90PDP Instruction Manual 90Plus Debye Plot Option for

Molecular Weight Determination

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Please Read

The 90PDP option consists of two parts: the 9k90MW software and the 90PFC flow cell. This manual describes the software and cell. Please read it carefully before making measurements. The “How To” section describes how to install the software and what the manual covers. You may familiarize yourself with some of the features of this software by reloading data files (Files/Database/Sample Data). If you have any questions or sugges-tions, please contact Brookhaven Instruments.

Software is never really finished, because there are always additions and changes. As these become available, they will be added to the back of this manual as appendices. Please look at the appendices if you cannot find the answer to your questions in the main part.

Please contact the factory at info@bic.com if you have questions. When you do contact the factory, please mention the instrument model number (90Plus or ZetaPlus/BI-MAS or ZetaPALS/BI-MAS), the serial number, and date of manufacture as indicated on the identification sticker affixed to the instrument. Please mention the 9k90MW software version number found by clicking Help on the main Menubar. Please also indicate from whom the instrument was purchased.

Remember the old saying: “When in doubt, read the instruction manual.” Sometimes the solution to your problem has already been addressed. You just need to find it. Thanks for purchasing a Brookhaven.

This program requires Windows 9X or higher and at least 8 Mb of RAM.

Important Warning

Never allow any liquid to dry inside the flow cell of tubing. Dried salts, poly-mers, and bacteria take time to remove. Always flush first with pure solvent so that salt or polymer does not precipitate. If the remaining solvent is not to be left in the cell for stor-age, flush with an intermediate solvent that is miscible both with the current solvent and the storage liquid. See Appendix B for recommendations. If you are not going to work with the cell for more than a day, AND you are working with a solvent in which bacteria may grow, flush the cell with one or more compatible solvents. Flush with one or more interme-diate solvents until you can replace the final liquid with ethanol or some other alcohol in which bacteria will not grow.

If a blockage occurs due to dried salt or polymer, or if the instrument was left

with water and bacterial growth is suspected, refer to Appendix A of this manual.

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Copyright Notice

Copyright (©) 2004 by Brookhaven Instruments Corporation. All Rights Reserved World-wide. No part of this manual may be reproduced, transmitted, transcribed, stored in a re-trieval system, or translated into any human or computer language, in any form or by any means, electronic, mechanical, magnetic, optical, chemical, manual, magical or otherwise, without the express written permission of Brookhaven Instruments Corporation, Brook-haven Corporate Park, 750 Blue Point Road, Holtsville, New York 11742-1832, USA.

First Printing: June 2004

Catalogue Number: 90PDP Manual Ver. 1.0

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Software License Agreement

Carefully read the following terms before using the software provided. Use of the software indicates your acceptance of these terms. If you do not agree with the terms, promptly re-turn the software. BIC refers to Brookhaven Instruments Corporation.

Terms:

1. In purchasing this software you are granted a nonexclusive license to use the software product on one computer.

2. BIC retains title to, and ownership of, the software product. The software product may not be modified without the express written consent of BIC.

3. Duplication of the software product for any purpose other than backup protection, in-cluding duplication for any commercial use, is a violation of the copyright laws of the United States of America and of other countries. We know that some of you, especially university students, feel that software is inherently free, and that this should be, if it is not already, one of the legal requirements of the United Nations. Based on this princi-ple, you see no problem in copying and distributing our software. Well, as soon as you can convince Bill Gates to give you free software, you are welcome to do the same with ours. Until then, please respect our right to earn a living by selling software to run our instruments. Thanks.

Information produced by using this BIC software and its manual, including the resulting displays, reports, and plots, are believed to be accurate and reliable. However, Brookhaven Instruments Corporation assumes no responsibility for any changes, errors, or omissions.

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Table of Contents

I. How to Use this Manual and Software

II. Theory

III. Flow Cell

IV. Calibration

V. Sample Preparation

VI. Making a Measurement

VII. Analyzing Data & Interpretation

VIII. Database

Appendix A: Clearing Blockages and Removing Bacterial Growth

Appendix B: Solvent Compatibility

Appendix C: Differential Refractive Index Increment, dn/dc

Appendix D: Rejection, Smoothing, Stability: Noise and Trend

Appendix E: Export File Format

Appendix F: Limits for Debye Plot Use

I-1

Section I: How to Use this Manual and Software

Introduction The 90PDP option consists of the 9k90Mw software and the 90PFC flow cell for

use in the 90Plus or with the BI-MAS option in either a ZetaPlus or ZetaPALS. The theory, which relates intensity of scattered light to Mw, the weight-average

molecular weight, and A2, the second virial coefficient, is discussed in Section II. Since the instrument is normally setup for use as a particle size or zeta potential analyzer, you must first insert the flow cell and arrange the tubing as described in Section III. Meas-urements of the scattered intensity are made at 90o scattering angle only. The instrument must be calibrated and this is described in Section IV. Sample preparation, described in Section V, is crucial if good results are expected. As described in Section VI, a measure-ment is made of the pure solvent, followed by measurements of the scattered intensity from a series of solutions of known concentration. Analyzing data is described by exam-ple in Section VII. If you prefer to fit the data using your own software, you will need to export the data as described in Section VIII.

Accurate Mw values are obtained if and only if the longest dimension of the poly-

mer is small compared to the wavelength of light. If the polymer’s longest dimension is less than or equal to 20-25 nm, the results are accurate. For random coils, this translates to a radii of gyration, Rg, less than or equal to 10-12 nm. A more quantitative criterion is developed in Section II on theory. Generally speaking, the method is absolute for globu-lar proteins, dendrimers, and other globular macromolecules, and for random coils with molecular weight less than approximately 100 kDa.

Before using the instrument, please read the 90Plus or BI-MAS manuals.

Make sure your instrument is operating properly by following instructions in the appropriate installation manual.

The 9k90Mw application program allows you to control the instrument, to collect the measured scattered light intensities and to plot the results. A Debye Plot is used to determine Mw and A2. The radius of gyration cannot be determined with a Debye Plot. If in doubt about the application of a Debye Plot, measure the Effective Diameter, equiva-lent to the hydrodynamic diameter, using the 90Plus or BI-MAS option. If the Effective Diameter is less than 25 nm, then the use of a Debye Plot is acceptable. Results can be printed, archived, and reloaded for future reference. An ASCII file can be created for use in spreadsheets and plotting programs.

This type of light scattering is variously known as static light scattering (SLS),

classical light scattering (CLS), and total or integrated light scattering (TLS or ILS). [The word integration here refers to the averaging over time.] It has even been called TILS for total intensity light scattering. If measurements are made at a single angle, it is called SALS for single-angle light scattering. Such acronyms eventually become irritating and

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tiresome, eventually when MALLS (multiangle laser light scattering) is used since it can also refer to a shopping center. The acronym MALS (multiangle light scattering) is mar-ginally better.

In this manual we prefer the term SLS to distinguish it from DLS, dynamic light

scattering, a form of light scattering typically used for particle size determination calcu-lated from the translational diffusion coefficient measurements obtained from analyzing the time dependence in the temporal fluctuations of the scattered light about the average intensity.

Software Installation

If you purchased 90PDP option at the time you purchased the 90Plus or BI-MAS

option on one of the zeta potential instruments, then the 9k90MW software is already in-stalled. If you purchased the 90PDP option subsequently, then follow these instructions.

To install the 9k90Mw software, place the installation CD in the appropriate CD

drive (here assumed to be the D: drive). Click on Window’s START button and select RUN. Type D:\9k90Mw\Setup. Press the Enter key. Follow any on-screen instructions. When finished, a BIC icon with the name Debye Plot Software will be added to your BIC program group that was created at the factory when you purchased the original instru-ment. References

Most good physical chemistry textbooks have a few pages on Zimm Plots and light scattering, though in most cases they describe instrumentation that is decades out of date, showing mercury arc lamps instead of vertically polarized lasers, for example. Nev-ertheless, these accounts serve as an easy introduction to the subject. However, most such textbooks neglect the simpler and original Debye Plot method. If you want more informa-tion than is available in undergraduate textbooks, read Section II: Theory.

Specialized information is also available in the references listed below. If you are

unfamiliar with the SLS method then read chapter 14 in reference 1 or chapter 5 in refer-ence 2. Both are presented at the undergraduate level. Reference 3 is an introductory textbook on classical light scattering from polymer solutions. Reference 4 is a review chapter on SLS presented at the intermediate level. Reference 5 is the classic text on SLS written mostly before the widespread introduction of lasers, personal computers, and DLS. It is, however, full of valuable data and insight. Long out of print, look in a univer-sity library to find a copy. Reference 6 is an advanced treatise on light scattering on branched polymers. Reference 7 is a textbook on DLS. Despite its title, it is suitable for use in a graduate level course.

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1. Allcock and Lampe, Contemporary Polymer Chemistry, Prentice-Hall

publisher, 1981. 2. Hiemenz and Rajagopalan, Principles of Colloid and Surface Chemistry,

Third Edition, Revised and Expanded, Marcel Dekker publisher, 1997. 3. Kratochvíl, Classical Light Scattering from Polymer Solutions, Elsevier

publisher, 1987. 4. Casassa and Berry, "Light Scattering from Solutions of Macromolecules",

chapter 5 in Polymer Molecular Weights, Part I, P.E. Slade editor, Marcel Dekker publisher, 1975.

5. M.B. Huglin, editor, Light Scattering from Polymer Solutions, Academic

Press, 1972. 6. W. Burchard, "Static and Dynamic Light Scattering from Branched Poly-

mers and Biopolymers", in Light Scattering from Polymers, Advances in Polymer Science series, Number 48, Springer-Verlag, 1983.

7. K.S. Schmitz, An Introduction to Dynamic Light Scattering by Macro-

molecules, Academic Press, 1990.

Though an understatement, this list of references is by no means complete. You can certainly find many other useful sources of information.

II-1

Section II: THEORY The Basic Equation

In the limit of low concentration, the data obtained from SLS measurements using a di-lute, homopolymer solution (also applies to globular proteins) in a single solvent can be ex-pressed as: H*c/∆R(θ,c) = 1/[MwPz(q)] + 2A2c . (1) The optical constant H is given by: H = 4π2n2

o(dn/dc)2/(Noλo4) , (2)

where no is the refractive index of the solvent. Typical values range from

1.30 to 1.60. dn/dc is the specific refractive index increment of the solution. Values

from -0.05 to 0.30 cm3/g are typical. See Appendix C. c is the polymer concentration. Values from 0.01 to 10 mg/cm3 are

typical. The lower concentration range is more common when measuring high molecular weight polymers, above 1 MDa, for example; the upper concentration range is more common when measuring low molecular weight polymers, below 100 kDa, for example. Though with the APD detector, the lower end of the range is accessible even for globular proteins.

No is Avogadro's Number, 6.022 x 1023 mol-1. λo is the wavelength in vacuum of the laser. For diode lasers in the

red it is typically 660 nm. θ is the scattering angle in degrees. ∆R is the excess Rayleigh Factor (also called Rayleigh Ratio) in units

of cm-1 calculated at different angles and concentrations. The ex-cess is the difference between the value for the solution and the value for the solvent. R is proportional to the scattered light inten-sity. The proportionality constant is determined by calibration against a substance (often toluene) with a known Rayleigh Ratio.

Mw is the weight-average molecular weight (molar mass). Values in the range from a few hundreds to tens of million g/mol (Daltons) are measureable, more commonly 103 to 5 x 106 Da, though for large dendrimers, values in the billions are possible.

Pz(q) is the z-average particle scattering function or particle structure function. (In more concentrated and strongly interacting systems a solution structure function is also important.) Pz(q) yields Rg.

q = (4πno/λo)sin(θ/2) is the magnitude of the scattering wave vector.

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A2 is the second virial coefficient. Values in the range 0 to 10-3 cm3·mol/g2 are typical. For polydisperse systems, A2 is also an av-erage quantity; however, the average is not a simply defined one like the weight- or z-average. Positive A2 values imply stability; negative A2 values imply unstable solutions (crystallizable).

In the polymer and light scattering literature, one often finds an alternate designation for

the second virial coefficient, Γ. The value of Γ typically varies from about 10 to 1,000 cm3/g, and it is a measure of molecular volume. Γ is the symbol often used in the discussion of the viscosity of polymer solutions. Γ is related to A2 as follows:

A2 = Γ/Mw (3) The factor 4 in the optical constant H is a result of using incident light that is linearly po-

larized perpendicular to the horizontal scattering plane. This is the most common configuration and is typically referred to as vertical polarization. The BI-MwA uses vertical polarization. For unpolarized incident light, the factor is 2. In older textbooks, you will see the factor as “2”.

The particle scattering function can be expanded in terms of q2, and the first three terms

are Pz(q) = 1 - (R2

g*q2)/3 + O(q4) , (4)

where Rg is shorthand for <R2g>0.5

z, the z-average, root-mean-square radius of gyration, a meas-ure of the molecular size. Rg is almost universally called the radius of gyration, even though that is a misnomer. It is a root-mean-square value. In fact, even for a monodisperse polymer system, where the z-average value equals the number- and weight-average values, Rg is still an average value. A random coil polymer takes up a large number of configurations and Rg, even for a single molecule, is thus an average value over time.

The coefficient of q2 is independent of the particle shape. Coefficients of higher order

terms do depend on shape. Therefore, the radius of gyration (more properly, the z-average, RMS radius of gyration) is a primary parameter obtained from light scattering: primary in the sense that no model for the shape is assumed.

The Zimm Plot

Combining Equations 1 and 2, and expanding 1/Pz(q) from Equation 3 to first order in q2 with a Taylor series, gives the following:

H*c/∆R(θ,c) = [1/Mw]·[1 + (R2

g·q2)/3] + 2A2c . (5) This equation is the basis for the famous Zimm Plot. Scattered light intensities are meas-

ured at several angles for each of several solution concentrations and for the pure solvent at each angle. Subtracting the solvent scattering from the solution value yields the excess intensity scat-tered by the polymer. After reflection, refraction and volume corrections, and calibration, the ex-cess Rayleigh Factors are calculated from measured intensities.

II-3

If the left hand side of Equation 5 is plotted against sin2(θ/2) + kp*c, where kp is an arbi-trary plotting constant chosen purely for convenience in viewing the results, a grid-like plot re-sults. Two sets of, typically, parallel lines make up the grid. One set consists of angular measurements at each concentration, and one set consists of concentration measurements at each angle. Extrapolating the angular measurements to zero angle for each concentration yields a straight line in c. The slope of this line yields A2. Extrapolating the concentration measurements to zero concentration for each angle yields a straight line in sin2(θ/2). The slope divided by the intercept of this line yields Rg.

The intercept of both extrapolated lines––the double extrapolation to zero angle and zero

concentration––yields Mw the weight-average molecular weight of the polymer in solution. Mw is the most important parameter of a polymer distribution. Light scattering offers an absolute∗ method for its measurement.

The value of dn/dc and a calibration constant must be known in advance in order to cal-

culate Mw and A2 from a Zimm Plot.

The Debye Plot When the longest dimension of a scatterer is small compared to the wavelength of light in

the liquid, then by definition the particle/polymer is called a Rayleigh scatter. In this case, the angular term in Equation 4 is negligible, and that equation reduces to:

H*c/∆R(θ,c) = 1/Mw + 2A2c . (6) This equation is the basis for the famous Debye Plot that predates the Zimm Plot. At one

angle, intensities are measured as a function of concentration. The results are plotted according to Equation 6. A2 is obtained from the slope/2 of this plot; the intercept yields 1/Mw. Typically the angle used is 90°, but this is not necessary. This angle is convenient because flare light should be negligible and because residual dust or microgel contributions are usually insignifi-cant.

For globular proteins, dendrimers, and other globular polymers, the Debye Plot is nor-

mally a good approximation. For random coil polymers below approximately 100 kDa a Debye plot is also usually acceptable. For a more quantitative analysis of the errors involved, see Ap-pendix F.

∗ Though commonly referred to as an absolute measurement, since calibration is required, it is not absolute in the sense of a first-principles measurement where there are no calibration or adjustable parameters. However, compared to viscosity measurements, where many more assumptions are required to obtain a molecular weight, light scattering is—if you will excuse the oxymoron—relatively absolute. In addition, compared to calibration using a polymer of known molecular weight, calibration with pure toluene is apt to result in a more accurate Mw since it is impossible to produce monodisperse, synthetic polymer distributions. So-called “standards” are in fact narrow distributions. In addition, calibration with a polymer standard requires accurate concentration measurements; whereas, calibration with pure toluene does not.

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Corrections for Depolarization For optically isotropic molecules, the polarization of the scattered light is parallel to the

polarization of the incident light. The most common configuration with a laser source is incident light that is linearly polarized perpendicular to the scattering plane. This is commonly called ver-tical polarization. For many, large, flexible-chain polymers depolarization effects are negligible, and, as a result, no polarization corrections are necessary. This is also true for spherically homo-geneous molecules such as dendrimers. For most globular proteins, it is also a good approxima-tion. Mw and A2 are correct as calculated from the Equations 6. [Many solvents are anisotropic scatterers and depolarize the scattered light significantly; however, these effects are negated upon subtracting the solvent scattering from that of the solution.]

For optically anisotropic molecules, the polarization of the scattered light has components

both parallel and perpendicular to the incident polarization. For short, flexible-chain polymers and chains in or near the rigid rod limit, depolarization effects are not negligible, and, as a result, polarization corrections are necessary. Under these circumstances Mw, Rg, and A2, as used in the equations above, should be considered apparent, not true values.

To make the corrections, two limiting cases of the worm-like chain model must be distin-

guished: flexible chain and rigid rod. In addition, each of these two cases can be measured in ei-ther of two common experimental setups: measurements with linearly polarized incident light perpendicular to the scattering plane and no analyzer Ruv (this is the case in the standard 90Plus); or, measurements with an analyzer set to pass only scattered light with polarization parallel to the incident polarization Rvv.

For Ruv measurements on flexible chain molecules: Mw,app = Mw*[1 + (7/5)δ2] = Mw*[(3 + 3ρv)/(3 - 4ρv)] , (7) A2,app = A2/[1 + (7/5)δ2] = A2/[(3 + 3ρv)/(3 - 4ρv)] , (8) Rg,app = Rg/[1 + (7/5)δ²]0.5 = Rg/[(3 + 3ρv)/(3 - 4ρv)]0.5 . (9) For Ruv measurements on rigid rod molecules: Rg,app = Rg*{[1 - (4/5)δ + (47/35)δ²]/[1 + (7/5)δ²]}0.5 . (10) For Rvv measurements on flexible chain molecules: Mw,app = Mw*[1 + (4/5)δ²] = Mw*[3/(3 - 4ρv)] , (11) A2,app = A2/[1 + (4/5)δ²] = A2/[3/(3 - 4ρv)] , (12) Rg,app = Rg/[1 + (4/5)δ²]0.5 = Rg/[3/(3 - 4ρv)]0.5 . (13)

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For Rvv measurements on rigid rod molecules: Rg,app = Rg*{[1 - (4/5)δ + (4/7)δ²]/[1 + (4/5)δ²]}0.5 . (14) In these equations δ is the molecular anisotropy and ρv is the depolarization ratio. The

depolarization ratio is an experimentally measured parameter. It is operationally defined as: ρv = Rhv(90°)/Rvv(90°) , (15)

where Rhv(90°) is the excess scattered light intensity measured at θ = 90° with polarization per-pendicular to the incident polarization, and Rvv(90°) is the excess scattered light intensity meas-ured at θ = 90° with polarization parallel to the incident polarization. The excess is defined by the difference between the value measured with the solution and the value measured with the solvent. Since many common solvents can depolarize the light significantly, one must use the excess values.

The molecular anisotropy can be written in terms of the experimentally determined depo-

larization ratio as: δ² = 5ρv/(3 - 4ρv) (16) Literature or measured values of ρv can be input, and its effect on recalculated values Mw,

Rg, and A2 determined. The 90PDP option does not provide for ρv measurements though our BI-200SM does.

For most polymer samples the depolarization corrections are negligible. This is so be-

cause the normally random orientation of dipole moments from the anisotropic monomeric units in a polymer cancel as the molecular weight increases. In fact, it is often stated that if the meas-ured depolarization ratio is not negligible, the measurement is probably wrong. The older litera-ture values of depolarization ratios are suspect. Be careful in applying these corrections. If in doubt, do not apply them. This is accomplished by setting ρv in the 9k90Mw program, to zero, the default value. With ρv equal to zero, there should be no effect on the calculation of Mw or A2 no matter which of the two models are selected: flexible chain or rigid rod.

For rod-like polymer molecules, for short-chain molecules where end-groups may con-

tribute significantly to depolarization, ρv may not be negligible and corrections may be neces-sary.

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WARNING Real samples and real measurements almost never fit exactly the simple theory just pre-

sented above. Polymer-polymer interactions may lead to nonlinear data. Though the fit will cer-tainly improve as the order of the polynomial is increased, the user must use judgment in accepting these results. Are they repeatable results? If not, then dust, microgels, and other su-pramolecular entities (colloids, perhaps) are most likely the problem. Look at the plotted points. If one or two are significant outliers, remove them by double clicking in the tabular area of the screen. See Section VII. If the scatter is too great, clean up the sample before proceeding. If the results are repeatable, do they make sense? If not, perhaps flare light is the problem; perhaps the calibration was not done with a clean solvent (repeat calibration and compare); perhaps the polymer concentrations are not correct (make new and more accurate concentrations); perhaps the value of dn/dc is wrong.

III-1

Section III: Flow Cell 90PFC: 90Plus Flow Cell

This is a 40 µL flow cell consisting of a 2 mm x 2 mm entrance/exit window and a 10 mm path length. The flow is horizontal. Black glass is used to minimize flare light. Either of the top ports can be used for the inlet, with the other port being used for the outlet. Always insert the square cell with the rectangular window facing the front of the instrument. The opposite-facing wall of the cell has no window from which light can emerge. This side of the cell should face the rear of the instrument.

The 30 cm long, orange, PEEK tubing of 0.50 mm (0.020”) I.D. with a Luer-lock fitting is the inlet. The 1 m long, white, TEFLON tubing of 0.75 mm (0.030”) I.D. is the outlet. It has no fitting on the free end. Cut this tube to an appropriate length and secure to whatever waste or collection vessel you choose. Arrange the free ends of the tubing such that they are held gently in place by partially closing of the sliding sample cell door on top of the instrument.

Never allow any liquid to dry inside the cell or tubing. Always flush the solute or polymer solution with a pure solvent. If you are not going to work with the instrument for more than a day, AND you are working with a solvent in which bacteria may grow, flush the instru-ment with solvent until any salt or polymer is removed. Then flush with ethanol or isopropanol to prevent bacterial growth. Finally, flush with methanol since it leaves less residue than either isopropanol or ethanol.

If a blockage occurs due to dried salt or polymer, refer to Appendix A of this manual.

NOTE: With some older machines, when you insert the cell the window may be a little too low for optimum alignment. After injecting any ample, raise the cell up and down a very small amount and see if the count rate reaches a maximum. That is the optimum position.

IV-1

Section IV: Calibration

Determine the Dark Count Rate Set the dark count rate for the detector as follows. Insert the sample cell with the

window-less wall facing to the right, the direction of the laser beam. Slide the sample cell door closed but not so tight as to crimp the inlet/outlet tubing. Click on the Experimental Parameters command button at the bottom of the main window. See Figure IV-1.

Figure IV-1: Experimental Parameters window. Setting the dark count rate.

Click on the Dark Count Rate command button. A dark count rate in counts per second, cps, should appear. The values are between a few tens of counts to several hun-dreds of counts per second. Repeat two or three times to make sure the value is a reason-able average value. REMEMBER: In photon counting the random error is proportional to the square root of the total counts. Thus, for a one second duration resulting in 256 cps, the standard deviation is +/- 16 cps. Therefore, 95% of the time another measurement should be within 2 x 16 or from 224 to 288; and 99.7% of the time it should be within 3 x 16 or from 208 to 304. By changing the Duration/Repeat to 10 seconds, you will get a larger total number of counts, a lower random error; but remember to return the value to 1 second before making any other measurement.

Avoiding Precipitation

If the last material in the 90PFC flow cell was a salt or a polymer solution, do not

initially use a liquid in which the salt or polymer is not soluble. If you do, the salt or polymer may precipitate, coming out of solution, and stick to surfaces or clog small ori-fices. Therefore, always flush with a compatible solvent before switching to a new liquid.

IV-2

Set the Dead Time

To calculate the correct intensity, the dead time correction must be applied. This correction depends on which detector you have: APD (150 ns) or PMT (25 ns). Click on Setup/Hardware Configuration and then select the appropriate detector. In most cases it will be the default APD choice. See Figure IV-2.

Figure IV-2: Setup/Hardware Configuration. Dead time correction selection. Preparing Syringes and Filters for Injection

Clean a 10 mL syringe glass syringe with soap and water, scrubbing all internal parts and the barrel. Rinse thoroughly in water and then with an intermediate solvent that is both miscible in water and with toluene, the calibration liquid. Acetone, methanol, ethanol, and cyclohexane should all work. High quality methanol leaves the least residue. See Appendix B, Solvent Compatibility, to determine a good intermediate solvent.

Use a fresh 100 nm (0.1 micron) Teflon or Nylon filter that is suitable for use

with the toluene. Since filters may have dried material on their surface from the manufac-turing process, flush with 5 mL of liquid before attaching to the BI-MwA. Calibration

A calibration constant is obtained by measuring the intensity of light scattered from a standard at 90°. It is assumed that Rc = kc*Ic, where kc is the calibration constant and Rc is the known Rayleigh Ratio. Rc is known for toluene and benzene at various laser wavelengths. These values are encoded in the 9k90Mw software. Rayleigh Ratios scale inversely with λ4. Such a calibration is only good if the flare light at the calibration angle, typically 90º, is insignificant.

IV-3

Click on the Sample Parameters command button in the bottom of the screen Figure IV-3 shows an example of what you will see. Make sure ‘Toluene’ is showing in the list box next to Calibration Liquid. Click on Calibrate Instrument. Follow instruc-tions and slowly inject the toluene, perhaps 2 mL. When finished, click the command button that says OK. Automatically, after approximately 20 to 25 seconds, the Trend and Noise traffic lights will remain green and the measurement is finished.

Figure IV-3: Sample Parameters window. Calibration of instrument. A new calibration constant will appear in the window. In this example, it is

1.137E-8. If in doubt, repeat the measurement and make sure that successive calibration constants agree to within 2%. Inject slowly. Be patient. Be steady.

Proper calibration ensures accuracy when calculating values for Mw and A2.

Given the wavelength of the instrument shown at the bottom of the window—a value automatically read by the software from the BI-MwA—the Rayleigh Ratio and refractive index are calculated and displayed as shown above in Figure IV-3 for the calibration liq-uid.

Since the absolute value of Mw will depend on the calibration constant, make sure

to use HPLC grade toluene. Once opened, a new bottle will begin to absorb moisture from the air. Therefore, do not use old bottles of toluene. Purchase small, new bottles of the purest grade available. Alternatively, use triple distillation to purify a reagent grade bottle of toluene. You will need about 10 mL, which includes enough for flushing and several repeated measurements.

IV-4

Once calibrated, an instrument should remain calibrated for many days. However,

since the calibration procedure is fast and simple, do it prior to any important set of new measurements.

V-1

Section V: Sample Preparation Sample Preparation: Generalizations

This is the single most difficult part of making a good light scattering measurement. Most errors can be traced to poorly prepared samples. This applies to the calibration procedure also. Be patient. Clean everything twice. Use pure materials. If you have enough sample, considering using a syringe pump. The steady injection from such a pump leads to more stable signals. If you have precious samples, such as a small amount of protein, use a small-volume syringe, a rinsed, 20 nm filter—Anatop is a common brand name as of the writing of this manual—and a slow, steady motion. Take care to remove visible bubbles from flasks of liquid and the syringes.

References 3, 4 and 5 in Section I: How to Use This Manual and Software each con-tain chapters devoted to sample preparation.

It is much easier to prepare samples in nonpolar liquids than it is in water. Water dis-solves more air, increasing the possibility that bubbles will form. Water is a polar liquid and keeps more charged impurities in suspension including dust which is often silica or other charged, colloidal particles.

Water that sits around for more than a day or so is usually not suitable as bacteria begin

to grow. Use freshly distilled or filtered water. In winter, when the temperature of water may be lower than usual, allowing more air to dissolve in the water, consider degassing it or letting it stand at room temperature and then sonicating it.

When using other solvents, do not use old, half-filled bottles, as these solvents are very likely to be contaminated. Use either triply distilled solvents or the very best HPLC or reagent grade solvents. The money spent on purchasing the best solvents and correct filters will be worth it because of the time saved in making good measurements.

Gravimetric methods are more exact than volumetric methods, even for the determination of the solvent volume. (Multiply by the solvent density determined to three significant figures and include a small temperature correction if available.) Yet, it is more convenient to determine the volume of solvent using either a volumetric flask or a calibrated, automatic pipette. Auto-matic pipettes are sometimes very accurate, but first verify they are correctly calibrated by weighing a liquid of known density. Never rely on the markings of a typical, thick-barreled sy-ringe for accurate volume determinations unless you have calibrated the syringe by weighing liquids of known density.

A minimum four-fold change in polymer concentration from the least to the most concen-trated sample measured is recommended. A 10-fold change is preferred. A minimum of three concentrations is required; we at recommend at least five for a good fit. The example shown in Section VII uses seven, or which two are deleted and the remaining five are used to make the fit.

V-2

Verify that Filtration does not effect Concentration If it is possible to dry a solution without decomposing the polymer itself or incorporating

some of the solvent into the newly dried polymer, then prepare a solution by weighing dried polymer and adding a known volume of liquid. Then filter. Then dry the solution and see how accurately the two polymer weights agree. It is best to cover the sample that is drying to prevent airborne materials from adding to the dried weight. This entails placing a low-lying canopy over the sample to be dried. You should expect concentrations to be accurate and repeatable to 1% or better. If not, a significant amount of polymer is still on the filter.

If evaporation to constant weight is not suitable, consider the following choices: UV ab-sorption (if appropriate) at a wavelength where the extinction coefficient is known or measured; measurement of the differential refractive index, ∆n, where dn/dc is already known (BI-DNDC).

Two Methods for Preparing a Set of Concentrations

You can prepare a single stock solution, quantitatively divide it into separate vessels, and

add known amounts of filtered solvent to each. Alternatively, you can prepare individual sample concentrations.

The advantage of the first method is that only solvent is filtered to make dilutions. If sig-

nificant change occurs upon initial filtration of the stock solution, only this filtered solution con-centration needs to be determined as described above. However, errors compound with serial di-lution, and an error made at any step propagates into all succeeding steps.

You must use a precision pipette or a calibrated, automatic pipette. Volume delivery is always more prone to error than the less convenient but more accurate method of weighing sam-ples. In addition, some polymers do not rapidly disperse when new solvent is added. You may have to wait for spatial homogeneity before injecting the freshly diluted sample into the 90PFC

Preparing individual sample concentrations is more time consuming, but it is the pre-

ferred method for experienced users.

Warning Some polymers take a long time to dissolve. It may take hours; it may take several days.

Be patient. Gently rolling samples can help. If the dried polymer is a thin flake, it will probably dissolve fast. If it is a chunky bit of plastic, it may take a long time. Low molecular weights dis-solve faster; high molecular weights take longer. Look for visual evidence that the solution is homogeneous by gently swirling it and noting the absence of any refractive changes in the light illuminating the sample.

V-3

Stock Solution Concentration

The scattered intensity depends on many factors including polymer concentration, mo-lecular weight, and specific refractive index increment, dn/dc.

As a first guess make a stock solution of 2 mg/mL for a polymer with Mw = 100,000

g/mol and dn/dc = 0.1 mL/mg assuming the detector is the BI-APD. If you have the PMT, start at 10 mg/mL. Since I ~ c*M*(dn/dc)^2, you can use these numbers to estimate a stock concentration given a guess for MW and knowing dn/dc for the unknown polymer. For example, given a typi-cal dn/dc of 0.18 mL/g for globular proteins in water, the stock concentration can be almost four times less. However, given the small, 40 µL cell volume, we recommend, even with the APD, no less than 1 mg/mL as the stock concentration from which more dilute samples will be made.

Preparing a Stock Solution

This procedure assumes you have plenty of dry polymer.

Wash with soap, water and a bottle brush any syringes, vials or dilution vessels including any screw caps. Wear clean, initially dry gloves to prevent finger oils from contaminating the glassware. If you are using a glass pipette, you must clean it too. Automatic pipettes with dis-posal polyethylene tips are better in this regard, but make sure you have calibrated the pipette and understand that a loose fitting pipette tip introduces a false volume reading.

Let glassware dry thoroughly.

Choose a filter and filter housing suitable for use with the solvents to be used. For water and similar, polar, non-aggressive solvents, standard cellulose filters are sufficient. For more ag-gressive solvents, or ones that will not wet cellulose, consider Nylon and Teflon filters and poly-carbonate housings. Disposable filters are convenient, though the traditional stainless steel filter housings and replaceable filters are also choices to consider.

Use a nominal 0.1 micron pore size filter for any polymer where the hydrodynamic di-

ameter is between 20 nm and 50 nm. Use a nominal 0.02 micron (20 nm) Anatop filter for globular proteins. Rinse the filter at least once with a syringe full of liquid to remove residue from the filter manufacturing process.

Prepare a 20 mL dilution vial with cap by rinsing cell, cap, and upper portions of the cell several times with filtered solvent. Cover it while it dries thoroughly. Weigh it. Weigh in roughly 100 mg of polymer. Add approximately 10 mL of filtered solvent. Weigh the vial. By subtrac-tion, determine the solvent’s weight. Use the density of solvent at the room’s temperature to cal-culate its volume. Calculate the stock solution concentration. In this example, it will be close to 10 mg/mL. Alternatively, use a calibrated, volumetric pipette to determine the volume of sol-vent.

Even though the solvent was filtered, it often happens that dust is introduced into the so-

lution from the surface of the dry polymer. Therefore, you may need to filter the stock solution.

V-4

If you have not done so already, verify that filtration does not significantly change the polymer solution concentration. If polymer is left on the filter, then you should use the dilution method discussed previously, and you must determine the filtered, stock solution concentration using one of the two methods previously discussed.

During the preparation of the stock solution and in the subsequent handling of polymer solutions, remember that volatile solvents will result in increasing concentration with time. Also, minimize contact between samples and lab air. It is laden with dust, and all your previous efforts are wasted if well-prepared samples are not capped.

The highest measured concentration, using any of the measurement schemes described

previously, should be about half the stock solution concentration. We recommend measuring five concentrations, though a minimum of three is required to

fit to a straight line using a linear least squares approach. Before You Take the Plunge --A Trial Measurement, Please

Do not start with the most difficult sample you can find. In particular do not try to meas-

ure that 30 million molecular weight DNA first; do not try to measure sucrose in water (300 g/mol) first; and do not try to measure the any exotic sample that you just synthesized first. There is, after all, only 3 micrograms of it in existence and you cannot get the Nobel Prize if there is no more left for another lab to verify your work.

Now that you have read this manual and played with the software using stored data, there

is an overwhelming tendency to make your very first SLS measurements on either your own samples or the most difficult one you can find. Resist the temptation until you have experience.

Instead, try something simpler to get use to the program; if you have never made SLS

measurements before, gain some experience with sample preparation. We suggest measuring polystyrene in toluene, perhaps in the range of 100,000 g/mol. It dissolves almost immediately; no gels are formed; scattering is good; the dn/dc is approximately 0.105 mL/mg; and inexpensive reference standards are available that are good to about ± 5 %. Check with a supplier of GPC/SEC standards for calibration of columns. They offer polystyrene “standards”.

Do not be fooled when purchasing GPC/SEC standards. Some are not narrow distribu-tions defined by Mw/Mn ≤ 1.05. For example, PEG’s are not narrow, but PS samples are. Some standards are characterized by Mp, the “peak” molecular weight obtained in a GPC/SEC frac-tionation. Advice: Be sure you know what the weight-average molecular weight, Mw, is sup-posed to be and its expected uncertainty.

Or, to practice with globular proteins, consider purchasing inexpensive Lysozyme, nomi-nally 14 kDa, with dn/dc = 0.18 mL/g.

VI-1

Section VI: Making a Measurement You must calibrate the instrument as described in Section IV prior to making any

measurements. Prior to calibration, you must determine and enter the dark count rate. Click the Experimental Parameters command button to initiate that procedure. And, of course, you need to verify that there are no leaks around the cell fittings by pushing liq-uid through the cell—with it removed from the instrument. Then make sure it is inserted with the blank wall facing the rear of the instrument.

Figure VI-1: The main window when entering the program. Click the Experimental Parameters command button at the bottom of the

screen. See Figure IV-2. Fill in an appropriate “Sample ID”. This name is used in the da-tabase and a little thought in assigning identification will make it easier as time passes to identify measurements. Fill in the “Operator ID” and add any “Notes”.

Select the “Solvent” from a pull-down list. If your solvent is one of several com-

mon ones found in the list, its refractive index will automatically be calculated and dis-played (grayed out: visible but cannot be changed). If your solvent is not in the list, select “Unspecified” and then type in the solvent’s refractive index.

VI-2

Enter an appropriate temperature. As discussed in Section II: Theory, the value of dn/dc is required. In order to cal-

culate an accurate Mw and A2, you must enter an accurate value for the sample’s specific refractive index increment, dn/dc. See Appendix C for more information.

For most random coil polymers, leave the “Depolarization Ratio, ρv” at its default

value of 0.000. If you know the value of ρv and the appropriate chain model, make those choices in this window. NOTE: If ρv is zero, it does not matter what chain model you se-lect. The answers for Mw and A2 are then not dependent on the model chosen.

Check the ‘Auto Save Results’ box and the results will be automatically saved to

whatever folder is currently opened under Setup/Database. You can always move or copy files between folders. See Section VIII for more details.

Check the ‘Excess Intensity’ box and you will be asked to inject solvent during

the measurement. In theory, it is the difference, or excess, between the light scattered from the polymer solution and solvent that is important. However, in special cases, where the solution scattering is very high and it is hard to clean the solvent, ignoring the differ-ence (click a checked box to remove the check) may be justified. Normally, always check this box.

Figure VI-2: Experimental parameters and calibration window.

VI-3

NOTE: You can always recalculate results by editing later the solvent’s refractive index, dn/dc, ρv, and the selected chain model.

Click OK to return to the main menu.

Use an Appropriate Filter

Most measurements require a filter on the end of the syringe to remove dust be-fore the liquid enters the tubing/cell. Use an appropriate filter.

If you have lots of sample, use a 0.1 mm pore size filter with a 25 mm O.D. dis-

posable filter housing. The holdup volume is on the order of ¼ cc. If sample is precious, use a smaller, 13 mm O.D. filter housing with a smaller holdup volume. Also, instead of using a new filter for each solution, push out the previous solution by forcing air through the filter using an empty syringe.

For aqueous and other types of non-aggressive solvents, use cellulose filters. For

aromatic solvents and aggressive solvents, use Nylon or Teflon filters and appropriate, disposable, filter housings. Consult lab supply catalogues for a description of appropriate filters for different liquids, samples, and applications.

Initiating a Measurement

Click on the Start command button in the lower left of the screen. If the instru-

ment has not been calibrated, you will be instructed to do so. You cannot make any meas-urements without performing this separate measurement first. Inject about 2 mL. Inject slowly, steadily, and be patient. Then click OK. After pressing OK, you will wait a time in seconds equal to N, the number of stability points (default 20). Red/green traffic lights will appear indicating whether or not the signal is stable.

Once stable, you will be asked to type in your first polymer concentration and

then inject the sample. Again, do not press OK immediately after injecting the sample. Wait for stability. Continue to follow the instructions on the windows requesting you to type in the polymer concentration, inject the sample, and press OK to enable data acquisi-tion.

Figure VI-3 shows the sequence for the fifth polymer solution concentration,

8.167 mg/mL. The box in the lower right shows the concentrations and the corrected, in-tensities I’. Corrections include dead time, dark count rate, and de-spiking. (At the end of the experiment, when solvent values are subtracted, excess intensities, I’

ex, are shown. It is the excess intensity that yields the excess Rayleigh Ratios used in calculating mo-lecular properties from light scattering data.)

There are five plateaus shown in the Intensity vs. Time graph. The lowest one to

the left is that for the solvent. The remaining four correspond to 1.026, 2.052, 4.055, and 6.077 mg/mL injections.

VI-4

Figure VI-3: The value for the 5th concentration is requested and filled in.

Enter the concentration. Press OK. The next window will instruct you to inject the solution. After having done so, wait a few seconds until the signal reaches a plateau. Then click OK and wait for the automatic stability criteria to establish an average inten-sity, I’.

As you add points, a Debye Plot will begin to form. It should look roughly linear.

If it doesn’t and the various plateaus are noisy and full of spikes, consider stopping the experiment and starting over with cleaner solutions.

You can click DONE to end a measurement. If you do so before collecting at

least five concentrations, you will receive a warning to add more concentrations. A minimum of three concentrations is required. When finished, a fit is made to all the data points, and Mw and A2 are displayed. See Section VII for instructions on data analysis and interpretation.

VII-1

Section VII: Analyzing Data & Interpretation

Figure VII-1 shows the plot before a fit is displayed. The X- and Y-values for the cursor position are shown in the lower left of the window. If any single point is signifi-cantly off the line established by the rest, click on it. The concentration for that point will be shown in reverse video in the table in the lower right of the screen. Double click on the reverse video line and it will be temporarily deleted. Double click again and it is re-stored.

Figure VII-1: Preliminary Debye Plot window. You can edit a concentration by scrolling through the numbered concentrations

listed above the table. Then make the change directly in the list box. To be safe, click File/Save and save the edited set of data with a new filename.

The tabular values displayed are the excess intensity, I’ex, at each angle for the se-

lected concentration. The ‘prime’ signifies the value has been corrected for dark count, dead time, spikes, and averaged using the Trend and Noise criteria described in Appendix D.

You can change the concentration if you wish by editing it; however, do not do this unless you have good reason to believe the originally entered concentration is incor-

VII-2

rect. If a concentration were too high, the points would be shifted to the right and high. If a concentration were too low, the points would be shifted to the left and down.

Click on the command button labeled Calculate when finished. Figure VII-2

shows the results for the data points remaining. This is a Debye Plot using a linear fit. The intercept of this line is 1/Mw. The slope of the line is 2A2. The results of this fit are displayed in the bottom half of the lower window.

Figure VII-2: Debye Plot results.

The X and Y values can be copied to a spreadsheet and plotted by the user to suit their needs. If you want the X & Y values for use in a spreadsheet or external plotting software, click Copy For Spreadsheet. This places tabular data on the clipboard. Then open an ASCII editor such as NotePad. Once in NotePad, type Ctrl V to paste the tabular data into the editor. Then SAVE it and name it for future importation into your favorite spreadsheet or plotting program. Figure VIII-3 shows a copy of tabular data saved in NotePad.

VII-3

Figure VII-3: Tabular data saved using Copy for Spreadsheet. The Y value for the zero concentration value represents 1/Mw. In this case, if you

invert 2.414E-5 mol/g, you get 41.4E+3 g/mol or 41.4 kDa, the same as shown in Figure VII-2. This is the extrapolated weight-average molecular weight. The other data points represent actual measurements, those that were not deleted.

If you choose to accept the plot as it is, click on Copy Plot. This places the plot

on the clipboard. Open a graphing program such as Paint and then paste (type Ctrl V) the contents of the clipboard to the empty Paint window. The plot can then be saved or printed as you like. Or, from the clipboard, you can paste it into any suitable document.

Click on the command button labeled Settings to return to the previous view. Do

this if you want to delete or restore points. Do this if you want to fit to a different order. Let us examine these choices in more detail. In this example, the nominal 14 and 10 mg/mL points were significantly off the

straight line determined by the other points. This was determined by first fitting all the points and then systematically removing points that were further off the line. This author preferred to keep five of the original seven points.

When editing your own data, you will most likely want to delete a few points. The

command buttons shown in Figure VII-1 allow you to do this. They are labeled First Data, Last Data, and Restore All. If you decide to restore individual points, locate them in the table and double click. If you decide to restore all the rejected points, click on Re-store All.

With a good measurement, with small, random errors about the fit, deleting one or

two points should not cause a large change in the result. The result is called robust if this is the case. Also use the RMS Error to guide you. When the root-mean-square error is a minimum, the fit, assuming random errors only, is optimum. Of course, if there are sys-tematic errors, you cannot find them this way. You may also have to change the Fit Or-der. It is worthwhile playing a little to determine if the final answer is robust and does not

VII-4

depend much on the removal of a few points. Of course, if you only have a few concen-trations, then your answer is not robust and will be determined by your bias.

It is best to stay with linear fits whenever possible. With only a few points, it is

hard to determine if second or third order fits are worthwhile. For an nth order, least-squares, polynomial fit, you need n+2 data points theoretically. [n+1 points determine the exact fit, not a least-squares fit.] For example, if you have five concentrations, you can fit up to a 3rd order polynomial.

Warning

Unless you have strong, consistent, visual justification for 2nd order and higher

polynomial fits, stay with the linear fits. Over fitting, to reduce the root-mean-square (RMS) error, may result in the wrong extrapolation for Mw and the wrong slope for A2.

Click on Graphs/Graph Settings and check the box marked Autoscale Y-Axis if you want to stretch the function over the entire display. Sometimes this makes it easier to spot an outlier suitable for deletion.

The Debye Plot is appropriate for a Rayleigh scatterer (Rg less than about 10 to 12 nm). In this case, there is no angular dependence and you obtain Mw and A2 but not Rg.

This 41.5 kDa polymer is a random coil and its Rg is too small to measure with

static light scattering. Thus, as expected, it is a good candidate for a Debye Plot. The value for A2 of (2.062 +/- 0.091)e-03 cm3mol/g2 was determined and it is reasonable.

Finally, it should be noted that if the fit using many points is good but the result-

ing value for Mw is wrong, the problem is most likely either the value used for dn/dc or with the calibration. Or, perhaps, your preconceived notion was incorrect.

VIII-1

Section VIII: Database Results are saved in the currently opened Folder as a File using the Sample ID, Date,

and Time as the file identifiers. Click on File in the menubar of the main window to access Folders and Files. Files are automatically saved when the Auto Save Results box, under the Parameters command button, is checked. If not checked, you can still save files using Save or Save As in the File menu. See Figure VIII-1.

To create folders, select Database from the File menu. Click on the Create Folder

command button. Enter a folder name; it can be more than 8 characters; it may include spaces and punctuation. Double click on the folder icon to open it. The file folder icon opens when the folder is active. Single clicking on a folder selects the entire folder but does not open it. When selected, but not opened, the entire folder and its contents may be deleted, printed, or archived by clicking on Delete Selected Folder, Print Selected Folder, or Archive Selected Folder.

Figure VIII-1: Database window, Folders & Files

VIII-2Select a single file in an open folder by clicking on it. Select a string of consecutive files

by clicking on the first, then, while holding down the Shift key, click on the last. Select a string of nonconsecutive files by clicking on the first, then, while holding down the Control key, click on any number of files, consecutive or not, one at a time. When selected, a single file or multiple files may be deleted, printed, or archived by clicking on Delete Selected File(s), Print Selected File(s), or Archive Selected File(s).

Once selected, single or multiple files can be moved or copied to another folder by

cutting and pasting (CTRL C and CTRL V) or by dragging and dropping. Files are archived in a binary format in the following path:

C:\Bicw32\9k90mw\Data\archive.bak

using the extension .bak by default. You may change the drive\directory, but you will then have to remember it. If you do not change the filename, the default filename, archive.bak, is used. You can archive an entire folder by selecting it, but not opening it. You can archive single files or groups of files. When archived to an existing .bak file, the selected folder or file(s) are added to it.

Click Reload Archive File when you want to reload an archived file. Click on the drive and directory where it was stored. The default path, mentioned above, is c:\bicw\dndcw\data. However, if you archived the folder\file(s) in another path, you must select that drive\directory and the correct filename. Files are reloaded and merged into the currently opened folder.

Double clicking on a file opens it. Alternatively, select the file by single clicking on it

and then clicking on Open File. Finally, you can export a selected file with an ASCII format. See Appendix E for details.

Appendix A-1

Appendix A: Clearing Blockages & Removing Bacterial Growth If liquid with salt or polymer solutions dry inside the cell or tubing, the signal stability

will suffer. The signal will drift continuously as the dried material is slowly desorbed off the tube/cell walls and back into solution.

The first line of defense is never to let any solution dry in the flow cell or tubing.

ALWAYS flush solutions with pure solvent. If the solvent is not water, and the flow cell will not be used for a long time, it is a good idea to force the remaining liquid out using the air from an empty syringe. If the solvent is water, and the flow cell will not be used for a long time, first flush the water with isopropanol or ethanol, and then use air to push the alcohol out. Bacteria do not grow in alcohols.

If something has dried in the cell and/or tubing, remove the cell with tubing from the

instrument, and place the cell in a suitable holder. Then slowly flush the cell with a suitable solvent. This may take a long time, depending on the solubility of the dried material. Use a syringe pump such as the BI-SPump. Alternatively, flush with two to ten millilitres of solvent many, many times and check the stability of the signal over time.

If solvent will not dislodge the dried particles or polymer, use 0.1 M nitric acid. Wear

gloves and safety goggles. Proceed slowly and with caution as the blockage is often near one end or the other in the tubing. If one end is blocked, try injecting from the other such that the acid can eat away at the dried material. You may have to repeat this several times to get flow. Alternatively, since the blockage is often near the end of the tubing closest to air, consider changing the tubing.

If the instrument is left with water, bacteria may grow and adsorb onto the walls of the cell. When flushed initially, the signal may drift for a long time just as if salt or polymer had dried in the system. This will also require slow flushing with alcohol to remove the bacteria.

You can determine when the instrument is stable by monitoring the signal as a function

of time using the Stability Test graph in the Setup menu. When the signal is flat, with only an occasional jump due to dust, then the cell and tubing are clean.

Appendix B-1

Appendix B: Solvent Compatibility 90PFC

The flow cell is made of quartz and so is resistant to almost any solvent likely to

be used except concentrated HF. The parts of the fittings that come in contact with liquid are made of Teflon and so are compatible with almost all liquids.

Never allow any liquid to dry inside the cell or tubing. Always flush the solute or polymer solution with a pure solvent. If you are not going to work with the instrument for more than a day, AND you are working with a solvent in which bacteria may grow, flush the instrument with solvent until any salt or polymer is removed. Then flush with ethanol or isopropanol to prevent bacterial growth. Finally, flush with methanol since it leaves less residue than either isopropanol or ethanol.

If a blockage occurs due to dried salt or polymer, refer to Appendix A of this

manual.

Tubing

The standard tubing is PEEK. It has an O.D. of 1/16” (1.59 mm) and an I.D. of 0.020” (0.50 mm). Per foot (30 cm), the volume contributed by the tubing is 60 µL. Tubing with 0.010” I.D. is also available. This lowers the volume/30 cm to 15 µL. However, considerably more force is required to push liquid manually through this smaller diameter tubing.

PEEK, poly(etheretherketone), can withstand temperatures up to 100 °C when

used continuously under pressure. It is an excellent choice for most applications except when used with these solvents:

Do NOT use these solvents, for an extended period, with PEEK tubing:

DMSO (dimethyl sulfoxide) CH2Cl2 (methylene chloride) Concentrated HNO3 (nitric acid) Concentrated H2SO4 (sulfuric acid)

Appendix B-2

Compatible Solvents Used For Flushing Methanol and ethanol are intermediate solvents that are miscible with water and

with less polar solvents like THF, ethyl acetate, toluene, and benzene. When changing from water to a non-polar solvent, first flush the salt or polymer

solution with water until the signal is stable (if you have software running). This should take about 1 mL. Then slowly flush (about 1 mL/minute) with an intermediate solvent like ethanol. Check for signal stability again. This should take about 1 mL. Finally, slowly inject the non-polar solvent.

When changing from a non-polar solvent to water, first flush the polymer solution

with the solvent until the signal is stable. This should take about 1 mL. Then slowly flush (about 1 mL/minute) with an intermediate solvent like ethanol. Check for signal stability again. This should take about 1 mL, depending on the miscibility of the two liquids.

We recommend using a syringe pump like the BI-SPump for slowly flushing

the system. The BI-SPump is a fixed-speed, syringe pump. With a 20 mL syringe, the speed is approximately 1 mL/minute.

By flushing the salt or polymer solution first with the solvent, you prevent salt or

polymer from precipitating and then clogging the small-diameter tubing. For example, if you flush a salt solution with an intermediate solvent, the salt may precipitate. Therefore, in this case, flush first with water and then ethanol or isopropanol, the intermediate solvent.

Appendix C-1

Appendix C: Differential Refractive Index Increment, dn/dc

Definition of dn/dc

The differential refractive index increment, sometimes referred to as the specific refractive index increment, or SRII, is the slope of ns vs. concentration at zero concentra-tion. Here ns is the refractive index of a polymer solution. The SRII is a limiting slope at zero concentration often referred to as just dn/dc. However, in most polymer/solvent samples ns vs. concentration is a straight line and the limiting slope is the same as the slope at finite concentrations, even up to 10’s of mg/mL.

These concepts are illustrated above and serve to define conceptually dn/dc. In

practice, the variation in ns with temperature is larger than its variation with concentra-tion, and the above plot is nearly impossible to obtain with precision unless extreme measures are taken for temperature stability. To avoid this problem, one should use a dif-ferential refractometer such as the BI-DNDC.

Differential Refractometer

In a differential refractometer, the solution and solvent are maintained at the same temperature in the same cell separated by a transparent partition. It is not important to know the exact temperature to within a few degrees; it is only important that the tempera-ture difference between the two sides of the cell is small, ≤ 0.01 °C. This is not a particu-larly stringent condition. It can be accomplished in a well-insulated, small cell by waiting for thermal equilibrium or by controlling the cell temperature to within ± 0.01 °C. The BI-DNDC differential refractometer is capable of maintaining the solvent and solution sides of the cell within ± 0.01 °C of each other from about 5 °C above ambient to about 80 °C.

n s

concentration

no, solvent Lim ∆n/∆c = dn/dc c → 0

Appendix C-2

The signal in a differential refractometer is proportional to the displacement of a

beam of light as it traverses the solution and solvents sides of the cell. To improve resolu-tion, the beam is reflected back through the cell to double the displacement. The dis-placement is proportional to the difference in refractive index of the solution and solvent-sides of the cell: ∆n ≡ ns – no. The basic plot is illustrated below.

The value of dn/dc normally varies from about 0.05 to 0.25 mL/g. Occasionally, negative values occur when the refractive index of the solvent is greater than that of the polymer molecule. Since dn/dc is squared in the equations used to determine Mw, a nega-tive dn/dc is physically acceptable. Establishing Error Limits

When using the batch mode of the 90Plus or BI-MAS with the 9k90MW soft-ware, the relative error in calculating Mw is twice the relative error in dn/dc. For example, if you want to know Mw to 5% using static light scattering, a reasonable error limit on Mw, then the error contributed by dn/dc must be less than 2.5%. Literature Values of dn/dc

Literature values for a very large number of common polymers in a variety of sol-vents are tabulated in:

1. Huglin, M.B., "Specific Refractive Index Increments", Chapter 6 in Light Scatter-ing from Polymer Solutions, M.B. Huglin editor, Academic Press, London & New York, 1972.

2. Huglin, M.B., "Specific Refractive Index Increments of Polymers in Dilute Solu-

tion", pp. IV-267 to IV-308 in Polymer Handbook, 2nd ed., J. Brandrup and

concentration

Lim ∆n/c = dn/dc c → 0

∆n

Appendix C-3

E.H. Immergut, editors, Wiley-Interscience, NY, 1975. Essentially a repeat of values tabulated in reference 1. There are also later editions of this book.

3. Timasheff, S.N., p. 372-382 in the Handbook of Biochemistry and Molecular Bi-

ology, 3rd edition, Vol. II, edited by G.R. Fasman, 1976. Values for proteins in water.

4. Refractive Increment Data-Book for Polymer and Biomolecular Scientists, com-

piled by A. Theisen, C. Johann, M.P. Deacon, and S.E. Harding, Nottingham University Press, 2000. Many entries are more recent than the classic compi-lations above.

The classic values (before the widespread use of lasers, say before 1970) are

given primarily at 436 nm and 546 nm, the mercury lines. Hg-arc sources were the light sources used in differential refractometers and light scattering instruments before lasers and LEDs became widely available. As shown below (Wave Length Dependence of dn/dc), fitting to A + B/λ2 using values known at two wavelengths is reasonable for cal-culating at laser wavelengths of 488 nm and 514.5 nm (Argon-ion laser lines) or 532 nm (newer, frequency-doubled, solid state lasers). However, using the fit to predict dn/dc at 632.8 nm (HeNe laser line) or 660 nm (“red”, diode lasers) is less acceptable, but may be necessary.

Without a direct measurement, literature values may be all that you have to work

with. It is important, however, to understand that dn/dc varies with the solvent’s refrac-tive index, impurities in the solvent and polymer, molecular weight of polymer, tempera-ture, and wavelength. Each of these variables is discussed below.

Effect of Solvent’s Refractive Index

If a particular polymer can be dissolved in several different solvents, it is best to choose the one with the greatest difference in refractive index. In this case, dn/dc will be a maximum (scattering intensity varies as dn/dc squared), and errors in determining dn/dc will become less important. While the shape of the molecule (affecting Rg) and its inter-action with the solvent (affecting A2) may change from solvent-to-solvent, Mw will not.

Appendix C-4

The variation of dn/dc with solvent refractive index is roughly linear. Here is an example.

The data is from Huglin’s book, reference 1 above. Note the approximate factor

of two in the spread of dn/dc. This leads to a factor of four in the scattered intensity. Us-ing acetone instead of chloroform will yield greater excess intensity, something easier to measure with greater confidence.

Effect of Impurities in Solvent and Polymer

Literature values from several authors for apparently the same polymer/solvent system often differ by several percent, even at the same temperature and wavelength. While this can be due to sample preparation, calibration, and measurement errors, it is sometimes due to impurities in the polymer or solvent. Solvent impurities will cancel when making the dn/dc measurements since they appear in both the pure solvent and the solvent used to prepare the solutions, but then your light scattering measurements have to be made with exactly the same polymer/solvent impurities as that used by the author of the literature article. As this is highly unlikely, it is better to measure dn/dc using your polymer/solvent.

Another manifestation of this same problem may occur if the solutions and sol-

vent have not been kept under the same conditions for both the dn/dc and light scattering

dn/dc of PMMA in Different Solvents

no (solvent)

1.34 1.36 1.38 1.40 1.42 1.44 1.46

dn/d

c (m

L/g)

0.04

0.06

0.08

0.10

0.12

0.14

acetone

ethyl acetate

n-butyl acetate

THF

dioxane

chloroform

t = 25 oC, λ = 546 nm

Appendix C-5

measurements. Ideally, the exact same solutions should be used for both measurements, and the solvent used to prepare the solutions should be kept under the same conditions (sealed, no additional moisture or other impurities allowed in contact). Otherwise, the subtraction involved in determining the excess scattered intensity and that involved in determining ∆n may be different.

Molecular Weight Dependence of dn/dc

Generally, dn/dc increases with molecular weight and reaches a plateau when the end groups are sufficiently far apart. Below approximately 1,000 g/mol, dn/dc varies con-siderably. It increases by a few percent up to ~10,000 to ~ 20,000 g/mol, depending on the solvent, polymer shape and end-group contributions to the refractive index. Above this range it is, typically, constant.

An early example from the literature involved polyethylene glycol in water. Here

are the results:

Generally, data like this fits reasonably well to dn/dc = α - β/M, so when M is large enough, dn/dc does not change. Given the fit above, the change in dn/dc is less than 2% when M > 1,064 g/mol. This is an unusual case and may arise because both solvent and polymer have hydroxyl groups.

Variation of dn/dc with M for PEG/Water

1/M x 103

(1/Da)

0 2 4 6 8 10 12 14 16 18

dn/d

c (m

L/g)

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

10 kg/mol

62 g/mol

dn/dc = 0.141 - 3/M

Appendix C-6

Polystyrene in cyclohexane is a more common case as shown in the next graph.

Here the rate of change with M is 9 times as large and the change in dn/dc is less than 2% when M > 7,750 g/mol. Both sets of data are tabulated in Chapter 6 of Huglin’s 1972 book and in the original literature, the references for which are found in Huglin’s book.

It is particularly important to realize that each set of data plotted here was meas-

ured by the same authors (Kratohvil, J.P. 1968 for PS/cyclohexane and Rempp 1957 for PEG/H2O). Therefore, it is safe to assume that the samples and corresponding solvents in each run were prepared under similar conditions for the different molecular weights.

If one simply compared a list of dn/dc values for the same solvent/polymer from

different authors, all at the same wavelength and temperature, one would be surprised to find variations of several percent. While it is tempting to think that this variation can be explained by differences in molecular weight, more often the reason is that the impurity levels in the polymers and solvents are different from author-to-author. Therefore, if you want to deduce the molecular weight dependence, one must rely on data from the same author.

Variation of dn/dc with M for PS/Cyclohexane

1/M x 1000 (g/mol)-1

0.0 0.1 0.2 0.3 0.4 0.5

dn/d

c (m

L/g)

0.166

0.168

0.170

0.172

0.174

0.176

0.178

0.180

0.182

2,180 g/mol

167,000 g/mol

dn/dc = 0.181 - 28/M

Appendix C-7

Temperature Dependence of dn/dc

The refractive index of liquids varies with temperature. For common organic sol-

vents, the range is from -3 x 10-4 K-1 to -5 x 10-4 K-1. Water’s value, an exception, is -1.1 x 10-4 K-1. Experimental temperature coefficients for dn/dc are usually linear from room temperature up to 100 °C and higher. The coefficients can be zero, negative, or positive, but the variation in the absolute value is typically in the range of 1 to 5 x 10-4 mL⋅g-1⋅K-1. Thus, a few degrees difference in the absolute temperature between the measurement of dn/dc and the light scattering experiment is not significant. It is also the reason that room temperature measurements of Mw using LS do not have to be temperature controlled. Wavelength Dependence of dn/dc

Experimental observations show that dn/dc decreases with increasing wavelength, with variations of 1 to 3% over the range of 436 nm to 546 nm. These two wavelengths, from a Hg-arc source, represent the two most common ones used in SLS measurements prior to the use of lasers. Since they span the 488 nm and 514.5 nm lines of an Argon-ion laser, and the 532 nm line of a frequency-doubled, solid state laser, one could interpolate (not linear interpolation, see equation below) values of dn/dc from those measured at the classical values. More uncertainty would accrue to values extrapolated to 632.8 nm, the wavelength of a HeNe laser, or to values extrapolated to ~670 nm, a common wavelength for a “red” diode laser. (Again, the extrapolation is not linear. See below.)

Except for absorption peaks in the spectrum of either the solvent or the polymer, the variation in wavelength is given by:

2/BAdc/dn λ+=

This equation is also applicable to the variation in refractive index of solvent and polymer (again, assuming no absorption in the wavelength range of interest) and is known as the Cauchy equation. If dn/dc is known at two wavelengths, this equation can be used to calculate it at a third. However, it is much better if three or more measured values fit well to a straight line.

Some investigators ignore the wavelength dependence, and this is usually a mis-

take. Although there are some polymer/solvent pairs that exhibit very little dispersion, there are others that exhibit quite a bit. For example, poly(vinylacetate)/MeOH has an 8.8% variation in dn/dc from 436 nm to 632.8 nm (see Page 40 of reference 4 listed above). In batch mode, such an error would result in nearly an 18% error in Mw; whereas, PVC/dioxane shows no change in dn/dc from 436 nm to 586 nm (see page 42 of refer-ence 4 listed above). In addition, many researchers working with proteins and protein-like structures, assume a constant dn/dc of approximately 0.18, ignoring wavelength and temperature corrections.

Since the errors in dn/dc arising from differences in samples, even samples

supposedly of the same chemical composition and with the same solvent, can be larger than the variations with temperature and wavelength, in order to find suitable A & B

Appendix C-8

the variations with temperature and wavelength, in order to find suitable A & B coeffi-cients for the equation above, one must choose examples from the same author. The hope is that at least the polymer/solvents were the same. Here is a selection obtained from ref-erences 1 and 4 above.

Polymer/solvent A B

Polystyrene/toluene + 0.1015 + 0.00200 Polystyrene/DMF + 0.1450 + 0.00500 Polystyrene/MEK + 0.1963 + 0.00675 Poly(methylmethacrylate)/Dioxane + 0.0486 + 0.00031 Sucrose/water + 0.1392 + 0.00115 Myosin/water + 0.1847 + 0.00121 BSA/0.1M NaCl + 0.1791 + 0.00378 Poly(acrylimide)/acetic acid + 0.1857 + 0.00253 Poly(dimethylsiloxane)/toluene - 0.0767 - 0.00504

The average value of B for all eight of the positive values is + 0.0028; for the

non-aqueous samples the average is a bit higher at + 0.0035; and for the aqueous-based samples the average value of B is a bit lower at + 0.0022. The table is obviously not ex-haustive, but the values do cover a range of polymer/solvents. B is calculated with λ in microns.

Here are examples of using the table to estimate small, first-order corrections. Suppose you measure dn/dc = 0.1500 mL/g for a random-coil polymer in an or-

ganic solvent using the 620 nm source in a BI-DNDC. You want to estimate dn/dc at 660 nm, the wavelength of the laser in your 90Plus. Assuming B = + 0.0035, calculate A = 0.1500 – 0.0035/0.6202. The result is A = 0.1409. Now calculate dn/dc at 660 nm. The result is dn/dc = 0.1409 + 0.0035/0.6602 = 0.1489 mL/g. The difference in dn/dc at 620 nm and 660 nm is 0.74%. The error in a calculated value of Mw using 0.1500 mL/g in-stead of 0.1489 mL/g is 1.5%, nearly insignificant compared to other errors. This case demonstrates why using the dn/dc values measured close to the laser wavelength is suffi-cient for many purposes.

Suppose you find a literature value of 0.1500 mL/g measured at 436 nm and you

want to estimate the value at 660 nm. Aside from the fact that the literature value may correspond to a polymer/solvent system with different impurities or molecular weights than yours, this large wavelength difference cannot be ignored. In this case A = 0.1500 – 0.0035/0.4362 = 0.1316, and the estimated value at 660 nm is dn/dc = 0.1316 + 0.0035/0.6602 = 0.1396 mL/g. Now the difference between the two dn/dc values is 7.4%. This could lead to a 15% error in Mw in the batch mode, something that is not acceptable.

Appendix C-9

Included in the table are two values that demonstrate atypical situations. First, note the negative value of A and B for poly(dimethylsiloxane) in toluene. This means that dn/dc is also negative. Negative values of dn/dc arise when the refractive index of the solvent is larger than that of the polymer. Since, typically, this is not the case, most dn/dc values are positive. Second, notice the rather small value of A and B for PMMA in diox-ane. This means that dn/dc is also small and it arises because the refractive indices of polymer and solvent are similar. It also demonstrates the fact that there are poly-mer/solvent combinations with near-zero dn/dc values. In these cases, the errors in light scattering measurements will be very large.

Appendix D-1

Appendix D: Rejection, Smoothing, Stability: Noise and Trend After injecting a new sample into the flow cell, it takes time for this new sample to com-

pletely replace the previous sample. During that time, the signal is not stable. Using stability cri-teria to automatically determine the acceptance of an averaged signal to be used in calculating molecular properties is therefore a suitable method for rejecting bubbles, dust, and mixtures of two different samples. In addition, smoothing a set of stable signals with random noise further improves the results.

The method used in the 9k90MW software starts with a set of values against which the

criteria are tested. The default values are show in Figure D-1.

Figure D-1: Trend/Noise window. Data are taken every second by default, or for however long was set in the Dura-

tion/Repeat box in the Experimental Parameters window. After N data points have been taken, where N is the number of stability points (20 by default), they are averaged and the standard deviation is calculated. In addition, the N data points are fitted to a straight line and the slope is determined. If 1000 times the slope divided by the average of the N points is less than or equal to the Trend Limit (1.00 by default), and if 100 times the ratio of the standard deviation divided by the average is less than or equal to the Noise Limit (5 by default), then the average is used in cal-culating molecular parameters. If either criterion is not met, an additional point is taken and the criteria are applied to the new set of N data points

In practice, with a clean sample (filtered solvent, generally), both criteria are often satis-

fied within the twenty to twenty five seconds after the intensity level has reached what appears to be new, level value. In cases that take longer than N seconds, you may see two “traffic lights”, each with a green (accept) and red (reject) light. One traffic light represents the Trend criterion and one represents the Noise criterion. When both traffic lights are “green”, then both criteria are satisfied and the average of the preceding N intensity values will be used in the equations to de-termine molecular properties.

Appendix E-1

Appendix E: Export File Format From within the Database, after selecting a data file or files, click on Export Selected

File(s). If you select but do not open a folder, you can export its entire content of data files by clicking on Export Selected Folder. Data files are appended with the extension “.dat”. When exporting more than one file, the program will automatically supply increasing numerical labels to the first file name you entered. The default name is 9k90mw.dat. Here is an example.

PEG in Water Sample ID Jlb Operator ID 16:31:55 Time 01/30/04 Date 90.0 Angle YES Solvent measured, yes or no. 0.000e00 Solvent concentration equals zero. 414 Solvent count rate 7 Number of Concentrations 2.011000e+00 1st concentration in mg/mL 1008 1st concentration’s excess count rate 4.073000e+00 2nd concentration in mg/mL 1418 2nd concentration’s excess count rate 6.045000e+00 3rd concentration in mg/mL 1668 3rd concentration’s excess count rate 8.067000e+00 4th concentration in mg/mL 1768 4th concentration’s excess count rate 1.015000e+01 5th concentration in mg/mL 2007 5th concentration’s excess count rate 1.208000e+01 6th concentration in mg/mL 2029 6th concentration’s excess count rate 1.413000e+01 7th concentration in mg/mL 2062 7th concentration’s excess count rate 656.0 Laser Wavelength 35.0 Temperature 1.329 Refractive Index of Solvent 1.137000e-008 Calibration Constant 1.483 Refractive Index of Calibration Liquid 1.212000e-005 Rayleigh Ratio Calibration Liquid 0.000 Depolarization Ratio 0.134 dn/dc in mL/g 1.0 Duration/Repetition in seconds

Appendix F-1

Appendix F: Limits for Debye Plot Use Strictly speaking, a Debye Plot should only be used to determine the Mw when the scat-

terers are small enough. Then they are called Rayleigh scatterers. The scattering per particle is then independent of the scattering angle. A simple rule of thumb that works well is that the larg-est dimension of the particle should be less than one twentieth of the wavelength of the light in the liquid. However, it is simple to be more quantitative.

How Small Is Small?

A very common statement in textbooks is that a Rayleigh scatterer is one whose largest dimension is less than 1/20th the wavelength of the light. What is meant, of course, is the wave-length of the light in the continuous media. Assume a wavelength in air of 660 nm and a refrac-tive index of 1.33 (water). One twentieth of 660/1.33 = 25 nm. If that is the diameter of a sphere, the radius is 12.5 nm. For spheres, the radius of gyration is 0.77 of the sphere radius. This sug-gests that a globular Rayleigh Scatterer (globular protein or dendrimer) should have Rg less than or equal to 9.6 nm. Interestingly, we come to very much the same conclusion for any shaped scatterer using the following argument.

When Rg is small enough, then Equation 5 in Section II: Theory reduces to Equation 6, the Debye result. In this case, (Rgq)2/3 << 1. Thus,

Using the values for the 90Plus, λo = 660 nm, θ = 90ο, and assuming water where no =

1.332, then Rg should be much smaller than 97 nm. Assume 1/10th is very small. Thus, under these conditions, a Rayleigh scatterer is defined as Rg = 9.7 nm or smaller.

Clearly, if the measurement is made at small enough angle, the condition holds. How-

ever, making measurements at small angles often has problems with flare light and scattering from dust. While such measurements can be made, it is easier to make them at higher angles.

Debye Plot Errors at Finite Angles

There is another way to look at the situation and be more quantitative about what error occurs in the calculated Mw using a Debye Plot at finite angles. The zero concentration intercept of a Debye Plot, when the angular-dependent term is not sufficiently small is given by:

Here, Mmeas is the apparent MW obtained by extrapolation and Mw is the true MW. De-

fining the percent error in the MW as:

( )/2sin(n4π/λ3R oog θ⋅⋅⋅<< (1)

1/Mmeas = [1/Mw]·[1 + (Rg·q)2/3] (2)

Appendix F-2 and substituting Equation (2) into the above yields, Using Equation (3), it is now easy to calculate the maximum value of Rg for a given

wavelength, scattering angle, and liquid refractive index at which a Debye Plot will yield an ac-curate Mw at specified percent errors. Table I shows the results under two conditions.

Table I: Maximum Rg values at which a Debye Plot yields the designated percent error in Mw due to extrapolation from a finite angle.

The conditions λo = 660 nm and θ = 90ο correspond to the 90Plus; the conditions λo =

633 nm and θ = 173ο correspond to an instrument using a HeNe laser and backscatter. From this table two points are obvious. For accuracy in the determined Mw of 1% to 2%, Rg should be less than about 10 nm when using a Debye Plot at these finite angles. This is yet further support of the statements made earlier. However, it is always better to use a lower angle. In these two ex-amples of experimental setups, the size can be 47% larger and the percent error is the same when measuring at 660 nm and 90o. Almost 90% of the 47% difference is due to measurement at 90o vs. 173o. The wavelength differences contribute just over 10% of the 47% difference.

wMwMmeasM

100%−

⋅=ε

(3) 3/)qR(1

3/)qR(100% 2g

2g

⋅+⋅

⋅=ε

%ε Rg (660 nm,90o)

Rg (633 nm,173o)

1 9.7 nm 6.6 nm 2 13.8 9.4 5 22.2 15.1

10 32.2 21.9