Precision Elucidate - The Molecular Materials Research Center
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1. e Jfa Precision Detectors PD4042 correlator module is employed access the Windows Device Manager and set USB Serial Port to Comm 4 1 4 GENERAL CONVENTIONS USED IN THIS MANUAL PrecisionElicidate 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 on 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 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 PrecisionElucidate Chapter 1 1 3 1 5 FOR ADDI2. 22 Commands seie a e n a a aae aeia ae aa aae oai E a Ea ceded TER 2 3 APAA RN EAI a1 PEA E EE E E E AE E E E E E E 2 3 DD Doe We MOM EE P A E A ATE dee est cutest E E AA E EEA E EAE A A TEE EE 2 3 AOA RTTE EAIA A n EEA A A E AE E EAE ATE ale da he AAE AE E E AEA EET 2 3 224 Measurement MENU rennen ae aS aE aaO eaa Rae ARE A aaie 2 3 0 T E E E E E T E E IIS OTD 2 3 2 3 The Measurement Mem iiss erane eneee a e E E a a E a a aE SS Ea 2 4 Dede di System DIEA RID TI A E A E A S EE E E 2 4 2 3 TT Tnstr ment C ntro laesies ene Ms Ron tenis Ae an Rent ei Me DAME oe 2 4 2 3 1 2 Configuration Options ccecceeseesceescesseeeeceecesecaecsaecseeeaeesseeseeseeeseeeeenseeeseceaeenseeeses 2 4 QS eledir Shutters 0 PEE 2d thew oct is isla bae aia Mesa ee ows ey cate coronas te aaah ocala eet 2 4 2 3 4 Intensity Control icc veces seseccti bhai densi n a gant uous tates A he aeah des eked 2 5 2 32 Starhx periments 2 lt hie E sok Ts ish gcn ade asesaeasigd a Bee beus yangen E 2 5 253 221 Damiing Parameter Seane e E a a a a A a EE a a a eaten 2 5 23 22 Experimental Parameters senno tence chen bie dees Ep E aaee ENE EES EEES 2 6 23I StopvExperimentt nire re eea E E E E a a E a e E a E aS 2 7 2 3 4 Run Queue Command ccccccccccccssscessecesseceeseccseceeseecsseceeseecessceeseecsseeeeseccsseseeseecssseeeseecseeeeeeeces 2 7 23y Temp Calibration renna E R E a e A e a E a a e wees dese inssse anaes 2 8 24A Establishing a Ruin Queu
3. lt lt T lt lt KAt This condition determines the choice of the sample time for the particular measurement To increase the statistical accuracy with which the correlation function is determined it is essential to maximize the number of count pairs whose products are averaged within the measurement time If the correlation function is being measured in M channels simultaneously ideally M products should be processed for each new count i e during sample time At The instrument capable of doing this is said to be working in the real time regime The real time regime means that the information contained in the signal is processed without loss The PDI correlator works in real time with a minimal sample time At of 1 microsecond and the length of the digital copy K 1024 The number of channels M processed in real time is determined by formula M 19 5 At 4 5 and cannot exceed 256 A 4 5 Brownian Motion Temporal fluctuations in the intensity of the scattered light are caused by the Brownian motion of the scattering particles The speed of the particles is related to the size small particles move faster than large particles Though each particle moves randomly in a unit time more particles leave regions of high concentration than leave regions of low concentration This results in a net flux of particles along the concentration gradient Brownian motion is thus responsible for the diffusion of the solute and is quantitatively characteriz
4. typical QLS data allow reliable determination of about three independent parameters of the size distribution of the scattering particles A 5 4 The Method of Cumulants T then are determined This method is only as good as the original guess of the The second approach is not to attempt to reconstruct the shape of the scattering particle distribution but instead to focus on so called stable characteristics of the distribution i e characteristics which are insensitive to possible fast oscillations In particular these stable characteristics are moments of the distribution or closely related quantities called cumulants 2 The first cumulant moment of the distribution D that gives the average diffusion coefficient D can be determined from the initial slope of the field correlation function Indeed using equation A 12 it is straightforward to show that Ing x 1 9 7 1D Dq dD Dg l A 12 The second cumulant moment of the distribution can be obtained from the curvature second derivative of the initial part of the correlation function As in the direct fit method the accuracy of the real QLS experiment allows determination of at most three moments of the distribution D The first moment D can be determined with better than 1 accuracy The second moment the width of the distribution can be determined with an accuracy of 5 10 The third moment which characterizes the asymmetry of the distributi
5. at the point of observation If the size of the aggregate is small compared to the wavelength of light A all waves scattered by individual monomers interfere constructively and the resulting wave has an amplitude mE Since the intensity of a light wave is proportional to its amplitude squared the intensity of the light scattered by the aggregate is proportional to the aggregation number squared mI o Where J is the intensity of scattering by a monomer The quadratic dependency of scattering intensity on the mass of the scatterer is the basis for optical determination of the molecular weight of macromolecules It is this dependency which is accounted for by the Mass Normalization function of PrecisionDeconvolve If the size of an aggregate particle is not small compared to the interference of the electromagnetic waves scattered by the constituent monomers is not all constructive and the phases of these waves must be taken into account If the phase of a wave scattered at the origin is used as a reference the phase of a wave scattered at a point with radius vector r is ger as shown in Figure A 1 The vector q is called the scattering vector which is a fundamental characteristic of any scattering process The length of the vector is indicated in equation A 1 4 q lq S sin0 2 where n is the refractive index of the medium X is the wavelength of light O is the scattering angle Partial cancellation of waves scattered by d
6. function D should be sought that produces via Equations A 3 and A 10 the function Ge T which is the best fit to the experimental data Unfortunately this simplistic approach does not work The underlying reason is that the corresponding mathematical minimization problem is ill posed meaning that dramatically different distributions D lead to nearly identical correlation functions of the scattered light and therefore are equally acceptable fits to the experimental data For example addition of a fast oscillating component to the distribution function D does not change GP t considerably since the contributions from closely spaced positive and negative spikes in the particle distribution cancel each other We discuss below three approaches for dealing with this ill posed problem A 8 PrecisionElucidate Appendix A A 5 3 The Direct Fit Method The simplest approach is the direct fit method In this method the functional form of D is assumed a priori single modal bimodal Gaussian etc and the parameters of the assumed function that lead the best fit of Go T to GZ functional form of D Moreover using the method can be misleading because it may confirm nearly any a priori assumption made It is also important to note that the more parameters there are in the assumed functional form of D the better the experimental data can be fit but the less meaningful the values of the fitting parameters become In practice
7. incident light beam is scattered in all directions upon interaction with particles in the beam Light is an electromagnetic wave and the light scattered by an ensemble of particles is the sum of light scattered by individual particles When the incident light is coherent the intensity variations or speckles are produced at the observation plane These speckles are due to the variation in phases of the waves scattered by different particles At one point waves arriving at different phases cancel each other more fully than at another As the scattering particles move over distances that are comparable to the wavelength of the incident beam the phases of the scattered waves and the speckle pattern are dramatically changed Monitoring the fluctuations of intensity of the scattered light passing through a small pinhole smaller than the size of the speckle make it possible to tell how fast the scattering particles diffuse over a distance equal to the wavelength of the scattered light In Precision Detectors systems this task is achieved by detecting the intensity of scattered light by an avalanche photodiode computing the correlation function of the photocurrent by a specialized correlator and deconvoluting this correlation function into contributions from particles with different diffusion coefficients Note A sample usually consists of a collection of particles with different molecular weights and sizes thus the Dynamic Light Scattering exper
8. information from the random fluctuations in the intensity of the scattered light For very large delay times T the photocurrents at moment and t t are completely uncorrelated and G co is simply the square of the mean current i At t 0 G 0 is obviously the mean of the current squared i Since for any i t i gt i the initial value of the correlation function is always larger than the value at a sufficiently long delay time The characteristic time within which the correlation function approaches its final value is called correlation time For example in the most practically important case of a correlation function that decays according to an exponential law exp t T the correlation time is the parameter T In the majority of practical applications of QLS the scattered light is a sum of waves scattered by many independent particles and therefore displays Gaussian statistics This being the case there is a relation between the intensity correlation function G and the field correlation function G Ga Hd yle N X A 4 PrecisionElucidate Appendix A Here g t G t G 0 is the normalized field correlation function I is the average intensity of the detected light and y is the efficiency factor For perfectly coherent incident light and for scattered light collected within one coherence area the efficiency factor is 1 If light is collected from an area J times larger than the coherence
9. light scattering are intrinsically more complicated than static light scattering since they involve measurements of spectral characteristics or related correlation properties of the scattered light PrecisionElucidate Appendix A A 1 A 3 LIGHT SCATTERING FROM MACROMOLECULES IN SOLUTION One may consider the solution as a homogeneous medium and ascribe light scattering to the spatial fluctuations in the concentration of a solute An alternative way is to consider each individual solute particle as a heterogeneity and therefore as a source of light scattering The first approach is more appropriate for solutions of small molecules in which the average distance between the center of the scatterers is small compared to the wavelength of light The second approach is more appropriate for solutions of large macromolecules and colloids when the average distance between particle centers is comparable to the wavelength of light When the size of the solute particles becomes comparable to the wavelength of light the description of the effects of orientational motion and deformation of the solute particles is much more straightforward when these particles are treated as individual scatterers Intensity of the light scattered by a single particle is dependent on the mass and the shape of the particle In this discussion we will consider an aggregate composed of m monomers and the amplitude of the electromagnetic wave scattered by an individual monomer is E
10. process dynamic light scattering data for macromolecules and particles greater than 1 nm in diameter PrecisionElucidate can be used with the following Precision Detectors system The PDExpert Workstation Platform which provides molecular size and conformation data from the autocorrelation of dynamic light scattering signals at any user selectable angle in 5 degree increments on a 360 platform The angular choice scattering capabilities provide exceptionally accurate measurements for hydrodynamic radius Rh and hydrodynamic radius distributions from any type of sample ranging from molecules protein and antibody to nanoparticles such as liposomes sols magnetic particles emulsions etc The 360 platform is a new concept of DLS measurement in a goniometer like instrument and provides ease of use and flexibility for all applications Many manually placed detectors can be multiplexed and with the unique shuttering mechanism measurements can be obtained at different angles in sequence The DLS detectors are interfaced with an APD avalanche photodiode detector for fast efficient and economical operation PrecisionElucidate Chapter 1 1 1 1 2 INTRODUCTION TO LIGHT SCATTERING Note This section provides the analyst with a qualitative description of the Dynamic Light Scattering method A detailed discussion of the technology is presented as Appendix A The term Light Scattering is used to describe the process in which light from an
11. show the difference in the signal between the two sensors for a given detector the difference is presumably due to random noise effects Ideally the two displays should be identical or very nearly so If there is a significant difference or you see a spike on one display but not the other this is evidence that the data is suspect Detector A 60 0 lapsed time seconds Figure 3 2 An Intensity Window The green red circles in the Jntensity window indicate the average intensity of the scattered light for the previous runs each point represents one run up to 2000 points can be displayed If desired you can change the vertical scale in the intensity window using up and down arrow keys and re center the line by pressing the space bar Each point in the intensity history plot represents one run The duration of the run is determined by Parameter Run time in the Measurement setup dialog box and may vary from one measurement to another In addition it should be noted that intervals between measurements are not shown so that the intensity history plot may not be a proper representation of the intensity time dependence and you cannot print the intensity history If you want to preserve and plot the intensity as a function of time during your measurements use the ntensity command on the Save sub menu of the File menu The black horizontal line is provided as a reference guide If the ntensity window is the active window pressing the
12. thermal equilibrium b Measure the temperature of the sample with a thermocouple or other accurate device c Click on the next available line on the Cuvette Temperature Calibration dialog box Enter the Target Temperature and Resulting Temperature d Repeat steps a c until the desired number of data points has been defined e Press the Export button to accept the calibration values 2 8 PrecisionElucidate Chapter 2 2 4 ESTABLISHING A RUN QUEUE A run queue is employed to automate data collection for a series of runs at different conditions i e data collection at 25 C 28 C 31 C 34 C 37 C To establish a run queue a Select Run Queue from the Menu menu to present the Run Queue dialog box Figure 2 7 Run Queue Sample Info Mode Run G Process Run Queue 5 i Cancel Figure 2 7 Run Queue Dialog Box b Right click in the dialog box to present a menu and select Add to present the Measurement Parameters dialog box Figure 2 4 c Enter the desired parameters for the first run and press OK The Run Queue dialog box will appear as shown in Figure 2 8 PrecisionElucidate Chapter 2 2 9 Run Queue PunSet FileName Sample Temperature Angle Eq Time Run Time Accumulations Repetitions Sample Info Operator Mode Sample dat Sample Name 25 0 Sample ln Operator Cross Cancel Figure 2 8 Run Queue Dialog Box d To add additional runs repeat steps b and c e Process th
13. wavelength of the laser that is being employed Scattering Angle Indicate the angle at which the scattering is being measured When the parameters have been established press OK to initiate the run The Start command will be deactivated and the Stop command will be activated 2 6 PrecisionElucidate Chapter 2 2 3 3 Stop Experiment The Stop command is used to halt data collection Data will be saved using the file name and directory indicated in the Measurement Parameters dialog box 2 3 4 Run Queue Command The Run Queue command accesses the Run Queue dialog box Figure 2 5 which is used to establish a series of data collection runs A detailed discussion of this feature is presented in Section 2 4 Run Queue Sample Info Mode L Ju t Process Run Queue F i Cancel Figure 2 5 Run Queue Dialog Box PrecisionElucidate Chapter 2 2 7 2 3 5 Temp Calibration The Temperature command presents the Cuvette Temperature Calibration dialog box Figure 2 6 which is used to indicate the expected temperature and observed temperature for the cuvette so that a temperature calibration relationship can be established Cuvette Temperature Calibration Cuvette Temperature Calibration Editable Target Temp Resulting Temp Difference R T Figure 2 6 The Cuvette Temperature Calibration Dialog Box To enter a calibration point a Set the sample holder with a sample in it to the desired temperature and allow it to come to
14. 0e 000 photons s Instrument Status Accumulating Data 0 accumulations from 1 measurements 30 Detector A Meant 0 000e 000 StdDevli 0 000e 000 photons s Instrument Status Idle log tau seconds Detector A ae x Detector B 60 0 J J 60 0 elapsed time seconds elapsed time seconds For Help press F1 Figure 2 1 The Main Window of PrecisionElucidate The contents of the Correlation Function window and the Intensity windows are discussed in detail in Chapter 3 PrecisionElucidate Chapter 2 2 1 The information panel in the upper right corner of the main window presents information about the sample and various instrumental parameters as shown in Figure 2 2 The panel is updated during data collection and cannot be edited by the user Data File Name BSAO60906c dat Date Time 06 09 2006 12 34 39 Sample Name BSA Sample Information BSA Solvent Buffer Ri 1 330000 Viscosity 0 008900 Poise Sample dride 0 167000 mL g Scattering Angle 90 degrees Desired Cell Temperature 25 0 C Current Cell Temperature 25 0 C Alignment Laser Status Laser is Off Laser Status Laser is On Laser Power 100 Temperature Control Enabled Remaining Equilibration Time O seconds intensity Cutotfs Detector 4 2 604e 005 Detector B 2 604e 005 photons s Detector A Current intensity 2 508e 005 photons s Detector B Current Intensity 25076 005 photons s Instrument Status Accumulating Data 60 accumulations from 60 measur
15. Main Laser Temperature C 125 Laser Power Full Power 1100 Index of refraction RIU 11 33 Wavelength nm 1809 Viscosity Poise 0 0089 Scattering Angle 30 Sample dnde mL g 10 167 Sample Concentation mg mL 11 314 Cancel Figure 2 4 Measurement Parameters Dialog Box File Name Directory Path Enter the desired file name for the data set and indicate the directory in which the data should be stored Note The file name must be manually updated by the operator for each new data set to eliminate the possibility of loss of data Sample Name Operator Sample Information Solvent Enter the desired alphanumeric information This information will be stored with the data 2 3 2 1 Timing Parameters Equilibration Time Indicate the period of time that the system should be held at when the desired temperature has been reached before data should be collected Run Time The Run time is the period of time at which the operator is updated on the current analysis and is the duration of an individual correlator run PrecisionElucidate Chapter 2 2 5 Accumulations The Accumulate parameter is the number of runs that the system should accumulate to obtain a single measurement The overall time for a single measurement is the product of the Accumulate and Run time parameters After the completion of data acquisition the results will be saved using the indicated file name and extension e g Jul20 001 You can change thi
16. NTIN Precision Detectors use a proprietary algorithm of superior quality PrecisionElucidate Appendix A A 9 All regularization algorithms produce similar results and incorporate the use of a parameter that determines how smooth the distribution has to be The choice of this parameter is one of the most difficult and important parts of the regularization method If the smoothing is too strong the distribution will be very stable but will lack details If the smoothing is too weak false spikes can appear in the distribution The rule of thumb is that the smoothing parameter should be just sufficient to provide stable reproducible results in repetitive measurements of the same correlation function Two facts are helpful for choosing the appropriate smoothing parameter First the lower are the statistical errors of the measurements the smaller the smoothing parameter can be without loss of stability This will yield finer resolution in the reconstructed distribution D Second narrow distributions generally require much less smoothing and can be reconstructed much better than can wide distributions This is because oscillations in narrow distributions are effectively suppressed by non negativity conditions The moments of the distribution reconstructed by the regularization procedure coincide closely with those obtained by other methods However the regularization procedure in addition gives unbiased apart from smoothing information o
17. PrecisionElucidate Data Acquisition and Instrument Control Software User Manual Created by Precision Detectors Inc Notices This product is covered by a limited warranty A copy of the warranty 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 precisiondetectors com Web site www prec
18. Refraction 2 6 Information Panel 2 2 Installation 1 3 Instrument Control 2 4 Intensity 2 5 Intensity Window 3 2 Interfacing the Computer 1 3 Introduction 1 1 PrecisionElucidate Index L Laser Enable 2 4 Laser Power 2 6 License Agreement iii Light Scattering 1 2 Load Default Settings on Startup 2 4 Main Window 2 1 Measurement Window 2 3 Oo On Line Help 1 3 Operator 2 5 P PDExpertWorkstationPlatform 1 1 Run Queue 2 7 Run Queue Command 2 7 S Sample Concentration 2 6 Sample dn dc 2 6 Sample Information 2 5 Sample Name 2 5 Scattering Angle 2 6 Signal Optimization Mode 2 4 Solvent 2 5 Start Experiment Command 2 5 Stop Experiment Command 2 5 System Defaults 2 4 T Temperature Calibration 2 8 Temperature 2 6 Temperature Control Enable 2 4 Timing Parameters 2 5 v View Menu 2 3 Viscosity 2 6 Ww Warranty iv Wavelength 2 6 Window Menu 2 3 1 2 PrecisionElucidate Index
19. 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 PrecisionElucidate 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 entit
20. TIONAL INFORMATION A detailed discussion about the processing and reporting of data collected via PrecisionElucidate please refer to the PrecisionDeconvolve User Manual General information about the instrumentation used to collect data is provided in the user manual provided with the detector system PrecisionElucidate Chapter 1 Chapter 2 The Main Window 2 1 COMPONENTS OF THE MAIN WINDOW The main window of PrecisionElucidate Figure 2 1 presents the correlation function window upper left corner an information panel upper right corner which presents sample and detector information and the signal from the each sensor employed in the cross correlation experiment bottom g PrecisionElucidate File View Window Measurement Help SH Seer PrecisionElucidate Function DER Instrument Status Data File Name Sample1 dat Date Time 06 22 2006 18 40 47 Sample Name Sample Name Sample Information Sample Information Solvent PBS Buffer Ri 1 330000 Viscosity 0 008900 Poise Sample dn de 0 167000 mLig Scattering Angle 65 degrees Desired Cell Temperature 25 0C Current Cell Temperature 273 1 C Alignment Laser Status Laser is Off Laser Status Laser is On Laser Power 100 Temperature Control Enabled Remaining Equilibration Time 0 seconds Intensity Cutoffs Detector A 0 000e 000 Detector B 0 000e 000 photons s Detector A Current Intensity 0 000e 000 photons s Detector B Current Intensity 0 00
21. area fluctuations in light intensity are averaged out and the efficiency factor is of the order of J J lt lt 1 Low efficiency makes the quality of measurements vulnerable to fluctuations in the average intensity caused by the presence of large dust particles in the sample or instability of the laser intensity A 4 4 Determination of the Correlation Function In PDI instruments the correlation function is determined digitally The number of photons registered by the photodetector within each of a number of short consecutive intervals is stored in the correlator memory Each count in a given interval termed the sample time and denoted A represents the instantaneous value of the photocurrent i t The series of K counts held in the correlator memory is a termed the digitized copy of the signal According to Equation 1 to obtain the correlation function G t at t nAt n 1 K the average product of counts separated by n sample times should be determined The number n is referred to as a channel number Up to K channels in principle can be measured simultaneously but usually a smaller subset of M equidistant or logarithmically spaced channels is used Clearly the shortest delay time at which the correlation function is measured by the procedure described above is At channel 1 The longest delay time cannot exceed the duration of the digitized copy KAt Thus it is important that the correlation time T fit into the interval At
22. artup This command is not active Signal Optimization Mode Used for system adjustment Autocorrelation Check this box if the autocorrelation feature is desired If the box is not checked a single channel will be monitored 2 3 1 3 Shutters Select the shutter that is to be open for this measurement and indicate the angle that the shutter is located Hardware Indicate the PD Electronics Module that is being used 2 4 PrecisionElucidate Chapter 2 2 3 1 4 Intensity Control Intensity Indicate the level for the Intensity line in the Intensity windows Intensity Limit photons s Used to indicate the maximum signal intensity that a data point above this level data will be automatically discarded 2 3 2 Start Experiment The Start Experiment command presents the Measurement Parameters dialog box Figure 2 4 which is used to enter the parameters for data acquisition When data is being collected the Start Experiment command is deactivated and the Stop Experiment command is active Lo PF Note This dialog box is also used to establish the individual runs when a run queue is established Section 2 4 Measurement Parameters File Name Sample1 dat Directory Path c data Sample Name Sample Name Equilibration Time s 0 Operator Operate aie Run Time s 2 Accumulations 160 Sample Information Sample cele Experiment Repetitions 10 Solvent PBS Buffer IV Enable Temperature Control M Enable
23. e Run Queue using the Save Run Queue button Execution of the run queue is described in Chapter 3 pa Note If desired the Run Queue can be saved and recalled via the Save Run Queue and Load Run Queue buttons 2 10 PrecisionElucidate Chapter 2 Chapter 3 Data Acquisition 3 1 Overview When data is acquired the correlation window Section 3 2 and the signal intensity windows Section 3 3 from both sensors are presented In addition this chapter presents information that will assist in optimizing the use of the system Additional detail is presented in the Precision Deconvolve User Manual 3 3 2 The Correlation Window The Correlation window shows the correlation function and is updated after each run A typical correlation window is presented in Figure 3 1 Precision Elucidate Function logitau seconds Figure 3 1 The Correlation Window The correlation curve presents the fit of the correlation function When new data is being collected the correlation function window updates after every run Duration of a run is determined by the Run time parameter in the Measurement dialog box eer Note You can change the scale of delay time axis via the left right arrows of the keyboard PrecisionElucidate Chapter 3 3 1 3 3 The Intensity Window The Intensity windows Figure 3 2 serve a number of roles e To show the intensity of individual data e To support intensity fluctuations management during measurements e To
24. ed by the diffusion coefficient D The laws of diffusive motion stipulate that over time df the displacement Ax of a Brownian particle in a given direction is characterized by the relationship Ax 2D 6 PrecisionElucidate Appendix A A 5 A 4 6 Determination of the Diffusion Coefficient D As explained earlier temporal fluctuations in scattered light intensity are caused by the relative motions of particles in solution Two spherical waves scattered by a pair of individual particles have at the observation point a phase difference of q r where r is the vector distance between particles As the scattering particles move over distance Ax q along the vector q the phases for all pairs of particles change significantly and the intensity of the scattered light becomes completely independent of its initial value The correlation time T is thus the time required for a Brownian particle to move a distance q along the vector q As stated above Ax 2D8t thus for Ax q Ta 1 Dq Rigorous mathematical analysis of the process of light scattering by Brownian particles leads to the following expression for the correlation function of the scattered light k exp Dq spe A 4 7 Determination of the Sizes of Particles in Solution According to Equations A 4 and A 5 measurement of the intensity correlation function allows evaluation of the diffusion coefficients of the scattering particles The diffusion coeff
25. ements Detector A Meant 2 476e 005 StdDevi 1 231e 003 photons s instrument Status Idle Figure 2 2 Information Panel 2 2 PrecisionElucidate Chapter 2 2 2 COMMANDS Note For the sake of brevity this manual will not describe commands and operations that are generally included in most Windows programs e g such as Open Save 2 2 1 File Menu File Includes a number of standard Windows utility commands that are used for archival purposes or printing of data Open Save Save As Print Print Preview Print Setup 2 2 2 View Menu View Includes standard Windows utility commands to indicate if the Toolbar and or the Status bar zs should be presented on the display The Refresh command is not active 2 2 3 Window Menu Window Includes standard Windows utility commands for selection of the active window on the workspace In addition this command can be used to indicate if the various windows should be presented as tiles or as a cascade The Arrange Icons command is not active 2 2 4 Measurement Menu Measurement Includes a number of commands to access windows that are used to establish data collection parameters and initiate data collection These commands are described in detail in Section 2 3 2 2 5 Help Help includes Help which accesses an on line help file and About which accesses a dialog bog that presents the version number PrecisionElucidate Chapter 2 2 3 2 3 THE MEASUREMENT MENU 2 3 1 System Defa
26. es sic ssccsenevsestonesseceoons estou ceseacecnieovienssivsvedge sisedesneesancavaavunestateslersateoeye 2 9 Chapter 3 Data Acquisition scccscssccsccccscsccccssccecssscecsscsesccesssscecsecssssecsesceesssceessessessscesscessssseeees 3 1 Bill SOVERVICW fates coe toss zecesal och se E E E ins ladies thatteteset van Peatessl O TA tines 3 1 3 2 The Correlation Window ccscccsccssscessceeeceseeesecsseeeseeesaecsaecsseceasensecsaecsseeseeseeeseeeseseeeneeesaeeaaes 3 1 3 3 Theclnitensrty WindoWr seere a A er R eed E a a R e 3 2 3 4 Selecting Data Collection Parameters ccccccccsseesseesssessecsecssecesecsseesecseeecseeseeseseeeeeeeeeaaes 3 3 Appendix A General Principles of Dynamic Light Scattering sesssesssssssssssesssosssesssesssesssesssesssese A 1 1D i C K EAE EEEE E TTA EE I 1 PrecisionElucidate Table of Contents v vi This page intentionally left blank PrecisionElucidate Table of Contents Chapter 1 Introduction 1 1 OVERVIEW The Precision Detectors PrecisionElucidate application software is designed for the collection of dynamic light scattering data using detectors that contain two sensors This program provides the ability to use cross correlation techniques to detect the presence of abnormal noise when a high pulse rate is employed Data collected with PrecisionElucidate is processed with the PrecisionDeconvolve application program These programs are designed to collect and
27. hat is rescattered at this location is not compensated for and some light will be observed in directions other than the direction of incidence and light scattering occurs Scattering of light can be viewed as a result of microscopic heterogeneities within the illuminated volume and macromolecules and supramolecular assemblies are examples of such heterogeneities A 2 LIGHT SCATTERING TECHNIQUES Static light scattering probes concentration molecular weight size shape orientation and interactions among scattering particles by measuring the average intensity and polarization of the scattered light Static light scattering measurements which are performed at different scattering angles provide information on the molecular weight size and shape of the scattering particles Measurements of the intensity of light scattering as a function of concentration yield the second virial coefficient which is the key characteristic of the strength of attractive or repulsive interactions between solute particles Quasielastic dynamic light scattering 2 probes the relatively slow fluctuations in concentration shape orientation and other particle characteristics by measuring the correlation function of the scattered light intensity Fast vibrations of small chemical groups which lead to significant changes in the frequency of the scattered light is the domain of Raman spectroscopy These latter two methods which probe the dynamics of the particles which cause
28. icient in an infinitely dilute solution is determined by particle geometry For spherical particles the relation between the radius R and its diffusion coefficient D is given by the Stokes Einstein equation __kT 6mnR A 6 where kp is the Boltzmann constant T is the absolute temperature n is the viscosity of the solution For non spherical particles it is customary to introduce the apparent hydrodynamic radius R defined as R app _ ky T 6nnb A 7 where D is the diffusion coefficient measured in the QLS experiment For non spherical particles it is important to note that the diffusion coefficient is actually a tensor the rate of particle diffusion in a certain direction depends on the particle orientation relative to this direction As small particles diffuse over a distance q their orientation may be changed many times QLS measures the average diffusion coefficient for these particles Particles of a size comparable to or larger than q essentially preserve their orientation as they travel a distance smaller than their size For these particles the single exponential expression of equation A 5 for the field correlation function is not strictly applicable A 6 PrecisionElucidate Appendix A For particles that are small compared to q the hydrodynamic radius is calculated numerically and in some cases analytically for a variety of particles shapes The important analytical formula for the prolate el
29. ifferent parts of the large aggregate reduces the intensity of light scattering by a factor of kl where a is an averaged value of the phase factors exp iq r for all monomers The factor a should be averaged over all possible orientations of the particle The result of this averaging yields the structure factor S q Expressions for the structure factors for particles of A 3 various shapes can be found elsewhere A 2 PrecisionElucidate Appendix A PMT LASER SAMPLE Ko Figure A 1 The Scattering Vector q The path traveled by a wave scattered at the point with radius vector r differs from the path passing through the reference point O by two segments 1 and 2 with lengths and respectively The phase a difference is Ad k l it L where k k ikl 2nn 2 is the absolute value of the wave vector k or k The segment is a projection of r on the wave vector of the incident beam k i e l re k k Similarly L rek k and thus Ad re k k rq Vector q k k is called the scattering vector A 4 METHOD OF QUASIELASTIC LIGHT SCATTERING SPECTROSCOPY QLS A 4 1 The Motion of Particles in Solution When light is scattered from a collection of N solute molecules at the observation point we also have a sum of waves scattered by individual particles Figure A 1 Each particle could be at any random location within the scattering volume the intersection of the illuminated volume and the volume fro
30. iment leads to a distribution for the diffusion coefficients The diffusion coefficient depends on particle size and shape and can be converted into related parameters such as e the hydrodynamic radius R of the macromolecule e the molecular weight of the molecule when the concentration is known e the diameter of the macromolecule 1 2 PrecisionElucidate Chapter 1 1 3 INSTALLATION 1 3 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 ia dialog box that presents the programs to load select PrecisionElucidate The password that is provided with the system will allow you to load the program Once you have loaded the software start PrecisionElucidate and select the System Defaults command on the Menu Configuration drop down menu and select the appropriate correlator module PD4042 PD4043 PD4046 or PD4047 1 3 2 Interfacing the Computer to the Correlator Module The correlator module is connected to the computer via a USB cable e Ifa Precision Detectors PD4043 PD4046 or PD4047 correlator module is employed the system configuration will be automatically performed
31. isiondetectors com Copyright 1997 1998 1999 2000 2002 2003 2005 2006 by Precision Detectors Inc Printed in the United States of America Precision Detectors Inc 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 relocate the
32. lipsoid with the long axis a and the ratio of lengths of the short axis to the long axis p is 2 R tip nee v p P The above formulae connecting the diffusion coefficient or hydrodynamic radius to particle geometry are strictly applicable only for infinitely dilute solutions At finite concentrations two additional factors significantly affect the diffusion of particles viscosity and interparticle interactions Viscosity generally increases with the concentration of macromolecular solute According to equation A 6 this leads to a lower diffusion coefficient and therefore to an increase in the apparent hydrodynamic radius Interactions between particles can act in either direction If the effective interaction is repulsive which is usually the case for soluble molecules otherwise they would not be soluble local fluctuations in concentration tend OA to dissipate faster meaning higher apparent diffusion coefficients and lower apparent hydrodynamic radii If the interaction is attractive fluctuations in concentration dissipate slower and the apparent diffusion coefficients are lower Thus depending on whether the effect of repulsion between particles is strong enough to overcome the effect of increased viscosity both increasing and decreasing types of concentration dependence of the hydrodynamic radius are observed In this context it should be noted that the interaction between large particles as compared to q 1 generally leads to a non ex
33. m which the scattered light is collected Since the size of the scattering volume is much bigger than q with the exception of nearly forward scattering where q 0 0 the phases of the waves scattered by different particles will vary dramatically As a result the average amplitude of the scattered wave is proportional to JN and the average intensity of the scattered light is simply N times the intensity scattered by an individual particle as expected The local intensity however fluctuates from one point to another around its average value The spatial pattern of these fluctuations in light intensity called an interference pattern or speckles is determined by the positions of the scattering particles As the scattering particles move the interference pattern changes in time resulting in temporal fluctuations in the intensity of light detected at the observation point The essence of the QLS technique is to measure the temporal correlations in the fluctuations in the scattered light intensity and to reconstruct from these data the physical characteristics of the scatterers PrecisionElucidate Appendix A A 3 A 4 2 Coherence Area There is a characteristic size for speckles in the interference pattern If the intensity of the scattered light is above average at a certain point it will also be above the average within an area around this point where phases of the scattered waves do not change significantly this area is called the c
34. ment 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 c 1 ii of 252 227 7013 iii 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 Precision De
35. n the shape of the distribution This shape cannot be extracted through use of the direct fit method nor from cumulant analysis In a typical QLS experiment regularization analysis can resolve a bimodal distribution with two narrow peaks of equal intensity if the diffusion coefficients corresponding to these peaks differ by more than a factor of 2 5 FOOTNOTES 1 R Pecora Dynamic Light Scattering Applications of Photon Correlation Spectroscopy Plenum Press New York 1985 2 K S Schmitz An Introduction to Dynamic Light Scattering by Macromolecules Academic Press Boston 1990 3 H C van de Hulst Light Scattering by Small Particles Dover New York 1981 4 A N Tikhonov and V Y Arsenin Solution of Ill Posed Problems Halsted Press Washington 1977 5 D E Koppel J Chem Phys 57 4814 1972 6 S W Provencher Comput Phys Commun 27 213 1982 A 10 PrecisionElucidate Appendix A Index A Accumulations 2 6 Additional Information 1 4 Alignment Laser Enable 2 4 Autocorrelation 2 4 c Commands 2 3 Copyright iii Correlation Window 3 1 D Data Acquisition 3 1 Diffusion Coefficient 1 2 Directory Path 2 5 Enable Main Laser 2 6 Enable Temperature Control 2 6 Equilibration Time 2 5 Establishing a Run Queue 2 9 Experiment Repetitions 2 6 Experimental Parameters 2 6 F File Menu 2 3 File Name 2 5 G General Conventions 1 3 H Hardware Command 2 5 Help 2 3 I Index of
36. oherence area Within different coherence areas the fluctuations in intensity of light collected are statistically independent Increasing the size of the light collecting aperture beyond the size of a coherence area does not lead to improvement of the signal to noise ratio because the temporal fluctuations in the intensity are averaged out For a monochromatic source the scattered light is coherent within a solid angle of the order of W A where A is the cross sectional area of the scattered volume perpendicular to the direction of the scattering Because the coherence angle is fairly small powerful 100 mW and well focused laser illumination and photon counting techniques are used in the PDI BATCH instrument A 4 3 The Correlation Function While the photodetector signal in QLS is random noise information is contained in the correlation function of this random signal The correlation function of the signal i t which in the particular case of QLS is the photocurrent is defined in equation A 2 G 0 lt i t i t t gt A 2 The notation G t is introduced to distinguish the correlation function of the photocurrent from the correlation function of the electromagnetic field G t which is the Fourier transform of the light spectrum G i lt E t E t 1 gt A 3 In the above formulae the angular brackets denote an average over time t This time averaging an inherent feature of the QLS method is necessary to extract
37. on usually can be estimated with an accuracy of only about 100 A 5 5 Regularization The regularization approach combines the best features of both of the previous methods The advantage of the cumulant method is that it is completely free from bias introduced by a priori assumptions about the shape of D assumptions that are at the heart of the direct fit method On the other hand reliable a priori information on the shape of the distribution function in addition to the experimental data improves significantly the quality of results obtained by the QLS method The regularization method assumes that the distribution D is a smooth function and seeks a non negative distribution producing the best fit to the experimental data As discussed above the ill posed nature of the deconvolution problem means that distributions differing by the presence or absence of a fast oscillating function produce very similar correlation functions The regularization requirement that the distribution should be sufficiently smooth eliminates this ambiguity allowing unique solutions to the minimization problem There are several methods that utilize this approach for reconstructing the scattering particle distribution function from QLS data All of these methods impose the condition of smoothness on the distribution D but differ in the specific mathematical approaches used for this purpose One popular program originally developed by Provencher is called CO
38. ponential correlation function that does not take the form of equation A 4 and therefore cannot be completely A 8 described by a single parameter D A 5 DATA ANALYSIS A 5 1 Polydispersity and the Mathematical Analysis of QLS Data Polydispersity can be an inherent property of the sample for instance when polymer solutions or protein aggregation are studied or it can be a consequence of impurities or deterioration of the sample In the first case the polydispersity itself is often an object of interest while in the second case it is an obstacle In both instances polydispersity significantly complicates data analysis For polydisperse solutions equation A 5 for the normalized field correlation function must be replaced with le gt LexpCD q t 0 i PrecisionElucidate Appendix A A 7 In this expression D is the diffusion coefficient of particles of the i th kind and J is the intensity of light scattered by all of these particles 7 N J where N is the number of particles of i th kind in the scattering volume and J is the intensity of the light scattered by each such particle For a continuous distribution of scattering particle size equation A 10 is generalized as follows I 1 l 7 I D exp Dqt dD A 10 where D dD N D I D aD is the intensity of light scattered by particles having their diffusion coefficient in the interval D D dD N D dD is the number of these particles in the scat
39. s parameter during measurements If it is set to a value less then the current accumulation the current measurement will end and next measurement will be started Experiment Repetitions The Repeat parameter is the number of accumulation processes that should be performed before the system stops If one measurement is desired set the repeat value to 1 At the conclusion of the accumulation process the data will be stored e g Jul20 001 using the name and the system will wait for another Start command If the value is greater than 1 the data will be stored the file name extension will be incremented e g Jul20 001 Jul20 002 etc the Repeat parameter will be reduced by one and another measurement will be initiated This process will be repeated for the indicated number of data accumulation processes Note If Repeat is set to zero the measurement will be performed but the results will not be saved If the user decides to save the results the Save command on the File menu should be employed Enable Temperature Control Check this box if the temperature of the sample should be monitored and equilibrated at the indicated temperature before data is collected Enable Main Laser Make certain that this box is checked so that the laser is powered up when the data collection is initiated 2 3 2 2 Experimental Parameters Temperature The temperature should be set to the desired temperature for the measurement A change in this parameter
40. space bar will shift the whole intensity curve so that the next point will be on this line Closing and reopening the ntensity window removes previous intensity data If intensity data becomes too long to fit into the Intensity window a horizontal scroll bar will automatically appear 3 2 PrecisionElucidate Chapter 3 When the intensity window is active e Clicking the right button the mouse sets the cutoff level to the Y coordinate of the point where the mouse was clicked e Pressing the space bar moves the whole graph up or down so that the current average intensity green line is on the black horizontal eye guide line e The left and right arrow keys scroll the display if scrolling is necessary PrecisionElucidate Chapter 3 3 3 3 4 This page intentionally left blank PrecisionElucidate Chapter 3 Appendix A General Principles of Dynamic Light Scattering A 1 WHAT IS LIGHT SCATTERING The propagation of light may be considered as a continuous rescattering of the incident electromagnetic wave from every point of the illuminated medium The amplitude of each secondary wave is proportional to the polarizability at the point from which this wave originates if the medium is uniform rescattered waves will have the same amplitude and interfere destructively in all directions except in the direction of the incident beam If however at some location the index of refraction differs from the average value the a wave t
41. tectors Inc 34 Williams Way Bellingham MA 02019 Your acceptance or decline of the foregoing Agreement was or will be indicated during installation iv PrecisionElucidate License Agreement Table of Contents Precision Detectors Inc Electronic End User License Agreement sccccscssssrccsccescccssscceeesceeees iii Chapter 1 Introduction e soesssesssesssesssoesscsssesssesssossseossosssosssseosocssoossoossoossoossoosssossssossosssossssssssssssesssee 1 1 Tel OVENI EW sires ae EE E E E E E lhe TOE O E E Ea 1 1 1 2 Introduction to Light Scattering cc ecccccssesssceeceeseeesseececsecesecesecsseececseeeseeeeeseceseeeseeeseesaes 1 2 13 gt Tista lati On ie eer seta ces riiin o ds CKE E eet vit okie EEEE AETA EERE e 1 3 3L Loading the Sowar Ese a a E RE ea a eens ee oe ees 1 3 1 3 2 Interfacing the Computer to the Correlator Module 0 0 0 0 ccceesceesceescesseeeceseceeeeaeeeseeneeeseeeeeeneens 1 3 1 4 General Conventions used in this Manual ccccccecsseessecesceeseceecesecesecseecseeeseeeesecaeeeseeeeeesaes 1 3 1 5 For Additional Information ccccccecccesscessscsseeeseeeeeeeecaecsaecsecesseeeecsseeseeeseseeeseceeesteeeneeesaes 1 4 Chapter 2 The Main Wind ow ccsscsscssssssssccscescsssssscecscccescccssssccesccsesscccesccessscesssessesscessscessssserees 2 1 2 1 Components of the Main Window c cesccesccesscesecesceeeeeeseeeseeeseecseecseeceseesaeceaeeeseeseeeseeeeneeenes 2 1
42. tering volume D is the intensity of light scattered by each of them The goal of the mathematical analysis of QLS data is to reconstruct as precisely as possible the distribution function D or N D from the experimentally measured function Go t It should be noted that polydispersity is not the only source of non single exponential correlation functions of scattered light Even in perfectly monodisperse solutions interparticle interactions orientation dynamics of asymmetric particles and conformational dynamics or deformations of flexible particles will lead to a much more complicated correlation function than described by equation A 6 These effects are usually insignificant for scattering by particles small compared to the length of the inverse scattering vector q but become important and often overwhelming for larger particles In those cases QLS probes not the pure diffusive Brownian motion of the scatterers but also other types of dynamic fluctuation in the solution A 5 2 Deconvolution of the Correlation Function an Ill Posed Problem The values of GO t contain statistical errors We have described previously the features of the QLS instrument that are essential for minimizing these errors It is equally important to minimize the distorting effect that experimental errors in G2 T have on the reconstructed distribution function 7 D The distribution D is a non negative function A priori then a non negative
43. ults The System Defaults command presents the System Defaults dialog box Figure 2 3 which is used to establish a variety of system parameters and enter the system configuration System Defaults Instrument Control Shutters IV Active C Shutter 1 Cell Temperature C Ch 25 C Shutter 2 V Laser Enable Shutter 3 Laser Power 100 Shutter 4 Alignment Laser Enable Hardware C PD4042 PD4043 V Temperature Control Enable Configuration Options Vv Intensity Control Signal Optimization Mode Intensity 2 5 V Autocorrelation Intensity Limit gqqo000 photons s Cancel Figure 2 3 System Defaults Dialog Box 2 3 1 1 Instrument Control Temperature Control Enable If you want the system to wait until it has reached a specific temperature before data is to be collected place a check mark and indicate the desired temperature Note A change in this parameter will automatically change the Temperature entry on the Measurement Ja Parameters dialog box Figure 2 4 Laser Enable If you want to set the laser to a specific percentage of laser power place a checkmark in the box and indicate the desired percentage Note A change in this parameter will automatically change the Laser Power entry on the Measurement Parameters dialog box Figure 2 4 Alignment Laser Enable If you want to use the alignment laser place a check mark in the box 2 3 1 2 Configuration Options Load Default Settings on St
44. will automatically change the temperature entry on the system default dialog box Note If a change is made on the Default Parameters dialog box Figure 2 3 this value will be automatically updated Index of Refraction The index of refractive of the sample should be obtained from the literature or measured in your laboratory For aqueous solutions the value 1 332 should be used at 25 C A table presenting the refractive index of water as a function of temperature is presented in Appendix B of the PrecisionDeconvolve User Manual Viscosity The viscosity of the sample should be obtained from the literature or measured in your laboratory The units for viscosity should be entered in Poise P For aqueous solutions the value is 0 0089 cP at 25 C A table presenting the viscosity of water as a function of temperature is presented in Appendix B of the PrecisionDeconvolve User Manual Sample dn dc 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 Sample Concentration Indicate the concentration of the sample Laser Power Enter the desired value for the laser power in Note A change in this parameter on the Default Parameters dialog box Figure 2 3 will automatically change the Laser Power entry on the Measurement Parameters dialog box Figure 2 4 Wavelength Indicate the
45. y 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 Agree
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