Precision MALS - The Molecular Materials Research Center
Contents
1. 3 1 3 3 Setting the Integration Rezinei ent a 3 3 3 4 3 5 Analyzing A 3 5 3 6 Calculations Settings Dialog BOX ccecccccccceeseneeeeeceeeeeeneeeeesseeeeesceesaeecnaeeeessnnseeeesenneeeens 3 7 3 7 Viewing Stored Datars 3 7 3 8 Results and Shape 3 8 Appendix A Theory of Light Scattering ccccsccsssscrccssccsssscccssssseesceceeesssssccessssssscccsssceeeees 1 senddecabaceceuasccecedasusscestaatecesenacesectan 1 1 PrecisionMALS Table of Contents vi This page intentionally left blank PrecisionMALS Table of Contents Chapter 1 Introduction 1 1 OVERVIEW This program is provided to process multi angle light scattering data to generate Zimm plots and determine a variety of macromolecular parameters including e Molecular Weight e Second Virial Coefficient e Radius of Gyration e Information about the shape of the molecule The program employs a two step process that involves e The determination of calibration constants for the system using a standard e Using the calibration constants to analyze from the sample This software is used with the PDExpert Workstation Platform A discussion of the theory of static light scatt2. Sphere The light scattering expression for a random coil is presented in Equation 3 2 gt sinv VCOS 9 3 2 where v 2 4 Rg D is diameter of the sphere Rod The light scattering expression for a rod is presented in Equation 3 3 2y 2 1 0 3 3 34 w y 0 where 1 2 q Rg L is the rod length Thin Disk The light scattering expression for a thin disk is presented in Equation 3 4 P 0 2 2 23 J 2w 3 4 where D diameter of disk Bessel function of the first kind Star The light scattering expression for a star is presented in Equation 3 5 1 22 7 f De sus AD where 8 3 Bf w k T f is the number of arms the star PrecisionMALS Chapter 3 3 9 Flexible Ring The light scattering expression for a flexible ring is presented in Equation 3 6 1 2 P O 201 a 3 6 where 5 u 12 _x2 2 Ip x e e at 0 Ip is Dawson s Integral n of statistical polymer segments b root mean square length of statistical segment A description of related mathematical functions such as Bessel s function Thin Disk model Dawson s Integral Flexible Ring model calculation of correlation coefficients can be found in mathematics reference books 3 10 PrecisionMALS Chapter 3 Appendix A Theory of Light Scattering 1 OVERVIEW Light Scattering refers to the process in which light
3. 2 3 THE DATA PANE When a file is opened the data pane presents the raw data A typical data pane is shown in Figure 2 2 and a typical plot containing analyzed data is shown in Figure 2 3 Batch66kPSSim 00 E Bs A Figure 2 2 Data Pane with Raw Data PrecisionMALS Chapter 2 2 3 BatchDOW1633Sim 00 Results 1 Figure 2 3 Data Pane with Analyzed Data Zimm Plot The format of the Raw Data plot and the Zimm plot can be edited by the user If you right click in the plot a pop up menu with the following commands will be presented Zoom Allows for expansion of a user selected region To define the region to be Zoom ed a Place the mouse at a corner of the desired region b Drag it to the opposite corner of the desired region c Release the mouse button Unzoom Returns the plot to a full scale presentation Grid Display Used to indicate if the major grid lines and or the minor grid lines should be presented on the plot The major and minor grids can be used for ease in reading the plot Legend Provides the identification color for each detector in the plot 2 4 PrecisionMALS Chapter 2 2 4 THE INFORMATION TREE The Information Tree which is on the right side of the display lists all files that have been loaded sample information about the various files calibration constants and results from the calculations Example of sample t
4. 017 K150 3 00197e 017 K165 3 00035e 017 PrecisionMALS Chapter 2 To add a raw data file to the information tree press Import Data File on the File menu Raw data files are indicated by a red icon while files which have been used for calibration are indicated via a green icon To add a workspace which includes raw data and calibration data or raw data calibration data and analyzed data press Load Workspace on the File menu When a file is used for calibration the calibration constant for each detector used to calibrate as well as the region used for the baseline and the integration and the response will be included When a file has been analyzed the Molecular Weight MW the Radius of Gyration Rgz the second virial coefficient A2 and the correlation coefficients for the various shape models will be presented in the information tree In addition the regions used for the baseline and the integration and the response will be included and can be viewed by expanding the menu To save data use Save Workspace As on the File menu To erase a file from the information tree highlight it right click and select Remove PrecisionMALS Chapter 2 2 7 2 8 This page intentionally left blank PrecisionMALS Chapter 2 Chapter 3 Creating a Zimm Plot 3 1 OVERVIEW The following steps are involved in the generation of a Zimm Plot a Open the file containing the data to be used for calibration b Define the Baseline
5. Agreement is found void and unenforceable it will not affect the validity of the balance of the Agreement which shall remain valid and enforceable according to its terms You agree that the Software will not be shipped transferred or exported into any country or used in any manner prohibited by the United States Export Administration Act or any other export laws restrictions or regulations This Agreement shall automatically terminate upon failure by you to comply with its terms This Agreement may only be modified in writing signed by the President of PDI 6 Notice to Government End Users If this product is acquired under the terms of i a GSA contract Use reproduction or disclosure is subject to the restrictions set forth in the applicable ADP Schedule contract ii a DOD contract Use duplication or disclosure by the Government is subject to restrictions as set forth in subparagraph 1 1 of 252 227 7013 11 a Civilian agency contract Use reproduction or disclosure is subject to 52 227 19 a through d and restrictions set forth in the accompanying end user agreement 7 Only Terms and Conditions These Terms and Conditions are the only terms and conditions related to the use of this software they supercede any previous agreement with respect to the software and may only be altered in a written agreement signed by PDI and you Unpublished rights reserved under the copyright laws of the United States Precisi
6. In this case depends on R and also on the shaper of the molecule as shown in Figure 2 1 2 0 Figure A 2 Values 0 as a function of q lt Rg gt for various particle shapes 1 Sphere 2 Gaussian Coils 3 Rods It is clear that all three molecular shapes yield the same value of P when q lt Rg gt is less than approximately 1 As the value of P O increases the shape of the molecule clearly influences the light scattering intensity 4 PrecisionMALS Appendix A 3 2 Using Refractive Index Measurements to Measure Concentration Refractive index measurements can be used in conjunction with static light scattering measurements to determine the concentration of the compound in the chromatographic slice The difference in refractive index between the solution under study and the pure solvent is measured by passing a light beam thru two cells as shown in Figure 7 3 One of the cells contains pure solvent and the other contains the eluant as it passes thru the cell after the column The cell with the pure solvent should be filled with the solvent prior to the separation and should be at the same temperature as the eluant The observed signal which corresponds to the deviation of the light beam is proportional to the difference in the refractive index of the fluid in the two cells as shown in equation A 10 RI dn dc A 10 where B is an instrumental constant is the
7. Region for the calibration data Section 3 2 Define the Jntegration Region for calibration data Section 3 3 d Press Calibrate e Open the file containing the data to be analyzed f Define the Baseline Region for the analysis data g Define the Integration Region for the analysis data h Press Analyze to present the Zimm plot If desired you can change the format of the Zimm plot via the Calculation Settings dialog box as described in Section 3 4 3 2 SETTING THE BASELINE REGION To set the baseline region a Select Set Baseline Region on the Region menu The cursor is changed to a plus sign b Move the cursor to the point where you want to start to define the baseline and depress the left button on the mouse c Drag the mouse over the desired baseline region The selected region will be indicated in red as shown in Figure 3 1 PrecisionMALS Chapter 3 3 1 Batch66kPSSim 00 mV spon 0520 A time min Figure 3 1 Setting the Baseline Region d Release the mouse button The selected region will be indicated by a narrow blue bar on the bottom of the plot Note Only one baseline region can be determined for a data set 3 2 PrecisionMALS Chapter 3 3 3 SETTING THE INTEGRATION REGION To set an integration region a Select Set Integration Region on the Region menu The cursor will be changed to a plus sign b Move the cursor to the point where you
8. angles because of interference effects caused by the fact that light scattered from one part of the molecule travels a different distance from another part of the molecule and is not in phase with light scattered This phenomenon can be quantified by defining the light scattering form factor equation A 6 A more detailed discussion of the form factor is presented in Section A 3 3 0 scattered intensity at angle scattered intensity at angle A 6 It should be noted that can be written as a series as shown in equation 7 1 1 3 A 7 where q 4 m n sin 0 2 A R is the radius of gyration of the molecule n is the index of refraction of the liquid 15 the wavelength of light in a vacuum For scattering at 15 and 90 equation 8 7 can be expressed as equations A 8 and A 9 respectively P 0 1 26 3 Rg A 8 P 0 1 0 0897 n A 9 We present a table of P values for 15 and 90 degrees as a function of molecular weight for molecules with molecular weight from 10 to 10 Daltons in Table A 1 These values assume that the molecules are random coils PrecisionMALS Appendix A A 3 Table A 1 Value of P 90 and P 15 for 685 nm n 1 5 Approx P 90 15 0 9993 1 0000 0 9993 0 9998 0 9993 0 9976 0 9780 0 7622 1 values depend on shape If the value of P 8 found in equation A 7 is below 0 7 higher order components become important
9. concentration of the sample in the solvent dn dc is the change in the index of refraction of the solution as function of concentration It is considered as a constant for any specified solvent solute pair under constant operating conditions A 3 3 The Form Factor The form factor at a particular angle is the ratio of the signal at that angle when compared to the signal expected at the theoretical angle of 0 where there is not form factor as indicated by equation 8 6 The importance of the form factor is that small molecules e g those which have a radius that is lt 10 nm which is small when compared to the wavelength of the incident light are studied generate comparable signals at all angles while large molecules generate signals that are smaller at higher angles and larger at small angles A 3 4 Characteristics of Low Angle 15 Light Scattering Low Angle light scattering data is collected at a 15 angle to the incident beam and is typically used for determination of the molecular weights of large molecules This measurement angle is especially useful for the study of proteins with molecular weight of greater than 1 000 000 Daltons and for random coils with molecular weight between 200 000 Daltons and about 10 000 000 Daltons In addition 15 data is also used with 90 data to measure Rg the radius of gyration of molecules over a limited range of sizes 12 150 nm using static light scattering analysis A 3 5 High Angle
10. entity provided that you transfer this Agreement with the Software 4 Warranty The Software delivered to you is PDI s current standard version and performs as described in PDI s brochures For a period of one year from the date of delivery PDI agrees to correct defects that the user identifies as not performing as described in PDI s brochures PDI DOES NOT AND CANNOT WARRANT THE PERFORMANCE OR RESULTS YOU MAY OBTAIN BY USING THE SOFTWARE OR DOCUMENTATION PDI MAKES NO WARRANTIES EXPRESS OR IMPLIED AS TO MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE IN NO EVENT WILL PDI BE LIABLE TO YOU FOR ANY CONSEQUENTIAL INCIDENTAL OR SPECIAL DAMAGES INCLUDING ANY LOST PROFITS OR LOST SAVINGS EVEN IF A PDI REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES OR FOR ANY CLAIM BY ANY THIRD PARTY Some states or jurisdictions do not allow the exclusion or limitation of incidental consequential or special damages or the exclusion of implied warranties or limitations on how long an implied warranty may last so the above limitations may not apply to you 5 Governing Law and General Provisions This Agreement will be governed by the laws of the State of Massachusetts United States of America excluding the application of its conflicts of law rules This Agreement will not be governed by the United Nations Convention on Contracts for the International Sale of Goods the application of which is expressly excluded If any part of this
11. move in solution Brownian motion The Stokes Einstein equation is used to determine Rh the hydrodynamic radius of the molecule Dynamic Light Scattering is described in Section A 4 Static and Dynamic measurements can be made on a sample in a cuvette or in a flowing stream such as that found in high performance liquid chromatography HPLC size exclusion chromatography SEC or gel permeation chromatography GPC In flowing streams measurements are made on each elution slice using a unique light scattering design and very fast digital signal processors which are essentially special purpose computers This chapter describes the fundamentals of the theory of light scattering A short list of references for additional reading is presented in Section A 5 PrecisionMALS Appendix A A 1 2 THE PHYSICAL BASIS OF LIGHT SCATTERING Light consists of perpendicular electric and magnetic fields that oscillate in a direction that is perpendicular to the direction of propagation of the light as shown in Figure A 1 When light strikes a molecule the electrons will experience a force due to the electric field and will move slightly This movement will induce an oscillating dipole moment that will radiate light in all directions at the oscillating frequency This radiated light is the scattered light that is detected and processed as described below Z scattered light incident Y molecule X Figure A 1 Light Scattered by a Molec
12. want to start to define the integration region and depress the left mouse button c Drag the mouse across the region that should be integrated The selected region will be indicated in red as shown in Figure 3 2 99 320 vo gt A 5 QS Q Figure 3 2 Setting the Integration Region d Release the mouse button The selected region will be indicated by a narrow green bar on the bottom of the display PrecisionMALS Chapter 3 3 3 3 4 CALIBRATION To calibrate the system a Open the file to be used to generate calibration factors b Select the Baseline Region as described in Section 3 2 c Select the Integration Region as described in Section 3 3 d Press Calibrate on the Calculations menu to present the Calibration dialog box Figure 3 3 Calibration Molar mass a mole Second virial coefficient 0002 mole mL Laser wavelength 1554 Sample concentration Sample dn de DENE Index of refraction 1408 810 Sample temperature 20 C OK Cancel Figure 3 3 Calibration Dialog Box e Enter the Molar mass and Second virial coefficient if the value of the Second virial coefficient is not known enter 0 00 f Press OK The calibration constants will be calculated and listed on the information pane 3 4 PrecisionMALS Chapter 3 3 5 ANALYZING A DATA FILE Analysis of a data file involves the a
13. 5 Information Tree PrecisionMALS Chapter 3 3 6 CALCULATIONS SETTINGS DIALOG BOX The Calculations Settings dialog box Figure 3 6 is used to indicate a variety of data presentation options for the Zimm plot If the desired element should be included in the plot check the appropriate box Calculation Settings Angular extrapolation lines Concentration extrapolation lines Zero angle extrapolation line Zero concentration extrapolation line Zimm Plot Scaling Factor 15000 OK Cancel Figure 3 6 Calculations Settings Dialog Box Angular extrapolation lines connect all points corresponding to a specific detector Concentration extrapolation lines connect all points corresponding to a given concentration Zero angle extrapolation line line connecting all zero angle points Zero concentration extrapolation line line connecting all zero concentration points Zimm Plot Scaling Factor The range is from 1 99999 These settings can be set before or after the Zimm plot is obtained 3 7 VIEWING STORED DATA Stored data can be retrieved via the Load Workspace command on the File menu The raw data will be presented in the Data Pane and the complete report including the calibration constants the regions used for baseline and integration and the results will be presented in the information Pane To view the Zimm plot press the Results entry on the information pane PrecisionMALS Chapter 3 3 7 3 8
14. Light Scattering Low angle light scattering data is collected at a 90 angle to the incident beam and is typically used with static light scattering analysis to measure the molecular weight of smaller molecules such as proteins with a molecular weight below 1 000 000 Daltons random coils with molecular weight below 200 000 Daltons and for lower molecular weight non spherical coil polymers In addition it is used with dynamic light scattering analysis to measure Rh the hydrodynamic radius of molecules and particles from 1 to 1 000 nm PrecisionMALS Appendix A A 5 A 5 REFERENCES FOR FURTHER READING C Tanford Physical Chemistry of Macromolecules John Wiley and Sons Inc New York 1961 Chapter 5 M Kerker Electromagnetic Scattering Pergamon Press Oxford 1963 Katime and J R Quintana Comprehensive Polymer Science Booth and Price eds Pergamon Press Oxford 1989 Chapter 5 A 6 PrecisionMALS Appendix A Index A Analyzing A Data File 3 5 Angular Extrapolation Lines 3 6 Calculations Menu 2 2 Calculations Settings Dialog Box 3 6 Calibration 3 4 Clear Regions 2 2 Concentration Extrapolation Lines 3 6 Copyright iti Creating a Zimm Plot 3 1 Data Pane 2 3 Diffusion Coefficient 1 1 E Exit 2 2 F File Menu 2 2 Flexible Ring 3 10 G General Conventions 1 2 Grid Display 2 4 H Help 2 2 Import Data File 2 2 Information Tree 2 5 Installation 1 1 Introduction 1 1 L Leg
15. PrecisionMALS Multi Angle Light Scattering Analysis Software User Manual Created by Precision Detectors Inc Notices This product is covered by a limited warranty and a software license A copy of the warranty and software license is included in this manual No part of this document may be reproduced in any form or by any means electronic or mechanical including photocopying without written permission from Precision Detectors Inc Information in this document is subject to change without notice and does not represent a commitment on the part of Precision Detectors Inc No responsibility is assumed by Precision Detectors for the use of this software or other rights of third parties resulting from its use The software described in this document is furnished under a license agreement and may be used or copied only in accordance with the terms of the agreement The user may make a single copy of the software for archival purposes Precision Detectors products are covered by US Patents 5 305 073 and 5 701 176 Additional patents applied for Precision Detectors PrecisionDeconvolve PrecisionElucidate PDDLS Batch and PDDLS CoolBatch are trademarks of Precision Detectors Inc All other brands and products mentioned are trademarks or registered trademarks of their respective holders Precision Detectors Inc 34 Williams Way Bellingham Massachusetts 02019 USA Tel 508 966 3847 Fax 508 966 3758 e mail info prec
16. RESULTS AND SHAPE INTERPRETATION The Results section of the Information panel presents the Molecular Weight the Radius of Gyration and the Second Virial Coefficient Figure 3 7 Results Mw 274106 g mole 24 7 A2 1 089e 006 mole cr g Figure 3 7 Results Section Information Panel The Shape Interpretation section Figure 3 8 of the Information panel presents the value of the correlation coefficient using the various calculations describing the shape of the particle The shape of the molecule is best described by the model with the highest value ofr Shape Interpretation Random Coil 0 99939 Sphere 0 96252 Rod 0 96247 Ring 0 99921 Disk 0 96242 3 Arm Star f 0 99933 4 Arm Star 0 99927 5 Arm Star f 0 99923 Arm Star 0 99919 Figure 3 8 Shape Interpretation Section Information Panel 6 527 Note The user should be aware that inhomogeneity in either the shape or the size of the particle may lead to ambiguity in the interpretation of the data The equations used for the various models include Random Coil The light scattering expression for a random coil is presented in equation 3 1 2u u 1 3 1 where nb u q Rg 2 a Rg is the radius of gyration n is the number of statistical polymer segments b is the root mean square length of the statistical segment 3 8 PrecisionMALS Chapter 3
17. are not described e g the Open dialog box is identical to that used in programs such as Word When we are describing a dialog box or window the name of the window will appear in italics Access the Correlation Function dialog box When a button or a command from a menu is to be chosen the button command is shown in italics To initiate data collection click Start on the menu bar On line help is available by pointing to the field of interest and pressing F1 1 2 PrecisionMALS Chapter 1 Chapter 2 The Main Window 2 1 THE MAIN WINDOW The Main window of the program Figure 2 1 consists of three regions Precision Detectors Batch MALS Untitled File Regions Calculations Help 3 Ry E 2 1 D a Figure 2 1 The Main Window Menu bar Section 2 2 e Data region Section 2 3 Information region Section 2 4 PrecisionMALS Chapter 2 2 1 2 2 MENU BAR 2 2 1 File Menu The File menu includes the following commands e Load Workspace Used to import a data file with calibration factors or with analytical results The file will be indicated in the information region e Import Data File Used to import a raw data file The file will be indicated in the information region e Save Workspace Used to save a data set with calibration factors or with analytical results using the present file name e Save Workspace As Used to save a data set with calibration factors or wit
18. end 2 4 License Agreement Load Workspace 2 2 Main Window 2 1 Menu Bar 2 2 PrecisionMALS Index On line Help 2 3 P Print 2 2 Print Preview 2 2 Random Coil 3 8 Regions Menu 2 2 Results 3 8 Rod 3 9 5 Save Workspace 2 2 Save Workspace As 2 2 Set Baseline Region 3 2 Set Integration Region 3 2 Setting the Baseline Region 3 1 Setting the Integration Region 3 2 Shape Interpretation 3 8 Sphere 3 9 Star 3 9 T Thin Disk 3 9 U Unzoom 3 4 vV Viewing Stored Data 3 6 Warranty iti 2 Zero angle extrapolation line 3 6 Zero concentration extrapolation line 3 6 Zimm Plot Scaling Factor 3 6 Zoom 3 4 This page intentionally left blank PrecisionMALS Index
19. ering is presented in Appendix A 12 INSTALLATION 1 2 1 Loading the Software To load the software onto the personal computer a Place the distribution diskette in the CD ROM drive If your computer is configured for Autorun a Welcome screen will be presented if your computer is not configured for Autorun select Setup exe on the CD to access the Welcome screen b The nstall program presents a series of dialog boxes that are self explanatory When you access the dialog box that presents the programs to load select PrecisionMALS The software license key that is provided with the system will allow you to load the program PrecisionMALS Chapter 1 1 1 1 3 GENERAL CONVENTIONS USED IN THIS MANUAL This program is a Windows application that follows general Windows conventions All windows dialog boxes controls short cut keys scroll bars etc operate according to standard Windows procedures For the sake of brevity we use the following conventions e It is understood that the OK button is to be clicked or the ENTER key on the keyboard is to be pressed to accept the settings and close a dialog box e It is understood that the CANCEL button is to be clicked or the ESC key the keyboard is to be pressed to close a dialog box and preserve the original settings e The APPLY button is to be clicked to change settings without closing the dialog box e Common dialog boxes and commands that are similar to other Windows programs
20. from an incident polarized laser beam is scattered in all directions when it interacts with a molecule or particle Light scattering is an everyday occurrence and was first described by Lord Rayleigh in the late 1800 s An example of light scattering is the scattering of sunlight by particles in the atmosphere the sky is blue because shorter visible wavelength radiation blue light is scattered more strongly by the gas molecules in air than light of longer wavelengths red light There are two general techniques for the measurement of physical properties of polymers synthetic polymers and natural polymers such as proteins and polysaccharides virons liposomes and particles Static Light Scattering also known as Rayleigh scattering or classical light scattering The intensity of the scattered light from the sample dissolved in the solvent This difference between the two measurements can be used to determine the average molecular weight and Rg radius of gyration To complete the molecular weight determination the concentration of the compound of interest is required typically obtained from a refractive index detector or an absorbance detector Static Light Scattering is described in Section A 3 Dynamic Light Scattering also known as Quasi elastic scattering Photocorrelation Spectroscopy or Beat Spectroscopy The fluctuations of the intensity of the scattered light is used to determine the diffusion coefficient of the molecules as they
21. h analytical results with a new file name e Print Prints the present plot raw data Zimm plot calibration constants if generated and results if generated e Print Preview Displays the present plot raw data or Zimm plot calibration constants if generated and Results if generated on the monitor e Exit Closes the program Any baseline definitions and data calibrations or results will be erased 2 2 2 Regions Menu The Regions menu includes the following commands e Set Baseline Region See Setting the Baseline Region for information Section 3 2 e Set Integration Region See Setting the Integration Region for information Section 3 3 e Clear Regions Presents a dialog box to indicate if the Baseline region or Integration region s that have been defined should be erased 2 2 3 Calculations Menu The Calculations menu includes the following commands e Calibrate Generates calibration factors from a data set e Analyze Generates results from a data set and calibration factors e Settings Presents the Calculation Settings dialog box which is used to indicate various options in the Zimm plot Section 3 4 2 2 4 Help Menu The Help menu includes the following commands e About Presents the version number and build number of the program Please provide this information to Precision Detectors when inquiring about this program e Help Accesses the on line help file 2 2 PrecisionMALS Chapter 2
22. isiondetectors com Web site www precisiondetectors com Copyright 2006 by Precision Detectors Inc Printed in the United States of America Precision Detectors Inc Warranty and Electronic End User License Agreement NOTICE TO USER THIS IS A CONTRACT BY INDICATING YOUR ACCEPTANCE DURING INSTALLATION YOU WILL BE ASKED TO ACCEPT ALL THE TERMS AND CONDITIONS OF THIS AGREEMENT This Precision Detectors Inc PDI End User License Agreement accompanies a Precision Detectors software product and related explanatory materials The term Software shall include all software packages delivered to you by PDI and any upgrades modified versions or updates of the Software licensed to you by PDI This copy of the Software is licensed to you as the end user for use by you and other users of a specific PDI hardware System purchased leased or rented by you Please read this Agreement carefully PDI grants to you a non exclusive license to use the Software provided that you agree to the following 1 Use of the Software a You may install the Software in a single location on a hard disk or other storage device install and use the Software on a file server for local execution over your network but not for the purpose of copying onto a local disk or other storage device for use only with the specific system b You may make backup copies of the Software c You may transfer the Software from one computer to another over your network or rel
23. les mole dn dc is the change in the index of refraction as a function of the change in concentration It is considered to be a constant for any specified solvent solute pair under constant operating conditions The oscillating dipole will radiate light in all directions at the oscillating frequency This is the origin of scattered light If a single molecule has dimensions that are small with respect to the wavelength of the incident light the intensity of the light can be defined by equation A 3 4 M sin dn de 1 2 R A 3 where I is the intensity of the radiated light I is the intensity of the incident light Aois the wavelength of light in vacuum and R are as defined in Figure 1 If we collect light from a volume V of a solution with a concentration c gm mL the intensity of scattered light can be found by multiplying equation 8 3 by the number of molecules in the volume V The number of molecules can be expressed by Nac V My Now if we solve for M we obtain equation A 4 My 2 I 4 2 My sin dn de I V A 4 Collecting all the constants and instrumental parameters into an overall instrumental constant A we obtain equation A 5 M I A 5 Equation 8 5 can be used to measure the molecular weight M of small molecules at any scattering angle It should be noted however that larger molecules scatter less light at high values of than at low
24. ocate the Software on your site but you may not copy it to additional sites over the network or make additional copies for use on additional networks or sites for use with other hardware d You may copy the Software to the personal computer of Users and such Users may use the software to examine recompute and print out files collected in conjunction with the System e You may obtain additional electronic copies of the Software directly from PDI for the cost of media handling and shipping 2 Copyright The Software is owned by PDI and its suppliers and its structure organization and code are valuable trade secrets of PDI and its suppliers The Software is also protected by United States Copyright Law and International Treaty provisions You agree not to modify adapt translate reverse engineer decompile disassemble or otherwise attempt to discover the source code of the Software You may use trademarks only to identify printed output produced by the Software in accordance with accepted trademark practice including identification of trademark owner s name Such use of any trademark does not give you any rights of ownership in that trademark Except as stated above this Agreement does not grant you any intellectual property rights in the Software PrecisionMALS License Agreement iii 3 Transfer You may not rent lease or sublicense the Software You may however transfer all your rights to use the Software to another person or
25. on Detectors Inc 34 Williams Way Bellingham MA 02019 Your acceptance or decline of the foregoing Agreement was or will be indicated during installation iv PrecisionMALS License Agreement Table of Contents Chapter 1 Introduction iicscccsssccscsccssscssscessocssnnsccesvsccuevsnnnsccessscessonandscccsveccvssennvoseescsessesenavssssesescesvess 1 1 LF e 1 1 1 2 Installation 1 1 1 2 1 5 1 1 1 3 General Conventions used in this 1 2 Chapter 2 2 1 2 1 The Main 2 1 252 Bart 2 2 2 2 2 2 2 Regions 2 2 22 3 4 542 2 2 224 ee 2 2 DS Th Data Pane 2 3 2 4 The Information 2 5 Chapter 3 Creating Zimm PlOt scccccccssccsssccssscccssssccccsscceseeceesssscscceesessssscccsscceseecesesssseees 3 1 3 1 ONVERVIEW 3 1 3 2 Setting the Baseline 1
26. pplication of the calibration constants to a raw data file to generate the Zimm plot Figure 3 4 BatchDOW1683Sim 00 Results 1242 1122 1 8 i j ai Figure 3 4 Zimm Plot Various elements of the Zimm plot can be deleted via the Calculations Settings dialog box Section 3 6 The results and shape interpretation data is indicated in the Results section of the Information tree Figure 3 5 A discussion of this data is presented in Section 3 8 PrecisionMALS Chapter 3 PDI Data 8 8 BatchSskPSSim 00 Calibration Constants mole t my p E E E E E amp 6 Results Mw 274106 g mole Rgz 24 7 nm 2 1 089 006 Shape Interpretation Random Coil 0 99939 Sphere 0 96252 Rod 0 96247 Ring 0 99921 Disk 0 96242 3 Arm Star 0 99933 4 Arm Star 0 99927 5 Arm Star 0 99923 6 Arm Stare 0 99919 1 Sample Information K10 2 99986e 017 K15 3 00177 017 K20 3 0031 7 017 25 2 99969e 017 K30 2 99992e 017 K35 2 99964 017 K40 3 00200 017 K45 3 00022 017 K50 2 99958e 017 3 00068 017 3 00143 017 3 00166 017 K90 3 00110 017 K100 2 99855e 017 K110 3 00350 4017 K120 3 00107 4017 K130 2 99859e 017 K140 2 99930e 017 K150 3 00197 01 7 K165 3 00035 01 7 Figure 3
27. rees are presented in Figures 2 4 and 2 5 Sim 00 El i Sample Information Polystyrene LS Simulation Temperature 20 Wavelength 684 nm Solvent THF a Refractive Index 1 408 0 184 9 concentrations 3 mg mL detectors 10 Baseline Regions i Integration Regions Figure 2 4 Typical Information Tree The information tree can present the results of the calculations as shown in Figure 2 5 PrecisionMALS Chapter 2 2 5 PDI Data We Batch66kPSSim 00 0 BatchDOW16835im 00 Calibration Constants mole t my p amp Figure 2 5 Results in the Information Tree Results Mw 274106 g mole Rgz 24 7 nm 2 1 089 006 Shape Interpretation Random Coil 0 99939 Sphere 0 96252 Rod 0 96247 Ring 0 99921 Disk 0 96242 3 Arm Star 0 99933 4 Arm Star 0 99927 5 Arm Star 0 99923 6 Arm Stare 0 99919 1 Sample Information K10 2 99986e 017 K15 3 00177 017 K20 3 0031 7 017 25 2 99969e 017 K30 2 99992e 017 K35 2 99964 017 K40 3 00200 017 K45 3 00022 017 K50 2 99958e 017 K60 3 00068e 017 3 00143 017 3 00166 017 K90 3 00110e 017 K100 2 99855e 017 K110 3 00350 4017 K120 3 00107 4017 K130 2 99859e 017 K140 2 99930e
28. ule Figure A 1 describes the spatial arrangement of the incident light and scattered light in the light scattering experiment The light is polarized in the vertical direction thus the electric field will oscillate in the Z direction and the magnetic field will oscillate in the X direction A diode laser which is a monochromatic source of light that can be focused to a very small point in the center of the sample cell is used in PDI light scattering systems Typical sources include a semiconductor laser that can provide 20 to 30 mW at 685 nm and another which provides 100 to 150 mW at 800 nm The scattered light is collected at a given angle and orientation e g 15 or 90 from the incident radiation and is used to deduce the desired molecular properties A 3 STATIC LIGHT SCATTERING A 3 1 Measuring the Molecular Weight Note Since Precision Detector systems include polarized laser light sources the equations presented in this chapter will be slightly different than those presented in discussions of light scattering when non polarized sources are used The electric dipole moment that is induced is shown in equation A 1 gt gt p aE A 1 where p is the dipole moment a is the polarizability E is the electric field A 2 PrecisionMALS Appendix The polarizability can be related to measurable parameters via equation A 2 M dn de 2aNq A2 where Mw is the molecular weight 15 Avogadro s number 6 02 x 107 molecu
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