ASTM D4001-93(2006)
(Test Method)Standard Test Method for Determination of Weight-Average Molecular Weight of Polymers By Light Scattering
Standard Test Method for Determination of Weight-Average Molecular Weight of Polymers By Light Scattering
SIGNIFICANCE AND USE
The weight-average molecular weight is a fundamental structure parameter of polymers, which is related to many physical properties of the bulk material, such as its rheological behavior. In addition, knowledge of the weight-average molecular weight, together with knowledge of the number-average molecular weight from osmometry, provides a useful measure of the breadth of the molecular-weight distribution.
Other important uses of information on the weight-average molecular weight are correlation with dilute-solution or melt-viscosity measurements and calibration of molecular-weight standards for use in liquid-exclusion (gel-permeation) chromatography.
To the extent that the light-scattering photometer is appropriately calibrated, light scattering is an absolute method and may therefore be applied to nonionic homopolymers that have not previously been synthesized or studied.
SCOPE
1.1 This test method describes the test procedures for determining the weight-average molecular weight Mw of polymers by light scattering. It is applicable to all nonionic homopolymers (linear or branched) that dissolve completely without reaction or degradation to form stable solutions. Copolymers and polyelectrolytes are not within its scope. The procedure also allows the determination of the second virial coefficient, A2, which is a measure of polymer-solvent interactions, and the root-mean-square radius of gyration (s2)1/2, which is a measure of the dimensions of the polymer chain.
1.2 The molecular-weight range for light scattering is, to some extent, determined by the size of the dissolved polymer molecules and the refractive indices of solvent and polymer. A range frequently stated is 10,000 to 10,000,000, but this may be extended in either direction with suitable systems and by the use of special techniques.
1.2.1 The lower limit to molecular weight results from low levels of excess solution scattering over that of the solvent. The greater the specific refractive increment dn/d c (difference in refractive indices of solution and solvent per unit concentration), the greater the level of solution scattering and the lower the molecular weight that can be determined with a given precision.
1.2.2 The upper limit to molecular weight results from the angular dependence of the solution scattering, which is determined by the molecular size. For sufficiently large molecules, measurements must be made at small scattering angles, which are ultimately outside the range of the photometer used.
1.3 The values stated in SI units are to be regarded as standard.
This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
There are no similar or equivalent ISO standards.
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: D4001 − 93(Reapproved 2006)
Standard Test Method for
Determination of Weight-Average Molecular Weight of
Polymers By Light Scattering
This standard is issued under the fixed designation D4001; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
1.1 This test method describes the test procedures for
determining the weight-average molecular weight M of poly-
NOTE 1—There are no similar or equivalent ISO standards.
w
mers by light scattering. It is applicable to all nonionic
2. Referenced Documents
homopolymers (linear or branched) that dissolve completely
without reaction or degradation to form stable solutions.
2.1 ASTM Standards:
Copolymers and polyelectrolytes are not within its scope. The
IEEE/ASTMSI-10American National Standard for Use of
procedure also allows the determination of the second virial
theInternationalSystemofUnits(SI):TheModernMetric
coefficient, A , which is a measure of polymer-solvent
System
interactions, and the root-mean-square radius of gyration
2 1/2
(s ) , which is a measure of the dimensions of the polymer
3. Terminology
chain.
3.1 Definitions—Units, symbols, and abbreviations are in
1.2 The molecular-weight range for light scattering is, to
accordance with IEEE/ASTMSI-10.
some extent, determined by the size of the dissolved polymer
molecules and the refractive indices of solvent and polymer.A
4. Significance and Use
rangefrequentlystatedis10,000to10,000,000,butthismaybe
4.1 The weight-average molecular weight is a fundamental
extended in either direction with suitable systems and by the
structure parameter of polymers, which is related to many
use of special techniques.
physical properties of the bulk material, such as its rheological
1.2.1 The lower limit to molecular weight results from low
behavior. In addition, knowledge of the weight-average mo-
levelsofexcesssolutionscatteringoverthatofthesolvent.The
lecular weight, together with knowledge of the number-
greater the specific refractive increment dn/dc (difference in
average molecular weight from osmometry, provides a useful
refractive indices of solution and solvent per unit
measure of the breadth of the molecular-weight distribution.
concentration), the greater the level of solution scattering and
4.2 Other important uses of information on the weight-
the lower the molecular weight that can be determined with a
average molecular weight are correlation with dilute-solution
given precision.
or melt-viscosity measurements and calibration of molecular-
1.2.2 The upper limit to molecular weight results from the
weight standards for use in liquid-exclusion (gel-permeation)
angular dependence of the solution scattering, which is deter-
chromatography.
mined by the molecular size. For sufficiently large molecules,
measurements must be made at small scattering angles, which
4.3 To the extent that the light-scattering photometer is
are ultimately outside the range of the photometer used.
appropriately calibrated, light scattering is an absolute method
and may therefore be applied to nonionic homopolymers that
1.3 The values stated in SI units are to be regarded as
have not previously been synthesized or studied.
standard.
1.4 This standard does not purport to address all of the
5. Apparatus
safety concerns, if any, associated with its use. It is the
5.1 Volumetric Flasks, 100-mL, or other convenient size.
responsibility of the user of this standard to establish appro-
5.2 Transfer Pipets.
This test method is under the jurisdiction ofASTM Committee D20 on Plastics
and is the direct responsibility of Subcommittee D20.70 on Analytical Meth-
ods.70.05). For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved March 15, 2006. Published April 2006. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1981. Last previous edition approved in 1999 as D4001-93(1999). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/D4001-93R06. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D4001 − 93 (2006)
5.3 Photometer, whose major components, described in particulate matter must be removed, sometimes with consider-
Appendix X1, are a light source, a projection optical system, a able difficulty. It should be understood that when this is done,
sample-cell area, a receiver optical system, a detector system, the remaining sample is no longer truly representative of the
and a recording system.Typical photometers are described and entire polymer. The extent of the difference from the original
summarized (1) in the literature. sample will depend on the removal techniques employed.
5.4 Differential Refractometer, with sensitivity of approxi-
NOTE 4—Reduction of sample particle size in a clean Spex or Wiley
–6
mill speeds solution and, with slow-dissolving materials, may be essential
mately 3×10 refractive-index units, capable of measuring
ifthemeasurementsaretobemadeinareasonabletime.Overheatingwith
the specific refractive increment dn/dc at the wavelength and
consequent sample degradation must be avoided during the milling
temperature of the scattering measurements (2).
process. Hard, tough samples or those with low melting points can be
handled by mixing with clean dry ice, milling the mixture, and then
NOTE 2—Specific refractive increments are tabulated (2,3) for many
allowingthedryicetosublime.Cleandryicemaybeobtainedbyopening
polymer-solvent systems.
a tank of carbon dioxide to the atmosphere. Commercial dry ice is usually
5.5 Refractometer, Abbé type or equivalent, capable of
contaminated.
measuringtherefractiveindicesofsolventsandsolutionsatthe
wavelength and temperature of the scattering measurements. 8. Preparation of Dust-Free Cell and Contents
8.1 Clean all glassware, including the scattering cell, with a
5.6 Spectrophotometer, capable of measuring the absor-
banceofsolutionsatthewavelengthofthescatteringmeasure- suitable detergent to remove grease and other contaminants.
Use of an ultrasonic cleaning bath is recommended. Rinse
ments.
glassware at least four times with distilled water to remove all
5.7 Laminar-Flow Clean-Air Station, to provide a dust-free
traces of detergent, and dry in a clean, dust-free drying oven.
area for preparing and cleaning solutions and filling the
scattering cell. NOTE 5—A laminar-flow clean-air station is recommended for provid-
ing a dust-free area for solution preparation and filtration. If a clean-air
5.8 Filters and Filter Holders, for cleaning solvents and
station is not used, a closed area in a location free of drafts and of
solutions. Membrane filters with pore sizes from 0.10 to 0.45
sufficient size to hold the filter unit, scattering cell, and other glassware
should be provided.
µm, used in glass or plastic filter holders, are recommended.
5.8.1 For water and aqueous solutions, and for organic
8.2 Filter solvent directly into the scattering cell. First rinse
solvents that do not attack the material, the use of polycarbon-
the cell several times with 5 to 10 mLof filtered solvent each,
ate (Nucleopore) filters is recommended.These filters have the
to remove dust particles. Be sure upper surfaces of the interior
advantages of high flow rate without the use of gas pressure,
of the cell are well washed down. Close the cell with a cap
minimal retention of solute on the filter, and efficient cleaning
similarly rinsed with filtered solvent.After rinsing, fill the cell
action. For other solvents, the use of cellulosic filters (Milli-
with the minimum amount of solvent required to bring the
pore or equivalent) is recommended.
liquid level above the point where the light beam in the
photometer passes through the cell.
NOTE 3—Sintered-glass filters may be used, but these are relatively
expensiveanddifficulttocleanbetweenuses.Centrifugationmaybeused,
NOTE 6—Use of a small filter holder fitting between a hypodermic
butthissteprequiresspecialcareandtechniques,orspecialscatteringcell
syringe and needle is convenient where only small quantities of liquids
design, to be satisfactory.
need be filtered. A cell cap, with a hole just large enough to insert the
needle, may conveniently be used.
6. Reagents and Materials
8.3 Place the scattering cell in the photometer, or in an
6.1 Solvents, as required. Since dn/dc is a function of
equivalent strong light beam, and examine it in the dark,
composition, solvents should be of high purity. Significant
viewingatsmallscatteringangles.Brightspecksofdustshould
errors in molecular weight, which depends on the square of d
notbevisible;iftheyare,thecellwasnotrinsedcompletelyor
n/dc,maybeincurredifliteraturevaluesofdn/dcareemployed
the filtration procedure is inadequate.
and the actual value of this quantity is different because of
8.4 Subsequent use of the clean cell for adding increments
impurities in the solvent.
of filtered solution or for replacing solvent with solution
6.2 12-Tungstosilicic Acid, as standard for calibration of
requires no further rinsing, except to ensure that residual
photometer.
solvent remaining, after the cell is emptied, is removed and
replaced with solution.
7. Sample
7.1 The sample must be homogeneous, and must be thor-
9. Procedure
oughly free of all foreign impurities. If at all possible, samples
9.1 Calibrate the light-scattering photometer. This calibra-
to be used for light-scattering measurements must be specially
tion is required to convert measurements of scattered light
treated from synthesis on to minimize exposure to or contami-
intensity from arbitrary to absolute values, an essential step in
nation with particulate impurities. Gels, which may consist of
thecalculationofmolecularweight.Thecalibrationprocedure,
very high-molecular-weight particles, are sometimes formed
which is lengthy and requires great care to obtain accurate
during synthesis and will interfere with the analysis. All such
results, is given in Appendix X2. The calibration constant of
most photometers remains stable for long periods of time,
however, so that the calibration procedure need be carried out
The boldface numbers in parentheses refer to the list of references at the end of
this test method. only infrequently.
D4001 − 93 (2006)
9.2 Prepare a stock solution of polymer, noting the precau- intensity at angles of 30°, 90°, 150°, and at least three pairs
tions of Sections 7 and 8, at a concentration estimated as between,symmetricallyplacedwithrespectto90°,asavailable
follows: For a polymer of M =100,000 in a solvent
on the photometer used.
w
such that dn/d c ≈ 0.2 mL/g (for example, polystyrene in
9.4.5 Reference—Turn the phototube to the specified refer-
2-butanone), the stock solution should be in the range from 10
ence angle, adjust amplifier gain or insert neutral filters as
to20g/L.SincescatteredintensityisproportionaltoM andto
w
required, insert the reference standard, and read and record the
the square of dn/dc, estimates of the stock-solution concentra-
indicated reference intensity.
tion required for other samples and systems can be made.
9.4.6 SolutionMeasurement—Prepareandfilterintothecell
Prepare no more stock solution than is required by the
the solutions required in 9.3. Mix thoroughly, allow a few
following procedure.
minutes for residual dust to settle out, and measure each
9.3 Select one of the following measurement schemes:
solution as in 9.4.4.
9.3.1 Where the volume of liquid required for measurement
9.5 Determine solution concentrations. Since filtration
in the photometer can be varied by at least a factor of two, it is
through membrane filters may result in retention of some
recommendedthatthescatteringfromtheminimumvolumeof
polymer on the filter, it is necessary to determine the solution
solvent be measured first, followed by measurement of solu-
concentrations after filtration.
tions prepared in the cell by the addition of weighed or
9.5.1 If successive concentrations are generated in the cell
volumetrically measured aliquots of filtered stock solution.
from a stock solution filtered under constant conditions, only
From four to six such solutions should be measured, the most
concentrated consisting of approximately equal volumes of the concentration of the filtered stock solution need be deter-
mined; otherwise, the concentration of each solution measured
solvent and stock solution if its concentration is selected in
accordance with 9.2, and the least concentrated being about must be determined.
one fourth this concentration. A specific example is given in
9.5.2 Determinetheconcentrationsofsolutions,asrequired,
Appendix X3.
by one of the following methods. Use standard analytical
9.3.2 If the volume of liquid in the scattering cell cannot be
techniques where applicable.
varied as in 9.3.1, it will be necessary to prepare and filter into
9.5.2.1 Evaporate a portion of the solution to constant
the cell from four to six separate solutions covering the range
weight. It may be necessary to do this at high temperatures,
suggested in 9.3.1.
namely, above the glass transition temperature and under
9.3.3 A further alternative, which is felt to be unduly
vacuum, to remove tightly bound solvent. Because solvent is
complicated, is to measure the most concentrated solution first
sometimes very difficult to remove, such a procedure for
(for this purpose, the stock solution concentration estimated in
determining concentration should be verified by other tech-
9.3.1 should be reduced by a factor of two), followed by
niques before being adopted.
successive dilutions with solvent. The scattering from the pure
9.5.2.2 Determine the ultraviolet absorbance of the solution
solvent must be measured in a separate step, and it may be
at a suitable wavelength.
necessary to start dilution sequences at two or more concen-
9.5.2.3 Determinethedifferenceinrefractiveindexbetween
tration levels to obtain the range specified in 9.3.1.
solution and solvent, using a differential refractometer, for
9.4 Measure the scattering of the pure solvent, filtered into
cases where the specific refractive increment is known.
the cell as described in Section 8, and of each of the series of
9.5.3 Forcaseswhereaseriesofsolutionsisproducedinthe
filtered solutions described in 9.3, following the instructions
cell, calculate the actual solution concentrations from that of
providedwiththepho
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