ASTM D4001-93(1999)
(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
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 (s ) 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/dc (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 the standard.
1.4 This standard does not purport to address all of the safety problems, 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 . Note 1-There are no similar or equivalent ISO standards.
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Designation:D4001–93 (Reapproved 1999)
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
1.1 This test method describes the test procedures for 2.1 ASTM Standards:
determining the weight-average molecular weight M of poly- E 380 PracticeforUseoftheInternationalSystemofUnits
w
mers by light scattering. It is applicable to all nonionic (SI)
homopolymers (linear or branched) that dissolve completely
3. Terminology
without reaction or degradation to form stable solutions.
3.1 Definitions—Units, symbols, and abbreviations are in
Copolymers and polyelectrolytes are not within its scope. The
procedure also allows the determination of the second virial accordance with Practice E380.
coefficient, A , which is a measure of polymer-solvent interac-
2 1/2 4. Significance and Use
tions, and the root-mean-square radius of gyration (s ) ,
4.1 The weight-average molecular weight is a fundamental
which is a measure of the dimensions of the polymer chain.
structure parameter of polymers, which is related to many
1.2 The molecular-weight range for light scattering is, to
physical properties of the bulk material, such as its rheological
some extent, determined by the size of the dissolved polymer
behavior. In addition, knowledge of the weight-average mo-
molecules and the refractive indices of solvent and polymer.A
lecular weight, together with knowledge of the number-
range frequently stated is 10 000 to 10 000 000, but this may
average molecular weight from osmometry, provides a useful
beextendedineitherdirectionwithsuitablesystemsandbythe
measure of the breadth of the molecular-weight distribution.
use of special techniques.
4.2 Other important uses of information on the weight-
1.2.1 The lower limit to molecular weight results from low
average molecular weight are correlation with dilute-solution
levelsofexcesssolutionscatteringoverthatofthesolvent.The
or melt-viscosity measurements and calibration of molecular-
greater the specific refractive increment dn/d c (difference in
weight standards for use in liquid-exclusion (gel-permeation)
refractive indices of solution and solvent per unit concentra-
chromatography.
tion), the greater the level of solution scattering and the lower
4.3 To the extent that the light-scattering photometer is
the molecular weight that can be determined with a given
appropriately calibrated, light scattering is an absolute method
precision.
and may therefore be applied to nonionic homopolymers that
1.2.2 The upper limit to molecular weight results from the
have not previously been synthesized or studied.
angular dependence of the solution scattering, which is deter-
mined by the molecular size. For sufficiently large molecules,
5. Apparatus
measurements must be made at small scattering angles, which
5.1 Volumetric Flasks, 100-mL, or other convenient size.
are ultimately outside the range of the photometer used.
5.2 Transfer Pipets.
1.3 The values stated in SI units are to be regarded as the
5.3 Photometer, whose major components, described in
standard.
Appendix X1, are a light source, a projection optical system, a
1.4 This standard does not purport to address all of the
sample-cell area, a receiver optical system, a detector system,
safety concerns, if any, associated with its use. It is the
and a recording system.Typical photometers are described and
responsibility of the user of this standard to establish appro-
summarized (1) in the literature.
priate safety and health practices and determine the applica-
5.4 Differential Refractometer, with sensitivity of approxi-
bility of regulatory limitations prior to use.
–6
mately 3 310 refractive-index units, capable of measuring
NOTE 1—There are no similar or equivalent ISO standards.
the specific refractive increment dn/dc at the wavelength and
temperature of the scattering measurements (2).
This practice is under the jurisdiction of ASTM Committee D-20 on Plastics
and is the direct responsibility of Subcommittee D20.70 on Analytical Methods
(Section D20.70.05). Annual Book of ASTM Standards, Vol 14.02.
Current edition approved Feb. 15, 1993. Published April 1993. Originally Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
published as D4001-81. Last previous edition D4001-81(1986). this test method.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D4001
NOTE 2—Specific refractive increments are tabulated (2,3) for many
8. Preparation of Dust-Free Cell and Contents
polymer-solvent systems.
8.1 Clean all glassware, including the scattering cell, with a
5.5 Refractometer, Abbé type or equivalent, capable of suitable detergent to remove grease and other contaminants.
measuringtherefractiveindicesofsolventsandsolutionsatthe Use of an ultrasonic cleaning bath is recommended. Rinse
wavelength and temperature of the scattering measurements. glassware at least four times with distilled water to remove all
traces of detergent, and dry in a clean, dust-free drying oven.
5.6 Spectrophotometer, capable of measuring the absor-
banceofsolutionsatthewavelengthofthescatteringmeasure-
NOTE 5—A laminar-flow clean-air station is recommended for provid-
ments.
ing a dust-free area for solution preparation and filtration. If a clean-air
5.7 Laminar-Flow Clean-Air Station, to provide a dust-free station is not used, a closed area in a location free of drafts and of
sufficient size to hold the filter unit, scattering cell, and other glassware
area for preparing and cleaning solutions and filling the
should be provided.
scattering cell.
5.8 Filters and Filter Holders, for cleaning solvents and 8.2 Filter solvent directly into the scattering cell. First rinse
solutions. Membrane filters with pore sizes from 0.10 to 0.45 the cell several times with 5 to 10 mLof filtered solvent each,
µm, used in glass or plastic filter holders, are recommended. to remove dust particles. Be sure upper surfaces of the interior
of the cell are well washed down. Close the cell with a cap
5.8.1 For water and aqueous solutions, and for organic
similarly rinsed with filtered solvent.After rinsing, fill the cell
solvents that do not attack the material, the use of polycarbon-
with the minimum amount of solvent required to bring the
ate (Nucleopore) filters is recommended.These filters have the
liquid level above the point where the light beam in the
advantages of high flow rate without the use of gas pressure,
photometer passes through the cell.
minimal retention of solute on the filter, and efficient cleaning
action. For other solvents, the use of cellulosic filters (Milli-
NOTE 6—Use of a small filter holder fitting between a hypodermic
pore or equivalent) is recommended.
syringe and needle is convenient where only small quantities of liquids
need be filtered. A cell cap, with a hole just large enough to insert the
NOTE 3—Sintered-glass filters may be used, but these are relatively
needle, may conveniently be used.
expensiveanddifficulttocleanbetweenuses.Centrifugationmaybeused,
butthissteprequiresspecialcareandtechniques,orspecialscatteringcell 8.3 Place the scattering cell in the photometer, or in an
design, to be satisfactory.
equivalent strong light beam, and examine it in the dark,
viewingatsmallscatteringangles.Brightspecksofdustshould
6. Reagents and Materials
notbevisible;iftheyare,thecellwasnotrinsedcompletelyor
6.1 Solvents, as required. Since dn/dc is a function of the filtration procedure is inadequate.
8.4 Subsequent use of the clean cell for adding increments
composition, solvents should be of high purity. Significant
errors in molecular weight, which depends on the square of d of filtered solution or for replacing solvent with solution
requires no further rinsing, except to ensure that residual
n/dc,maybeincurredifliteraturevaluesofdn/dcareemployed
and the actual value of this quantity is different because of solvent remaining, after the cell is emptied, is removed and
replaced with solution.
impurities in the solvent.
6.2 12-Tungstosilicic Acid, as standard for calibration of
9. Procedure
photometer.
9.1 Calibrate the light-scattering photometer. This calibra-
tion is required to convert measurements of scattered light
7. Sample
intensity from arbitrary to absolute values, an essential step in
7.1 The sample must be homogeneous, and must be thor-
thecalculationofmolecularweight.Thecalibrationprocedure,
oughly free of all foreign impurities. If at all possible, samples
which is lengthy and requires great care to obtain accurate
to be used for light-scattering measurements must be specially
results, is given in Appendix X2. The calibration constant of
treated from synthesis on to minimize exposure to or contami-
most photometers remains stable for long periods of time,
nation with particulate impurities. Gels, which may consist of
however, so that the calibration procedure need be carried out
very high-molecular-weight particles, are sometimes formed
only infrequently.
during synthesis and will interfere with the analysis. All such
9.2 Prepare a stock solution of polymer, noting the precau-
particulate matter must be removed, sometimes with consider-
tions of Sections 7 and 8, at a concentration estimated as
able difficulty. It should be understood that when this is done,
follows: For a polymer of M =100 000 in a solvent
w
the remaining sample is no longer truly representative of the
such that dn/dc ' 0.2 mL/g (for example, polystyrene in
entire polymer. The extent of the difference from the original
2-butanone), the stock solution should be in the range from 10
sample will depend on the removal techniques employed.
to20g/L.SincescatteredintensityisproportionaltoM andto
w
NOTE 4—Reduction of sample particle size in a clean Spex or Wiley the square of dn/dc, estimates of the stock-solution concentra-
mill speeds solution and, with slow-dissolving materials, may be essential
tion required for other samples and systems can be made.
ifthemeasurementsaretobemadeinareasonabletime.Overheatingwith
Prepare no more stock solution than is required by the
consequent sample degradation must be avoided during the milling
following procedure.
process. Hard, tough samples or those with low melting points can be
9.3 Select one of the following measurement schemes:
handled by mixing with clean dry ice, milling the mixture, and then
9.3.1 Where the volume of liquid required for measurement
allowingthedryicetosublime.Cleandryicemaybeobtainedbyopening
in the photometer can be varied by at least a factor of two, it is
a tank of carbon dioxide to the atmosphere. Commercial dry ice is usually
contaminated. recommendedthatthescatteringfromtheminimumvolumeof
D4001
solvent be measured first, followed by measurement of solu- 9.5 Determine solution concentrations. Since filtration
tions prepared in the cell by the addition of weighed or through membrane filters may result in retention of some
polymer on the filter, it is necessary to determine the solution
volumetrically measured aliquots of filtered stock solution.
concentrations after filtration.
From four to six such solutions should be measured, the most
9.5.1 If successive concentrations are generated in the cell
concentrated consisting of approximately equal volumes of
from a stock solution filtered under constant conditions, only
solvent and stock solution if its concentration is selected in
the concentration of the filtered stock solution need be deter-
accordance with 9.2, and the least concentrated being about
mined; otherwise, the concentration of each solution measured
one fourth this concentration. A specific example is given in
must be determined.
Appendix X3.
9.5.2 Determinetheconcentrationsofsolutions,asrequired,
9.3.2 If the volume of liquid in the scattering cell cannot be
by one of the following methods. Use standard analytical
varied as in 9.3.1, it will be necessary to prepare and filter into
techniques where applicable.
the cell from four to six separate solutions covering the range
9.5.2.1 Evaporate a portion of the solution to constant
suggested in 9.3.1.
weight. It may be necessary to do this at high temperatures,
9.3.3 A further alternative, which is felt to be unduly
namely, above the glass transition temperature and under
complicated, is to measure the most concentrated solution first
vacuum, to remove tightly bound solvent. Because solvent is
(for this purpose, the stock solution concentration estimated in
sometimes very difficult to remove, such a procedure for
9.3.1 should be reduced by a factor of two), followed by
determining concentration should be verified by other tech-
successive dilutions with solvent. The scattering from the pure
niques before being adopted.
solvent must be measured in a separate step, and it may be
9.5.2.2 Determine the ultraviolet absorbance of the solution
necessary to start dilution sequences at two or more concen-
at a suitable wavelength.
tration levels to obtain the range specified in 9.3.1.
9.5.2.3 Determinethedifferenceinrefractiveindexbetween
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
providedwiththephotometerorintheliterature(4),beingsure
the stock solution by standard volumetric or gravimetric
that the following steps are included. (This procedure is based
analytical methods.
on the scheme of 9.3.1.)
9.6 If the specific refractive increment d n/dc is not known,
9.4.1 Instrument Check—See that the photometer is pre-
determineitusingsolutionsofknownconcentrations;thesame
paredformeasurement,withthelamplit,highvoltagesupplied
solutions used for light scattering measurements can be uti-
to the photomultiplier detector, and all components fully
lized. The specific refractive increment is the slope of the
warmed up and stabilized.
straight line relating solution-solvent refractive-index differ-
9.4.2 Solvent Preparation—Fill the cleaned scattering cell
ence, D n, to solution concentration, c. Since the relation is
with filtered solvent as described in Section 8
...
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