po tential In principle three contributions to the latter charge are possible which can not be distinguished from the proton binding isotherms the charge of the pDADMAC sites which are not adsorbed and thus present in the bulk solution the pDADMAC charge compensated by Cl and OH ions which are incorpo rated in the adsorbed layer and the charge of the pDADMAC sites which are adsorbed but not in the proximity of the surface whereby their contribution to the surface potential is reduced The adsorbed amounts as calculated from the excess charge present at the point of zero charge Nj are in a reasonably good agreement with the result of the batch experiments Neglecting the influence of different sample prepara del tion for the titration and batch experiments it may be concluded that NE actually corresponds to the residual pDADMAC in the solution and not to the adsorbed sites which have less influence on the surface potential due to their dis tance from the surface or incorporation of the counterions into the pPDADMAC layer Therefore for low polyelectrolyte loadings the majority of the adsorbed pDADMAC charge actually influences the surface potential Unfortunately the adsorbed charge can not be determined from the proton binding isotherms at higher loadings The presented models although very simple are giving some insight into the distributio
33. for setting the ionic product of water depends on the temperature pKw 14 00 at 298 K Burette settings Dispensing speed The control for setting the dispensing rate The value depends on the tubing diameter Maximum dispensed volume The security setting for the maximum vol ume that can be dispensed from a burette during an experiment 158 12 13 14 15 16 ve 18 19 Const_I_mode switch Lets the user choose between the constant ionic strength and standard titrations in spite of the fact that the constant ionic strength are commonly done and could be called standard Constant ionic strengths button The button triggers the subroutine where the ionic strengths are being set Cnst_I_par vi pH limits switch Previewed for the choice between the mode where the pH is swept in a pre defined range and a mode where the pH range is not defined so that the experiment is terminated according to the conditions defined through controls 33 to 36 or manually However at the time of this manuscript this option was not implemented pH_init The control for setting the initial pH in the experiment The initial solution is automatically dosed to achieve the initial pH If the cell contains a substance that undergoes dissociation manually dosed prior to starting the experiment the pH will be automatically adjusted to the initial value pH end The final pH i
34. for various standard systems HAc EDA Alanine etc with respect to the literature values performance of the described method and the accuracy of the proton binding isotherms and the corresponding pKa values figure 1 20 is a statistic of the fitted values from various experiments with ethylene diamine and acetic acid as analytes 1 9 Conclusion A high precision computer controlled potentiometric titrator with four burettes and a high impedance voltmeter was developed The four burette setup is very convenient to perform constant ionic strength titrations The advantage of this system is that it enables the adjustments of the ionic strength in the titration cell without having to change the analyzed solution nor any of the burette solutions The data treatment which includes fitting of the experimental blank titration curves is advantageous because it enables an insight in the electrode quality and gives insight in the possible sources of errors High precision potentiometric titrations appear as a powerful tool for study 39 ing the concentrations of the charged species in a solution If all the sources of errors are under good control the absolute error of the determined analyte con centration is not higher than 1076 mol Thus 100 mL of analyte solution with initial concentration of 1075M can be easily be analyzed with only 1 error The pH scale is defined by the blank titration curve parameters The accuracy of the pH
35. from the 20 solutions which were purchased from Aldrich The purchased solutions were used without any 118 further purification The concentration of the purchased solutions were verified with the total carbon and nitrogen analyis which have as well shown a correct stoichiometric ratio of carbon and nitrogen The adsorption of pDADMAC was carried out in the following manner First the silica suspension 10 20 ml was added into a polyethylene container of 30 ml The measured pH of the pure silica suspension is around 5 Then pDADMAC solution was added The concentration of the pDADMAC stock solution is ad justed so that the addition of pDADMAC is of the order of a few milliliters The mixture was shaken and the pH was adjusted to pH 7 5 by carefully with an automatic burette adding KOH 0 25M The mixture was shaken for several minutes and transferred into the titration cell Titrations were performed with the Jonction titrator see appendix in the same way as described in chapter 4 The studied pH range was 4 lt pH lt 8 5 Higher pH values were not stud ied in order to minimize the dissolution of silica and constant ionic strengths were maintained throughout titrations at 0 01 0 05 0 10 0 50 1 00 by addi tions of 3 M KCl and de carbonized water The burette concentrations of HCl and KOH were 0 25 M The titration mixture was degassed with nitrogen which was previously passed through conc KOH water and 0 1 M KCI so
36. is of great interest in for example food and paper industry or purification of waste water The colloidal stability is greatly affected by the charge carried by particles in suspensions 55 Furthermore the surface charge as well as the poly electrolyte charge and the concentrations of ionic species within the adsorption layer are playing an important role for the conformation and structure of the adsorbed or grafted polyelectrolyte layers While the scaling theory set forward by de Gennes 56 led to a breakthrough in understanding the conformations of the adsorbed polyelectrolyte layers 57 58 However the ionic distributions in the adsorbed layers still require explicit computations by means of Monte Carlo simulations 59 83 An insight into the charging processes at interfaces can be gained through the shear or plane potential which can be experimentally determined from the electrophoretic mobility or streaming potential measurements By applying the theory of Derjaguin Landau Vervey and Overbeck DLVO 60 an insight about the shear plane potential may be gained from the measurements of the aggregation rates in the initial stages of the particle aggregation where dimers are formed from monomers 61 In these studies the aggregation rates are usually compared with the electrophoretic mobilities and the fast aggregation regime typically coincides with the isoelectric point 62 63 As well an evidence of the charge
37. nearest neighbor pairwise interactions as parameters The model can be used for assessment of both macroscopic and microscopic protonation mechanism In the case of poly amidoamine dendrimers the proton binding isotherms can be described even for a large number of protonation sites by using only six parame ters The cluster parameters can be unambiguously fitted from the experimental proton binding isotherms by starting from GO where only three parameters are needed and proceeding towards higher generations by using always the same values of cluster parameters In turn the macroscopic pK values could be calcu lated from the site binding model The comparison between the pK values which were obtained by direct fitting of the proton binding isotherms and the pK values calculated from the cluster parameters has shown a very good agreement Further analysis of the proton binding isotherms of poly amidoamine den drimers was carried out in terms of a microscopic protonation mechanism where the protonation species are distinguished by the distribution of the bound protons among the sites as described in chapter 3 It was shown that for high genera tions the plateau in the proton binding isotherm at 0 1 2 corresponds to an intermediate protnation microspecies where the outermost primary amine sites are protonated while the rest of the sites are deprotonated The intermediate species is evident at 7 lt pH lt 8 The microcopic protonation m
38. of four burettes Metrohm Dosimat 765 cylinder volume 5 mL containing KOH and HCl at 0 25 M KCl at 3 M and water The electromotive force is measured with a high impedance voltmeter Microlink PH4 S which is embedded in a computer interface Microlink 3000 for the communication with external units burettes stirrer For that task separate glass and Ag AgCl reference electrodes both purchased from Metrohm AG were used The home made plexiglass reaction vessel minimum and maximum volume of the titrated system is 45mL and 450 mL respectively was thermostatized at 25 C by an external thermostat Haake DC 10 and the solution was constantly degassed with nitrogen previously washed with concentrated KOH water and 0 1 M KCl solution The potentiometric titration experiments are fully controlled by the computer First blank titrations were performed where the electrode readings were recorded after a drift criterion of 0 1mV min was satisfied which is usually achieved in less than 3 minutes except in the region around pH 7 where up to 5 minutes were needed Then the samples of the composite PDADMAC carboxylate latex suspensions were transferred to the titration cell The experiment begins with an addition of HCl KCl and water in order to reach the initial conditions pH 3 the ionic strength of 10 mM and total volume of 100 mL At the beginning the pH is corrected in a rapid step wise manner through acid and base additions
39. of the proton binding isotherms for different pDADMAC latex mixture composi tions The adsorbed and dissolved amounts were calculated from the charge at point of zero charge Stern capacitance is denoted Cs pDADMAC TN TON loading sites nm sites nm sites nm Cs Fm ph 0 56 0 35 0 21 6 95 4 00 1 50 1 18 0 32 3 02 5 82 2 44 1 91 0 53 2 90 6 84 3 15 227 0 88 2 40 7 76 1 00 gt 9 0 electrophoretic mobilities are presented in figure 4 9 The lines in the top fig ures were calculated by means of the modified Stern model as described in the introduction to this chapter and using the parameters listed in table 4 3 The coincidence between the point of zero charge as obtained from the proton bind ing isotherms and the isoelectric points as obtained from the electrophoretic mobility measurements is obvious The lines in the bottom figures represent the predictions of the O Brien 81 and White theory for the electrophoretic mobili ties For this the shear plane potential was calculated from the surface potential wo by means of the Gouy Chapman theory the fitted shear plane distances are given in table 4 4 The calculation of the electrophoretic mobilities from the shear plane potential is described in the paper of O Brien and White In the present work the mobilities have been obtained by interpolation from databases which contain mobilities for various values of the shear plane potential 105
40. preset channel Real value indicator indicates the current calibrated signal Display for the time dependency of the reading value in millivolts or cali brated value depending on the position of the switch 3 The array of calibration points i e the raw values left and some calibrated values that are known a priori right Add point buttons the user can set as many as ten calibration points Remove point button To remove points Correlation indicator indicates the coefficient of correlation for the cali bration data 167 12 13 14 15 16 17 18 Slope indicator the slope of the calibration line Offset indicator the offset of the calibration line Update calibration data button upon pressing the calibration parame ters slope and offset are saved for the experiment Indicators of the calibration parameters for each channel Load and Save buttons serve for loading the parameters from a file or saving them Communication with HighImp4 buttons serve to transfer the calibration parameters and the used units to the voltmeter which will change the value displayed on the voltmeter display Quit button serves to quit the calibration subroutine and return to the main program pH adjustment subroutine SV adjust pH vi Controls and indicators Current measure indicator the user ca
41. right respective to the main frame Conductivity meter and conductivity cell optional Conductometric titrations are one more option of the Wallingford titrator For that one needs a Metrohm 712 conductivity meter connected to the Microlink 3300 interface through a RS 232 module During this work it was established that the con ductivity meter should be connected at an address which is higher than all the burette addresses Otherwise the communication may fail The settings for the conductivity meter are baud rate 9600 data bit 7 stop bit 1 parity even handshake none RS232 control ON Other conductivity meter specifications are Measurement range 0 20 S cm Max conductivity resolution 4 5 digits The conductivity cell used in this work is an epoxy body Accumet Cat no 13 620 161 cell with two platinum electrodes The cell constant is 0 1 em The epoxy sleeve around the platinum plates was removed to achieve a better flow of the solution into the space between the electrodes 145 PC Since the Wallingford titrator software is running under DOS the require ments for the PC are rather minimal an IBM compatible PC with installed DOS However from my experience the communication with the Microlink 3200 inter face is not achievable with any computer the reasons could be in the talk listen delays or data buffering properties of a particular PC This can change from one PC to another Software The Wallingford titrator
42. s diff rent en pr sence et en absence d un poly lectrolyte de charge posi tive En absence de celui ci le potentiel de surface est toujours n gatif et les xl isothermes de protonation montrent toujours une charge n gative augmentent avec le pH En pr sence du poly lectrolyte adsorb la charge de surface peut tre invers e par les protons li s et le potentiel de surface est gal z ro autour d une valeur de pH donn e soit au point de charge nulle Pour cette raison les isothermes de liaison des protons forces ioniques diff rentes se croisent dans une troite r gion de pH Le point de charge nulle peut tre modul par la quantit de poly lectrolyte adsorb D ailleurs la charge mesur e au pointe de charge nulle peut tre utilis e pour d terminer le taux d adsorption et cela est en tr s bonne ad quation avec les mesures directes La d pendance du point de charge nulle avec l adsorption pour deux masses molaires diff rentes s est montr e gale ce qui ne souligne aucune influence de la masse molaire du poly lectrolyte sur le comportement lectrostatique de l interface xii Introduction Polyelectrolytes are polymers which are charged in aqueous solutions Strong and weak polyelectrolytes can be distinguished one carrying strong and the other weak acidic or basic moieties In water solutions polyelectrolyte molecules present a source of an excess charge which stems from the conjug
43. set to 0 for further calculation Then the salt addition can be calculated 2 I Vtinit sum Vs Vtinit A 6 5 i 2 cs Vtinit sum ca Va cb Vb cain Va n cb_in Vb_in absacid cs_in Vs_in nsin 1000 A 7 absacid ca Va ca_in Vain cb Vb cb_in Vb_in A 8 174 Finally the water addition is the difference between the initial total volume Vtinit and the acid Va base Vb salt Vs and sample additions Vsample Vw Vtinit Vsample Va Vb Vs A 9 Input global parameters initial pH pHinit initial ionic strength I 1 total volume Vtinit sample volume Vsample Va_in ca_in Vb_in cbin Vsin cs_in ns_in and Vsample see the above definitions The pH adjustment procedure Constant addition mode This sub routine is used to adjust the pH to the pHinit value at the beginning of the experiment or in the scenario with one way titrations see A Constant vol umes of the titrant V_ad_dose are added until the pH exceeds the initial value pH_init Then the addition volume is split by half and the titrant is changed to acid if initially it was base and vice versa This procedure is repeated until the convergence criterion pH_init pH lt delta pH init is satisfied Input global parameters the initial pH pH_init constant titrant addition V_ad_dose the convergence criterion for the procedure delta pH init 175 Ionic strength
44. software is actually a programming language with a structure similar to Fortran The language consists of settings and commands In the settings the user can define the features that are constant during an experiment This includes the hardware settings e g the devices that are used the burettes settings and other features like the electrode reading criterion stirring status etc The commands can be regarded as subroutines which can be called from the main routine The experimental procedure is defined in the main routine which can contain loops conditional statements and calculations User defined or pre defined e g current reading of the EMF dosed volumes etc variables can be used as arguments for commands or for programming purposes These programming features provide enough flexibility to develop even very advanced titration routines More details about this language can be found in 16 Some minor problems connected with the Wallingford titrator software were spotted in the course of this thesis The drift reading conditions are not obeyed and the salt additions upon using the TITRATI command were observed as not precise The latter can be bridged by programming the constant ionic strength routines from scratch by using the very neat programming possibility of the Wallingford titrator software However for an unexperienced user this might be time consuming 146 A to PC to electrodes _ Al D
45. the system is approximately 100mL the detection limit can be expressed in terms of concentration and it equals 1075 M If the solutions are prepared with care the burettes functioning impeccably and the CO dissolution is lowered to minimum the forward and backward curves should coincide Figure 1 11 nicely shows the influence of the CO dissolution Here the fitted H Acidities were subtracted from the experimental as shown in the previous figure and multiplied with the total volume As explained in section 1 6 the conversion of H Acidities into amounts in moles is necessary to discard 22 0 000 H Acidity moldm 0 001 pH Figure 1 10 Forward and backward blank titrations at J 0 1M The markers represent the experimental data o forward e backward and the lines represent the fitted functions The burette concentrations are c HCl 0 25 M c KOH 0 25 M c KCl 3 00 M The aimed pH increment is 0 17 units the total volume dependency of the data without this the subtracted acidities at different pH could not be compared The experiment was started at pH 3 and the titration was performed up to pH 11 After the solution was exposed to a basic pH the CO started dissolving which is apparent from an increase of the residuals in the backward run The solution was again freed to a certain extent of the CO due to the degassing in the acidic region This process repeats at all the examined ionic strengths and c
46. v reading value acquisition subroutine acquisition subroutine is depicted in the figure A 12 The core of this subroutine is the middle part where the c r v Calibrated reading value drift and standard deviation are being calculated The calibrated reading value is the value acquired as a valid reading according to the drift or time out criterion in the units of the calibrated signal The calculation is done in the following manner The raw signal is continuously acquired and recalculated into the calibrated signal during a time T see figure A 13 Time T is divided 170 calibratedsignal pH t s Figure A 13 Calibrated signal versus time during one reading period T Depicted are the two significant time periods A and Ag P1 and P2 are the points for the drift calculation into three parts A41 Ay and T A Ag The c r v is the mean value of the calibrated signal acquired during A2 The drift is the slope of the straight line through two points mean of the calibrated signal acquired during A1 Aj 2 and mean of the calibrated signal acquired during A T A 2 Standard deviation is calculated from the calibrated signal acquired during Ag The formulas for calculating the c r v drift and standard deviation of the signal are T f pH dt _ fa cy f dt PAS 171 Al T J pH dt J pH dt 0 T A2 Al T J dt f dt 0 T A2 drift TA A 1 2 T J pH crv dt stdev
47. value of 2 13 reported for ethylenediamine 6 This increase is probably caused by the presence of the amido side chains coordinat ing the nitrogen atoms Note that e decreases within increasing ionic strength while and are virtually ionic strength independent This difference can be 50 understood by realizing that the nearest neighbor interactions parameterized by c and act mainly along the hydrocarbon backbone while the interactions be tween the primary amines parameterized by e act through the solution and is thus more influenced by the ionic strength due to effects of screening 6 39 The trend in the increase of e with the generation number is similar to the sequence of conformations observed by small angle scattering 27 The negligible interac tion between the primary amine groups for GO and G1 reflects the open structure of these dendrimers while its increase for higher generations is in line with the increasingly compact structure of the larger dendrimers The microscopic ionization constants of the amine groups are generally lower than the corresponding values for aliphatic amines but show the same trends otherwise For primary amine groups pk in the range 9 4 9 7 have been reported while for tertiary amine groups pk lies around 7 5 6 As shown in Tabs 2 and 3 the site binding model can equally well predict the fitted macroconstants pK obtained from eq 2 11 This feature illustrates that t
48. y Eo and A The choice was to fix the acid 21 burette concentration c since this solution is stable regarding the dissolution of CO so it s analytical concentration is more accurate than that of the KOH After examining the correlations between the fitted parameters by plotting them against each other in this manner the cross correlations are visualized it was observed that either or A have to be fixed not fitted see figures 1 16 and 1 17 The features of the blank titration curve fitting will be discussed in more detail in section 1 8 1 7 Results A typical result of a forward and backward blank titration at ionic strength of 0 1 M obtained through the procedure described in section 1 6 is shown in figure 1 10 The fitted parameters from forward titration curve are c KOH 0 2506 M Eo 384 14mV yH You 0 82 and from the backward titration curve c KOH 0 2505M Eo 383 5mV Yq You 0 80 Other parameters from function 1 17 were not fitted but fixed at the following values c HCl 0 2500M A 59 0mV Kw 107 Figure 1 11 is showing the residuals calculated from the fitting To discard the volume dependency see section 1 6 the residuals are represented as charge in units of mols The fitting is usually very good with a mean residual value averaged over all the experimental points of the order of 10 mol see figure 1 11 which is considered as the detection limit Since the total volume of
49. 0 000 0 000 0 000 0 000 vi reference Va_dosage Vb_dosage Vs_dosage Vw dosage JE 0 000 0 000 0 000 0 000 0 000 Total_Vol Old_Meas 0 00 End_Experiment Figure A 6 Main program user interface The controls in the lower part can not be changed by user 153 the message Idle in the status indicator The commands that can be given at this point by clicking one of the buttons are Calibration Parameters for titration Titration or Quit Clicking on the Parameters for titra tion button will again launch the subroutine for parameter setting if a check or change is desired while the Quit button will stop the experiment and LabView will be closed The button Calibration will launch the calibration subroutine see SV_HighImp4_Set_Calib_Parms vi If the calibration parameters are a pri ori known the calibration is not necessary Then the parameter values have to be entered in the Slope and Offset fields see figure A 6 Once the cali bration parameters are defined the titration may be launched by pressing the Titration button At that event the timer is started The program continues by initializing the data file and writing Start titration the date and time to it and filling burette cylinders The titration starts by an addition of water salt and acid or base in order to achieve the initial pH ionic strength and the initial total volume the calcu
50. 1 One of the possible protonation microstates for the macrostate de fined with N 14 and m 6 The state vector s defines the microstate statistical mechanical experssions which enable the assesment of the microscopic protonation constants microstate probabilities and other microscopic properties Again the basis for these calculations are the cluster parameters which in the case of poly amidoamine dendrimers are the same as presented in chapter 2 3 2 Microscopic protonation equilibria To define all the possible distributions of the bound protons among the proto nation sites the sites are enumerated with 7 and a two valued state variable si Oorl 0 for deprotonated 1 for protonated is assigned to each site The microscopic protonation state alternatively microstate or microspecies is de fined by a state vector s as demonstrated for the first generation dendrimer molecule in figure 3 1 The microscopic protonation constant K s is at tributed to an unprotonated site j when the molecule attains a microstate s The site binding model is defined in the previous chapter through equation 2 6 However the probability of a given microstate depends on the proton activ 59 ity ay 6 43 p si Shame SFA 3 1 The normalization constant can be interpreted as the partition function of the polyelectrolyte with respect to different states of protonation a X ae PRs 3 2 si As ment
51. 2 147 PC requirements To run Labview the PC should be equipped with a 200 MHz processor unit 32 MB RAM and Windows 98 version installed Though higher speed processors and more RAM are desirable for code development From the hardware side the PC has to be equipped with at least five serial ports one for the HighImp4 and the rest for the burettes Software The software for Jonction titrator is fully developed under the Labview platform LabView is a very powerful application software intended for the control of pe ripheric instruments by a PC acquirement and modulation of meter readings virtual signal processing etc While the possibilities of this software seem end less we have used only the least necessary to develop the constant ionic strength potentiometric titration procedures In general LabView programs consist of two parts namely the user interface and the code The user interface is presented as a console of a virtual instrument and contains all the input and output variables organized as controls or indicators The controls can be modified by the user and are displayed in forms of buttons for boolean variables numeric fields or turnable buttons for numeric variables etc The indicators are just showing the current values of variables and are being displayed in forms of led indicators for boolean numeric fields for numeric variables graphs for numeric arrays etc All the values of these variables are constantly u
52. 3 14 desktop while the main program is running until the switch is set to off Start titration button The button starts the experiment Titrating led indicator The indicator is lit on while the experiment is running Status indicator Indicates the current activity of the instrument Time elapsed indicator Indicates the time elapsed after the titration was launched by clicking Start titration button Current ionic strength indicator Indicates the ionic strength Quit button The button terminates the program and LabView Error led indicator Indicator is lit on if some error occurred during the run Global parameters SV Titr enter par multi test vi In this subroutine the user has to define all the paramteres that are used to control the experiment in the code they are located in the global parameter cluster global parameters are the parameters which are accessible to all subroutines Description of the user interface controls and indicators Common controls 1 Waiting time after dispensing control Lets the user set the time for which the titrator will wait after dispensing acid base salt and water Or example this time could be needed for mixing Drift criterion The user must enter the drift in pH s here pH refers to the unit of the calibrated reading value that the titrator will use as the reading criterion 1
53. 3280 13286 2002 Berne B J and Peccora R Dynamic Light Scattering Wiley New York 1976 O Brien R W and White L R Journal of the chemical society Faraday transactions IT 74 1607 1626 1978 Wagberg L Pettersson G and Notley S Journal of Colloid and Interface Science 274 480 488 2004 Meszaros R Thompson L Bos M and de Groot P Langmuir 18 6164 6169 2002 Szekeres M Dekany I and de Keizer A Colloids and Surfaces 141 327 336 1998 Shubin V Samoshina Yu Menshikova A and Evseeva T Colloid and Polymer Science 275 655 660 1997 Beltran S Hooper H H Blanch H W and Prausnitz J M Macro molecules 24 3178 3184 1991 191 88 89 cs 91 i 92 lb 93 97 98 Park S Y Barrett C J Rubner M F and Mayes A M Macromolecules 34 3384 3388 2001 Bolt G H Journal of Physical Chemistry 61 1166 1169 1957 Tadros Th F and Lyklema J Journal of Electroanalytical Chemistry 17 267 275 1968 Yates D E and Healy T W Journal of Colloid and Interface Science 55 9 19 1976 Wells J D Koopal L K and de Keizer A Colloids and Surfaces 166 171 176 2000 Hiemstra T and van Riemsdijk W H Journal of Colloid and Interface Science 179 488 508 1996 Meeussen J C L Filius J D Hiemstra T and van Riemsdijk W H Journal of Colloid and Interface Science 244 31 42 2001 Boily J F Persson P and S Sjoberg Ge
54. 46 44 646 su ba dd 408 de 8 139 181 A 2 Scheme of the signal processing by the HighImp4 instrument 147 A 3 Scheme of the Jonction titrator software hierarchy 149 A 4 Experimental scenarios with Jonction titrator 150 A 5 Titration curves obtained with a dynamic and b constant titrant addition MOUS s roso Aa ke ae Dae eo AOR ee ALE ae a 150 A 6 Main program user interface 153 A 7 The user interface of the parameter assignment subroutine 157 A 8 The user interface for defining the initial cell composition 162 A 9 The user interface for burette assignment 164 A 10 The user interface for the electrode calibration 166 A 11 The data acquisition subroutine flowchart 170 A 12 The calibrated reading value acquisition flowchart 170 A 13 Calibrated signal versus time 171 A 14 Dynamic addition calculation be a ee eee ee at a 173 182 List of Tables 1 1 1 2 2 1 2 2 2 3 3 1 3 2 4 1 4 2 4 3 4 4 5 1 5 2 The fitted mixed deprotonation constants versus the corrected lit erat re vales s o Le Sw SSL Ne RM ee de 28 Davies formula parameters 31 Cluster parameters of the poly amidoamine dendrimers 44 Macroscopic ionization constants pK of the PAMAM dendrimer Sl 4 a oe Oe RSG eS A Go Si oe ae de we OH FE 48 Macroscopic io
55. 56 2 Joe Ave fi0 00 6 Jo 7 100 000 8 450 000 9 aw 14 00 oso ffo 7500 Not used NoName oo Figure A 7 The user interface of the parameter assignment subroutine 157 10 11 Drift monitoring time The control for setting the time during which the drift is monitored If the reading criterion is weak this will be the time gap between two readings see Calibrated reading value acquisition Delta t1 First reading period see Calibrated reading value acquisition paragraph below Delta t2 Second reading period Time out for drift The control for setting the maximum waiting time for satisfying the drift criterion Initial total volume The control for setting the initial volume in the titration vessel Minimum initial total volume is determined by the cell geometry and the electrodes the limitation is that the electrodes have to be sufficiently immersed into the solution For the cell in figure 1 4 it is cca 45 mL However this volume has to be larger than the sum of the sample volume and the initial dosages of acid or base and salt Otherwise the initial burette additions can not be calculated Maximum total volume The control for setting the maximum volume that can be achieved in the experiment if the total volume condition is chosen see control 34 This volume is determined by the size of the cell pKw The control
56. Protonation behavior of hyperbranched polyamines The concepts presented in the introduction to this chapter will be demonstrated on several examples of branched polyamines These will include the zeroth and the first generation of the poly amidoamine and poly propyleneimine den drimers and a dendrimer with a structure similar to the poly propyleneimine dendrimer but with a shorter core unit To the best knowledge of the author of this text the latter molecule was not yet synthesized but could exert some inter esting protonation properties to be discussed It will be referred to as 2 3 den drimer The structures of poly propyleneimine and 2 3 dendrimers are shown in figure 3 2 and of poly amidoamine dendrimer in figure 2 1 The microscopic mechanisms estimated for the lowest two generations will be applied to predict the microscopic picture of protonation for the higher generations The number of sites for different generations can be calculated according to the formula Nm 3 7 where G denotes the generation number which is zero for the smallest molecule The assessment of the microscopic protonation mechanism refers to predic tion of the probabilities of the microspecies with respect to pH The macroscopic mechanism gives the probabilities of the macrospecies The microscopic mecha nism gives the probabilities of the microspecies and the microscopic protonation 57 constants which can be assigned to each unprotonated s
57. UNIVERSIT DE GEN VE FACULT DES SCIENCES D partement de chimie min rale Professeur Michal Borkovec analytique et appliqu e Charging behavior of polyamines in solution and on surfaces A potentiometric titration study TH SE pr sent e la Facult des sciences de l Universit de Gen ve pour obtenir la grade de Docteur s sciences mention chimique par Du ko Cakara de Zagreb Croatie Th se N 3555 GEN VE Atelier de reproduction de la Section de physique 2004 Contents R sum en fran ais Introduction 1 Potentiometric titrations 1 1 Modem Le A DNS Va dar Lada Re a 1 2 Potentiometric titration method 2 1 4441444a4u 1 3 Experimental setup 2 4224 464 864 646 44 64 44 ex 14 Materials LS Ua eS ee ER ee es Tea se 1 5 Experimental procedure 24 4 8 44 bn eu ob oem oo 6 da 1 6 Data treatment 4 4 6 0 04 66 san es vases bete Wt Results cccream eu NE RIRE Nada dela ha Le D S IEN sy i Ge ae AN Na DR RATE Bh Es de 1 9 Concl sion a s sa sisina s pao a Be Gate ee voeu ee 2 Protonation of poly amidoamine dendrimers 2 1 Introduction se 2 2 Macroscopic protonation equilibria in polyelectrolyte solutions 23 Experimental 222444444244 RL No Ree SS ee 2k RESUS 222 os bbw oboe ee OLS Se ee eB ee 2 5 Modelling and Interpretation 42 lt 425 5865568 544 4 20 Conclusiot s s o secs so aoe ey oea oreo be ee oak ou 10 15 15 16 22 28 39 3
58. a M and Chiba H Nature 415 509 511 2002 Sideratou Z Tsiourvas D and Paleos C M Langmuir 16 1766 1769 1999 Lee I Athley B D Wetzel A W Meixner W Baker Jr J R Tomalia D A and Baker J R Macromolecules 35 4510 4520 2002 Perrin D D Dempsey B and Serjeant E P pKa Prediction fpr Organic Acids and Bases Chapman and Hall London 1981 Russel W B Saville D A and Schowalter W R Colloidal dispersions Cambridge University Press Cambridge 1989 de Gennes A Scaling Concepts in Polymer Physics Ithaca NY 1979 Fleer G J Stuart M A Scheutjens J M H M Cosgrove T and Vincent B Polymers at Interfaces Chapman and Hall London 1993 Tran Y and Auroy P Journal of the American Chemical Society 123 3644 3654 2001 Belloni L Journal of Chemical Physics 119 7560 7565 2003 Evans D F and Wennerstrom H The Colloidal Domain Wiley VCH New York 1999 Behrens S H Christ D I Emmerzael R Schurtenberger P and Borkovec M Langmuir 16 2566 2575 2000 189 66 67 68 69 70 71 72 74 Yu W L Bouyer F and Borkovec M Journal of Colloid and Interface Science 241 392 399 2001 Bouyer F Yu W L Robben A and Borkovec M Langmuir 392 399 17 5225 5231 2001 Vermeer A W P and Koopal L K Langmuir 14 4210 4216 1998 Rojas O J Ernstsson M Neumann R D and Claesson P M Langmuir 18 1604 1612 2002
59. a larger distance from the surface than the others In this case the point of zero charge depends on the density distribution of the adsorbed pDADMAC 99 and this complicates the prediction of the adsorbed amount from the point of zero charge Furthermore Cl ions which may be present in the adsorbed pDADMAC layer neutralize the charge of the quaternary amine groups to a certain extent which in turn reduces the effect of the pDADMAC charge on the surface potential As discussed in the data treatment we can express the excess charge present at the point of zero charge as the excess amount of the quaternary amine sites If we subtract the excess quaternary amine sites from the total added pDADMAC sites we obtain the portion of adsorbed positive charge that affects the surface potential Figure 5 5 is showing the same dependency of the point of zero charge upon the adsorbed pDADMAC charge that affects the surface potential for two different molecular weights of pDADMAC From this and in the light of the previous discussion two conclusions can be made First that the surface density of the adsorbed pDADMAC sites at the point of zero charge is the same for two different molecular weights of pDADMAC and at the same time the Cl ions 127 have the same effect in both Second the effect of a difference in the surface density of pDADMAC sites on the surface potential for two different molecular weights of pDADMAC is matched through a
60. accessible quantities are all the volumes and the electromotive force of the electrode couple The rest of the quantities are parameters Ca Cp Kw y Eo and A It could be argued that the concentrations of the burette solutions can be known from the sample prepara tion but since the blank titration curve is more sensitive to these concentrations than the accuracy of the preparation it makes more sense fitting them Non linear least squares fitting and the cross correlations between the blank titration curve parameters As mentioned in the description of the data treat ment non linear least squares fitting of the blank titration curves is performed in order to obtain the blank titration data at the pH values of the analyte titra tion curve The advantage of this approach in front of a simple interpolation procedure is that in this manner one can verify the experimental precision by 20 comparing the values of the fitted parameters with some expected or literature values However in order to obtain unambiguous values from fitting one has to establish the set of parameters which can be simultaneously fitted In the case of the blank titration curves the sum of the squares function can be obtained by combining equations 1 18 and 1 19 CaVai CbVbi 1 Ey EMF A Ey EMF A pKw 12 sum gt A 10 0 10 1 20 where is the counter of the experimentally measured data In the case of func tions with a number o
61. an be tracked in figure 1 11 In order to test the instrument the experimental procedures and data pro cessing titrations of simple acids and bases were performed In this chapter the results for ethylene diamine and acetic acid are presented The pK values obtained by non linear least squares fitting were compared with the literature values 11 The comparison between the fitted and the literature value serves as an estimation of the precision of the pH scale 14 The proton binding isotherms in terms of charge in mol units see section 23 10 H AcY syp H ACY saic V mol pH Figure 1 11 The differences between the experimental and the calculated H Acidities for forward and backward titrations at different ionic strengths Open symbols denote the forward runs and closed symbols the backward runs o J 01M O 0 5M A I 1 0M 24 H ACYepa H Acypiank V mol pH Figure 1 12 Titration curve of ethylene diamine at three different initial con centrations at J 0 1M Open symbols denote the forward and closed the backward titration runs o EDA 5 0mM EDA o 2 5mM A EDA 1 0 mM 1 6 of ethylene diamine at three different initial concentrations are presented in figure 1 12 These experiments were performed in order to verify the precision of the charge calculated from the titration curves The proton binding isotherms from the same experiments at th
62. an intermediate microspecies around pH 7 where the primary amine sites and the sites in each second shell counting from the outermost are protonated Consequently a plateau in the proton binding isotherm is present at 0 2 3 The imaginary dendrimer which is also discussed is built from a short inner core unit with two carbon atoms as in poly amidoamine den 2 drimer and the hyperbranched part with arms of three carbon atom chains as in poly propyleneimine dendrimer The microscopic protona tion mechanism shows features characteristic for both poly amidoamine and poly propyleneimine dendrimers At 5 lt pH lt 7 a microspecies with alter nated protonated and deprotonated shells is present which is the same as the one 80 observed in the poly propyleneimine dendrimer mechanism A less pronounced microspecies present at pH amp 8 5 with protonated primary amine sites is the same as the one observed in the mechanism of the poly amidoamine dendrimer The latter microspecies is becoming more important for low generations due to the fact that for higher generations the structure of this dendrimer is dominated by the hyperbranched part 81 Chapter 4 Charging of carboxylated latex particles in the presence of pDADMAC 4 1 Introduction Adsorption of polyelectrolytes at solid surfaces is widely used to control the col loidal stability and the hydrodynamic properties in colloidal suspensions which
63. and the pH is automatically adjusted to the pre defined initial value This is necessary only in the case of analyte titrations otherwise the initial automated dosing will result with a solution where pH equals the initial pH Then a sequence of titration steps is repeated until the final pre defined pH value is achieved Each step in the titration consists of an acquirement of the reading values namely the electromotive force EMF all the added volumes the total volume and additions of the burette solutions The measurement of the pH is recorded after 15 the solution has reached thermodynamic equilibrium which can be seen from the drift of the electrode signal After the final pH is achieved the forward run is finished and the sense of the pH sweep is reversed The sequence of titration steps is repeated in the backward run These two runs are repeated at all the pre defined ionic strengths The experiment is terminated after all the forward and backward titrations were effectuated at all the desired ionic strengths The details about all the algorithms EMF measurement etc can be found in the Appendix 1 6 Data treatment The automatization of the experiment enables accumulation of many data points Therefore fast data analysis procedures were programmed in which the experi mental data from different titration runs were separated and analyzed The evaluation of the concentration of the proton binding species at a certain pH
64. ant l isotherme de protonation Ceci est utile pour la d termination quantitative d adsorption de pDADMAC sur la surface de latex Observ e de cette mani re l adsorption coincide bien avec celle mesur e par l analyse de carbone et d azote totaux dans la solution comme le montre la figure la page suivante Le m me comportement lectrostatique pr c demment observ pour le syst me mixte pDADMAC latex carboxyl est remarquable pour le syst me pDADMAC silice La surface de la silice exerce un comportement acide dans la r gion de pH d tude ce qui est montr sur la figure la page suivante Cependant quand le pDADMAC est pr sent la surface les isothermes de proto nation font remarquable le point de charge nulle Dans les exp riences pr sent es dans le cinqui me chapitre l effet de la masse molaire du pDADMAC sur la compensation de la charge de surface de la silice est tudi en comparant les d pendances du point de charge nulle au taux de charge du DADMAC adsorb cela pour deux masses molaires savoir 100 et 500 kDa La figure pr sent e a la page xi ne rev le aucun effet de masse molaire La m thode de titrage potentiom trique s est montr e adapt e pour effectuer ix Adsorbed DADMAC sites nm Added DADMAC sites nm Comparaison entre l adsorption d termin e par
65. antitative up to a saturation limit after which the adsorbed amount can not be further increased but remains constant upon further additions In the present case when the adsorption is carried out at pH 10 the saturation limit is not reached in the range of loadings examined The presence of the adsorbed oppositely charged polyelectrolyte is promoting the development of the negative charge at the latex surface which is in turn promoting the adsorption 69 82 83 However at pH 4 lower adsorption was observed and in this case the adsorption is not of the high affinity type The increased adsorption at higher pH is not surprising having in mind that the charge present at the surface of the carboxylate latex particles is increasing with an increasing pH This points out that in the studied low range of loading adsorption of pDADMAC to the carboxylate latex surface can be regarded as an example of the screening reduced regime according to de Keizer et al 84 The proton binding isotherms of the pure latex suspension fig 4 4 are show ing typical protonation behavior for weakly acidic particles 6 8 The experi mental data could be reasonably well fitted with the simple double layer model The value of 4 2 obtained for the microscopic pKa of a carboxylic surface site 107 seems a bit too low the reported values are usually around 4 9 61 85 and for comparison the pKa of acetic acid in solution is 4 6 11 However t
66. ants can be determined for GO and fourteen for G1 with reasonable confidence A disadvantage of this classical picture is that it is becoming impractical with in creasing generation number as the number of macroconstants increases quickly Furthermore as will be discussed in chapter 3 it does not lead to insight into the microscopic protonation mechanism of the molecule Both disadvantages can be overcome with the site binding model discussed now The cluster parameters are illustrated in Fig 2 4 Since the ionizable amine groups are relatively far apart we assume pair interactions only Nearest neighbor interactions act along bonds namely one containing the amide bond with an interaction parameter and the ethyl chain in the center of the dendrimer with an interaction parameter As we shall see a nonzero next nearest neighbor interaction parameter between the primary amine groups must be introduced similarly as in the description of the charging behavior of carboxylated dendrimers 34 The microconstant of the primary amine groups is denoted by pk O For the tertiary groups two different microconstants must be distinguished due to different chemical environments The microconstant of the innermost tertiary IT amines is denoted by pk while for all others the same value of pk D will 47 Table 2 2 Comparison of macroscopic ionization constants pKm of the PAMAM dendrimer GO from direct fit of the titration curves
67. arge present at silica surface at the point of zero charge 125 5 4 Discussion The proton binding isotherms of the silica particles in the presence of adsorbed strong cationic polyelectrolyte pDADMAC exhibit the point of zero charge as was observed for the carboxylate latex particles in the presence of pDADMAC At the point of zero charge the surface potential equals zero This fact has important consequences and in the case of homogeneous surfaces e g metal oxide can provide an insight into the charge distribution near the surface In the case of metal oxide at the point of zero charge the surface charge density equals zero and in the case of a monovalent inert electrolyte the amounts of positive and negative counterions in the diffuse layer are perfectly matching The aim of the following discussion is to explain the charge distribution at the point of zero charge for the case of the composite system of a weakly charged surface in the presence of an adsorbed strong polyelectrolyte Although amphoteric bare silica surface can bear only negative charge in the studied pH range above 3 which is in agreement with previous findings e g 74 89 Since the second protonation step can be discarded above pH 2 in the case of pure silica the same charging model can be applied as for the carboxylate latex particles which is demonstrated in the figure 5 3 The obtained parameters are in a good agreement with the already published
68. assing apparatus vou 4 yd de ele Ge y Se we a A photo of the Jonction titration setup Experimental potentiometric titration curves Titration curves and charging curves of acetic acid The charging curve of acetic acid ue os lt a bau eee eg eu Forward and backward blank titrations Experimental and calculated H Acidities for forward and backward CITACIONS s o peci Som a Nan TS CT Ie NT Oe Titration curve of ethylene diamine Proton binding isotherms of ethylene diamine Proton binding isotherms of acetic acid at three ionic strengths 1 Proton binding isotherms of ethylene diamine at three ionic Strengths 2 oc dou a dacs we be wl eee Be ee oe we The cross correlations between Eo andy The cross correlations between Aandy The activity coefficients y Influence of various parameters on the blank titration curve 179 1 20 2 1 2 2 2 3 2 4 3 1 3 2 3 3 3 4 3 9 3 6 3 7 3 8 3 9 3 10 3 11 Statistics of the fitted pK values Chemical structure of the poly amidoamine dendrimers Potentiometric titration curves of PAMAM dendrimers Potentiometric titration curves of PAMAM dendrimers at ionic Bremen Mo Ste Oe nk me SAR ES Se ES So ee ee se Cluster parameter assignment for the poly amidoamine dendrimer
69. ate pairs of acid or base groups The conformation of polyelectrolytes as well as their mutual interactions are both closely related to the charge 1 2 This is important for many of the solution properties such as the viscosity 1 3 aggregation stability and aggregate structure 4 the response to the electrical and mechanical fields 5 etc On the other hand the charge present on weak polyelectrolytes is tunable by the solution conditions pH ionic strength which can be used to control the solution properties 1 6 The behavior of polyelectrolytes at a solid liquid interfaces is interesting partly due to the importance in industrial and environmental processes and partly due to the complexity of such systems For example polyelectrolytes can be used to stabilize suspensions of particles or induce their precipitation which is extensively used in industry paper production construction materials food pro duction purification of waste waters by flocculation etc As well adsorption of polyelectrolytes at charged particles is important in production of spherical membranes by self assembled monolayers which gained huge interest during the past decade 7 In all the above cases a handful of colloidal properties such as the viscosity colloidal stability electrophoretic mobility permeability of the polyelectrolyte layers for small molecules etc strongly depend upon the surface charge One of the goals of the present study
70. ated by choosing Stop from the Operate menu Or clicking at the stop icon in the toolbar the communica tions with burettes are not properly terminated and the control over them is not switched to manual In that case to gain manual control over the burettes one needs to reset their power supply Here follows the description of the controls and indicators 1 Channel control Lets the user choose the HighImp4 channel that will be used for the electrode reading 2 Calibration trigger button The button will start the calibration subrou tine which is described below 3 Slope and Offset controls The two controls let the user enter the parameters of the calibration line which will be used to convert the reading signal into pH These fields are used if the calibration line parameters are a priori known and no electrode calibration is needed 4 Titration curve graphic The graphic displays the complete titration curve of the most recent run 5 Parameters button The button triggers the SV_Titr_Enter_Par_Multi_test vi subroutine where most of the important controls for the titration are being set 6 Parameter file indicator Indicates a filename if the parameters have been saved 7 View drift switch The switch triggers the window for a graphic that displays electrode reading versus time This window will be active on the 155 10 11 12 1
71. ation see table 3 4 The procedure to obtain the cluster parameters from the experi mental proton binding isotherms for poly amidoamine dendrimers was described in chapter 2 For poly propyleneimine dendrimers the cluster parameters were obtained in a similar manner 33 For 2 3 dendrimers the cluster parameters for the zeroth generation were taken from 44 3 4 Poly amidoamine vs poly propyleneimine dendrimers The cluster parameters obtained by fitting the proton binding isotherms of poly amidoamine dendrimers are shown in table 2 4 in chapter 2 For the poly propyleneimine dendrimers the cluster parameters were used as reported in 33 and the values at J 0 1M are presented in table 3 4 For the explanation of the seven different parameters see figure 3 3 60 Figure 3 3 The assignment of the cluster parameters for the poly propyleneimine dendrimers The proton binding isotherms of poly amidoamine and poly propyleneimine dendrimers calculated from the cluster parameters are presented in fig 3 4 In both cases the isotherms for higher generations all follow the same curve and a deviation from this curve can be observed for the lowest two generations Since the site binding model is inherent to the type of the protonation groups and the pair interactions and is insensitive to the number of the protonation sites the appearance of the common proton binding isotherm at high generations can be explained by t
72. ations and it turns out that for silica the only protonation reaction which takes place in the experimental pH range of 3 5 lt pH lt 9 0 is that one where a proton is bound to a singly coordinated oxygen Binding of the second proton to the singly coordinated and the first proton to the doubly coordinated oxygens would occur at much lower pH values Therefore the surface charge on the pure silica surface originates from the SiO surface species according to the reaction SiOH SiO Ht 5 1 The pK of this reaction is around 7 5 so at pH gt 3 similar to the carboxylate latex particles silica is weakly acidic and negatively charged The CD MUSIC model is found to be suitable for describing adsorption charging behavior and particularly surface speciation of the adsorption sites in the case of adsorption of small molecules to metal oxide surfaces 92 95 A problem that may arise when studying the pH dependent charging is that sil ica dissolves and the dissolution rate increases with pH 96 However it was established that the dissolution of silica prepared according to the St ber pro cedure starts playing an important role around pH 9 74 Therefore the experimental window for the potentiometric titration studies is constrained to 116 3 lt pH lt 9 A very large number of studies dealing with the polyelectrolyte adsorption on silica or silicon oxide are available 66 67 83 84 97 The importance of
73. both 50 and 60 Hz interferences Eight high impedance inputs can host up to four ion selective reference electrode couples The ion selective electrode inputs are BNC sockets while the reference electrode inputs are standard banana sockets Other specifications are Voltage range 1 9999 V 1 9999 V Input current 10pA Input impedance 1 TQ A D converter 4 5 digit precision dual slope integrating Conversion time 400 ms Integration time 0 1s rejects 50 and 60 Hz Accuracy 0 03 of reading 2 Les digits RS 232 module The RS 232 modules are used for the control of the burettes and the conductivity meter Attention should be paid to the cables that are used to connect the Metrohm 762 Dosimat burettes with the module The pin assignment is different at the two ends This is due to the fact that the RS 232 module belongs to data terminal equipment DTE standard while the computer belongs to data communication equipment DCE standard The cables must be adapted according to the scheme which can be found in the instrument manual or 16 The baud rate parity stop bits and XON XOFF modes are preset by the manufacturer An address set by DIP switches that are found on the integrated 144 circuit board is assigned to each module and is normally preset by the man ufacturer It should be adjusted if the ports of the modules are changed The sequence of the module addresses has to go from lower to higher numbers from left to
74. btained with the Davies formula 1 22 Both figures are showing remarkable correlation between the electrode parameters and the activity coefficient The parameters Ey and A depend on the electrodes that are used for the experiment The electrode response is changing upon time which is caused by the changes in the electrode solutions wearing of the glass and the ceramic diaphragm of the reference electrode etc This is evident from figures 1 16 and 1 17 where a change of the electrodes has caused a parallel shift of the data The fitted activity coefficients are compared with the values calculated from the Debye Hckel limiting law at J lt 0 002 M and Davies formula for higher ionic strengths see figure 1 18 E 1 22 y 2 where J is the ionic strength in M and a and b are empirical coefficients a 1 022 29 sae ge Be E 0 E wae z m Ay 4 gt 2 _ my ae j g sa A 4 a ae ne 0 2 0 1 0 0 0 1 0 2 0 3 Figure 1 17 The cross correlations between A and y from various experiments with two different electrode couples The slope A is presented with respect to the value obtained from the calibration of the electrodes with standard buffers A and y with respect to the Davies value y The parameters Ey and A were obtained by fitting the set Eo A y and cp and b is given in table 1 2 Although the fitted values are significantly scattered a trend is noticeable which is similar to the prediction of the Dav
75. con tribute significantly to the overall degree of protonation In the second step at 4 lt pH lt 7 the rest of the sites protonate almost randomly with an exception of one of the core sites which protonates last around pH amp 3 5 The inter mediate protonation microstate with the protonated outermost primary amine sites is prominent for the plateau value in the overall proton binding isotherm at 0 1 2 In the case of the poly propyleneimine dendrimers the plateau value at 0 1 3 is a consequence of the existence of an intermediate microspecies with alternating protonated and deprotonated shells which is depicted in fig 3 10 The primary amine groups protonate at 8 5 lt pH lt 11 As can be inferred from pk and the proton binding isotherm see fig 3 4 the rest of the sites lead ing to the shell like intermediate structure protonate around pH 8 This occurs in a step which is not clearly distinguished from the protonation of the primary amine sites Thus in the proton binding isotherm this appears as a less steep continuation of the steep part at high pH One of the innermost tertiary amine sites protonates next but this contribute significantly to the overall degree of protonation for higher generation poly propyleneimine dendrimers As can be inferred from the microconstants within the intermediate microstate the second step at 3 lt pH lt 6 can be divided in two sub steps which are not distin guishable from the
76. ction normal to the surface the distribution might assume different shapes as some simulation results are pointing out 86 87 with different proportions between the tails loops and trains Both the lateral and the vertical distribution of the adsorbed sites could have a pronounced influence on the surface potential Furthermore the conformation of the adsorbed pDADMAC is pH and ionic strength dependent and it is very likely that it dynamically changes during the described titration experiments The response of the counterions K and CT in the diffuse layer to the pres ence of the adsorbed ppDADMAC can be qualitively predicted by the presented extended Stern model The charge balance between the surface and the diffuse layer which has to equal zero at all time leads to the conclusion that upon the adsorption of pPDADMAC some positive counterions i e potassium ions have to be depleted from the diffuse layer into the solution In fact the coincidence of the point of zero charge and the isoelectric point see figure 4 9 is indicating that there is an equal distribution of counterions K and CI in the adsorbed pDADMAC layer 4 7 Conclusion All of the presented results are demonstrating the usefulness of the potentiomet ric titrations for studying the charging mechanisms in the system consisting of pDADMAC adsorbed to oppositely charged carboxylate latex surface In com bination with the surface complexation models the e
77. e charge of the adsorbed pDADMAC which influences the surface potential from the pDADMAC charge which is not adsorbed or does not influence the surface potential due to compensation with the bulk solution ions or the Cl ions which are present within the adsorbed layer It was concluded that the latter case may as well occur if some fraction of the pDADMAC charge is displaced from the surface and is therefore less effective in neutralizing the surface charge In this chapter a charging behavior of the silica particles will be studied in the presence of pDADMAC The emphasis will be made on the effect of the molecular weight 115 of the polyelectrolyte In particular it will be investigated whether the polyelec trolyte molecular weight influences the effect of the adsorbed positive charge on the surface Silica is silicon oxide and as such it is amphoteric This was confirmed in many studies of the charging behavior of silica suspensions 88 91 The proto nation of pure silica can be well interpreted in terms of the 1 pK MUSIC 76 77 model The advantage of this model is that it is able to predict the surface charge according to the actual crystallographic structure of the surface According to the MUSIC model theoretically one or two protons can bind to singly or doubly coordinated oxygens of silicon oxide The pK values for these four protonation reactions can be calculated further explanations can be found in the above pub lic
78. e others and the change in pH does not cause a change in speciation Special are the pro ton binding isotherms of polyelectrolytes and interfaces which are broader than the proton binding isotherms of simple acids These substances have a buffering capacity in a broader pH range A very important feature of the proton binding isotherms are the trends with respect to the ionic strength These trends can be interpreted through the activity coefficients As a rule of a thumb at J lt 0 2 M for acids the pKa shift to lower values with an increasing ionic strength The opposite is valid for bases The activity coefficients actually express the deviation in the behavior of ions with respect to the ideal solutions This deviation is influenced by the electrostatic potential of the counterion which is positive in the case of a base and thus fa vorable for deprotonation The acid counterion is negative thus electrostatically attractive for protons which is favorable for protonation The electrostatic po tential experienced by the protons depends on the ionic strength and is higher at lower ionic strength At J gt 0 2M the trend in the activity coefficients with respect to the ionic strength is reversed which reflects hydration layer influence on the deviation from ideality The hydration layer of an ion is growing with decreasing electrostatic potential 18 The accuracy of the experimental proton binding isotherms and the experi mental pH
79. e scale of the degree of protonation coincide very well as presented in figure 1 13 This result testifies about a very good experimental accuracy as mentioned before the detection limit is ca 1075 M even at concentrations of the analyte of 1 mM The proton binding isotherms of acetic acid at three different ionic strengths are shown in figure 1 14 The solid lines represent the fitted proton binding isotherms The only fitted parameter is the mixed pKa The ionic strength dependence of this parameter reflects the variation of the activity coefficient of the charged species The proton binding isotherm of ethylene diamine exhibits two well distinguished steps and a plateau value at 1 2 as can be seen in figure 25 degree of protonation 6 Figure 1 13 Proton binding isotherms of ethylene diamine at different concen trations o EDA p 1 0 mM O EDA 2 5 mM A EDA 5 0 mM degree of protonation 6 AN N AR EN TR ay N R AN Pa DN TA Lt gt a gis spas ee Figure 1 14 Proton binding isotherms of acetic acid at three ionic strengths o I 0 1M functions I 0 5M A I 1 0M Full lines represent the fitted 26 degree of protonation 6 pH Figure 1 15 Proton binding isotherms of ethylene diamine at three ionic strengths o J 0 1M I 0 5M A J 1 0M Full lines repre sent the fitted functions The fitted values of pkg are summarized in t
80. e software side all what is needed to run an experiment is to know how to use LabView interfaces of the main program and the upper level subroutines see figure A 3 In the chapters below follow the descriptions of the experimen tal steps and the according interfaces in a sequence as they appear in an actual experiment The relevant controls and indicators are found in the upper parts of the windows The lower parts contain only indicators that are of no importance for the user and are therefore shaded out In later chapters more information will be given about the other non interactive subroutines and the actual code of Jonction titrator program The experiment usually consists of two indepen dent parts calibration of the electrodes and titration The program needs the calibration parameters for the conversion of the raw electrode reading into pH Jonction titrator main program Titrator_dusko vi The main program is contained in the LabView file Titrator_dusko vi Opening this file by double clicking on it will start LabView and the user interface of the main program will appear on the screen see figure A 6 The user has to launch the program by pressing Ctrl R or by choosing Start from Operate menu or clicking on the white flesh in the toolbar Immediately after launching the program initializes HighImp4 which is announced on the screen After that the pro gram is calling the subroutine for entering various experimenta
81. echanism further 132 reveals that the primary amine groups protonate in the first step which occurs at 7 5 lt pH lt 10 The inner part of the molecule protonates in the second step which occurs at 4 lt pH lt 7 The last site to protonate is one of the innermost sites This occurs at pH amp 3 5 The mechanism is the same for the low genera tions of poly amidoamine dendrimers i e GO and G1 except that the proton binding isotherms of these molecules attain a slightly different shape due to a different proportion between the outermost primary the innermost tertiary and the rest of the sites A comparison between the protonation mechanisms of three different den dritic polyamine structures is presented in chapter 3 These include the poly amidoamine and poly propyleneimine dendrimer and the 2 3 den drimer where the structure is the same as in the poly propyleneimine den drimer but with a short spacer between the innermost two sites The agree ment between the microscopic protonation constants for poly amidoamine and poly propyleneimine dendrimers is showing that the microscopic pK is inherent to a certain type of the protonation group and its chemical environment The comparison of the pair interaction parameters is showing that they depend on the spacer length between the neighboring protonation sites The microscopic protonation mechanisms of the three studied dendrimer structures turns out to be different The poly
82. ed for a setup with only two burettes but so far not implemented and will therefore be omitted in the further text Output files There are several output files of Jonction titrator The data file and the log file are created automatically during the experiment There are possibilities to save the experimental parameters and calibration data into files with extensions par and cal respectively Data output file txt This file contains the output data which are written to the file every time a reading has been acquired The data are organized in columns in the following order total volume of the solution in the cell includ ing the sample burettel burette2 burette3 burette4 volumes in milliliters calibrated reading value usually pH see Calibrated reading value acquisition drift standard deviation explanations of these terms can be found in paragraph Calibrated reading value acquisition subroutine Log file txt log The log file serves for recording the actions that were taken during an experiment and the times when they occurred As well at the be ginning of this file all the experimental parameters are found Actually most of the reported actions are automatically taken by the program e g acquirements of the electrode reading salt addition to increase the ionic strength or changing the direction of the pH change between forth to back etc 151 Running Jonction titrator From th
83. ed with the charge in Coulombs per surface area or the number in moles of elementary charges per surface area 1 2 Potentiometric titration method For the experimental determination of the proton binding isotherms it is nec essary to measure the concentrations of the charged dissociation species upon a variation of pH in the solution Many quantitative analytical methods can serve for the measurement of the charged species equilibrium concentrations for example spectrophotometry NMR conductometry voltammetry etc Never theless the most common way to obtain the proton binding isotherm are the potentiometric titrations 8 Potentiometric titration is a method where the pH of the solution is varied by controlled and measured additions of strong acid or base e g HCl or KOH and simultaneously measured by a pH sensitive electrode couple The usual mini mal experimental setup includes a burette that contains a strong acid or base at a known concentration a pH measurement couple combined glass electrode or separated glass and reference electrodes with a high impedance voltmeter the titration vessel and a stirrer 12 Although the existence of the first auto mated titrators was reported already in the late sixties 13 the appearance of the personal computers triggered the wide use of such systems one example of the first PC controlled titrator stems from 1978 14 The earliest review of the au tomated potentiometric ti
84. erature scientifique car pas encore synth tis Nous le nommons alors ici dendrim re 2 3 Les isother mes de protonation pour la quatri me g n ration des tous les dendrim res sont r pre sent es sur la figure ci dessus Les m canismes de protonation de trois types de dendrim res se pr sentent diff rement Le dendrim re poly amidoamine est proton en deux tapes distinctes Dans une premi re zone du pH comprise entre 10 et 7 5 les sites amines primaires sont proton s et le reste l est de pH 7 4 Dans la r gion de pH entre ces deux zones appara t une micro esp ce avec vi poly amidoamine poly propyl neimine proton O deproton Micro esp ces interm diaires pr sentes autour du pH 7 pour les dendrim res poly amidoamine et poly propyl neimine des sites amines primaires proton s ce qui donne un plateau dans l isotherme de protonation au degr de protonation gal un demi Pour le dendrim re poly propyl neimine l isoth rme du protonation montre deux zones Le pla teu interm diaire se situe au degr du protonation gal deux tiers L les sites amines primaires et tous les autres sites qui se situent dans les anneaux impairs en comptant l anneau avec les sites primaires comme tant le premier sont proton s Le dendrim re 2 3 montre des caract ristiques dans le m canisme de protona tion qui ont des ressemblances avec les deux dendrim res poly amidoamine et pol
85. es 62 poly amidoamine dendrimers L GO G1 G2 G3 degree of protonation poly propylene dendrimers degree of protonation Figure 3 4 Proton binding isotherms of the first five generations of the poly amidoamine top and poly propyleneimine bottom dendrimers The proton binding mastercurve for poly amidoamine dendrimers exerts a plateau value of 0 1 2 at pH amp 7 5 63 BP 12 8 85 8 85 of fs negligible 1 2 9 00 35689 6408 PRT 100 98 100 degree of protonation Figure 3 5 Bottom macrospeciation diagram of the zeroth generation poly amidoamine dendrimer as a function of pH broken lines where m de notes the number of protons bound to the molecule macrospecies The overall titration curve is represented with a full line Top the most prominent mi crospecies for a certain protonation step where the micro pK values are assigned to the unprotonated sites 64 9 97 0 3 8 92 8 92 of ths 0 5 3 5 76 9 97 53120 622 PR 02 99 5 96 100 degree of protonation Figure 3 6 Bottom macrospeciation diagram of the zeroth generation poly propyleneimine dendrimer as a function of pH broken lines where m de notes the number of protons bound to the molecule macrospecies The overall titration curve is represented with a full line Top the most prominent mi crospecies for a certain protonation step where the micro pK values are assigned to the unprot
86. es of the 2 3 dendrimer 79 4 1 The system composed of PDADMAC and carboxylate latex particles 87 A2 Stern models sise 2288 eee eRe eee Bo eee ee 89 4 3 Experimental proton binding isotherms of the pDADMAC carboxylat latex Mure ca coarae we Eee oe Eh phe EES 96 4 4 The proton binding isotherm of carboxylated latex suspension at three ionic strengths ace LIL AR di Sb ek ee a eS 98 4 5 Proton binding isotherms of pDADMAC at five different ionic Strengths ae oo ee ee ee dos RR ee eee eh oh eS a 99 4 6 Adsorbed amounts calculated from the potentiometric titration EXPETENDIS LIL Le a aue a ewe Se ee Sw we od we HY 101 4 7 Proton binding isotherms of carboxylated latex suspension in the presence of pPDADAMAC 2 4 46 6 Lu a ee ee es 103 4 8 Predictions of the proton binding isotherms 104 4 9 Proton binding isotherms versus the pH dependence of the elec trophoretic mobility lt lt lt sais 4 ee Soe esse 106 5 1 TEM of the heated silica particles 118 5 2 The excess positive surface charge at the point of zero charge 120 5 3 Proton binding isotherms of the silica particles 122 5 4 Proton binding isotherms of the silica particles in the presence of POADMAG das dun ee ew we ee Bw Seok 124 5 5 The point of zero charge versus the adsorbed positive surface charge for pPDADMAC silica 125 A 1 Wallingford titrator 6
87. eters on the blank titration curve a Solid line curve obtained with parameters ca 0 25M cq 0 25 M pKw 14 00 y 0 90 Eo 380 00mV A 59mV b Dashed parameters the same as in a except y 0 70 c Dash dotted parameters the same as in a except Eo 420 00 mV d Dotted line parameters the same as in a except A 45mV an influence on the curve see 1 18 Also it is worth mentioning that if the electrode response is perfectly linear with pH then an error in the electrode parameters Ep and A will not necessarily cause an error in the whole examined pH scale If a reference pH scale is de termined through electrode parameters Ej and A the two scales will coincide around pH Eb Eo A A The proton binding isotherms are functions which are reflecting the protona tion steps The normalization of the charging curves with respect to the maximum charge of the acidic or basic species 1 6 gives the degree of protnation with ver sus pH The degree of protonation can attain values between 0 and 1 and reflects the protonation state of the species The steps in the proton binding isotherms occur in the pH regions around the pKa values where the equilibrium is chang ing in favor of one species depending on the direction of the change in pH In 32 these regions the solution has a higher buffering capacity 8 The plateau values reflect the regions in pH where one species predominates over all th
88. eved through a PC card In that case one first has to install the driver 142 software which is supplied together with the interface The Microlink 3300 interface contains power supply and a control card that handles the communication with the computer It can port a number of various modules which appear as integrated circuit boards The modules can serve for various tasks ranging from time counting analogue signal aquirement and modulation high speed signal scanning to digital signal processing and device control by means of relays This gives the Wallingford titrator setup the flexibility to be used in conjunction with various other devices The standard Wallingford titrator setup makes use of nine modules Two pH measurement modules PH4 S six RS232 interface modules for burette and conductivity meter communication and a relay module for the stirrer control This allows connection and reading of up to eight ISE reference electrode couples a conductivity meter five burettes and the stirrer which makes use of only one of the eight relays In principle the RS232 and relay modules could as well be used for other purposes but the Wallingford titrator software is not suitable for that 143 PH4 S module This module combines eight high impedance analogue inputs and an integrating A D converter with a 4 5 digit resolution The integrating period of 400 ms allows up to 2 5 readings per second and is sufficiently long to eliminate
89. f e Four Metrohm 712 Dosimat burettes with tubings e pH measurement electrode couple e Microlink 3300 interface with modules e Titration cell e Pure nitrogen degassing apparatus e Conductivity meter optional e PC Stirrer These components are connected according to the scheme depicted in figure A 1 139 Metrohm 712 Dosimat burettes and the tubings Metrohm 712 Dosimat burettes consist of the main body that embeds all the mechanic and electronic parts and of an exchange unit that embeds the bottle containing the dispensed liquid the dispensing cylinder and tubings The exchange units can vary in the size of the dispensing cylynder In this work both 5 mL and 10 mL exchange units were used without an observable difference in the precision of the results An advantage of the 10 mL in front of the 5 mL unit is that the dispensing cylinder is less frequently filled which in turn may prolongue the lifetime of the exchange unit and the mechanical parts of the burette Highest care should be made that no air or gas is being dispensed which would produce an error of the measured volume Therefore all the tubing connections should be well sealed Operating the burette is simple and while the titrator is not running it can be accessed manually via the touchpad interface Although the overall impression is that they are reliable and durable occasional checks are recommended Tubing fittings every time after disconnectin
90. f parameters that are to be fitted the least squares method may not be free of ambiguities Namely sets of parameters may occur which give the same minimum in the sum of the squares function cross correlations between parameters 19 Let s now examine the sets of parameters which can not be fitted simultane ously For example if we vary simultaneously the parameters Ca and cp the rest of them we keep fixed we could find different values which give exactly the same sum of the squares the change in the left term in equation 1 20 can be compensated by a change in the right term if we choose an appropriate y Thus we can not fit those parameters simultaneously In the same manner we can deduce that combinations ca ch pKw Eo A and pKw Eo 7 can not be fitted Furthermore parameters pK and y could be simultaneously tuned without affecting the sum of the squares function which means that they can not be fitted in combination with each other Equation 1 20 shows that distinguishing of ca and cp is possible only if there is a significant difference between the added amounts of strong acid and base Vai and V respectively Otherwise when Vai Vii the first term becomes VailCa amp Vii In this case only the difference ca cp can be obtained from fitting and the two concentrations can not be deduced Having in mind the above demonstrations the most reasonable set of fitted parameters might be ca or ch
91. f the NMR techniques 46 47 This approach has substantially become important for the studies of biologically im portant molecules like oligophosphates 48 49 or aminoacids 50 As well the insight into the protonation of specific proton binding sites within a molecule is important in the case of metal complexation 21 51 or incorporation of small molecules 52 The microscopic charging mechanism of the dendritic polyamine molecules is not immediately obvious and has prompted quite some discussion in the lit erature 29 31 33 35 37 53 The charging behavior of poly propyleneimine 53 dendrimers has been studied in substantial detail by potentiometric titrations 33 and N NMR 36 and it was shown that these dendrimers protonate in two steps with an intermediate plateau at a degree of protonation of 2 3 Briefly during the first step occurring around pH 10 the primary amine sites and the sites in each second shell counting from the rim protonate In the second step around pH amp 5 the rest of the sites protonate However it was as well suggested that in the poly propyleneimine dendrimers the primary and tertiary amines protonate almost independently leading to two distinct protonation steps 35 Since in a larger dendrimer the number of primary and tertiary amine groups is almost the same this model would incorrectly predict an intermediate plateau at 1 2 and not at 2 3 as observed experimentally The charging mec
92. fective charge of the strong polyelectrolyte is always the same fraction of the total adsorbed polyelectrolyte charge which is situated in the close vicinity of the surface the rest of the polyelectrolyte charge is compensated with the counterions Second for different molecular weights of polyelectrolyte the difference in the surface densities of the charged polyelec 128 trolyte sites is matched by a difference in the amount of counterions which are incorporated into the adsorption layer 129 Conclusions Potentiometric titrations have been used to study the charging properties of vari ous systems These included pure solutions of poly amidoamine dendrimers col loidal suspensions of carboxylate latex and silica particles and composite systems where strong cationic poly dimethyl diallylammonium chloride PDADMAC is adsorbed onto carboxylated latex or silica particles The methodology of the potentiometric titrations in determinations of the excess charge in water solutions and suspensions was presented in chapter 1 To obtain the proton binding isotherms of the above systems the blank acid base titration curves were subtracted from the titration curves of the systems of in terest The pH scale of the proton binding isotherms was calculated from the parameters of the blank titration curves which were obtained by fitting and verified through determinations of the pK values of standard systems namely ethylenediamine and
93. ference in pH which is constant for the whole run see figure A 5 In the constant mode the titrant additions are pre defined and constant see figure A 5 The direction selection is possible only in the dynamic mode and defines whether the dynamic mode will be used for both directions or the constant mode will be applied during the back run This is useful if the back run is preferred to be accelerated for some reasons It is emphasized that in all scenarios the titrator 149 FORTH CONSTANTAS DITIONS ra ec emia SCENARIO 2 Figure A 4 Experimental scenarios with Jonction titrator The bare arms in the flowchart denote directions which were still not implemented at the time of this manuscript ji Te Tj LA e ee i6 7 fz b BL _ ZT a 6 4 4 J e e e e 4 e e X nl ia 4 o FIL Le 0 0 02 04 06 08 1 0 12 00 02 04 06 08 1 0 1 2 V KOH ml V KOH ml Figure A 5 Titration curves obtained with a dynamic and b constant titrant addition modes 150 performs forth and back titration runs The ionic strength control lets the user choose whether the titrator should attempt to maintain a pre defined constant ionic strength in the system during the titration A constant ionic strength can be maintained by adding salt or water in order to correct for the change produced by an acid or base addition The variable ionic stength scenario is preview
94. first step due to four symmetrically equivalent outermost groups A common feature of the GO mechanism for both dendrimers is that the macrostate with four bound protons exerts three distinct microspecies out of which the one with the protonated primary amine groups is largely predominant over the two with one deprotonated primary group In principle another microspecies with two unprotonated primary amine sites can be imagined but it turns out that the probability of that one is lower than one per thousand A difference in these mechanisms can be noticed regarding the last protonation step In the case of poly propyleneimine GO dendrimer the inner two sites are protonated in a single step at 5 lt pH lt 7 In the case of poly amidoamine GO dendrimer the protonation of the inner two sites occurs in two separate steps around pH amp 6 and around pH amp 3 5 This difference can be explained by the dependence of the pair interaction parameter on the distance between the sites 6 44 For poly propyleneimine dendrimers where there are four carbon atoms in between the inner two sites the pair interaction parameter is lower than for the poly amidoamine dendrimers These sites are separated by only two carbon atoms The macrostate probability diagrams of the first generation poly amidoamine and poly propyleneimine dendrimers are shown in fig 3 7 The main differ ence is in the probabilities of the most pronounced intermediate macrostat
95. g them the glass cylinders have to be cleaned if they appear dirty or contain precipitate and the pistons replaced if damaged The taps can easily be replaced if they become blocked by some precipitate A check by an official Metrohm mechanic is recommended after cca 5000 hours of usage for all the mechanical and electronic parts within the main body It is recommended to check the precision of the piston walk on the same occasion Directions for manually operating and maintaining the burettes can be found in the Metrohm burette manual In order to dispense volumes smaller than the size of a drop the tubing endings were submerged into the solution To minimize the diffusion flux of the ions through the tubing openings the tubing endings were made of 0 2 mm inner diameter teflon tubing Therefore in order to minimize the dispensing pressure the dispensing rate should not exceed 5 mL min Otherwise leakages may occur 140 Electrodes The pH measurement couple consists of two separate electrodes glass electrode Metrohm 6 0123 100 and Ag AgCl reference electrode Metrohm 6 0733 100 pH measurement couple specifications e Glass electrode pH measuring range 0 14 Membrane glass type U Membrane resistance 150 500 MQ Electrode slope gt 97 of the ideal Nernst value Electrode zero point 0 15 mV e Ag AgCl reference electrode Diaphragm Ceramic pin Reference electrolyte KCl c 3M Diaphragm flow rate 5 15 wL h
96. gligible pair interactions between the primary and the outermost tertiary sites In the case of the first generation poly propyleneimine dendrimer the most interesting microspecies is for m 10 with protonated primary and the in nermost tertiary amine sites as can be seen by inspecting figure 3 9 Another difference with respect to the mechanism of the poly amidoamine dendrimer is that the difference in the probabilities of the two microspecies at m 13 is less pronounced which is a consequence of a smaller difference between pk and the pk in the case of poly propyleneimine dendrimer Apart from the above differences the microscopic mechanisms of the G1 poly amidoamine and 66 a poly amidoamine dendrimer G1 degree of protonation 0 8 0 6 0 4 degree of protonation Figure 3 7 The macrospeciation diagrams for the first generation poly amidoamine and poly propyleneimine dendrimers The most important macrospecies are denoted with m the number of bound protons per molecule 67 9 00 6 70 9 00 6 00 5 85 5 55 6 70 o 3 85 9 00 91 nag 570 m 0 5 85 7 css 25 3 85 239 10 5 70 5 70 9 00 3 85 5 55 3 9 5 70 SEB 5 70 82 eae 6 70 3 70 555 m 9 5 70 5 70 16 9 00 53 5 70 D BE 385 5 55 3 85 8 85 5 70 m 10 0 25 5 70 5 55 38 5 70 0 25 vo ir 8 3 70 5 55 5 70 a 6 55 62 570 SEB 5 55 m 11 4 3 70 3 85 m 12 40 6 40 22 5 70 5 55 5 55 1 2 5 55 2 98 m 13 2
97. hanism of poly amidoamine dendrimers was suggested to involve two independent protonation steps of the primary and tertiary amine groups 53 while others have surmised that poly propyleneimine and poly amidoamine dendrimers should protonate similarly 31 In this chapter it will be demonstrated that the protonation mechanism of poly amidoamine dendrimers is very different from the poly propyleneimine dendrimers and for higher generations indeed involves the almost independent protonation of primary and tertiary groups which is consistent with the observed intermediate plateau at 1 2 However this picture is only partially correct for lower generations since the two innermost tertiary groups interact strongly and protonate in two distinct steps Furthermore it will be demonstrated that the protonation mechanisms of poly propyleneimine and poly amidoamine dendrimers can be combined in the case of a dendrimer with a structure similar to poly propyleneimine dendrimer but with a short core carbon chain which will be referred to as 2 3 dendrimer The microscopic protonation mechanisms presented hereby have been ob tained by applying the same microscopic site binding model which was intro duced in chapter 2 The cluster expansion of the free energy of protonation 6 33 36 37 42 is used in the same manner as presented there with a set of 54 protonated i 14 deprotonated s 1 0 1 0 0 0 0 1 0 1 1 0 1 1 Figure 3
98. he classical description in terms of the macroscopic equilibria is inherent to the site binding model In contrast to the classical picture however the site binding model is capable of quantifying the protonation behavior within an entire homologous series with a limited number of parameters With the site binding model one can further address the microscopic proto nation mechanism in detail as will be discussed in chapter 3 2 6 Conclusion Poly aminido amine PAMAM dendrimers of generations GO G1 G2 G3 G4 and G6 were investigated by potentiometric titrations and the data analyzed in terms of classical macroscopic protonation equilibria and a site binding model While both descriptions are equivalent the site binding model offers further the possibility to model the titration curves of the higher generation dendrimers 51 and to describe all dendrimers within a common set of parameters These pa rameters involve the microscopic ionization constants for each group in the fully deprotonated state and nearest neighbor pair interaction parameters 92 Chapter 3 Microscopic protonation mechanisms of dendritic polyamines 3 1 Introduction In the microscopic picture of protonation the species are distinguished by both the number of bound protons m and their distribution among the protonation sites 6 45 The studies of the protonation species at the molecular level were first become feasible with the development o
99. he fixed respective amounts of different types of sites For example for high generations of poly amidoamine dendrimer there are only two types of sites that play an important role with two distinct pK values namely the pri mary amine groups and the tertiary amine groups there is only one significant pair interaction parameter namely In the case of high generations the in nermost sites are greatly outnumbered by the rest and the ratio of the primary amine groups to the total number of sites N is approaching 1 2 Consequently the proton binding isotherm exerts a plateau at 0 1 2 The proton binding isotherms of high generations of poly propyleneimine dendrimers are showing a plateau at 0 1 3 The source of the plateau in these curves can be rationalized 61 by inspecting the most prominent microspecies presented in fig 3 10 as will be discussed later The microscopic protonation mechanisms for the zeroth generation of poly amidoamine and poly propyleneimine dendrimers are shown in figures 3 5 and 3 6 respectively In the lower part of these figures the macroscoopic speciation diagrams and the overall proton binding isotherm are presented The proton binding isotherm shows a pronounced protonation step at 8 lt pH lt 10 for poly amidoamine and at 9 lt pH lt 11 for poly propyleneimine where two thirds of the sites are protonated The microscopic mechanisms show that the peripheral sites are protonated in the
100. he table 1 2 1 15 It can be noticed that the titration steps are somewhat broader than for the acetic acid The same treatment as for the acetic acid can be performed for ethylene diamine The two pKa can be obtained by fitting and their values depend upon the ionic strengths The values are summarized in table 1 1 together with the literature values 11 It should be noticed that the constants reported in Martell and Smith are the concentration constants defined as Keone eus 1 21 To compare the fitted mixed deprotonation constants see the definitions 1 3 and 1 4 with the literature values a correction of the mixed constants for the activity coefficient of the proton is required The ionic strength dependence is more pronounced than in the case of acetic acid which is due to the interactions of the protonated sites as will be discussed in chapter 2 From table 1 1 it can be verified that the experimentally obtained deprotonation constants fit very well with the literature values The only exception is in the case of ethylene diamine at 27 Table 1 1 The fitted mixed deprotonation constants versus the corrected litera ture values 1 step 224 step Substance I M fit literature 11 fit literature 11 Ethylene diamine 0 1 10 02 10 02 el 7 02 0 5 10 14 10 15 7 44 7 43 1 0 10 21 10 29 7 54 7 56 Acetic acid 0 1 4 70 4 66 0 5 4 62 4 62 1 0 4 64 4 67 1 0 M ionic strength where the data are less accu
101. his was the highest value that could be used in order to describe the data in terms of the double layer model or the basic Stern layer model A possible source for such a low pKa value might be the specific adsorption of negative counterions in this case Cl 8 As well a higher surface charge 600mCm than usual has been observed 61 85 which could be due to the surface roughness The proton binding isotherms of pDADMAC figure 4 5 are showing a fairly constant charge of the quaternary amine groups upon the variation of pH It has to be stressed that pDADMAC does not contribute to the total net charge in the solution since the charge of the quaternary amine groups is fully compensated by the charge of the counterions Cl and in this respect pDADMAC acts as a monovalent strong electrolyte However when adsorbed to the carboxylate latex surface these counterions are to a certain extent depleted from pDADMAC which gives rise to the positive surface charge of the adsorbed pDADMAC 67 Although the adsorption isotherms from the batch experiments are showing a dependence of the equilibrium adsorbed amount on the pH a very good reversibil ity of the titration curves was achieved by fast titration experiments which was established by comparing the data from the forward and backward titration runs at same pH and ionic strength This and the fact that the common intersection points can be easily recognized in the proton binding isotherm
102. iagrams with the according most prob able microspecies for the zeroth top and first bottom generation of 2 3 dendrimer 76 55 9 40 7 50 7 50 86 7 50 82 16 5 7 50 1 0 5 30 4 50 5 50 6 50 5 50 5 50 9 a 4 50 4 78 12 4 50 5 30 A 5 50 7 50 8 1 4 30 Ke 70 5 50 8 m 11 26 4 50 5 50 o 330 4 50 3 30 Ke 450 8 2 3 82 64 4 30 5 50 10 Tia a 4 50 89 11 Figure 3 13 The microscopic mechanism of the first generation 2 3 den drimer The most important microspecies are presented for several distinguished macrospecies denoted with m see figure 3 7 A probability is assigned each microspecies and the micro pK values are assigned to the unprotonated sites 17 The most convincing evidence that the protonation mechanism of the 2 3 dendrimer would exert intermediate microspecies characteristic for both poly amidoamine and poly propyleneimine dendrimer is demonstrated in figure 3 14 The prominent microspecies at pH 8 5 has the outermost primary amine sites protonated as in the case of poly amidoamine dendrimer At 5 lt pH lt 7 the prominent microspecies is featured with alternated protonated and deproto nated shells as in the case of the poly propyleneimine dendrimer Therefore the proton binding isotherm of the fourth generation of the 2 3 dendrimer pre sented in fig 3 11 is featured with a clear plateau at 0 2 3 as in the case of poly pro
103. ibria for polyelectrolytes more complicated than in the case of simple or oligo acids or bases as was confirmed in numerous experimental studies 1 In the present thesis this problem is addressed by applying a simple site binding model similar to the Ising model 9 which includes only several parameters and can be resolved by applying statistical mechanics Within this model the same set of parameters can be applied for different types of molecules and its usefulness is demonstrated in the third chapter where a comparison of the detailed microscopic charging mechanisms is presented for three types of dendritic polyamines namely the poly amidoamine poly propyleneimine and 2 an imaginary dendrimer which has a structure similar to poly propyleneimine dendrimer but with a short core unit Fourth chapter presents a study of the charging properties of weakly acidic carboxylate latex particles in the presence of poly dimethyldiallylammonium chloride which is a strong polycation It is demonstrated that the adsorbed amount of polyelectrolyte can be inferred from the proton binding isotherms The applicability of the basic Stern model and a modified version of that model was investigated for the interpretation of the experimental data Particularly interesting results were obtained with the modified Stern model In the fifth chapter the charging behavior of silica in the presence of adsorbed poly dimethyl diallylammonium chloride i
104. ide limits which were set as parameters or it had to be corrected see the chapter about the dynamic titration procedure 5 Titration curve graphic all the points c r v titrant volume of the current titration run are displayed 6 Error led indicator this will indicate some errors that may occur during the titration e g a burette was not properly assigned to the titrant solu tion the maximum dispensing volume for the titrant burette was exceeded etc Algorithms Data acquisition subroutine SV_read_all_and_write_to_data vi The flowchart of the data acquisition subroutine is presented in the figure A The 169 F Calibrated reading value acquisition J 7 s Write to data N i i 1 Reading the volume from Y 7 Burettei Figure A 11 The data acquisition subroutine flowchart JS Fa N NS Start chrono Read Higlmp4 during T calculate CRV drift stdev N 27 drift lt drift criterion N Y lt OR p timeout EXIT NY N N Figure A 12 The calibrated reading value acquisition flowchart C r v is acquired simultaneously as the volumes from all the burettes These values are being written to the data file The time delay for this subroutine is given by the time delay for the c r v acquisition Calibrated SV_HighImp4_Acq_Drift vi The flowchart of the c r
105. ies equation at low to moderate ionic strengths At J 1 0M the discrepancy is significant which could be due to an experimental error these points stem from the titrations which were performed as the last in the course of an experiment at which stage the system contains more dissolved CO The parameters obtained from fitting are determinant for the experimental pH scale Figure 1 19 is showing several modeled blank titration curves with different parameters It can be concluded that y influences the curve at high and low pH Parameter Ep shifts the titration curve parallel with the pH scale while parameter A causes a shift and broadening of the titration curve The ionic strength influences the curve through the activity coefficients shifting it in high and low pH regions The influence of pK is growing with pH and it is becoming predominant over pH at pH pX 2 At low pH pKw does not have 30 Table 1 2 Parameter b from the Davies formula and the corresponding activity coefficients I M b logy y 0 1 0 46 0 10 0 80 0 5 0 37 0 12 0 76 1 0 0 34 0 09 0 82 1 0 0 9 0 8 0 7 0 6 0 5 0 0 0 2 0 4 0 6 0 8 1 0 1 moldm gt Figure 1 18 The activity coefficients y obtained from the blank titration curve fittings versus the ionic strengths The solid line is calculated by means of the Davies formula 31 0 001 0 000 H Acidity moldm 0 001 pH Figure 1 19 Influence of various param
106. ijer E W and M Borkovec Journal of the American Chemical Society 119 6512 6521 1997 Borkovec M and Koper G J M Analytical Chemistry 72 3272 3279 2000 Huang Q R Dubin P L Moorefield C N and Newkome G R Journal of Physical Chemistry 104 898 904 2000 Welch P and Muthukumar M Macromolecules 31 5892 5897 1998 Pericet Camara R Papastavrou G and Borkovec M Langmuir 20 3264 3270 2004 Niu Y Sun L and Crooks R M Macromolecules 36 5725 5731 2003 Borkovec M and Koper G J M Journal of Physical Chemistry 98 6038 6045 1994 Borkovec M and Koper G J M Macromolecules 30 2151 2158 1997 van Duijvenbode R C Rajanayagam A Koper G J M Borkovec M Paulus W Steuerle U and Haussling L Physical Chemistry Chemical Physics 24 5649 5652 1999 Noszal B Journal of Physical Chemistry 90 4104 4110 1986 Rabenstein D L Journal of the American Chemical Society 95 2797 2803 1973 Rabenstein D L and T L Sayer Analytical Chemistry 48 1141 1146 1976 Mernissi Arifi K Schmitt L Schlewer G and Spiess B Analytical Chem istry 67 2567 2574 1995 188 58 59 60 61 Felemez M Bernard P Schlewer G and Spiess B Journal of the American Chemical Society 122 3156 3165 2000 Zhang X X Oscarson J L Izatt R M Schuck P C and Li D Journal of Physical Chemistry 104 8598 8605 2000 Yamamoto K Higuchi M Shiki S Tsurut
107. ion In the first case the system can be described by means of the basic Stern model If the fixed positive charge is considered as displaced from the surface origin the first step towards modeling could be to place this charge at the origin of the diffuse layer as depicted in fig 4 2 The latter approach will be referred to as the modified Stern model where the negative electrostatic potential in the 0 plane has a higher magnitude due to a smaller influence of the positive pDADMAC sites This modification is equivalent to the model which includes the specific adsorption of the counterions with an infinite binding constant 73 for the cations The basic Stern model is a classical approach for solving the charging equi libria at homogeneous surfaces 6 8 74 where the interface is divided into two compartments namely the surface and the diffuse layer As a consequence of the electroneutrality condition the charge in the diffuse layer 7g has to neutralize the surface charge do Oa 00 4 1 The Gouy Chapman equation can be invoked to calculate the potential in the diffuse layer Wa 2kT e arcsinh eoa 2kT eerk 4 2 where e is the elementary charge og is the charge per surface area at the origin of the diffuse layer coe is the permittivity of the medium kT the thermal energy and the inverse Debye length Der 2 4 3 n eiT 4 3 where J is the ionic strength in units of number of ions per m On the other
108. ioned earlier the fully unprotonated molecule is taken as the reference state The number of microstates for a macrostate m grows with the number of sites as eal 6 The probability of a microstate can be expressed as a product ps 7 si Pn an 3 3 where m s denotes the conditional probability of the microstate s within the macrostate m This probability is given by m si Kate orton 3 4 It should be noted that the probability 7 s does not depend on pH and can be easily interpreted as the mole fraction of the microspecies within a macrospecies m Once all cluster parameters are known the microscopic protonation constants for all the unprotonated sites within all the microstates can be calculated in a straightforward fashion If we label the unprotonated site with j the association equilibrium can be written as A 5 H A s 3 5 where s s for all i j but s 0 and si 1 Using expansion for the free energy eq 2 6 the microscopic pK value for the reaction given by eq 3 5 follows as 42 J 56 This relation defines the change in the microscopic protonation constant of a group in the presence of another protonated group and reflects the group ad ditivity concept for the estimation of protonation constants 54 In the present approach the microconstants from eq 3 6 represent secondary parameters which can be easily evaluated once the primary cluster parameters are known 3 3
109. is to reduce the current deficit in experimental surface charge data and contribute to the understanding of pH dependent charging of surfaces in the presence of adsorbed polyelectrolytes The most straightforward method for measuring the equilibrium excess charge in a system which contains acid or base is the potentiometric titration 6 8 The methodology for estimating the solution excess charge from the potentiometric titration data will be presented in the first chapter of this thesis This will include a thorough description of potentiometric data analysis which will be supported with experimental examples the tests of precision and accuracy and discussions of error sources Within the present thesis a computer controlled high precision titrator was developed A peculiarity of this setup is the facility of performing repeated titration experiments at constant ionic strengths including real time data monitoring A thorough technical description of this setup directions for programming and running are presented in the appendix The focus of the second and the third chapter is on the protonation behavior of hyperbranched polyamines in solutions In the second chapter the proton binding isotherms of six different generations poly amidoamine dendrimers are reported at different ionic strength The fact that the protonation state of one site can influence the protonation constant pK of another site makes the solution of the acid base equil
110. ite within a certain macrostate The probabilities of the protonation species can be interpreted in terms of abundances in the solution The presence of the microspecies can be experimentally confirmed by means of spectroscopic methods in particular NMR 6 36 37 and UV VIS and IR techniques 6 The microstates will be presented schematically as shown in fig 3 1 and the macrostates will be simply denoted with m which is the number of bound protons to the molecule The microscopic mechanisms will be presented as schemes of the most prominent microspecies for a certain macrostate together with the according probabilities and all the micro constants The macroscopic protonation mechanisms will be presented in terms of the speciation diagrams P pH e g fig 3 7 which are directly reflected in the proton binding isotherms as can be concluded from the eq 2 2 In this man ner a comprehensive picture of protonation can be gained for all the molecules studied The protonation mechanism can be deduced once all the cluster parameters are assessed The conditional probabilities of the microspecies within a certain macrospecies can be calculated according to formula 3 4 and the microconstants according to eq 3 6 The difference in the microstate probabilities reflects the difference in the free energies of microspecies which can be calculated according to eq 2 6 In other words the microstate probability is weighted by the free energy The p
111. k CH3COO7 OH H K CI 1 13 The activities of all the dissociation species are mutually dependent 10 Therefore at a fixed initial composition of the solution the overall speciation can be regulated by changing the activity of one single species Since the proton activity is easily measurable it is convenient to express the concentrations of the dissociation species versus pH This also enables a comparison of the speciation in different solutions e g two different acids with the same total concentrations this is the reason for which pH is called the master variable 8 Proton binding isotherm is the dependency of the overall degree of protonation of an acid or a base upon pH 6 pH see figure 1 1 proton binding isotherm reflects the dissociation speciation in the solution and is fully defined by pKa values and the pH For example for acetic acid when pH lt pKa the protonated CHCOOH species dominate over the deprotonated charged CH3COO species 7 degree of protonation 6 2 4 6 8 10 Figure 1 1 Example of a modeled proton binding isotherm of acetic acid at 0 1 M ionic strength The dashed line denotes pH pky 4 66 11 When pH gt pKa the situation is reversed In the case where the initial acid or base concentration is proportional to some other measurable quantity e g the surface area of a particle with acidic or basic surface groups the degree of protonation 0 can be replac
112. k ground electrolyte The charge reversal occurs when the sum of the PDADMAC charge experienced by the carboxylate sites and the charge of the protons bound to them equals the negative charge of the deprotonated carboxylic groups The pH value of the charge reversal can be referred to as the point of zero charge PHpzc or P Z C where the electrostatic potential at the surface origin where the carboxylic groups reside Wo equals zero 78 This point depends on the surface charge concentration of the carboxylate groups the surface concentration of the adsorbed pDADMAC and the solution pH but does not depend on the background electrolyte concentration The point of zero charge in the composite system depends on the adsorbed pDADMAC charge which in the low range of pDADMAC less than one pDADMAC site per one surface site turned out to be tunable by the polyelectrolyte loading In the pH range above the point of zero charge when the surface charge is negative the surface is acting as a weak acid Conversely in the pH range below the point of zero charge the surface charge is positive and the surface is acting as a weak base The presence of the point of zero charge in the experimental proton bind ing isotherm enables distinguishing the adsorbed from the dissolved pDADMAC charge The adsorbed charge is the fraction of the added pDADMAC charge 109 which has an influence on the surface potential The dissolved charge estimated as the
113. l 9 reference electrode as measured by a high impedance voltmeter and the volumes of the added solutions were collected at pre defined ionic strengths which were kept constant during one titration run Successive forward and backward titra tion runs were performed throughout this text forward titration means the pH sweep from the initial to the final pre defined pH value and backward is the opposite direction at different ionic strengths which were adjusted after a forward and backward titration cycle 1 3 Experimental setup In this work with an invaluable effort of Stephane Jeannerret a computer controlled high precision titration setup was built from scratch The experience with the Wallingford titrator 16 was very helpful to fulfill this task The new titrator is called the Jonction titrator The scheme of the Jonction titrator setup is presented in figure 1 2 All the technical details about the Jonction titrator and the details about the software needed to run the constant ionic strength titrations are presented in the appendix of this thesis The hardware of the Jonction titrator consists of the following the numbers in the list correspond to the scheme presented in fig 1 2 1 Four Metrohm 712 Dosimat burettes with tubings 2 pH measurement electrode couple 3 Voltmeter with A D converter 4 Titration cell 5 Pure nitrogen degassing apparatus 6 PC 10 voltmeter A D conve
114. l for weakly acidic particles 6 61 The maximum charge which is achieved above pH 10 equals 600 20 mCm which corresponds to 3 74 elementary charge units per nm At low pH typically below pH 4 the surface charge approaches zero The lines in figure 4 4 represent the best fit of the basic Stern model to the experimental data The model parameters are presented in table 4 5 Better fitting could not be achieved by a lower value for the Stern capacitance The basic Stern model in which the Stern capacitance equals infinity is equivalent to 97 0 0 0 1 0 2 0 3 0 4 0 5 surface charge Cm 0 6 Figure 4 4 The proton binding isotherm of carboxylated latex suspension at three ionic strengths o e 0 01M O08 0 05M A a 0 10 M The maximum surface charge equals 600 mC m Open and closed symbols represent the forward and the backward titration runs respectively The lines represent the Basic Stern model predictions the parameters are presented in table 4 5 the simple double layer model which does not include a capacitor 74 78 The proton binding isotherms of the pure pDADMAC solution are shown in figure 4 5 In this case 0 0161 g of the pure pDADMAC was titrated which corresponds to 0 1 mol of nitrogen quaternary amine sites The amount of pDADMAC monomer units corresponds to cca 600 mC g by considering every monomer unit as one elementary charge 100 quaternization The curves are showing a
115. l parameters see SV Titr_enter_par_ multi test vi The user interface of that subroutine automat ically appears on the screen After user closes that the subroutine for burette assignment see Prod_assign vi is called Upon quitting on command the main program performs burette initialization where the communication is established and some settings are passed to them limiting volumes filling and dispensing rates which should take less than 5 seconds After that the program will ini tialize the log file and then wait for further commands This is announced by 152 Titration Channel Titration PES Calibration er b D Slope 710 0000 pH 4 60 c SeS ey ql Offset 0 00000 Arid 4 20 Parameters for Titration A gt S 4 00 ee a 3 3 80 3 5 3 60 8 View Drift 3 40 On sag Titration C Titratin J Jor C g 3 20 3 00 7 D D 1 1 1 D 1 D i 1 0 35 0 40 0 45 0 50 0 55 0 60 0 65 0 70 0 75 0 80 0 85 Status Volume mL MB Lune alia Calibrated value i a eS CH Time elapsed 0 si Current ionic strgth 10 000 mo error Old_values 0 List of Channels EU Manual Dosimat Access 0 Old Vol 5 000 pH_Array Index 0 00 A _ Old_Meas 5 500 j Vol_Array 0 VISA_acid Acid_Used Base_Used Salt Used Water_Used al Chronometring VISA_base delta_pH_init 0 00 v refnum data Vsample VISA_salt el refnum log VIEN Reroun 0 00 v Sl Volumes VISA_water H Va_total Vb_total Vs_total Vw_total
116. lation of the additions is previously performed by a non interactive subroutine see init_dose_calc vi After that an adjustment of the initial pH in the cell is performed see SV_adjust_pH vi Usually this step is needed only when the initial solution contains some substance undergoing dissociation and not needed for the blank titrations Then the titrations are performed under the conditions that have previously been defined several pos sible experimental scenarios are described in figure A 4 The subroutine which performs the dynamic constant ionic strength titration in one direction between pre defined initial and final pH is SV_titra dyn_cnst_I forth1 vi For the dynamic mode forth and back titrations at constant ionic strength it is invoked in loops where the directions inner loop and ionic strengths outer loop are varied Af ter the titrations have been finished at the highest defined ionic strength the program will close the data file stop the chronometer and wait for further com mands Idle state waiting for command is announced in the status indicator If desired the experiments can be repeated the system in the titration cell has 154 to be exchanged though or the main program can be quitted by clicking the Quit button In the latter case the communications with burettes are termi nated the burettes are switched to manual control the log file is closed and LabView is quitted If the program is termin
117. lution 5 3 Data treatment and results The data treatment of the potentiometric titration experiments was performed in the same way as described for the pDADMAC latex system chapter 4 In a first correction the charge of all the free Cl and K ions which were added with pDADMAC and during pH adjustment for the adsorption was subtracted from the experimental raw proton binding isotherms The resulting proton binding isotherms showed an excess positive charge which can be considered as dissolved charge Njiss at the common intersection point Following the same argument as described in the data treatment for the pDADMAC latex system 119 adsorbed DADMAC sites nm 00 02 04 06 08 1 0 added DADMAC sites nm Figure 5 2 The excess positive surface charge as calculated from the positive charge at the point of zero charge see text recalculated into sites per nm is plotted versus the loaded amounts of pDADMAC o low molecular weight pDADMAC 100 200 kDa O high molecular weight pDADMAC 400 500 kDa chapter 4 this charge was used to calculate the adsorbed charge The values of the adsorbed and the dissolved charge are listed in table 5 2 In the second correction the dissolved charge N was subtracted from the proton binding isotherms so that the presented data exert a common intersection point at zero surface charge In figure 5 2 the adsorbed amount of quaternary amine sites calcula
118. mely that of 100 200 kDa and 400 500 kDa the points of zero charge were found to coincide for the same adsorbed amounts The modified Stern model as presented in chapter 4 was here as well found to be appropriate for describing the proton binding isotherms As a part of this thesis and with an invaluable effort of the department elec tronic workshop an automated titrator was developed and called Jonction titra tor The routines were developed in order to perform potentiometric titrations at pre set constant ionic strengths The development of this setup is described in the appendix 135 136 Appendix A Automated potentiometric titrator Introduction In the initial stage of this work constant ionic strength acid base potentiometric titrations were performed with the Wallingford titrator introduced and described by Kinniburgh and Milne 16 The Wallingford titrator is featured with very good flexibility and to my knowledge it is the most widely used setup for this kind of experiments Although not very user friendly this setup can be applied for a variety of titration tasks including the conductivity titrations A new titration system called Jonction titrator was set up during the later stage of this work based on the experience with the Wallingford titrator For the new setup Mr Stephane Jeannerret at the Department of inorganic analytical and applied chemistry at the University of Geneva has built a high im
119. micro constants of particular protonation sites are indicated 79 between the protonated sites Due to the symmetry of the molecule only a limited number of cluster parameters is necessary for an assessment of the protonation mechanism for even very large molecules The poly amidoamine and poly propyleneimine dendrimers exert different microscopic protonation mechanisms due to a difference in the structure of the two molecules In the case of poly amidoamine dendrimers the core carbon chain is short while the arms of the hyperbranched part are long and vice versa for the poly propyleneimine dendrimer For poly amidoamine dendrimers this causes the mechanism to be mainly sensitive to the pA parameters the pair interaction parameter is playing a role only for the protonation of the last core site at low pH In the case of poly propyleneimine dendrimer both the pki and the pair interaction parameters play an important role The difference in the microscopic protnation mechanisms of the poly amidoamine and poly propyleneimine dendrimers affects the overall pro ton binding isotherm In the case of poly amidoamine dendrimer the inter mediate microspecies is present at 7 lt pH lt 8 where the outer rim sites are protonated and the tertiary amine sites deprotonated This is reflected in a plateau in the proton binding isotherm at 0 1 2 The protonation mecha nism of the poly propyleneimine dendrimers is featured with
120. n a titration run Delta_pH_init control Lets the user set the convergence criterion for the initial pH setting see SV_cnst_mode vi Cell composition at start button The button triggers the subroutine where the user can enter the content of the cell that was manually dosed prior to the current experiment see cell_comp vi Titration curve settings Titration mode switch Lets the user choose between dynamic and con stant additions mode see the paragraph about the experimental modes If the constant mode is used then the controls 21 to 24 are not accessible 159 20 21 22 23 24 25 26 27 28 24 30 31 Direction switch Lets the user choose between One way and Froth and back modes Delta vol min control The minimum volume of the titrant that can be dispensed in the dynamic mode It is recommended to set this to a low value e g 0 005 mL Delta vol max control The maximum volume of the titrant that can be added in dynamic mode It is recommended to set this to a value between 0 2 and 1 0 mL depending on the concentrations of acid and base in the burettes Delta pH The control for setting of the aimed pH increment Attenuation factor The control for setting the attenuation factor see SV _titra_dyn_cnst_I_forth1 vi Constant additions The constant additions of the titrant used in the constan
121. n binding isotherms of the silica particles Open symbols rep resent the forward titrations and closed symbols the backward titrations Ionic strengths o 0 e W 0 01 M A V 4A Y 0 10M 9 0 89 1 00 M The lines represent the prediction by the basic Stern model with the parameters enlisted in the table 5 3 Table 5 1 The parameters of the basic Stern model obtained from fitting the experimental proton binding isotherms of silica where pKa is the microscopic dissociation constant and o total surface concentration of the protonation sites from 76 fitted with the MUSIC model Stern capacitance To pKa Fm sites nm 7 5 3 5 8 122 Table 5 2 The results obtained from the proton binding isotherms of the com posite pDADMAC silica system Adsorbed and the dissolved sites Nj are explained in detail in the data treatment section in chapter 4 The Stern ca pacitance is obtained by fitting the modified Stern model see chapter 4 to the experimental proton binding isotherms The upper part of the table refers to pDADMAC with Mw 100 200 kDa and the lower part to pDADMAC with Mw 400 500 kDa DADMAC DADMAC DADMAC loading adsorbed dissolved Cs sites nm sites nm sites nm Fm pH 0 26 0 12 0 14 2 90 5 78 0 45 0 26 0 19 1 26 6 71 0 44 0 28 0 16 1 26 6 72 0 68 0 53 0 15 1 10 1 12 0 37 0 36 0 01 1 62 6 78 0 60 0 50 0 10 1 05 7 68 0 94 0 83 0 11 1 05 8 70 The prot
122. n equilibria of polyprotic acids where the macroscopic protonation state or macrostate is defined by the number of the protonated sites m and the total number of protonation sites N 6 11 Thus there are N protonation steps and to each step a macroscopic protonation constant is assigned _ _ GA Km Alaa 2 1 The degree of protonation 0 can be calculated from the probabilities of the macrostates Pm 1 N a 3 2 2 38 NH H Figure 2 1 Chemical structure of the zeroth first and second generation of poly amidoamine dendrimers 39 The probability of a macrostate can be expressed through the macroscopic pro tonation constants m ae K 2 Miz L 2 3 1 el ayy Tien Ki Equations 2 2 and 2 3 define the proton binding isotherm 0 pH However the m macroscopic picture of protonation equilibria does not give information about the distribution of bound protons among the different protonation sites For the convenience of the following discussions it is also useful defining the cumulative protonation constant for a macroscopic protonation state m Kn Ke 2 4 Thus from eq 2 3 and eq 2 4 the macrostate probability can equivalently be expressed as UR Pan T t 2 5 Lee ye Protonation equilibria of polyprotic acids or bases can be described with a site binding model which is analogous to the classical Ising model 6 33 36 37 42 To each protonation site i a state
123. n exchange of the Cl ions with the solution The two conclusions can not be distinguished from the current experiments Therefore it can not be clearly stated whether the difference in the pDADMAC charge experienced by the silica surface presented in figure 5 2 for two different molecular weight of pDADMAC reflects a difference in the adsorbed amount the density of the adsorbed sites or an exchange of Cl ions with the solution A combination of these effects is possible as well 5 5 Conclusion Silica particles are suitable for studying the charging behavior in a system com posed of weakly charged particles and adsorbed strong polyelectrolyte The presented proton binding isotherms can give important information about the charging behavior in these systems An interesting feature of the proton binding isotherm is the point of zero charge which is tunable by the adsorbed amount of pDADMAC If there are no counterions present within the adsorbed layer and the strong polyelectrolyte is adsorbed in a conformation where all the sites reside at the surface the excess charge which is present at the point of zero charge can be attributed to the polyelectrolyte in the solution The coincidence between the point of zero charge observed with two different molecular weights of pDADMAC at the same adsorbed pDADMAC charge i e the pDADMAC charge which actually influences the surface potential is point ing out in two directions First the ef
124. n of charges in the electrical double layer at the particle solution in terface The basic Stern models with two surface components at the surface two types of sites with two different pK values is not capable of reproducing the experimentally determined point of zero charge see figure 4 8 This deviation is becoming larger with an increase of the adsorbed amount of PDADMAC This is due to an overestimation of the pDADMAC charge influence at the surface potential wo On the other hand the modified Stern model can give good pre dictions of the point of zero charge which is a consequence of the fact that the 110 pDADMAC sites are modeled to be at a certain distance from the surface see fig ure 4 2 such that the surface potential Yo is less influenced by the pPDADMAC charge The presence of the pDADMAC charge which does not influence the surface potential is in agreement with the picture of the pDADMAC sites as displaced from the surface as the distance of the positive pDADMAC sites from the surface is increased their effect on the surface potential wo decreases The decrease of the effectiveness of the pDADMAC sites will be compensated by an uptake of protons by the surface so that the degree of surface protonation is increased This uptake corresponds to a shift in the bulk pH towards higher values which explains the difference in the predictions of the point of zero charge between the basic and modified Stern model It i
125. n read the current c r v Split dose led indicator flashes when the titrant dose was decreased by half see SV _cnst_mode vi Exit led indicator flashes when the convergence criterion was satisfied and the subroutine automatically closed View drift switch the user can turn on the time dependency of the calibrated signal graphic same as switch 7 in Titrator_dusko vi Variable regulation switch turns on the controls for the below variables Convergence criterion control same as 17 in section SV _Titr_enter_parmulti_test vi 168 7 Initial pH control the user can adjust the pH that is being set However this will not affect the initial pH variable set in the subroutine for entering the parameters SV_Titr_enter_par_multi_test vi 8 Constant addition control the user can adjust the additions of the acid or base used in the pH adjustment procedure Dynamic mode titration procedure SV_titra_dyn_cnst_I_forth1 vi Commands and indicators 1 Current volume indicator indicates the volume of the titrant dispensed in the current titration run 2 Current measure indicator displays the last acquired c r v pH 3 Index indicator indicates the number of the data point currently ac quired or the total number of acquired points in the current titration run 4 Limited led indicator indicates whether the calculated addition volume was ins
126. n the case of polyelectrolytes adsorbed to the particles one should as well consider the polyelectrolyte charge In that case one should tune the electrode charge according to the polyelectrolyte For example in the case of positively charged polyelectrolyte adsorbed on a nega tive surface e g pDADMAC adsorbed onto carboxylated latex the electrodes should be conditioned in 0 1M HCl Very unstable response especially in the basic pH region was observed after using the electrodes in suspensions of metal oxides e g SiO2 TiO2 In the case of silica this is probably due to deposition at the glass electrode surface and blocking of the reference electrode ceramic diaphragm by the particles While a good rinse with a surfactant solution 1 Hellmanex is sufficient for the glass electrode one should condition the reference electrode in 1 M HNO for several hours Changing the inner solution after con ditioning the reference electrode is recommended Finally if the electrodes are showing bad response even after conditioning they should be replaced Microlink 3300 interface and PC requirements Microlink 3300 is an inter face that provides computer control over all the hardware used in the Wallingford titrator setup It belongs to a wider family of Microlink 3000 series interfaces with a GPIB connection to the PC Other models 3200 3301 etc can be con nected via RS 232 Ethernet or both The GPIB connection at the PC end can be achi
127. namic addition calculation The red line is the titration curve blank HCI KOH titration V1 pH1 and V2 pH2 are the two recently measured data points 173 culated according to the initial pH pHinit initial ionic strength I 1 total volume Vtinit sample volume Vsample and all the components that were added to the cell prior to the experiment Va_in ca_in and Vb_in cb_in are the volumes and concentrations of added of acid and base solutions respectively Vs_in and cs_in are the volume and concentration of added salt solution ns_in is the amount of added solid salt in moles and Vsample is the total volume of all added solutions for example it can include the volume of some sample of a weak acid and the volumes of the acid and base added to the cell previously The initial pH ionic strength total volume sample volume and the concentrations of the burette solutions of acid ca base cb salt cs are set in the global param eter subroutine The initial additions of acid base salt and water additions are calculated in the following manner First the acid or base addition is calculated according to the initial pH Vtinit 10 PHinit 1 QPHinit pKw _ ca in Va in cb_in Vb in a A 4 a A 4 Vb Vtinit 10PHinit pKw _ a cbin Vb_in cain Va in A 5 C If the calculated acid or base addition is smaller than 0 pHinit lt 7 then Vb lt 0 otherwise if pHinit gt 7 then Va lt 0 it is
128. nd poly propyleneimine dendrimers is cor rect the microscopic protonation mechanism of the 2 3 dendrimers should exert features of both poly propyleneimine and poly amidoamine dendrimers For the low zeroth generation the protonation mechanism should be more similar to the poly amidoamine dendrimer and for the higher genereations where the branched part dominates the structure the mechanism should be similar to the poly propyleneimine dendrimer The cluster parameters used to infer the protonation mechanism for the 2 3 dendrimer from the site binding model were used as reported in 44 They are listed in table 3 5 and presented in fig 3 14 the scheme refers to the fully 72 poly amidoamine poly propyleneimine 10 lt pH 6 lt pH lt 8 1 lt pH lt 5 3 pH lt 3 Figure 3 10 The most important microspecies of the fourth generation poly amidoamine left and the poly propylene right dendrimers indicating the protonation mechanism The pH ranges in which these microspecies occur and the microconstants for particular protonation sites are indicated 73 Table 3 2 Cluster parameters of the site binding model for the 2 3 dendrimer pKa pk 7 50 9 40 2 20 1 00 unprotonated molecule It was assumed that one pk value is satisfactory for all the tertiary amine sites As well the pair interaction parameters were assumed to depend purely on the spacer length between the sites In this manner
129. nded to higher pH values The surface charge of the pre treated silica is negative in the whole examined pH range At pH lt 3 silica is positively charged 88 89 but such low pH was not experimentally examined in the present work The maximum surface charge at high pH can not be experimentally determined because the highest experimentally reachable pH is around or slightly below pH 9 Above that pH the dissolving of silica is becoming pronounced 90 At pH 9 the charged fraction of the protonation sites is around 8 to 15 per cent of the total protonation sites considering the value of 8 sites per nm for the total surface concentration of the protonation sites 77 depending on the ionic strength A very good description of the experimental proton binding isotherms of pure pre treated silica suspension with the basic Stern model can be noticed in figure 5 3 The parameters obtained from fitting are listed in table 5 3 However it has to be stressed that in this case as opposed to the case of carboxylate latex particles the fitting is not free of ambiguity Namely the total surface concentration of the protonation sites is calculated from the slope of the proton binding isotherm which is as well influenced by the Stern capacitance Cg In other words in the absence of a clear plateau in the data at high pH these two parameters are correlated 121 0 00 H 0 05 0 10 surface charge C m Figure 5 3 Proto
130. ne by extending the mechanism for the first generation The most prominent species for the fourth generation poly amidoamine and poly propyleneimine dendrimers are presented in fig 3 10 69 8 19 8 40 6 52 9 97 8 40 6 53 54T 8 19 9 67 6 52 7 14 8 19 FE 69 5 6 52 m 8 40 75 6 53 Ke 247 8 09 9 97 9 97 1 0 18 5 7 58 5 47 6 52 744 6 52 e 6 52 8 19 6 52 me n 5 47 Fes F 5 47 7 04 8 40 25 Fi 9 97 lt 547 71 6 53 5 ar 5 47 7 58 15 6 52 6 52 _ 5 8 19 2 1 5 47 ace 5 47 se 6 52 i 59 5 48 5 47 11 10 a 57 6 52 m 12 D f 7 14 37 548 5 47 0 Fe 6 53 T f 6 52 35 67 33 Figure 3 9 The microscopic mechanism of the first generation poly propyleneimine dendrimer The most important microspecies are presented for several distinguished macrospecies denoted with m see figure 3 7 A probability is assigned each microspecies and the micro pK values are assigned to the unprotonated sites 70 A difference in the microscopic protonation mechanisms of the higher gen erations of the two types of dendrimers is evident from the proton binding isotherms for high generations As discussed in the previous chapter in the case of poly amidoamine dendrimer the outermost primary amine groups pro tonate almost randomly in the first step at 7 5 lt pH lt 10 One of the innermost sites protonates around pH amp 7 but for higher generations this does not
131. ngths o 0 01 M O 0 05M A 0 10M v 0 50M 1 00 M 96 The outcome of the second correction is shown in the figure 4 3 right Af ter the correction at the common intersection point point of zero charge the surface charge equals zero Assuming that N4__ corresponds to the charge of diss dissolved pDADMAC it makes sense subtracting this quantity from the total added pDADMAC charge and comparing with the adsorption isotherm which is shown in fig 4 6 Both of the above corrections were performed only in the case of the composite pDADMAC carboxylate latex system data The proton binding isotherms of the pure latex are presented as obtained by the standard data treatment as explained in chapter 1 In the case of pure pDADMAC titrations the charge of the CI ions added with pDADMAC was subtracted 4 5 Results The proton binding isotherms of pure carboxylate latex suspension are presented in figure 4 4 The total amount of the titrated sites in this experiment is 0 1 mmol For this total amount of titratable sites the accuracy of the calculated surface charge equals 2 within the experimental window 4 lt pH lt 10 Open symbols represent experiments in which the initial pH in the titration was set to 3 0 and the final pH to 11 0 forward titration runs The closed symbols represent the opposite direction titration run The data are showing a monotonic dependence of the surface charge upon pH which is typica
132. nization constants pX of the PAMAM dendrimer Glee shee es ee Oe eee hee es eee he Wee eo de 49 Cluster parameters of the poly propyleneimine dendrimer 60 Cluster parameters for the 2 3 dendrimer 74 Sample preparation for the titration experiments 92 The parameters of the basic Stern model for the pure carboxylate Fae og oe ke es ee eS SO ee oe a 99 Stern model parameters 2 6 36 es ee eee eee ee ee 105 The shear plane distances for the O Brien and White calculations 107 The parameters of the basic Stern model for the pure silica particles 122 The results obtained from the proton binding isotherms of the composite pDADMAC silica system 123 183 Bibliography Dautzenberg H Jaeger W K tz J Philipp B Seidel Ch and Stscherbina D Polyelectrolytes Carl Hanser Verlag Munich Vienna New York 1994 Zimmermann R Kratzmu ller T Erickson D Li D Q Braun H G and C Werner Langmuir 20 2369 2374 2004 Scherrenberg R Coussens B van Vliet P Edouard G Brackman J de Brabander E and Mortensen K Macromolecules 17 456 461 1998 Biesheuvel M P and Cohen Stuart M A Langmuir 31 2785 2791 2004 Hoagland D A Smisek D L and Chen D Y Electrophoresis 17 1151 1160 1996 Borkovec M Jonsson B and Koper G J M In E Matijevic editor Sur face and Colloid Science volume 16 Kluwer Academic Plenum Publishers New York 2001 Decher G
133. nt The modulator frequency was set to 1 kHz Each data point was measured six times For each measurement the count rates of the scattered photons were accumulated for 30 seconds The sample preparation for the batch experiments were performed in the following manner The latex suspension stock solution at 0 160 mg L was dialyzed against the Milli Q water which was daily exchanged until a constant conductivity of cca 1uScm in the surrounding water The pDADMAC was used as purchased and several stock solutions were prepared in order to cover a wide range of the final sample concentrations 14 17 g of latex suspension was mixed with a comparable volume of the pDADMAC stock solution Then the pH and the ionic strength were adjusted by using 0 1 M HCl and KOH solutions and a 1 M KCI solution Thus the resulting mixture has a particle concentration of 800 mg L After mixing the samples were gently stirred for 24 hours Then the majority of the particles was sedimented by centrifugation for 4 hours at 24000 rpm 103864 G at 25 C Ultra centrifuge Beckman Coulter Avanti J30 I The rest of the particles were separated from the supernatant by filtration Millex hydrophilic PVDF filters pore size 0 1 um The supernatant was analyzed by the total carbon and nitrogen analysis For this the calibration was done by using potassuim hydrogenphtalate and KNO as standards 94 4 4 Data treatment This section contains an important explanati
134. ochimica et Cosmochimica Acta 64 3453 3470 2000 Rietra R P J J Hiemstra T and van Riemsdijk W H Geochimica et Cosmochimica Acta 63 3009 3015 1999 Hiemstra T and van Riemsdijk W H Journal of Colloid and Interface Science 136 132 150 1990 Mahltig B Rehahn M and M Stamm Polymer Bulletin 45 501 508 2001 Mahltig B Gohy J F Jerome R and Stamm M Journal of Polymer Science B 39 709 718 2001 192 99 Ennis J Sj str m L Akesson T and J nsson B Journal of Physical Chemistry 201 2149 2164 1998 100 Eisenman G Bates R Mattock G and Friedman S M The Glass Elec trode Wiley New York 1965 101 Jeannerret S Highimp4 user s guide Technical report Department of inorganic analytical and applied chemistry University of Geneva 2004 193
135. oconjugate Chemistry 4 372 379 1993 186 25 27 lt 3 28 29 is 30 35 Kukowska Latallo J F Bielinska A U Johnson J Spindler R Toma lia D A and Baker J R Proceedings of the National Academy of Sciences 93 4897 4902 1996 Prosa T J Bauer B J and Amis E J Macromolecules 34 4897 4906 2001 Nisato G Ivkov R and Amis E J Macromolecules 33 4172 4176 2000 Ramzi A Scherrenberg R Joosten J Lemstra P and Mortensen K Macromolecules 35 827 833 2002 Ottaviani M F Valluzzi R and Balogh L Macromolecules 35 5105 5115 2002 Chen W Tomalia D A and Thomas J L Macromolecules 33 9169 9172 2000 Betley T A Banaszak Holl M M Orr B G Swanson D R Tomalia D A and Baker J R Langmuir 17 2768 2773 2001 van Duijvenbode R C Koper G J M and Bohmer M R Langmuir 16 7713 7719 2000 van Duijvenbode R C Borkovec M and Koper G J M Polymer 39 2657 2664 1998 van Duijvenbode R C Rajanayagam A Koper G J M Baars M W P L de Waal B F M Meijer E W and Borkovec M Macromolecules 33 46 52 2000 Kabanov V A Zezin A B Rogacheva V B Gulyaeva Z G Zanso chova M F Joosten J G H and Brackman J Macromolecules 31 5142 5144 1998 187 39 40 Er 41 42 43 as 44 45 er 46 Koper G J M van Genderen M H P Elissen Roman C Baars M W P L Me
136. od agreement with the values which were determined in batch experiments In this system the point of zero charge is tunable by the amount of adsorbed pDADMAC However the point of zero charge can be observed only for low adsorption where the ratio between the adsorbed pDADMAC sites and the surface sites is lower than unity At higher adsorbed amounts the surface charge is overcompensated by pDADMAC and the surface can no longer bind protons in the experimental pH window The point of zero charge determined from the proton binding isotherms coincides with the isoelectric point determined from the electrophoretic mobility measurements The proton binding isotherms of the carboxylate latex particles in the presence of adsorbed pDADMAC were interpreted in terms of Stern model The basic Stern model has shown as inappropriate since it could not reproduce correctly the point of zero charge Much better results were obtained by implementing a modification of the basic Stern model where the pDADMAC sites were treated as displaced from the surface origin Having in mind the simplicity of this model the fitting is surprisingly good The effect of the molecular mass of adsorbed pDADMAC on the protonation behavior of silica is shown in the last chapter In this case as well the proton binding isotherms are featured with a point of zero charge which was used to de termine the adsorbed amounts of pDADMAC For two studied molecular masses 134 na
137. of low molecular weight top figures and high molecular weight bottom fig ures Loadings of pPDADMAC a 0 07 mgm b 0 12mgm c 0 12mgm d 0 18mgm e 0 10mgm f 0 16mgm h 0 25mgm Ionic strengths o 0 01 M O 0 05M A 0 10M Y 0 25 M gt 1 00 M 124 8 5 a P oO ae D 80 a Oo 5 gt 7 Pia 79 d o 5 65 eo 6 0 0 2 0 4 0 6 0 8 l 2 loaomac sites nm Figure 5 5 The point of zero charge versus the adsorbed positive surface charge as calculated from the excess charge at the point of zero charge NYiss see data treatment section in chapter 4 for high and low molecular weight pPDADMAC o M 100 200 kDa O Mw 400 500 kDa as pDADMAC As was established in chapter 4 the adsorbed charge calculated in this manner could be lower than the total positive charge carried by the adsorbed ppADMAC molecules because the influence of the quaternary amine sites on the surface potential decreases with an increasing distance of these sites from the surface origin However figure 5 5 is showing a coincidence of the point of zero charge for both studied molecular weights of ppADMAC when repre sented as a function of the adsorbed charge As will be discussed in the following section this observation may be pointing out that the molecular weight of the polyelectrolyte does not affect the surface density of the charged quaternary amine groups which compensate the negative ch
138. on binding isotherms of silica particles in the presence of adsorbed pDADMAC are presented in figure 5 4 The upper part of the figure is showing the data for several different loadings of PDADMAC Mw 100 200kDa The lower figures are presenting results which were obtained with pDADMAC of a higher molecular weight M 400 500kDa As was observed in the case of carboxylate latex chapter 4 the proton binding isotherms in figure 5 4 are showing a point of zero charge which is tunable by the loading of the pPDADMAC The lines in these figures are the best fittings of the modified Stern model as described in chapter 4 The parameters obtained from fitting are presented in table 5 2 Figure 5 5 is showing the point of zero charge determined from the pro ton binding isotherms versus the adsorbed charge of the quaternary amine sites from pDADMAC which is expressed as the number of elementary charges or sites per surface area The adsorbed charge was determined by subtracting the excess charge at the point of zero charge from the total positive charge added 123 ppapmac Mw 100 200 kDa a b 0 05f 0 00 2 0 00 9 5 0 05 o 0 05 S 3 0 10 2 wn 0 10 0 15 C 0 05 d z 0 05 0 00 0 00 S 0 05 S 8 0 10 0 05 a N 0 15 a 0 05 0 00 surface charge C m Figure 5 4 Proton binding isotherms of the silica particles in the presence
139. on of two corrections that are be ing performed on the raw proton binding isotherms of the composite system pDADMAC carboxylate latex The first correction has to be carried out in or der to subtract the charge of the free ions added during the sample preparation These include K ions which were added to the sample as KOH in order to adjust the pH to the adsorption value and Cl ions which were added with pDADMAC The net excess charge which stems from these strong electrolyte ions causes a shift in the proton binding isotherms parallel with the y axis Therefore the difference between these two concentrations was subtracted from the raw proton binding isotherms The corrected proton binding isotherms are presented in the figure 4 3 left In the second correction the charge of the quaternary amine sites which does not influence the surface potential in the point of zero charge is subtracted from the proton binding isotherms These sites will be referred to as not adsorbed and their charge denoted Nj It has to be mentioned that N4 diss includes the charge of adsorbed pDADMAC sites which are displaced from the surface wherefore their charge is compensated by the the bulk solution ions Their influence on the surface potential is mitigated and they can not be distinguished from the dissolved sites in the proton binding isotherms Thus the total charge of the added pDADMAC is split into two terms namely adsorbed N and dis
140. onated sites 65 which are causing a plateau in the proton binding isotherm In the case of poly amidoamine dendrimer it is the species with m 8 while in the case of poly propyleneimine dendrimer it is the one with m 10 The microscopic mechanisms will be used to establish the most probable microstates for these two macrostates which play an important role for the overall proton binding isotherms The microscopic protonation mechanism for the first generation poly amidoamine dendrimer is presented in fig 3 8 The most prominent microspecies are shown with the according probabilities and the microconstants are presented for each unprotonated site The increased complexity of the mi croscopic protonation picture for the first generation as compared to the zeroth generation is not surprising having in mind that the number of microstates for a certain macrostate grows as A The most prominent microspecies can be spotted by inspecting the probabilities of the microstates In the case of poly amidoamine dendrimer these are the microspecies at m 8 with the protonated primary amine sites and at m 9 with the protonated primary and one of the core tertiary amine sites These microspecies have significantly higher probabilities than the others For m gt 9 there is one more significant microspecies with the protonated primary and one of the outermost tertiary amine sites which is a consequence of the long chains thus almost ne
141. pdated in real time Jonction titrator program has a hierarchical concept as shown in figure A 3 The user has to start the main program which is calling various subroutines As well as the main program the subroutines too have an user interface The user has to be acquainted only with the interfaces of the two highest levels in order to run experiments While some subroutines are interactive which means that the user is asked for input the others are not These are just displaying some indicator variables and performing calculations in the background If it does not 148 Main program Upper level Lower level Drivers LabView Shell Figure A 3 Scheme of the Jonction titrator software hierarchy The arrows define the directions in the communication between different levels contain any important information the user interface of a subroutine is hidden while the main program is running Experimental modes There are several experimental scenarios see figure A 4 which are defined by a choice of three boolean controls titrant additions constant or dynamic direction one way or forth back and ionic strength variable or constant The titrant addition control defines the mode which is used to calculate the titrant additions in the dynamic mode for each titration step the addition is calculated in order to achieve a pre defined dif
142. pedancs voltmeter with an A D converter unit as a replacement of the robust Microlink 3000 interface of the Wallingford titrator The rest of the hardware namely the burettes and the stirrer are the same The basic routines for the communication between the hardware and the PC as well as the electrode reading routines 137 were all developed by Mr Stephane Jeannerret For all his effort the author of this thesis owes him a huge credit The constant ionic strength titration routines have been programmed by the author of this thesis Our new software is programmed upon the LabView platform which provides user friendliness although it requires a considerable amount of programming time This text contains a brief description of the Wallingfdord titrator with a summary of my experience with that setup and a thorough description of our own built system However the main purpose is to provide a user manual for the Jonction titrator 138 GPIB Microlink 3300 relays pa Ww f HCI KOH KCI H 0 C modified RS232 water 298 K Figure A 1 Wallingford titrator Wallingford titrator Hardware The Wallingford titrator 16 hardware consists o
143. presented in figure 1 7 The H Acidity versus pH curves are called the titration curves and are calculated from the experimental data The curve that represents the overall excess charge concentration in the analyte titration with respect to the blank solution at the same pH is called the charge titration curve or simply the charging curve It is the difference between the analyte and the blank titration curves In the above figure the data shown are from a simulated experiment thus do not include experimental errors Two features of the presented data are impor tant First in contrast to the proton binding isotherm figure 1 1 the charge 17 titration curve closed squares is not constant at high pH it shows a slight de crease of the CH3 COO with an increasing pH This is due to the fact that the concentrations depend upon the total volume and the latter varies in the real titration experiment it increases with increasing pH in the presented figure To discard this artefact the concentration CH3COO can be either multiplied by the total volume to give an amount in moles or recalculated into the degree of protonation through division by the total concentration CH COOH o which varies with the total volume in the same way as CH3 COO Second the ex perimental points from the blank and the analyte titrations do not coincide on the pH scale To obtain the interpolated values analytical function for the blank tit
144. propyleneimine dendrimers pro tonate with a prominent intermediate microspecies where the sites in the odd shells counting from the rim are protonated The rest of the sites which reside in even shells counting from the rim are deprotonated This leads to a plateau in the proton binding isotherm at 0 2 3 The lowest generation of the 2 3 den drimer protonates with a mechanism which is similar as for the poly amidoamine dendrimer while the higher generations protonate with a mechanism which is similar to poly propyleneimine dendrimers However the microspecies which was observed for poly amidoamine dendrimers at 0 1 2 can be noticed even for high generations of the 2 3 dendrimer but is less prominent than the mi 133 crospecies with the shell like protonation pattern The proton binding isotherms of the carboxylate latex particles in the pres ence of adsorbed strong cationic pDADMAC are presented in chapter 4 At different ionic strength the proton binding isotherms are crossing in a common intersection point where the surface potential equals zero In this manner this composite system is showing a behavior which can be compared with the pro tonation behavior of amphoteric systems like the metal oxides The common intersection point corresponds to the point of zero charge and can be used to evaluate the amount of adsorbed pDADMAC For different pDADMAC loadings the adsorbed amounts obtained in this manner are in a go
145. proton binding isotherm In the first of these two sub steps around pH amp 5 5 protonate the outermost tertiary amine sites and the second core site while the other tertiary amine sites stay unprotonated In the case of the fourth generation the latter unprotonated sites contribute only with around 71 6 to the total number of sites For high generations this number is found to converge to 8 3 All of these unprotonated sites protonate around pH amp 4 8 which leads to the fully protonated molecule A peculiarity of the intermediate microspecies of the poly propyleneimine dendrimer is that the protonation state of the alternately protonated shells changes if the generation number is increased by one 3 5 Poly propyleneimine dendrimer with ethylenediamine core 2 3 dendrimer The protonation of the poly propyleneimine dendrimer with ethylenediamine core which will be addressed to as 2 3 dendrimer is interesting due to the structure featured with a short ethane carbon chain in the middle of the molecule as shown in figure 3 2 The three carbon atom chains in the branched part are the same as in the poly propyleneimine dendrimer Therefore this molecule has structural features of both poly propyleneimine and poly amidoamine den drimers The hyperbranched part is the same as in poly propyleneimine and the core as in poly amidoamine dendrimer Therefore if the site binding model presented for the poly amidoamine a
146. pyleneimine dendrimer However a less pronounced plateau at 6 1 2 can be noticed which is characteristic for the poly amidoamine dendrimers For the generations higher than the first the proton binding isotherm is mostly af fected by the protonation of the hyperbranched part of the molecule which is similar same as in the poly propyleneimine dendrimer This is the reason why the protonation mastercurve resembles the poly propyleneimine mastercurve with a pronounced plateau at 0 2 3 3 6 Conclusion The presented site binding model is very useful for prediction of the protonation mechanisms Precise microscopic protonation mechanisms which include the probabilities of all the microstates can be obtained for polyprotic molecules with a very large number of sites For this a symmetric arrangement of the sites is necessary as is the case for dendrimers However for molecules with less than thirty sites the symmetric arrangement is not essential The microscopic protonation mechanism can be fully inferred from the cluster parameters which include microscopic pK values for the unprotonated molecule and the nearest neighbor pair interaction parameters The pK values are inherent to a particular site and the pair interaction parameters depend on the distance 78 5 lt pH lt 7 Figure 3 14 The most prominent microspecies of the 2 3 dendrimer at pH values which correspond to a plateau in the overall titration curve The
147. r interactions which in principle could play a role will be omitted in the present approach The parameters pK and 6 are also called the cluster parameters The model which is defined through eq 2 6 also called the Ising Hamiltonian 42 allows us to calculate all the quantities related to both macroscopic and the microscopic equilibria from the cluster parameters and the pH The total number of bound protons can be calculated for each microstate by N ee 2 8 i 1 The probability of a particular macrostate is given by 42 Plan Kae 2 9 where the normalization constant can be interpreted as a partition function Sage PFs 2 10 si and the are the cumulative protonation constants which can be expanded as 42 k 5 e BF ons a 2 11 si Al The Kronecker symbol is denoted as 0 with 6 1 and vanishes other 29 wise The commonly used macroscopic step wise dissociation constants eq 2 1 can be expressed in terms of the cumulative constants as pK logio Km logip Km Km _1 Eq 2 11 is also being referred to as the binding polynomial It becomes clear that the site binding model can be used to express the overall degree of protonation 0 by introducing eq 2 11 into eq 2 5 and 2 2 9 1 ee nK ar 2 12 N Ea Kray Alternatively the degree of protonation can be expressed as 42 ay Olog 0 2 13 N Oax The cluster parameters can be determined by fitting the mac
148. rate due to the CO dissolution which is becoming more pronounced in the later stage of the experiment 1 8 Discussion The quality of the blank titration fitting is usually very good However this does not necessarily mean that the obtained parameters have physical meaning Namely the fitting of non linear functions with several parameters can be ambigu ous due to the cross correlations between the parameters 19 or the insensitivity of the function value to a parameter in a certain range of the domain In order to verify the cross correlations between the parameters Ey A and y which by analytical inspection of the sum of the squares function see section 1 6 do not appear as correlated the values obtained from fitting were plotted against each other figures 1 16 and 1 17 Since the absolute values of Eo and A are not very significant by themselves 20 they are compared to the calibra tion values and A In these representations the activity coefficients y are 28 iia 40 es gt 30 ur 20 a P i A Le is y Bi 0 A 0 2 Figure 1 16 The cross correlations between Ey and y from various experiments with two different electrode couples Parameter is presented with respect to the value obtained from the calibration of the electrodes with standard buffers Ej and y with respect to the Davies value y The parameters Ey and A were obtained by fitting the set Eo A y and cp compared to the values o
149. ration curve was used which enables computation of the OH Alkalinities of the blank solution at the experimental pH values from the analyte titration The blank titration curves were fitted to an analytical function by means of the least squares method a fast converging Newton method was used acquired from the NAG library 17 This has enabled a comparison of the fitted parameters with the literature values and a cross check of different experiments In turn the lit erature values of the blank titration curve parameters were used as a calibration of the whole experiment All the data analysis programming was done in the FORTRAN language The volume dependency of the charging isotherms see figure 1 7 can be discarded by either converting the H Acidity into the degree of protonation 1 6 or by multiplying the H Acidity with the total volume In the latter case the amount of charge in the units of mols is obtained As an example figure 1 8 is showing the raw titration curves and the charging curves of acetic acid The volume dependence is apparent from the difference between the forward and backward titration data Figure 1 9 is showing the two volume independent representations charge in units of mols and the degree of protonation Here the forward and backward titration data coincide The analytical expression for the electromotive force as a function of the 18 3 H Acidity mmoldm O0G000C ops 3 4 9 6 7 8 pH
150. re presented in Fig 2 2 The solid lines are model calculations to be discussed below The titration or charging curves show the characteristic dependence with the 43 Table 2 1 Cluster parameters of the site binding model of the poly amidoamine dendrimers has to be recalculated into the next nearest neighbor parameter by using formula 2 14 I M pk pk pA UT A 0 1 9 00 6 00 6 70 0 15 2 85 0 14 0 5 9 20 6 50 7 00 0 15 2 85 0 07 1 0 9 30 6 70 7 30 0 15 2 85 0 06 ionic strength for a polybase which is becoming more acidic with decreasing ionic strength 6 33 It was further verified that the titration curves were fully reversible and independent of the dendrimer concentration within experimental error indicating that dendrimer dendrimer interactions are negligible The titration curves undergo a characteristic transition with increasing gen eration number This transition is more clearly illustrated in Fig 2 3 where the titration curves for the different generations at fixed ionic strength of 0 5 M are plotted The smallest dendrimer GO has 6 ionizable sites 4 primary and 2 tertiary amine groups see Fig 2 3 and Tab 2 4 and shows three protonation steps and two intermediate plateaus at 0 4 6 and 5 6 On the other hand the largest dendrimer G6 with 510 ionizable sites shows two protonation steps and an intermediate plateau at 6 1 2 The differences between titration curves of the smaller dendrimers are subs
151. re 3 11 The proton binding isotherms of the first five generations of 2 3 dendrimers calculated from the cluster parameters for the zeroth generation 44 In the proton binding mastercurve a plateau at 0 2 3 is pronounced another one can as well be noticed at 0 1 2 similar as in the case of the poly propyleneimine dendrimer But contrary to the poly propyleneimine dendrimer macrospeciation the species at m 10 is not pronounced The above considerations already point out that the mechanism for the 2 3 dendrimer may show combined characteristics of both poly amidoamine and poly propyleneimine dendrimes Figure 3 13 is showing the detailed microspeciation for the 2 3 dendrimer As a consequence of a distinction between the pK values for the primary and tertiary amine sites pK pkK 1 90 and significant pair interactions the num ber of the significant microspecies is lower than in the case of poly amidoamine and poly propyleneimine dendrimers For example for m 9 there are only two significant microspecies while in the case of poly amidoamine and poly propyleneimine dendrimers there are four of them Similarly for m 8 there are only three significant microspecies while there are four and five for poly amidoamine and poly propyleneimine respectively 75 9 40 33089 5 508 PP 50 100 100 100 fraction macrospecies degree of protonation Figure 3 12 The macroscopic speciation d
152. repancies between the measured adsorbed amounts The adsorbed amounts obtained from the proton binding isotherms may not be the equilibrium amounts since these experiments were not performed in conditions of equilibrium adsorption Generally the adsorbed amounts may depend on pH and the ionic strength thus may vary during the titration experiments How ever from the agreement between the titration and the batch experiment data at low loadings it may be assumed that the adsorption of pDADMAC does not substantially change during the titration The fact that the charge reversal oc curs in a narrow pH range i e the common intersection point points out in the same direction For all the model calculations which will be presented further the adsorbed amounts were used as obtained from the titration experiments the values are listed in table 4 5 This is reasonable because neither the charge of the pDADMAC in the solution nor the quaternary amine sites in the surface vicinity that are compensated with Cl ions affect the protonation behavior of latex The proton binding isotherms for all the studied mixtures at several different ionic strengths and corrected only for the amount of chloride ions added through pDADMAC and potassium ions added during the sample preparation are pre sented at the left side in figure 4 3 As discussed in the data treatment section the positive charge present at the common intersection point Nj could be u
153. results for the same type of silica 77 As a simplest model of the silica surface with an adsorbed pDADMAG let us imagine a situation where all the quaternary amine sites reside in the plane at the surface origin together with the protonation sites of silica Then at the point of zero charge where the surface potential equals zero the number of deprotonated silica sites has to equal the number of the adsorbed quaternary amine groups of pDADMAC Thus any positive charge which appears in the proton binding isotherm at the point of zero charge after subtraction of the excess charge C17 added with pDADMAC or K added during the sample preparation to adjust 126 the pH to the adsorption value could only be attributed to the quaternary amine groups of the dissolved PDADMAC In this case the calculation of the adsorbed amount of pDADMAC at the point of zero charge would be straightforward The adsorbed amount would equal the difference between the loaded amount of pDADMAC and the amount of elementary charge units present at the point of zero charge The basic Stern model can not reproduce the proton binding isotherms of the composite system in particular the point of zero charge as was shown in chapter 4 Therefore it is sensible to assume that the quaternary amine sites from pDADMAC do not influence the surface potential with the same efficiency This could in the first place occur due to a fact that some of these groups reside at
154. roscopic titration curves based on the site binding model In contrast to the macroconstants the number of cluster parameters remains the same for all dendrimer generations For moderately sized molecules N lt 30 the model was evaluated numerically by direct enumeration of all states For larger molecules the model was also solved exactly employing a transfer matrix technique A detailed description of this technique is given elsewhere 43 2 3 Experimental In this stage of the thesis the Wallingford titrator was used to perform the potentiometric titration experiments for details see appendix The burettes containined 0 25 M HCl Merck Titrisol 0 25 M CO2 free KOH Baker Dilut It 3 0 M KCI Merck p a and pure water All solutions were prepared with water from a MiliQ A10 UV UF Milipore system from which the residual CO was eliminated through boiling The double wall potentiometric plexiglass cell was thermostatized to 25 C and continuously flushed with moist CO free nitrogen The potential between a separate glass electrode and an Ag AgCl 42 reference electrode was measured with an high impedance voltmeter Microlink PH4 S after the drift criterion of less than 0 1 mV min has been achieved A typical run started with the titration of acidified solution with KOH and was then back titrated with HCl The instrument maintains a constant ionic strength during such a titration The acid base and base acid titrations
155. roton binding isotherms can be obtained from the cluster parame ters in the following manner The energy spectrum of the molecule is calculated according to eq 2 6 and the cumulative macroscopic constants can then be calculated from eq 2 11 The degree of protonation can be obtained from the cumulative protonation constants in a straightforward fashion by introducng the macrostate probabilities from eq 2 5 into eq 2 2 The number of cluster parameters in the case of studied molecules is small a very good fitting of the proton binding isotherms of the high generation poly amidoamine dendrimers was achieved by using effectively only five differ 58 NH FE HN NH a H 5 NL aN mi UNH G2 G1 En 2 3 dendrimers Figure 3 2 Chemical structures of the studied molecules 59 Table 3 1 Cluster parameters of the site binding model for the poly propyleneimine dendrimers for J 0 1M 33 generation pAUM pkK DKU pK e e 0 9 02 9 97 0 61 1 05 Il 8 19 9 66 9 85 0 61 1 05 1 57 2 8 19 7 99 9 72 9 79 0 61 1 05 1 57 3 8 19 8 02 9 71 9 70 0 61 1 05 1 57 4 8 19 7 95 9 66 9 56 0 61 1 05 1 57 ent cluster parameters see chapter 2 and only three parameters in the case of the zeroth generation In the case of poly propyleneimine dendrimers according to 33 seven parameters are needed to fit the proton binding isotherms of the second and higher generations four for the zeroth and six for the first gener
156. rs since the proper fitting will pollute the right value All the occurrences which are affecting the titration curve parameters equa tion 1 17 for blank titration can be sources of errors for the pH scale because they have to be exactly the same for the blank and the analyte titration These can be changes in the electrode reading conditions between the analyte and the blank titrations Then the parameters Eg and A are changed and so is the pH scale The error can as well arise if the experimental temperature is not the same for the blank and the analyte titration all the titration curve parameters are temperature dependent to a larger or lesser extent Furthermore the tempera ture affects all the pK values so that the proton binding isotherms at different temperatures are not comparable Because the literature values for pKa values are reported at 25 C this is the standard working temperature The measure for the experimental accuracy are the proton binding isotherms of the simple acids and bases performed at the initial concentrations of interest and the agreement of the fitted pKa with the literature values Good analyte standards for this are the ethylene diamine and the acetic acid Their only disadvantage is a rather high volatility in both cases To give an insight in the 34 0 4 0 3 a Cc 2 0 2 D 0 1 0 0 0 2 0 1 0 0 0 1 0 2 pK exp pK literature Figure 1 20 Statistics of the fitted pK values
157. rter Figure 1 2 Scheme of the Jonction titrator an automated potentiometric titra tion setup with four burettes These components are connected according to the scheme depicted in figure 1 2 The RS232 standard cables are used for the connections of the burettes and the voltmeter to the PC Automatic burettes serve for high precision dosing of all the solutions to the titration vessel precision of 1 uL The additions are defined by the computer The bottles have to be well sealed to prevent the dissolution of CO The burette tubing endings were fitted with ca 15 cm of a narrow teflon tubing 1 16 OD x0 01 ID see figure 1 3 These tubings were fitted with PEEK fittings 1 16 ID and 1 8 ID Alltech cat 37172 and 37168 respectively by using the Easy Flange tool Alltech cat 35900 and joined with a PEEK union Alltech cat 20088 Custom teflon caps with five holes were produced in order to introduce these tubing endings into the titration cell These caps are produced according to the Metrohm standard for the electrode sleeves so that they could be placed into a standard Metrohm titration cell lid see below The pH measurement electrode couple used in this work is a separated glass and an Ag AgCl reference electrode The voltmeter and an A D converter are 11 fittings 0 01 ID es E SR me ee to burette union tubing ending Metrohm standard Figure
158. rvene in the titrator code A warning will appear in the message box if the burettes are ambiguously assigned e g acid assigned to more than one burette This subroutine closes upon clicking the OK button 163 Figure A 9 The user interface for burette assignment 164 Description of controls and indicators 1 Burette n control Here the user has to assign acid base salt and water to each burette i e VISA address 2 Warnings Indicates a warning if the same solution is assigned to different burettes Otherwise OK is displayed Calibration SV Highimp4 Set_Calib_Parms vi Due to the analog digital conversion the values sent to the PC by the HighImp4 instrument are not calibrated on the absolute voltage scale but rather some raw values For the calibration standard buffer solutions are needed thermostated to the ex perimental temperature The a priori known values can be given in pH units millivolts etc which will in turn determine the units of the calibrated signal To update the calibration the user has to enter a known value in the field at right and then click on the field at left 165 Channel E LE 2 Average 5 dt Add Point Cc 9 Remove Point 10 gt 11 Correlation 0 0000 12 Slope 10 0000 Calibration Click on on a Raw cell to measure Raw PH or mY 0 00 0 00 13 Offset 10 0000 Update
159. s is leading to a conclusion that the adsorbed amounts of pDADMAC did not change to a great extent during the titrations The main feature of the proton binding isotherms of the carboxylate latex particles in the presence of adsorbed pDADMAC is the common intersection point of the curves at different ionic strengths which indicates the reversal of the surface charge This can be clearly explained by inspecting figure 4 7 If the latex particles and pDADMAC would be separated in the water medium with the supporting electrolyte this mixture would titrate as indicated by the sum 108 of the components The particles would be exerting a negative surface charge or zero at low pH while pPDADMAC would not contribute to the overall charge due to the compensation with the counterions The protons that are exchanged between the particle surface and the solution would always experience neg ative electrostatic potential The screening effect would in that case cause a shift of the proton binding isotherms towards lower pH values upon an increase in the background electrolyte concentration and there would be no common in tersection point 18 However the presence of the adsorbed positively charged pDADMAC in the vicinity of the carboxylate sites is giving rise to a possibility of a surface charge reversal In this case the carboxylate surface sites can behave similarly as amphoteric species upon the electrostatic screening by the bac
160. s apparent that the modified Stern model although overly simple can satisfactorily reproduce the measured proton binding isotherms in particular the dependence of the point of zero charge upon the variation of the adsorbed amount of pDADMAC The trend of the Stern capacitance see table 4 5 might be pointing out that the center of mass of the adsorbed pDADMAC is becoming more displaced from the surface with an increasing adsorbed amount Consequently the fraction of the pDADMAC sites which do not influence the surface potential increases Figure 4 6 supports this conclusion since it shows more dissolved pDADMAC sites at higher loadings the dissolved amount does not increase with loading at the same rate as the actually adsorbed amount In spite of the above successes of the extended Stern model the quantitative prediction of the proton binding isotherms in the whole pH range is still lacking The causes for the discrepancy may be as follows The model does not assume any particular distribution of the adsorbed pDADMAC sites in the electric double leayer and the sites are uniformly distributed in a plane at some distance from the surface Consequently we are not able to draw more precise conclusions about the actual conformation of the pDADMAC layer from the proton binding isotherms For example in the directions parallel to the surface the distribution 111 of the adsorbed pDADMAC sites may not be uniform but patch wise In the dire
161. s et des esp ces microscopiques L esp ce macroscopique est d finie par le nombre des protons li s la mol cule m Ceci est aussi appell l tat de protonation macroscopique Les tats microscopiques sont definis par la distribution des protons li s parmi les sites de protonation Pour un macro tat donn les tats microscopiques peuvent tre d finis en utilisant un vecteur de dimension m compos d une variable binaire s assign e chaque site i Donc les esp ces microscopiques sont definies par le vecteur s o 1 m L nergie d un tat microscopique peut tre modelis e en utilisant l expansion BF si 2 1 i o la sommation est effectu e sur tous les sites 7 les pki d notent des constantes de protonation microscopiques d notent des interactions entre les sites voisins et 1 kT Toutes les probabilit s statistiques des esp ces macroscopiques ainsi que microscopiques peuvent tre calcul es en utilisant l quation ci dessus Dans ce cas la les probabilit s statistiques correspondent aux abondances des esp ces dans la solution Par ailleurs il est possible de calculer les constantes de protonation macroscopiques et microscopiques Pour un micro tat donn les constantes microscopiques sont la mesure de l energie de liaison d un proton a un site particulier les pA sont des microconstantes du micro tat dans lequel la mol cule est compl tement d proton e et a
162. s reported There the focus is on the influence of the polyelectrolyte molecular weight on the adsorption and the protnation behavior of silica Chapter 1 Potentiometric titrations at constant ionic strengths 1 1 Introduction In water solutions charged species are produced through dissociation reactions For monoprotic acids and bases the dissociation can be noted as HA Ht A5 F e 1 1a QHA B H O H BOH oe 1 1b apt where ax represents the equilibrium activity of the species X by definition ac tivity of water equals unity and K represents the dissociation equilibrium con stant The analytical concentrations of the species X cx or alternatively X are related to their activities through the activity coefficients a eee 1 2 cx It is also useful mentioning the mixed constants 8 1 3 ay BOH B These constants are not the true thermodynamic constants to which they can Ks 1 4 be related through the activity coefficients Equations 1 1a and 1 1b can be extended for polyprotic acids and bases which will be discussed in the chapter 3 For example for a simple diprotic acid we can define the equilibirum constant for each step HA H HAS ie Re 1 5a AH A HA Ht A7 ee 1 5b QHA where Kg denote the equilibrium constants for each step 1 The overall degree of protonation of a polyprotic acid or a base 0 is defined as Ek 4 n X
163. scale obtained in this manner is 0 04 units The pH scale calculated from the blank titrations can easily be verified through titrations of substances with known dissociation constants pkg For this purpose ethylene diamine and acetic acid have shown to be convenient standards because their proton binding isotherms exert well defined protonation steps Ethylene diamine is turned out to be more convenient since it protonates in two well defined steps around pH 10 and pH 7 5 so that the pH scale can be verified in a range of several units Furthermore in the case of ethylene di amine the ionic strength trends of the proton binding isotherms are sufficient to be experimentally distinguished 36 Chapter 2 Proton binding isotherms of poly amidoamine dendrimers 2 1 Introduction During the past two decades dendritic polyamines have invoked great interest of the polyelectrolyte community due to their unique properties and potential applications as metal complexing agents 21 22 nanoreactors for particle syn thesis 23 light harvesting devices 22 or as gene vectors 24 25 Their unusual properties have been studied by numerous authors 26 39 Their conformation has been investigated in solution mainly by scattering 26 28 and spectroscopic methods 29 30 while in the adsorbed state on surfaces with AFM 31 40 and reflectometry 32 Their charging behavior was studied by electrochemical techniques 33 35 NMR 36
164. sed to calculate the adsorbed amount of pDADMAC by subtracting it from the loaded pDADMAC The proton binding isotherms to the right in figure 4 3 100 Adsorbed DADMAC sites nm Added DADMAC sites nm Figure 4 6 Adsorbed amounts calculated from the potentiometric titration ex periments e compared to the adsorbed amounts measured in the batch exper iments at J 0 1M o pH 4 O pH 10 The solid line represents the high affinity adsorption straight line with unit slope and zero intercept where all added pDADMAC is adsorbed The dissolved amount of pDADMAC sites is indicated for the highest loading 101 which are corrected for charge N7 will be used to test the models In the diss case of the highest loading 1 00 mg m the common intersection point is not clearly detectable Therefore N4 a could not be estimated and calculation of the model curves was not possible A comparison of the proton binding isotherms of the mixture with the pro ton binding isotherms of all the components pure latex suspension and pure pDADMAC solution is presented in figure 4 7 The charge of the components these experiments are described in figures 4 4 and 4 5 is normalized to the con centrations actually present in the mixture The lines represent the sum of the component charges For this s
165. set to true If it is the total cell volume the value from control 8 is displayed Otherwise one of the values from controls 11 will be displayed depending on the choice of the burette in 34 Here the total time stop condition value is being set only if the total time condition was chosen in 33 Error indicator Some of the common errors in the parameter values which can be recognized by the program are indicated If there are errors the led indicator in this field flashes Return trigger button Terminates the subroutine 161 Figure A 8 The user interface for defining the initial cell composition Cell composition at start cell comp vi In this subroutine the composi tion of the cell prior to the titration experiment has to be defined The cell can contain strong acid or base 1 1 salt in form of solution or solid water or some unknown liquid sample In the case of strong electrolytes the volumes and the concentrations of the added solutions have to be transmitted to the program so that it could account for the ionic strength change caused by this Water and unknown sample are just accounted as an extra volume Description of the controls and indicators 1 V acid V base and V salt The controls for input of volumes of strong acid strong base and salt 1 1 respectively added to the cell prior to the titration experiment 2 c acid c base and c salt
166. sing of the titration cell with pure nitrogen is necessary to prevent con tamination of the titration system with carbon dioxide Before being introduced 12 Sr 49 26 9a Figure 1 4 The titration cell is composed of the inner part which is scooped out of one piece of plexiglas and the outer wall which is sealed around the cell The space between the inner part ant the outer wall serves for thermostating into the cell the gas is washed by passing it through conc KOH solution then pure water and then 0 1 M KCI solution see figure 1 5 The solutions should be periodically changed since the KOH solution is loosing it s CO neutralizing capacity upon time The pH of the KOH solution can be checked with pH paper and should be above 13 Although the compositions of the final washing solution and the solution in the titration cell should be as close as possible during all the described experiments the final washing solution was always 0 1 M KCl The degassing tubing can either be kept above the solution surface or submerged below The advantage of the latter is that the nitrogen stream can be broken into very small bubbles by the stirrer which in turn can accelerate the degassing of the solution In the other hand this can cause foaming in some suspensions All other details and the acquired experience about this hardware are sum marized in the Appendix 13
167. solved ING dsl SO that the electroneutrality condition reads as K HT Nga ING ads diss C17 OH COO 4 8 The point of zero charge where the surface potential equals zero corresponds to the common intersection point of the proton binding isotherms at different ionic strength 78 6 This enables estimation of the dissolved pDADMAC diss charge N from the proton binding isotherms 95 after subtracting K CI after subtracting N giss K Cl a DADMAC f T T T T T T T S loading 0 0 5000 amp 015mgm 01 1000 4 gt An Po o Ya Co D 0 2 L An O 4 G YA So A Po 0 3 H YOg 4 8 Re Le 04 L han a LE 0 5 H 1 1 fi 1 1 H b _ 0 40 mgm 9 iT T T T T T 7 Q oO D oO ke oO 8 N c _ T T T T T T T 0 65 mgm h 03 D 0 3 Lun 4 eae 0 2 4 0 2 E y E D a8 0 1 S ptit jissa J a6 8 T N diss 0 0 01 wn 0 1 0 2 H d _ 0 5 i 04 Q 5 03 gt 202 oO 8 0 1 8 0 0 Figure 4 3 Experimental proton binding isotherms of the pDADMAC carboxylate latex mixture at four different loadings of pDADMAC Left proton binding isotherms corrected for the Cl from pDADMAC and K from the sam ple preparation Right after subtracting the excess charge present at the com mon intersection point Nj Ionic stre
168. t mode This value is also used for the first step addition in the dynamic mode Control for entering the concentration of the acid in the burette Control for entering the concentration of the base in the burette Control for entering the concentration of the monovalent salt in the burette Saving the parameters entered in the fields on the disk Loading the parameters from a par file Filename for the data The control for entering the filename and the full path for the data file 160 32 33 34 35 36 37 38 Exists led indicator Flashes if the data file already exists In that case it will be overwritten Stop conditions Dispensed volume and Total time switches Let the user choose be tween two conditions for automatic stopping the experiment volume and time see further If the user chooses the volume condition for terminating the experiment he has to specify which one the total volume in the cell choice 0 or the dispensed volume from one of the burettes choices 1 4 It is recommended to use the total volume condition as a prevention from overflowing the cell if not stopped by finishing the experimental task see A the experiment will stop if the total volume of the solution exceeds the maximum value defined in control 8 Volume indicator it indicates the volume at which the experiment will be terminated only if the Dispensed volume switch is
169. t we have set e 0 The ionization constants increase with the ionic strength and the values are given in Tab 1 While a slight decrease of the interaction parameters with increasing ionic strength could be found the data can be equally well described by assuming these parameters to be ionic strength independent This approach was adopted here for simplicity For the dendrimers G2 G3 G4 and G6 it was observed that a good fit cannot be obtained without introducing an interaction between the primary amines While the data for all dendrimer generations can be obtained with the same clus ter parameters one further observes that increases with increasing generation number It was found that this dependence can be modelled as A k 1 2 14 where k is the generation number k gt 1 and A is ionic strength dependent and is given in Tab 1 For GO and G1 k 0 1 it was found that the interaction parameter is negligible e 0 From Figs 2 2 and 2 3 it can be inferred that this five parameter model describes all experimental data at a given ionic strength to good accuracy The interaction parameters for the amide bond 0 15 has not been re ported in the literature before but this value is well comparable with the corre sponding value of 0 18 for an alkyl chain with the corresponding number of car bon atoms as in hexamethyleneamine 6 The interaction parameter 2 87 is somewhat larger than the
170. tantial while the titration curves of the dendrimers G4 and above are minor and reflect the large molecule limit This limit where the titration curves becomes independent of molecular weight is characteristic for polyelectrolytes 44 degree of protonation degree of protonation degree of protonation Figure 2 2 Potentiometric titration curves at different ionic strengths in KCl of PAMAM dendrimers of generations G0 G1 G2 G3 G4 and G6 Solid lines are calculations with the site binding model 45 degree of protonation Figure 2 3 Potentiometric titration curves of PAMAM dendrimers of generations G0 G1 G2 G3 G4 and G6 at at ionic strength 0 1 M in KCl Solid lines are calculations with the site binding model 46 2 5 Modelling and Interpretation The macroscopic equilibria of GO and G1 poly amidoamine dendrimers is de scribed in classical terms by fitting the pK values directly from the proton bind ing isotherms and by calculating them according to the site binding model by using the relations presented in sect 2 2 The proton binding isotherms are in terpreted in terms of the site binding model where the degree of protonation was calculated from the site binding model The macroscopic ionization constants have been determined by a least squares fit of the experimental titration curve cf eq 2 12 The resulting macroscopic protonation constants pK are summarized in Tabs 2 5 and 2 5 Six macrocon st
171. ted from the excess charge at the point of zero charge is presented versus the total added amount of quaternary amine sites The presented adsorbed amount of the quater nary amine sites does not include the sites which are displaced from the surface since their influence on the surface potential is mitigated However in chapter 4 a good agreement between the adsorbed amount calculated from the excess charge at the point of zero charge and the adsorbed amount measured in batch experiments was observed This is pointing out that the dissolved pDADMAC is the major contribution to the excess charge at the point of zero charge 120 The proton binding isotherms are showing typical protonation behavior for St ber silica particles pre treated by heating 91 The titrations were repeatedly performed with acid and base at the same ionic strength for pH lt 9 Since the proton binding isotherms from titrations with acid and with base do not show any significant difference it can be concluded that in the studied pH range the dissolution of the pre treated silica can be neglected This finding is in agreement with previous findings 90 91 which show that the dissolution rate of silica is low at pH lt 9 and starts growing at higher pH values The proton binding isotherms of silica which was not pre treated have shown differences hysteresis between the titrations performed with acid and base The same is the case if the pH range is exte
172. the parameters which were estimated for the zeroth generation in 44 were used for all the higher generations The proton binding isotherms of the first five generations of the 2 3 den drimer are presented in fig 3 11 Some of the features which were established for poly amidoamine and poly propyleneimine dendrimers can be noticed here as well The proton binding isotherm of the zeroth generation is distinguished from the other curves which are becoming more similar to a common curve as the generation number is growing The proton binding isotherm of the zeroth gener ation shows three distinguished titration steps while for the higher generations two well distinguished steps are noticeable In fig 3 12 the macroscopic speciation diagrams and the according most probable microspecies are presented for the zeroth and the first generation 2 3 dendrimer In the case of the zeroth generation two intermediate macrostates are determinant for the overall proton binding isotherm and the microscopic protonation mechanism is very similar to that of the poly amidoamine dendrimer see fig 3 5 The macroscopeciation diagram for the first generation 2 3 fig 3 12 shows pronounced species at m 8 m 9 and m 13 As a reminder this is similar to the macroscopic speciation of the poly amidoamine dendrimer However the macrospecies at m 8 is less dominant than the species at m 9 which is 74 degree of protonation Figu
173. tions have been performed at all the pre defined ionic strengths For the electrophoretic mobility measurements the sample preparation ad sorption of pPDADMAC for the electrophoretic mobility measurements was done in a similar way as for the potentiometric titrations The total amount of pDADMAC per surface area was the same as for the titration samples as given in table 4 3 The final latex concentration in the samples was 5mg L In or der to achieve approximately the same additions of the pDADMAC and the latex the stock solutions were diluted to 20mg L and 0 32mg L for latex and pDADMAC respectively The final pH was varied in a range of several pH units such as to include an anticipated isoelectric point assumption was that the isoelectric point will coincide with the point of zero charge The pH 93 was measured with a standard Metrohm 691 pH meter equipped with a com bined pH electrode Metrohm 6 0234 110 The values were acquired after there was no pH drift registered by the instrument but for a maximum time of five minutes In this manner the pH measurement conditions in the electrophoretic mobility measurements resemble as much as possible to these conditions in the titrations Electrophoretic mobilities were measured with a doppler velocimeter setup Malvern Zetasizer 2000 The cell potential was set to 75 V for the mea surements at J 0 1M and to 100 V for the measurements at J 0 01 M in order to optimize the curre
174. tir des isother mes de protonation symboles noirs et des mesures directes symboles blancs 0 05 0 10 surface charge C m Isothermes de protnation de la silice trois forces ioniques dif ferentes Les courbes d notent du mod le de Stern 8 5 a P oO ae D 80 a Oo 5 Du Pia oO Yo N 70 f o 5 65 ic 6 0 0 2 0 4 0 6 0 8 2 loaomac sites nm Point de charge nulle pour silice en pr sence du pDADMAC en fonction d adsorption les tudes du comportement lectrostatique des esp ces charg es en milieux aqueux notamment des poly lectrolytes des surfaces collo dales et des m langes des deux Les tudes des m canismes de protonation des dendrim res polyamines ont confirm le mod le de protonation suivant lequel les interactions lectrostatiques entre les sites voisins jouent un r le tr s important ainsi que les valeurs des pK microscopiques inh rents aux sites eux m mes Dans ce sens le dendrim re poly amidoamine selon lequel les sites de protonation voisins sont distants rev le un m canisme de protonation determin uniquement par les valeurs de pK microscopiques Au contraire le dendrim re poly propyl neimine dont les sites voisins sont plus proches est caract ris par un m canisme o la protonation des sites voisins est vit e pour raison de r pulsion lectrostatique Le comportement lectrostatique d une surface faiblement acide s est montr tr
175. ton binding isotherms of carboxylated latex suspension in the pres ence of pDADAMAC at a loading of 0 65 mgm at five different ionic strengths Closed symbols represent the isotherms of pure components pure pDADMAC solution in the upper part and the pure latex suspension in the lower part of the graph recalculated to the concentrations present in the mixture The lines represent the sum of the interpolated isotherms of the pure components Open symbols represent the experimental proton binding isotherm of the mixture Ionic strengths o e 0 01 M O W 0 05M A a0 10M 103 Basic Stern model Modified Stern model surface charge Cm v o surface charge Cm Qa surface charge Cm a 2 surface charge Cm Figure 4 8 A comparison between the predictions of the proton binding isotherms lines for four different surface compositions as indicated in table 4 5 of the basic Stern model left and the modified Stern model right The parameters used for the basic Stern model calculations are the same as for the modified Stern model listed in table 4 5 except for the Stern capacitances given in Fm a oo b 5 00 c 1 50 d 1 00 Ionic strengths o full line 0 01 M O dashed 0 05 M A dash dot 0 10 M V dot 0 50 M dash dot dot 1 00 M 104 Table 4 3 The parameters used to calculate the modified Stern model predictions
176. tration methodology known to this author originates from 1968 15 The measured quantities are the electromotive force of the pH sensitive elec trode couple the volumes of the strong electrolyte s added to the system and the total volume of the system sum of the initial volume and the added volume s From these data the experimental titration curves OH Acidity versus pH are calculated The term blank titration will be used for a titration of a system which contains only strong acid and strong base counterions at concentrations that are regulated through the additions from the burettes protons and hydrox yle ions For the system which in addition to this contains a substance for which the proton binding isotherm should be calculated e g acetic acid the term analyte titration will be used In the present work a method for automated potentiometric titrations at constant ionic strengths was developed The setup resembles to the Wallingford titrator 16 and includes four burettes each containing strong acid strong base 1 1 salt solution at high concentration and water For each titration step the additions of all of the burette solutions are calculated by the computer The titra tions were automatically performed at pre defined and controlled constant ionic strengths In particular this means that the pH was swept in a controlled way and the titration data the glass electrode potential with respect to an Ag AgC
177. tri butions of the ions and the polyelectrolyte segments are found by means of 84 Monte Carlo algorithms The self consistent mean field model invokes number of Flory Huggins coefficients which describe the interactions between different constituents of the system poleyelectrolyte segments surface groups inert elec trolyte ions solvent molecules 72 In this chapter the primary aim is to present the potentiometric titration data of the strong cationic polyelectrolyte poly dimethyl diallylammonium chlo ride PDADMAC adsorbed onto carboxyl latex particles see figure 4 1 The fraction of the total added pDADMAC charge which influences the surface po tential at the point of zero charge will be evaluated from the proton binding isotherms and compared to the adsorbed amount of pDADMAC sites The experimental proton binding isotherms will be interpreted with the Stern model 6 which is extended for a specific adsorption of oppositely charged ions 8 73 The model is treating the dissociation of the surface sites through a discrete site binding model similar to those which were developed for the metal oxides 74 77 with a difference that it accounts only for negative carboxylate sites In the case of adsorbed polyelectrolytes the model is able to reproduce the point of zero charge by considering the presence of positively charged ions at the surface which do not undergo dissociation The ratio of the positive polyelec
178. trolyte sites to the negative carboxylate sites depends on the adsorbed amount So far interpretation of the proton binding isotherms of the charged surfaces with adsorbed oppositely charged polyelectrolytes has not been reported in terms of the Stern model which presents a mean field approach Our aim is to explore the advantages and limitations of such an approach when applied to adsorbed poly electrolytes The basic Stern model was first developed for the interpretation of the ionic distributions and the corresponding electrostatic potentials near homo geneous charged surface namely that of a mercury drop in water Some decades ago it became widely used for inorganic surfaces with discrete charging sites like metal oxides 75 and surfaces with organic acidic or basic surface moieties 74 The applicability of the Stern model is increased through extensions such as to 89 include the specific adsorption of ions 73 78 or different proton binding sites 79 86 Dee N Cr TN poly dimethyl diallylammonium chloride PDADMAC water suspension KCI Figure 4 1 The system under investigation is composed of poly dimethyldiallylammonium chloride which is adsorbed on the surface of the carboxylate latex particles The particles are suspended in water which contains KCl 87 4 2 Extension of the Basic Stern model The pDADMAC sites can be considered to be situated in the 0 plane or displaced towards the solut
179. ummation the charges of pDADMAC at the pH values of the pure latex isotherms were computed by interpolation A significant disagreement between this sum and the experimental proton binding isotherms of the actual mixture becomes apparent Modeling of the proton binding isotherms of the carboxylate latex particles in the presence of the adsorbed pDADMAC was attempted with two models namely the basic Stern model and the modified Stern model for the specific adsorption of counterions The basic Stern model with a pKa value for the carboxylate sites of 4 9 is not able to reproduce the curves as can be seen in the figure 4 8 left column The Stern capacitance influences the slope of the curves the lower the capacitance the lower the slope but does not affect the position of the point of zero charge which can in this case not be correctly reproduced in the modeled curves Much better descritpion was achieved with the modified Stern model which was described in the introduction to this chapter The parameters that resulted in the best fitting are presented in the table 4 3 The fitting was also attempted with a protonation constant value of 4 2 as obtained from the fitting of the proton binding isotherms of the pure latex suspension see figure 4 4 and table 4 2 but resulted with worse fits The proton binding isotherms as compared to the pH dependencies of the 102 a pDADMAC experiment surface charge Cm Figure 4 7 Pro
180. used in the present work is known for a long time e g 14 It is based on the electroneutrality condition and the principle can be described by taking the solution of acetic acid as an example To calculate the degree of protonation see definition 1 6 the concentration of the charged species CH3COO has to be evaluated it is assumed that the total concentration CH3 COOH p is known from the sample preparation __ CH3 COOH CH3 COO7 a CH3COOH The concentration CH COO7 can be calculated by subtracting the H Acidty of the solution which contains acetic acid the analyte H Acylnac H pac OH nac CH3COO7 Cl yac K Hac 1 15 from the H Acdity of a blank solution H Acy piank H OH C KT 1 16 16 D O E 0 00 gt D lt 0 01 HE 0 02 Figure 1 7 Experimental potentiometric titration curves o blank titration curve Acetic acid titration curve M Acetic acid charging curve This subtraction has to be done for all the measured pH values The H Acidities are determined by the concentrations of the strong acid and base counterions CI and K respectively and thus can be calculated from the experimental concentrations of the added strong acid and base The charges of the ions com ing from highly dissociated salts like KCl cancel out in the electroneutrality expression The result of a typical potentiometric titration experiment is
181. variable s i 1 2 N is assigned such that s 1 if the site is protonated and s 0 if the site is deprotonated The pro tonation microstate is then specified by the set of state variables 51 59 SN abbreviated as s Neglecting the intermolecular interactions in a dilute solu tion the free energy of a particular microstate relative to the fully deprotonated state and for unit activity of protons can be written as an expansion BF BF si m 10 D Si J DLL sj 2 6 where the sums run over all the sites pki is the microscopic protonation con stant of the site given all other sites are deprotonated are pair interaction parameters and 8 1 kT 6 42 43 The parameters can be related to the 40 free energy of the electrostatic repulsion between the protonated sites E c PE z ln 10 2 7 The symmetry relation j is obeyed and e 0 The multiplication of amp with s and sj in equation 2 6 ensures that only the interactions between the protonated sites are taken into account It is essential to realize that within the present model the pair interactions act through the molecular backbone and their magnitude is supposed to decrease quickly with increasing distance between the ionizable groups 44 Thus in the first approximation we can consider only the nearest neighbor interactions in which case the presented model is equivalent to the Ising model 9 Triplet and othe
182. vec ils forment les param tres cluster La sym trie mol culaire des dendrim res permet l tablissement des param tres cluster toujours selon le m me principe dont le nombre de ces param tres reste mod r Il est possible de calculer toutes les constantes de pro tonation en utilisant ces param tres et r ciproquement il est possible d obtenir les param tres cluster des isothermes de protonation de mani re similaire la r gression non lin aire iii Ho H T HN ven o z Ynn ait H HI o o wh TT H HN NH H N uah we n AV Le l t a HN i L NH dendrim re poly amidoamine ho HAN pus HN MH TOO UE ere LNH NA NH FF NH HN gt Nr 2 do N an HN H Oe a s U NE dendrim re poly propyl neimine a As HN H dendrim re 2 3 Les dendrim res tudi s de g n ration G2 degree of protonation M canisme de protonation macroscopique de dendrim re poly amidoamine G1 Par la suite les isothermes de protonation des six premi res g nerations du dendrim re poly amidoamine ont t analys es par le mod le Six param tres cluster sont d termin s ceci suffisant pour une tr s bonne description des courbes exp rimentales Les constantes de protonation macroscopiques sont cal cul es en utilisant les param tres cluster Puis la connaissance des constantes macroscopiques permet d tablir les diagrammes d abondance des esp ces macro scopiques par rapport
183. were repeated at ionic strengths of 0 1 M 0 5 M and 1 0 M The whole sequence of acid base titrations at different ionic strengths was carried out automatically within a single titration experiment Blank titrations were used to calibrate the glass electrode in a pH range be tween 3 and 11 at ionic strengths in the range of 0 1 1 0 M The exact base concentration and the activity coefficients were determined by a least squares fit Starburst polyamidoamine PAMAM dendrimers Dendritech Corporation Midland USA were titrated at total concentrations of amine groups of 10 and 20 mM By taking the difference between the titration curves between the sample and the blank the charging curve of the dendrimers is obtained The titration curves were normalized with the known concentration of the dendrimers and are reported as the overall degree of protonation as a function of pH The estimated errors are 0 04 for 0 and 0 02 for pH respectively The overall performance of the system was checked with titrations of ethylenediamine and acetic acid The resulting ionization constants were in accord with literature values 11 within the expected error The dendrimer concentrations were determined from the titration curves and were within 2 of the values expected from the sample dosage 2 4 Results Potentiometric titration curves of PAMAM dendrimers at ionic strengths 0 1 0 5 and 1 0 M in KCl for the different generations GO G1 G2 G3 G4 and G6 a
184. window are important for assessment of the sources of errors These can be divided in two groups namely error in the calculated degree of protona tion and the error of the pH scale The degree of protonation can be falsely calculated due to the following In the low and high pH regions the H Acidities have high values whereas the charge concentration which obtained by subtracting the blank H Acidity form the analyte H Acidity can have a very a low value In effect one subtracts two big numbers to obtain a small one This is sensitive to errors because a small 33 relative error in the H Acidities will cause a big error in the charge concentration This error is scaling with the initial concentration of the analyte Thus the initial concentration is a determining factor for the pH window which can be experi mentally studied This error can be noticed in figure 1 13 from the broadening of the curves at high pH the curve at EDA o 1mM is laying slightly above the others at high pH An error in the calculation of the initial concentration of the analyte can occur due to a poor dosing control during the preparation of the analyte solution or e g due to a fact that the concentration of the stock solution is not known An error in the preparation of the burette solutions causing an error in e g Ca Which is not fitted from the blank An erratic preparation of the burette solution which concentration is fitted will not cause any erro
185. xperimental proton binding isotherms can give a deeper insight in the surface concentrations of ions and their distributions along the interface The pDADMAC charge which has an influence on the surface potential can be determined from the proton binding isotherms at the point of zero charge The comparison between the adsorbed amount as calculated from the proton binding isotherms and measured independently in the 112 batch experiments is showing that at low pDADMAC loading lt 0 6 mg m all the added pDADMAC sites influence the surface potential However at higher loadings this is no longer the case The best fitting of the experimental data were achieved by applying an exten sion to the basic Stern model where the adsorbed polyelectrolyte sites are con sidered to be displaced from the surface The Stern capacitance obtained from fitting the extended Stern model to the experimental proton binding isotherms is showing that the distance of the center of mass of pDADMAC to the surface is increasing with an increasing adsorbed amount 113 Chapter 5 pH dependent charging of silica particles in the presence of pDADMAC 5 1 Introduction In the previous chapter the proton binding isotherms of weakly acidic car boxylate latex particles in the presence of a strong cationic polyelectrolyte poly dimethyldiallylammonium chloride pDADMAC have been presented The measured proton binding isotherms enable distinguishing th
186. y propyl neimine Pour la g n ration z ro le m canisme est proche de celui du dendrim re poly amidoamine et pour les g n rations suivantes il ressem ble plus au m canisme du dendrim re poly prolpyl neimine Les micro esp ces interm diaires pr sentes autour de pH 7 donn es par les m canismes micro scopiques pour les dendrim res poly amidoamine et poly propyl neimine sont pr sent es sur la figure ci dessus Le comportement lectrostatique des surfaces collo dales charg es en absence vil hppa 4g b ES p a pDADMAC 0 2 CEA N SS N VORA A E OG Na JOE amp oO CORR ar experiment 0 0 SK D O D O O T 5 a Isothermes de protonation de latex carboxil pur de pPDADMAC pur et de latex en pr sence de pDADMAC adsorb Les courbes repr sentent la somme des charges des composants purs et en pr sence d un poly lectrolyte de charge oppos e est present dans les deux derniers chapitres Dans le chapitre 4 les isothermes de protonation des partic ules de latex carboxyl sont tudi e en absence et en pr sence du poly chlorure de dimethyldiallylammonium pDADMAC La structure de la surface est present e sur la figure 4 Les isothermes du protonation pour le latex en absence du pDADMAC montrent le comportement typique d une surface avec des sites acide faible Les isothermes de protonation du pDADMAC pur ne montrent aucune d pendance en charge par rapport

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