AlllOb 3bD351

NBS SPECIAL PUBLICATION 260-42

I, Standard Reference Materials:

The Characterization of

Linear Polyethylene SRM 1475
NATIONAL BUREAU OF STANDARDS

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* Part of the Center for Building Technolog.v.
The Characterization of

Linear Polyethylene SRM 1475

Herman L. Wagner and Peter H. Verdier, Editors

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

Reprinted from the National Bureau of Standards

Journal of Research, Section A. Physics and Chemistry

Vol. 76A, No. 2, March-April 1972 (The original page numhers of each paper have been

retained for citation purposes)

U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretary

NATIONAL BUREAU OF STANDARDS, Lawrence M. Kushner, Acfing Director.

Issued September 1972

L .- ;^ too- ^
Library of Congress Catalog Card Number: 72—600250

National Bureau of Standards Special Publication 260-42

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-42, 39 pages (Sept. 1972)

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.10:2v^0-42). Price45 cei.ts.
CONTENTS

THE CHARACTERIZATION OF LINEAR POLYETHYLENE SRM 1475:

PAGE

I. INTRODUCTION, C. A. J. Hoeve, Herman L. Wagner

and Peter H. Verdler 137

II. DETERMINATION OF TOTAL METHYL CONTENT BY

INFRARED SPECTROPHOTOMETRY, James E. Brown 141

III. DENSITY DETERMINATION, James E. Brown 143

IV. MELT FLOW RATE, John R. Maurey 145

V. SOLUTION VISCOSITY MEASUREMENTS, Richard G.

Christensen 147

VI. PREPARATION OF CALIBRATING FRACTIONS, Richard G.

Christensen 149

VII. DIFFERENTIAL REFRACTIVE INDEX OF POLYETHYLENE

SOLUTIONS, Herman L. Wagner 151

VIII. LIGHT- SCATTERING STUDIES ON POLYETHYLENES IN

1-CHLORONAPHTHALENE, Lois J. Frolen, Gay Ion S.

Ross, Andrew M. Wims , and Peter H. Verdier 156

IX. NUMBER AVERAGE MOLECULAR WEIGHT OF FRACTIONS BY

MEMBRANE OSMOMETRY, James E. Brown and Peter H.

Verdier 161

X. GEL PERMEATION CHROMATOGRAPHY, Gaylon S. Ross and

Lois M. Frolen 163

iii
The Characterization of Linear

Polyethylene SRM 1475

Herman L. Wagner

and

Peter H. Verdier, Editors

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

The National Bureau of Standards has issued a linear

polyethylene standard reference material, SRM 1475.

This material is certified for weight average molecular weight (M,^) , number average molecular weight

(Mj^), Z average molecular weight (Mg) , molecular

weight distribution, limiting viscosity numbers in

several solvents, melt flow rate, and density. The

experimental details of the determination and certification of these properties are given in these collected papers previously published in the Journal of

Research of the National Bureau of Standards.

Key words: Density; differential refractive index; gel permeation

chromatography (GPC) ; light scattering; linear polyethylene; melt flow

rate; molecular weight distribution; number average molecular weight;

osmometry; refractive index; standard reference material; viscosity;

weight average molecular weight; Z average molecular weight.

iv
The Characterization of Linear Polyethylene SRM 1475

I. Introduction.

C. A. J. Hoeve,* Herman L. Wagner, and Peter H. Verdier

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

The National Bureau of Standards has issued a hnear polyethylene standard reference material, SRM 1475. In this report a general description of the sample is given, and the characterization work

described in the subsequent reports is outlined. Some peUet-to-pellet variabiUty was found and

estimated.

Key words: Fractionation; linear polyethylene; molecular weight; molecular weight distribution; National Bureau of Standards; pellet variability; standard reference material.

1. Purpose

The National Bureau of Standards has issued a

linear polyethylene standard reference material, SRM

1475,** to fill the need for a well-characterized sample

of this polymer. The sample may be used for the

calibration of instruments for measuring molecular

weight and molecular weight distribution, such as

light scattering photometers and gel permeation

chromatographs. It should also be useful in other

areas of polymer research such as dilute solution

studies, polymer rheology, and polymer crystal

physics.

2. Properties Measured

The characterization results which are described in the succeeding papers in this series [1] ^ include a determination of:

(1) Weight average molecular weight by light

scattering,

(2) molecular weight distribution by gel permeation chromatography and, from this distribution, weight average, number average, and Z

average molecular weights,

(3) limiting viscosity number in 1-chloronaphthalene, 1,2,4-trichlorobenzene, and decalin,

(4) melt flow rate by a melt index type apparatus,

(5) density by ASTM procedures.

No attempt was made to determine number average

molecular weight of this whole polymer by osmometry

•Present address: Department of Chemistry, Texas A & M University, College Station, Texas 77843.

** Available through the Office of Standard Reference Materials, National Bureau of Standards, Washington, D.C. 20234.

' Figures in brackets indicate the literature references at the end of this paper.

since diffusion of even small amounts of low molecular

weight species through the membrane makes such a determination meaningless. However, by calibration of

the gel permeation chromatograph with fractions that were well characterized by light scattering and

osmometry, it was possible to determine number

average molecular weight as well as weight average

and molecular weight distribution. With these data,

SRM 1475 may be used conveniently for the precise

caHbration of other gel permeation chromatographs.

In the papers which follow, the various techniques

are described. More detail is given in those cases where

there has been some deviation from the usual pro- cedure. The certificate for SRM 1475 is reproduced at the end of this paper.

3. Sample Description

The sample of hnear polyethylene chosen for SRM

1475, an ALATHON 7050, was kindly donated by the

E. I. duPont Company, Wilmington, Delaware.* The

material is in the form of pellets, each weighing about

20 mg. An antioxidant, tetrakis[methylene-3-(3',5'-dii-butyl-4'-hydroxyphenyl)propionate] methane, known

commonly as Irganox 1010 (Geigy Chemical Company),

was added to the polymer at a concentration of 111

ppm by the manufacturer. The Unearity of the polymer

is demonstrated, as shown in part II [1], by infrared

analysis. Ash content, determined by ashing a 10- gram portion of the sampl*^ at 750 °C, was found to be

0.002 percent.

*Certain commercial equipment, instruments, or materials are identified in this paper

in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available

for the purpose. 137
The determination of volatile components, or at least those components soluble in xylene, was made

as follows. Three grams of polyethylene and 7 grams

of xylene were sealed in one container and 7 grams

of xylene was sealed in another as a control. These

containers were heated at 140 °C until the contents

dissolved. They were cooled to precipitate the polyethylene, opened, and samples of Uquid from each were analyzed by gas chromatography.

It is estimated that any xylene-soluble volatiles that amounted to as much as V2 percent of the polyethylene could be readily detected by this method.

No evidence of such volatile material was found.

4. Sampling

The sample was received in forty 50-lb bags. To

determine the conditions necessary for uniform sampUng, polymer variabiUty from pellet-to-pellet and bagto-bag was determined. The bags were numbered at random from 1 to 40 and samples were taken from the

top and bottom of each of bags 1 to 20. Several grams

of each of these were mixed and samples drawn from

this "pool" to make up blended samples for light

scattering, limiting viscosity number, and gel permeation chromatography. These blends were made up of several hundred pellets dissolved in xylene at 140 °C

and precipitated in ethanol at room temperature.

PeUet-to-peUet variabiUty was determined by solu- tion viscosity measurements [Id] in 1-chloronaphthalene at concentrations of from 0.06 to 0.12 g/dl at 130 °C on individual pellets and on samples of the

blends. The viscosity number, (tj — tjoVCt/oc), in dl/g,

where r) is the viscosity of the solution, rjo is the vis- cosity of the solvent, and c is the concentration in g/dl,

is plotted against concentration in figure 1. The

viscosity numbers obtained for the blended samples were fitted by least squares to a hnear function of concentration, yielding the straight hne shown in the

figure. The standard deviation in viscosity number

obtained from the least-squares analysis for the

blended samples was 0.0034 dl/g (0.38%). The root- mean-square deviation from the straight line of the

viscosity numbers obtained for solutions made up from

individual pellets was found to be 0.028 dl/g (3.1%).

Thus the standard deviation of a single measurement

is 0.38 percent and the standard deviation due to pellet-to-peUet variation is

[(3.1)2- (0.38)2]i/2 = 3.1%.

Since the coefficient of variation is 3 percent, it is recommended that all determinations be performed on

samples containing at least 50 pellets or one gram of

polymer (or material from a blend of one gram). This

wiU reduce the expectation of the standard error due

to pellet variability to less than 0.5 percent.

Details of the method of measurement of melt

flow rate and the results obtained are discussed else- where [Ic]. These measurements were employed to investigate variations in material taken from different regions of the entire material. Forty-two samples for

0.02 0.04 0.06 0.08 0.10 012 0.14 0.16 CONCENTRATION, 9/dl

Figure 1. The viscosity number of a blended sample and of indi- vidual pellets of SRM 1475 plotted against concentration.

melt flow rate determination were taken from 13

different regions in seven of the bags. The standard

deviation for samples within a region was found to be

2.1 percent, based on 29 degrees of freedom. The

standard deviation between regions was found to be 1.7 percent, based on 12 degrees of freedom. We conclude

that variations from region to region are too smaU to be

detected by this method.

5. References

[1] The Characterization of Linear Polyethylene 1475:

(a) Brown, J. E., Paper II, Determination of Total Methyl

Content by Infrared Spectrophotometry, J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 2, 141-142

(Mar.-Apr. 1972).

(b) Brown, J. E., Paper III, Density Determination, Ibid, 76A

(Phys. and Chem.), No. 2, 143-144 (Mar.-Apr. 1972).

(c) Maurey, J. R., Paper IV, Melt Flow Rate, Ibid, 76A (Phys. and Chem.), No. 2, 145-146 (Mar.-Apr. 1972).

(d) Christensen, R. G., Paper V, Solution Viscosity Measurements, Ibid, 76A (Phys. and Chem.), No. 2, 147-149 (MaiApr. 1972).

(e) Christensen, R. G., Paper VI, Preparation of Calibrating

Fractions, Ibid, 76A (Phys. and Chem.), No. 2, 149-150

(Mar.-Apr. 1972).

(f) Wagner, H. L., Paper VII, Differential Refractive Index of Polyethylene Solutions, Ibid, 76A (Phys. and Chem.), No.

2, 151-155 (Mar.-Apr. 1972).

(g) Frolen, L. J., Ross, G. S., Wims, A. M., and Verdier, P. H., Paper VIII, Light Scattering Studies on Polyethylenes in 1-Chloronaphthalene, Ibid, 76A (Phys. and Chem.), No. 2, 156-160 (Mar.-Apr. 1972).

(h) Brown, J. E., and Verdier, P. H., Paper IX, Number Average

Molecular Weight of Fractions by Membrane Osmometry,

Ibid, 76A (Phys. and Chem.), No. 2, 161-163 (Mar.-Apr.

1972).

(i) Ross, G. S. and Frolen, L. J., Paper X, Gel Permeation Chromatography, Ibid, 76A (Phys. and Chem.), No. 2, 163-

170 (Mar.-Apr. 1972).

(Paper 76A2-706)

138
U. S. Departjhsnf of Commerce

MauriceJS. Stans Rational ^mtm of ^inndnxd^

Certificate

Standard Reference Material 1475

Linear Polyethylene

(Whole Polymer)

C. A. J. Hoeve, H. L. Wagner, J. E. Brown,

R. G. Christensen, L. J. Frolen, J. R. Maurey, G. S. Ross, and P. H. Verdier

This Standard Reference Material is intended for the calibration of instruments used in polymer

science and technology for the determination of molecular weight and molecular weight

distribution. Estimated

Quantity

Molecular Wei^t

Wei^t-average molecular wei^t^

Number-average molecular weight

j Wei^t-average molecular weight I Z-average molecular weight U

Ratio of molecular weights Mj.;M^ iM^ I Molecular weight distribution I

Limiting Viscosity Number (dl/g) In 1-chloronaphthalene at 130 °C

In 1,2,4-trichlorobenzene at 130 °C

In decahydronaphthalene*^ at 130 °C

Melt-Flow Rate (g/10 min)^

Density (g/cm')*

*By light scattering in 1-chloronaphthalene at 135 °C. ^By gel-permeation chromatography.

''"Technical" grade, which assayed at approximately equal proportions of cis- and trans- decahydronaphthalenes.

•^By a procedure similar to Procedure A, ASTM Method D1238-65T, Test Condition D, 190 °C, load 325 g. «By ASTM Method D1505-67; sample prepared by Procedure A, ASTM Method D1928-68.

Average Standard Deviation

Values of Average

52,000 2,000

18,310 360

53,070 620

138,000 3,700

7.54:2.90:1

See Table 1

0.890 0.0032

1.010 .0086

1.180 .0032

2.07 .0062

0.97844 .00004

Measurements leading to the certification of this material were performed in the Molecular

Properties and Characterization Section of the Polymer Division.

Washington, D.C . 20234 J. Paul C ali. Chief

November 6, 1969 Office of Standard Reference Materials

(Revised December 2,1971)

(over)

139
The methyl group content as determined by ASTM Method D2238-68 is 0.15 methyl groups

per 100 carbon atoms. This shows the polyethylene to be essentially linear. A pellet to pellet coefficient of variation of 3 percent in the limiting viscosity number was found. All determinations

should consequently be performed on samples containing at least 50 pellets or one gram of polymer

(or material from a blend of one gram). This will reduce the expectation of the standard error due

to pellet variability to less than 0.5 percent.

Table 1 . Cumulative Molecular Weight Distribution by

Gel-Permeation Chromatography

Wt. Wt. Wt.

log M % log M % log M %

2.800 0.0 4.014 15.2 5.065 90.7

2.865 0.005 4.070 18.1 5.113 92.2

2.929 0.020 4.126 21.5 5.161 93.7

2.992 0.052 4.182 25.2 5.209 94.8

3.056 0.105 4.237 29.3 5.256 95.8

3.119 0.185 4.292 33.7 5.303 96.6

3.181 0.343 4.346 38.5 5.349 97.3

3.243 0.475 4.400 43.4 5.395 97.9

3.305 0.706 4.454 48.5 5.440 98.4

3.366 0.999 4.507 53.5 5.485 98.7

3.427 1.38 4.560 58.3 5.530 99.1

3.488 1.88 4.612 62.9 5.574 99.3

3.548 2.51 4.664 67.3 5.618 99.5

3.607 3.30 4.715 71.4 5.662 99.7

3.667 4.28 4.766 75.1 5.705 99.8

3.725 5.46 4.817 78.5 5.789 99.9

3.784 6.87 4.868 81.6 5.87 100.0

3.842 8.56 4.918 84.4

3.900 10.50 4.967 86.7

3.957 12.7 5.016 88.9

The sample of linear polyethylene was obtained from E. I. du Pont de Nemours and Company of

Wilmington, Delaware.

This sample of linear polyethylene has an ash content of 0.002 percent. No volatiles were

detected by a gas-chromatographic procedure capable of detecting 0.5 percent volatiles. The manufacturer added 111 ppm of the antioxidant, Irganox 1010 (Geigy), which is tetrakis [methylene3-(3',5'-di-t-butyl-4'-hydroxyphenyl)propionate] methane.

The differential refractive index in 1-chloronaphthalene, required for the calculation of

molecular weight by light scattering, was found to be —0.193 ml/g at 135 °C and 546 nm.

The maximum rate of shear in the Ubbelohde viscometer was about 1500sec'i. All measure- ments were carried out at specific viscosities (0.1 or less) which were sufficiently low for negligible

dependence on rate of shear. A series of reports describing investigations required for this certificate will be published in the

Journal of Research of the National Bureau of Standards, Volume 76 A, No. 2, 1972.

140
The Characterization of Linear Polyethylene SRM 1475. II. Determination of Total Methyl Content by Infrared

Spectrophotometry.

James E. Brown

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

An ASTM method was used to determine the methyl content of linear polyethylene SRM 1475 by measuring the absorbance at 1378 cm"' (7.25 nm) of methyl groups on compensated infrared spectra. The methyl content of this polymer was found to be 0.15 methyls per 100 carbon atoms. Considering

the methyls to be polymer end groups, the number average molecular weight computed approximates

that determined by gel permeation chromatography within the experimental error. These values indicate

that the polymer is essentially free of branching.

Key words: Infrared; linear polyethylene; methyl; methylene; number average molecular weight;

spectra; spectrophotometry.

1. introduction

The total methyl group content in polyethylene may

be used to estimate the amount of branching in the

polymer. If, for example, it is assumed that all chainends are methyl groups, then the methyl-group content

of the polymer may be combined with its numberaverage molecular weight, M„, to yield an estimate of the average number of chain ends per molecule.

In the characterization of SRM 1475, the total methyl

content was determined to obtain an estimate of the

polymer's linearity. Infrared spectrophotometry was

used to determine the methyl content from the absorb- ance at about 1378 cm~' due to methyl groups. This

band is overlapped by bands at 1368 and 1352 cm~\

and therefore cannot be used directly to estimate

methyl group content. However, it has been shown

[1-5] ^ that both the latter two bands and another

band at 1304 cm~' arise from methylene-groups in the

amorphous or disordered regions only, while the 1378

cm"* band arises from methyl groups in both amor- phous and crystalline regions. If we assume [5] that the spectrum of solid polyethylene is a superposition of

contributions from amorphous and crystaUine regions,

then the spectrum arising from methyl groups alone

may be obtained as a difference spectrum between two

films of the same polymer, but different degrees of

crystallinity and appropriately different thicknesses. In this paper, we report the results for total methyl

content in SRM 1475 by the method described in American Society for Testing and Materials (ASTM)

Designation: D 2238-68, "Standard Method of Test

for Absorbance of Polyethylene Due to Methyl Groups

' Figures in brackets indicate the literature references at the end of this paper.

at 1378 cm"*." - By this method, the absorbance is measured at the methyl frequency (1378 cm~*) on

films which are largely crystaUine while compensating

for the amorphous methylene absorbance with thinner,

less crystalline films. Graphically, the absorbance

resulting only from methyl groups is interpolated to the point of zero methylene absorbance at 1304 cm"'. Each of the absorbanccs at 1378 and 1304 cm"* is corrected for the effect produced by the difference in thickness and density of the crystalline and amorphous

films. The resulting absorbance at 1378 cm"* is then

used to calculate the number of methyl groups per

100 carbon atoms. The conversion of absorbance to methyls per 100 carbon atoms is computed from the

absorbance at 1378 cm"* due to methyl groups in n-hexadecane (cetane).

2. Experimental Procedure

Films were prepared from SRM 1475 pellets taken

from each container and blended as described in the

first paper of this series [6]. In accordance with the

ASTM procedure, several films ranging in thickness

from 0.01 to 0.04 cm were molded in a hydrauhc

press heated to 168 °C. The molten polyethylene in the mold assembly was then quenched in an ice-water

mixture. Films prepared in this manner are designated

reference films. Four films about 0.05 cm thick were

also molded from the SRM pellets by the above pro- cedure except that these films were annealed so as to produce an increase in density of at least 0.02 g/cm^

greater than the density of the quenched reference

films. The annealed films will later be referred to as

' Available from American Society for Testing and Materials, 1916 Race Street, Phila- delphia, Pennsylvania 191U3. 141
samples I through IV. Diflference spectra of each

sample (high crystalline content) were obtained with

three or four of the thinner reference films (low

crystalline content). The spectra were recorded in the region from about 1430 to 1250 cm~* using the

prism optics of a double-beam, infrared spectrophotometer, (Perkin-Elmer Model 221).^ From these

spectra, which range from partial to over-compensation of the absorption due to amorphous methylene

groups, the absorbance at the methyl frequency,

Ai378, and that at the methylene frequency, A1304, were

determined as directed by the ASTM method.

3. Results and Discussion

Effective absorptivities, a, at 1378 and 1304 cm~^

were calculated from the difference spectrum of each

sample-reference pair by the relation a = AI{dsts — drtr), where A is absorbance and dg, tg, dr and tr are sample density, sample thickness, reference

density, and reference thickness, respectively. The

resulting pairs, (ai304, aisrs), were plotted as shown in figure 1, together with the straight line determined by a hnear least squares fit. The value of ai378, on the least squares hne, corresponding to ai304= 0 is the absorbtivity in cm^g at 1378 cm"' at which the methylene

absorptivity at 1304 cm"* is completely compensated.

This quantity is designated K' in table 1. The number

of methyl groups per 100 carbon atoms is also shown

in table 1. The methyl concentration is computed

from the product of K' and a calibration factor derived

from measurements on cetane, as described in the

ASTM procedure.

High density (Unear) polyethylene chains may be

presumed to be terminated with methyl groups as demonstrated by WiUbourn [4] in a study of chain

branching in polyethylene. If we assume two methyl

groups per chain, then our estimate of 0.15 methyl

groups per 100 carbon atoms leads to an estimate of

18,7()0 for the number-average molecular weight,

Mn- This value closely approximates the M„ (18,310)

from the gel permeation chromatography measurement

as shown in Paper X of this series [7]. This correlation

and the density [8] suggests that the polymer, SRM

1475, is essentially free of branching.

^ Certain commercial equipment, instruments, or materials are identified in this paper

in order to adequately specify the experimental procedure. In no case does such identifi- cation imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.

£2.0

SAMPLE I SAMPLE n

SAMPLE m 0

SAMPLE •

-

-

1 1 1

1

1 1 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0

(%'|304

Figure 1. Ordinate: Absorptivity, a^3^s, cm^lg; Abscissa: Absorptivity, ai304, cm^lg.

The Une shown in this graph represents a least squares fit of the absorptivity at 1378 cm"'

resulting from methyl groups against the absorptivity at 1304 cm"' arising from amorphous

methylene groups. The slope is equal to 0.51 ±0.03 with the intercept at 1.74 ±0.05 where

the symbol ± stands for the standard deviation in these quantities inferred from the linear least-squares fit. The intercept represents the methyl absorption at perfect compensation

for the methylene groups.

Table 1. Results of methyl group determination from compensated

spectra

Absorptivity K', cm^/g

Sample standard

deviation of K' CH3 groups per

100 C atoms

1.74 0.053 0.15

K' in cm^/g is the reduced absorptivity of methyl groups, at complete compensations for the absorption due to methylene groups determined for SRM 1475.

4. References

[1] Cross, L. H., Richard, R. B., and Willis, H. A., Discussions Faraday Soc, No. 9, 235 (1950).

[2] Nielsen, J. R. and Holland, R. F., J. Mol. Spectr. 4,488 (1960).

[3] Okada, T. and Mandelkern, L., J. Polymer Sci. A-2 5,239(1967).

[4] WiUbourn, A. H., J. Polymer Sci. 34, 569 (1959).

[5] BCrimm, S., Liang, C. Y., and Sutherland, G. B. B. M., J. Chem.

Phys. 25, 549 (1956).

[6] Hoeve, C. A. J., Wagner, H. L., and Verdier, P. H., J. Res. Nat.

Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 2, 137-140

(Mar.- Apr. 1972). Paper I of this series.

[7] Ross, G. S. and Frolen, L. J., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 2, 163-170 (Mar.-Apr. 1972). Paper X of this series.

[8] Brown, J. E., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and

Chem.), No. 2, 143-144 (Mar.-Apr. 1972). Paper III of this series.

(Paper 76A-707)

142
The Characterization of Linear Polyethylene SRM 1475. Ill

Density Determination

James E. Brown

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

The density of SRM 1475 at 23 °C was determined by ASTM method D 1505-67 on samples pre- pared by Procedure A of ASTM method D 192«-68, with the result 0.9784 g/cm^.

Key words: Crystallization; degree of crystallinity; density; linear polyethylene; polymer;

recrystaUization.

1. Introduction

The density of polyethylene crystallized from its melt is sensitive to a number of factors which influence

the degree of crystallinity. Among these factors are: the polymer's previous thermal history and crystallization temperature which affect the perfection and rate of

crystal growth [1-4],* the average molecular weight

and its distribution [3], and the amount of branching

[5-6]. In this paper we report the results of the density

measurements on linear polyethylene SRM 1475. The

density measurements and the sample preparation were performed using standard methods of the

American Society for Testing and Materials (ASTM).

It was necessary to specify closely the preparation of

the samples used in this determination since the

density of polyethylene depends to such an important

extent on the polymer's previous history. From our

experience, it should be possible to duplicate these

results closely provided that the same methods are

followed.

2. Experimental Procedure

Three composite samples, weighing about 100 g each, were made up separately as described in the

first paper of this series [7] by blending equal amounts

of the SRM 1475 pellets taken from the tops and

bottoms of each of the original containers. These

three composite samples will subsequently be referred

to as blend I, II, and III. Test samples (plaques) were prepared from blend I by Procedure A of ASTM Designation: D 1928-68,

"Standard Method for Preparation of CompressionMolded Polyethylene Test Samples." ^ In accordance

with this procedure, the pellets of blend I were made

' Figures in brackets indicate the literature references at the end of this paper.

' Available from the American Society for Testing and Materials, 1916 Race Street, Philadelphia, Pennsylvania 19103.

into a crepe on a roll mill. The polyethylene was

milled for about four minutes at a temperature suffi- ciently high to cause the polymer to flux but not to

drip. Pieces were cut from the cooled crepe and compression molded into 3 mm thick plaques at 178 °C

using picture-frame-like chases.^ The mold assembly

containing the molten polyethylene was removed from

the press and quenched to room temperature in a water

bath. The mold assemblies containing the quenched

plaques were then placed in a heated oven and maintained at 170 °C, well above the crystal melting point,

for 1 h or more in order to destroy the polymer's pre- vious thermal history. The temperature of the oven was then lowered to 50 °C at a rate of 5 °C/hr. After the

plaques had come to room temperature, several speci- mens (2-3 mm on a side) were cut from each plaque

for the density measurements.

As a check on the sensitivity of the ASTM pro- cedure to variations in the preparative technique,

plaques of blends II and III were prepared somewhat

differently. Plaques of blend II were prepared as described above except that the milling time (about

2 minutes) was just long enough at about 125 °C to cause the pellets to fuse into a sheet. The plaques of

blend III were not molded from a milled crepe. These

plaques were compression-molded from the pellets.

Except for the milling process, the test samples

(plaques) of blend III were quenched, recrystallized,

and cooled to room temperature by the same techniques described for blends I and II. The density of the three blends was determined by

the procedure given in ASTM Designation: D1505-67,

"Standard Method of Test for Density of Plastics by

the Density-Gradient Technique." ^ The density of

each specimen taken from the recrystallized plaques was determined by graphical interpolation of its equihbrium height in the density-gradient liquid

^ Although paragraph 5.6 of the ASTM procedure calls for a preheating period of 5 min, we have employed a time of 15 s. 143
maintained at 23 ±0.1 °C. Isopropanol and water were

used as the density-gradient liquids. The column was

calibrated by a series of glass beads whose density was known to within ±0.0001 g/cm^. The sensitivity of the column was found to be about 0.0002 g/cm^ per

mm column height, and the position of beads and

specimens could be read to about 1 mm.

3. Results and Discussion

The molding and recrystallization of the plaques

and the density measurements were performed on

several different days according to ASTM procedures

for sample preparation and density measurement.

No significant day-to-day variation was found in the

results. It was concluded that the preparation and

recrystalhzation of the samples were consistent

from one experiment to the next to within the precision

of the density determination. The average density

of twelve specimens taken from five samples (plaques)

of blend I was found to be 0.97844 g/cm^ with a sample

standard deviation of a single determination of 0.00014

g/cm^. The sample standard deviation of the mean of the twelve determinations is therefore 0.00004 g/cm^.

These values of the mean density and the sample

standard deviation of the mean are reported on the

certificate for SRM 1475. The range of the measure- ments was from 0.9784 to 0.9786 g/cm^.

The average of ten density measurements on blend

II was found to be 0.97817 g/cm^ with a standard

deviation of a single determination of 0.00010 g/cm^.

The density measurements for blend III gave a result of 0.97493 g/cm^ with a standard deviation of a single

measurement of 0.00045 g/cm^, based on 21 measurements. These results are summarized in table 1. From

the sample standard deviations and the systematic

uncertainties associated with the calibrating beads.

Table 1. Density at 23 °C ofLinear PolyethYlene SRM 1475

Blend I Blend II Blend III

Average density, g/cm^ *0.97844 0.97817 0.97493 Standard deviation of a single measurement 0.00014 0.00010 0.00045 Number of measurements 12 10 21

* Certificate value. The samples of blend I were prepared from pellets of polyethylene

which had been fluxed and milled twice as long (about 4 minutes)

as blend II. The samples of blend III were molded from the poly- ethylene pellets.

we conclude that the overall accuracy of our measure- ments is well within the 0.05 percent limit cited in the

ASTM procedure.

Although the 0.03 percent difference between the

densities of blends I and II is statistically significant, for practical purposes this difference is unimportant

in view of the 0.05 percent estimate of accuracy given

in the ASTM procedure. On the other hand, the density

of blend III (unmiUed samples) is materially lower

than that of blends I and II, and its standard deviation

of a single measurement is much larger than those of blends I and II. These differences cannot be ascribed

to differences in the crystaUinity of the samples, for the parts of the procedure which might be expected

to affect crystaUinity (molding, quenching, recrystallization) were identical for all three blends. Nor can the

differences be attributed to the lack of mixing of the

individual pellets during the preparation of blend III, since pellet-to-peUet variation would be expected to yield a larger sample standard deviation for blend III than for blends I and II, but the same mean density.

The most likely explanation of both the lower mean

density of blend III and its larger sample standard

deviation seems to be the presence of small voids

resulting from the lack of miUing and fluxing. This

explanation is reinforced by the fact that specimens

taken from plaques of blend III, even though carefully

selected, appeared to contain small regions of en- trapped air. We conclude that the preparatory miUing and fluxing

stipulated in the ASTM procedure is essential if the

stated precision of the procedure is to be realized.

4. References

[1] Mandelkern, L., in Growth and Perfection of Crystals, Ed.

R. H. Doremus, B. W. Roberts, and D. TurnbuU, p. 467 (John Wiley and Sons, Inc., New York, N.Y., 1958).

[2] Mandelkern, L., Posner, A. S., Diorio, A. F., and Roberts,

D. E., J. Appl. Phys. 32, 1509 (1961). [3] Chiang, R. and Flory, P., J. Am. Chem. Soc. 83 , 2857 (1961). [4] Weeks, J. J., Jr., J. Res. Nat. Bur. Stand. (U.S.), 67A (Phys. and Chem.), No. 5, 441-451 (Sept.-Oct. 1963).

[5] SteUa, C, Compt. Rend. 248, 1819 (1959). [6] Sperati, C. A., Franta, W. G., and Starkweather, H. W., Jr.,

J. Am. Chem. Soc. 75, 6157 (1953).

[7] Hoeve, C. A. J., Wagner, H. L., and Verdier, P. H., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 2, 137-140

(Mar. — Apr. 1972). Paper I of this series.

(Paper 76A2-708)

144
The Characterization of Linear Polyethylene SRM

1475. IV. Melt Flow Rate.

John R. Maurey

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

The melt flow rate of SRM 1475 was determined to be 2.07 g/10 min at 190 °C under a load of 325

g by a method similar to procedure A of ASTM method D 1238-65T. This value is the average of determinations on 42 samples with a standard deviation of a single measurement of 0.040 g/10 min, and a range of 1.991 g/10 min to 2.132 g/10 min.

Key words: Extrusion plastometer; load; melt flow rate; orifice; orifice die; preliminary extrudate;

test extrudate.

1. Introduction

Meh flow rate is widely used in polymer tech- nology as a product specification since this value,

which includes a statement of the load and temperature

under which it is obtained, gives an indication of the

processing properties of the polymer. The value of

melt flow rate is expressed as the mass of polymer

melt pushed from the heated cyhnder of the extru- sion plastometer through its precision bore orifice by its piston in a period of time, the standard units

of the value being grams per ten minutes (g/10 min). In this paper, we report the determination of melt

flow rate for linear polyethylene SRM 1475. Use of

the same measurements to investigate the uniformity

of the material is described elsewhere [1].^

2. Experimental Procedure

2.1. Instrument and Method

The melt flow rate determinations were made

with a commercial extrusion plastometer,^ by

a method similar to Procedure A described in "Tentative Method of Measuring Flow Rates of Thermoplastics by Extrusion Plastometer," ASTM Designation: D 1238-65T.4

The dimensions of the plastometer cylinder, piston

assembly and orifice, and the combined masses of

the piston and passenger weight were found to comply

with the instrument specifications described by the

ASTM method.

' Figures in brackets indicate the literature references at the end of this paper. ^Certain commercial equipment, instruments, or materials are identified in this paper

in order to adequately specify the experimental procedure. In no case does such identi- fication imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available

for the purpose.

^ Model 3, Tinius Olsen Testing Machine Company, Willow Grove, Pennsylvania 19090.

* Available from the American Society for Testing and Materials, 1916 Race Street, Philadelphia, Pennsylvania 19103.

In compliance with the ASTM method, the temperature indicator of the extrusion plastometer was cali- brated with respect to a standardized iron-constantan

thermocouple rhounted in an undisturbed column of

polymer melt in the plastometer cylinder. The thermocouple junction was fixed at the axis of the cyhnder,

12.7 mm above the top surface of the orifice die in the bottom of the cylinder. An equilibrium temperature reading of 189.9 °C was observed on the mercury

column thermometer in the cyhnder while the thermocouple indicated the equilibrium temperature of the

polyethylene melt to be 190.0 °C at the prescribed

calibration point. Thus, prior to each series of flow

rate determinations, the cylinder of the extrusion

plastometer was brought to thermal equiUbrium with

a constant reading of 189.9 °C on the mercury column

thermometer.

Further study of the temperature at other dis- tances up to 48 mm above the orifice, under conditions required by the calibration procedure, indi- cated that the temperature was uniform above the

12.7 mm height in the undisturbed melt column.

However, the temperature of the melt 1 mm above

the orifice was 0.7 deg lower than the temperature

of the melt 12.7 mm above the orifice. This thermal

gradient at the bottom of the undisturbed melt column

is probably at least partially erased in an actual

flow rate determination by the downward flow of the

piston-driven melt through the orifice. A separate study of the effect of temperature indi- cated that the flow rate of SRM 1475 was not significantly altered by a temperature change of 1 deg

from the specified test temperature, 190 °C. The orifice die was found to have a bore diameter

of 2.096 mm, well within the ASTM specification

tolerance limits. Bore diameter tolerance gauges were used to test the bore of the orifice die frequently

between series of flow rate determinations. According to this test, no detectable change occurred in

145
the bore diameter during the entire course of the

flow rate study.

2.2. Procedure

Because of the relatively high fluidity of the melt

of the Hnear polyethylene, the light load of conditions

D of the ASTM method was chosen for the flow rate determination. Conditions D of the ASTM method

specify the temperature of the melt to be 190 °C, and

the load (combined apparent masses of piston as- sembly and passenger weight) to be 325 grams.

In accordance with the ASTM procedure, each

sample was first preheated in the plastometer for 6

minutes, and the preliminary extrudate cut from the

bottom of the orifice. Test segments were then cut from

the extrudate at 1 minute intervals for 11 minutes,

and were examined for bubbles as they emerged from

the plastometer. The ASTM procedure calls for the use of bubble-free samples obtained during the first 3 minutes. We found, however, that it was virtually

impossible to obtain bubble-free samples of SRM 1475

within 3 minutes. Attempts were therefore made, as suggested in the ASTM procedure, to eliminate the

bubbles by manually forcing out some of the melt

during the preheat period. These attempts were unsuccessful and this modification was therefore not employed. Among the first five segments collected, however, at least two were completely free of bubbles, and

generally one or two additional segments contained

only bubbles so few and small that their individual

flow rate values were not distinguishable from the

values for the completely bubble-free segments. The

extrudate from the fourth through the eleventh 1 min

intervals contained no bubbles. In order to obtain

measurements on bubble-free materials while staying

as close as possible to the conditions specified by the

ASTM procedure, we therefore determined flow rate

for the certificate from the bubble-free segments

obtained during the first 5 min. In order to investi- gate the eff"ect of exceeding the prescribed time of 3 min, we also determined the flow rate from all the

bubble-free segments obtained during the entire 11 min

interval. The results obtained are described in the

following section.

It was found unnecessary to apply the severe

orifice-cleaning techniques, described in the ASTM

method, between flow rate determinations of this particular polyethylene. It was found satisfactory to ram

out the residual polyethylene with a soft copper wire

of diameter nearly as large as that of the orifice bore,

while the die was still hot. No effect on the flow rate values could by detected when this technique was

applied between determinations.

3. Results and Discussion

Flow-rate measurements were obtained on a total of 42 samples, taken from thirteen diff"erent regions of

the total supply of SRM 1475. As described elsewhere

[1], no variation could be found from region to region.

The results for the 42 samples were therefore pooled.

The mean flow rate, based on segments obtained

during the first 5 min as described in the preceding

section, was found to be 2.07 g/10 min, with a sample

standard deviation of 0.040 g/10 min, a range of 1.991

to 2.132 g/10 min, and a sample standard deviation of

the mean of 0.0062 g/10 min. The mean value and the

sample standard deviation of the mean are the values

reported on the certificate for SRM 1475. Measurements on segments collected during the

entire 11 min period, well beyond the 3 min limit specified in the ASTM procedure, yielded a mean flow rate of 2.06 g/10 min, with a sample standard deviation of

0.038 g/10 min and a range of 1.987 to 2.142 g/10 min.

The close agreement between the two calculations in mean value, standard deviation, and range suggests

that either a longer preheat period or a longer measure- ment period could be used for this material without

aff'ecting the observed flow rate.

4. References

[1] Hoeve, C. A. J., Wagner, H. L., and Verdier, P. H., J. Res. Nat.

Bur. Stand. (U.S.), NBS 76A, (Phys. and Chem.), No. 2, 137-

140 (Mar.-Apr. 1972). Paper I of this series.

(Paper 76A2-709)

146
The Characterization of Linear Polyethylene SRM 1475.

V. Solution Viscosity Measurements

Richard G. Christensen

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

The limiting viscosity numbers of linear polyethylene SRM 1475 were determined at 130 °C in 1,2,4-trichlorobenzene, 1-chloronaphthalene, and decaUn. Technique, including use of a novel solution transfer method, is described.

Key words: 1-chloronaphthalene; decalin; Unear polythylene; Umiting viscosity number; solution

viscosity; 1,2,4-trichlorobenzene; viscometer.

1 . Viscosity Measurements

Limiting viscosity number is a readily measured

physical property which can be related empirically to molecular weight. A number of empirical relation- ships between limiting viscosity number and molecular weight of polyethylenes have been published

[1-6V

The limiting viscosity number [17] is defined as the

limit as the concentration c approaches zero of the

viscosity number, (tjs ~T7o)/(i7oc), where tjs and tjo are the viscosities of the solution and solvent, respectively,

in the limit of zero shear rate. Thus, [tj] may be

determined by measuring the viscosity number over

a range of finite concentrations and extrapolating to zero concentration, provided the solution and solvent

viscosities are independent of shear rate. The limiting viscosity number of SRM 1475, de- scribed in Part I of this series [7], has been determined

in several solvents so that data can be compared with

that cdready published, and also so that the sample

can serve as a basis fcr interlaboratory comparison

of technique.

Viscosity measurements were made in a Ubbelohde

viscometer fitted with a removable sintered glass filter in the neck through which the viscometer is filled. Such a viscometer is described in ASTM D 1601-61.^

Solutions were made up by weight in 25 cm^ flasks. The solvents used and their densities at 130 °C

were: 1-chloronaphthalene, 1.098 g/cm^; 1,2,4-tri- chlorobenzene, 1.323 cm^; and decalin, 0.801 g/cm^.

The polymer was weighed on an electric microbalance.

Dissolution of the polymer was accomplished by

heating at 140 °C with occasional vigorous agitation by

magnetic stirrer. Usually an hour of heating and

stirring sufficed. The 1-chloronaphthalene was carefully purified

and appeared to be about 99.5 percent pure by gas

Figures in brackets indicate the literature references at the end of this paper.

' Available from the American Society for Testing and Materials, 1916 Race Street, Philadelphia, Pennsylvania 19103.

chromatographic analysis. The 1,2,4-trichlorobenzene was technical grade and appeared to be about 98.5

percent pure by gas chromatographic analysis. The

decalin used was technical grade which had been

subjected to a simple vacuum distillation to remove

gross impurities. An assay showed approximately

equal proportions of cis- and traras-decahydronaphthalenes. AW solvents used contained 0.1 percent 2 ,6-di-tert- butyl-4-methylphenol (lonol) as an antioxidant, and

the automatic viscometer used kept the solutions

under nitrogen during measurement. It is beUeved

that degradation of the polymer was negUgible under

these conditions, since httle change in the flow times

occured even when the solutions were left in the

viscometer as long as overnight. Also, dilutions were

not made, but rather a separate solution was used for each concentration. Under conditions such as long

heating to dissolve high molecular weight fractions,

significant degradation can occur. This is usually

evinced by much larger scattering of points in the plot for the extrapolation to limiting viscosity number,

since the extent of degradation is likely to vary from

sample to sample.

The solutions were transferred into the viscometer

by a wash-bottle-Hke siphon (see fig. 1) which was

found to be more convenient than a heated pipette.

Due to the low thermal mass of the fine glass tubing,

it was found unnecessary to preheat the siphon. The

viscometer was rinsed twice with about 4 cm^ of the

solution^then about 10 cm^ was siphoned in for the flow

time measurement. An automatic viscometer timer

(Hewlett-Packard Model 5901B Autoviscometer^) was used to operate the viscometer and measure the

flow times, while the viscometer was thermostatted in a Hewlett-Packard 5901A Constant Temperature

Bath. 3

^ Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.

147
Table 1.

Limiting viscosity number versus Solvent number, dl/g concentration,

(dl/g)2

l-chlororitiphthiileiie " 0.890 ±0.0032 0.48 1^,4-trichlorobenzene L010± .0086 .55 decahydronaphthalene' 1.180 ± .0032 .72

" Uncertainties quoted are estimated standard deviations obtained from linear least squares fits of viscosity number versus concentration.

^ Technical grade, which assayed at approximately equal proportions of cis- and trans- decahydronaphthalenes.

Figure 1. Solution transfer siphon.

Advantages of an automatic viscometer timer are

that the same amount of hquid is automatically drawn

up to each time and that the flow time is measured to 0.001 seconds. The former contributes to the uniformity

of the measurement, the latter makes possible the use

of very dilute solutions, which greatly facihtates reh- able extrapolations to zero concentration. A third

advantage is that the cleanhness of the viscometer can

be judged by the reproducibility of the flow times.

Ordinarily, flow times wiU fall in a range of 0.03 seconds or less. In the presence of Unt or dust the flow

time will drift or will be randomly erratic with a range of up to 0.2 seconds.

Kinetic energy corrections were made in all cases

[8]. These amounted to about 1.2 percent for 1,2,4-

trichlorobenzene solutions, and about 0.3 percent for the decalin and 1-chloronaphthalene solutions. The

rate of shear in the Ubbelohde viscometer used was

about 1000-1500 seconds"^ Measurements on a

higher molecular-weight hnear polyethylene fraction

(M„ = 355,300, M„, = 688,000) at shear rates from

20 to 1500 s~^ reveal no dependence of measured

viscosity number on shear rate. We therefore assume

that the measured viscosity numbers of SRM 1475

exhibit no shear-rate dependence in this region.

Since the flow time (corrected to allow for kinetic

energy of the effluent from the capillary) in a Ubbelohde viscometer is proportional to solution viscosity, the viscosity number can be written (tg — to)l (toc)

,

where c is concentration and ts and to are flow times

for solution and solvent respectively. The standard

deviation in the viscosity number of aUquots of the same solution was found to be sHghtly less than

0.3 percent. The viscosity numbers were fitted by

least squares to hnear functions of concentration;

the Hmiting viscosity numbers were obtained as the

resulting constant terms. The results are given in table 1. The viscosity numbers are plotted against

concentration in figure 2, which also shows the straight

lines obtained from the least-squares analysis.

Considerable care must be exercised in making vis- cosity measurements when decalin is used as the sol1.2

I.I

cr

0.9

DECALIN

_^„^—"a^

TRICHLOROBENZENE

-CP" l-CHLORONAPHTHALENE

0 0.04 0.08 0.12 0.16 Q20 CONCENTRATION. 9/dl

Figure 2. Limiting viscosity numbers ofSRM 1475.

vent. Errors can easily arise due to the widely differing

properties of the cis- and frans-isorners of decahydronaphthalene. The ci5-isomer has a boihng point about

10 °C higher, a density about 3 percent greater, and a

viscosity about 20 percent higher than the ^rans-isomer.

If the solutions are made up by weight, density must be

measured for each batch of solvent. Since the isomers

differ in volatility, condensation in the upper part of

the viscometer can change the isomeric composition in the solution. The resulting error in flow time can cause

errors of 5 percent or more in the viscosity number.

These errors were minimized in he present work by

repeatedly equihbrating the viscometer with fresh

portions of solvent. After reproducible solvent flow

times were obtained, the flow times of the solutions were measured. We beheve that by the use of these

techniques, the errors due to the variable composition

of decahn have been reduced to less than 1 percent.

148
2. References

[1] Wesslau, H., Makromol. Chem. 20, 111 (1956).

[2] Francis, P., Cooke, R., Jr., and Elliott, J., J. Polymer Sci. 31,453

(1958).

[3] Kotera, A., et al, Rept. Progr. Polymer Phys. Japan 3, 58 (1960).

[4] Chiang. R., J. Polymer Sci. 36, 91 (1959).

[5] Tung, L., J. Polymer Sci. 36, 287 (1959).

[6] de la Cuesta, M., and Billmeyer. F. Jr., J. Polymer Sci. A 1, 1721 (1963).

[7] Hoeve, C. A. J., Wagner, H. L., and Verdier, P. H., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 2, 137-140

(Mar.-Apr. 1972). Paper I of this series.

[8] Allen, P. W., Techniques of Polymer Characterization, p. 180

(Butterworths, London, 1959). (Paper 76A2-710)

The Characterization of Linear Polyethylene SRM 1475.

VI. Preparation of Calibrating Fractions

Richard G. Christensen

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

Fractions for use in calibrating a gel permeation chromatograph were prepared by a Desreux column extraction method. The construction and operation of the fractionating system are described.

Key words: Column extraction fractionation; fractionation; linear polyethylene.

1. Introduction

In the process of determining the molecular weight

distribution of SRM 1475 [1]^ it was necessary to calibrate a gel permeation chromatograph [2] with

linear polyethylene. Fractions of linear polyethylene were used for this purpose. The fractions were subsequently used to establish relations between limiting

viscosity number (intrinsic viscosity) and molecular

weight [3]. The requisite fractions were prepared by a column extraction [4] technique, using a solvent system

which has been described in considerable detail by

Chiang [5] and others.

2. Experimental Procedure

The fractionation apparatus was constructed as depicted in figure 1. The column temperature is maintained by surrounding it with a narrow, deep oil bath, 20 X 20 X 90 cm. The stirrer and heater are placed

inside a long tube to promote efficient thermal ex- change between the top and bottom of the tank.

The solvent inlet to the column is a small concentric

tube reaching to the bottom of the packed column. The

efflux collects above the column packing and is periodically drawn off through a slightly larger tube concentric with the inlet tube. The liquid is forced out by

nitrogen pressure. The 8 cm diameter column is packed

Figures in bracicets indicate the literature references at the end of this paper.

Figure 1. Section offractionation apparatus.

(a) nitrogen inlets; (b) preheating flaslc; (c) efflux siphon; (d) o-ring flange; (e) heater; ( stirrer; (g) tanic; (h) pacited column; (i) effluent liquid; tj) inlet tube; (k) thermoregulatoi

(1) circulating tube. 149
with Johns-Manville Celite No. 545^ to a depth of about

55 cm. The free liquid volume of the packed column is about 2000 cm".

In operation, the column was heated to 127 °C, the

polymer in xylene was allowed to flow in, and the

column was allowed to cool slowly overnight. All of the

polyethylene except a small amount of low molecular

weight was thereby precipitated in the column. The

cooling rate at 90 °C was about 0.2 °C/min. The cooled

(50 °C) xylene was displaced by a poor solvent, 2- butoxyethanol, while the precipitated polyethylene was retained in the column. The column was reheated

to 127 °C, causing the polyethylene to melt and swell

with the poor solvent. The column was then extracted

with mixtures of xylene and 2-butoxyethanol which

were successively better solvents. The solutions

of extracted polyethylene were siphoned into flasks containing cold ethanol. The polyethylene was filtered out, washed with ethanol, air dried, and then dried in vacuum at .50 °C. AU solvents contained 0.1 percent lonol (2,6-ditert.-butyl-4-methylphenol) as an antioxidant. They

were preheated under nitrogen to over 130 °C before

3eing admitted to the column. This served to degas the

solvent, preventing the formation of bubbles in the

column. Typical input concentration was 1 percent

^ Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.

polymer in xylene. Extracting mixtures were 15-55

percent xylene. Recovery was ordinarily 97-98

percent, but no great effort was made to obtain absolutely quantitative recovery of material.

Samples PE 7 to PE 180 were prepared by fraction- ating SRM 1475. Yield was three to six grams of

each sample. Samples PE 200 to PE 600 were prepared

from Phillips Marlex 6002. These fractions contained

two to four grams each.

Light-scattering [6], osmometry [7], and gel permeation chromatography [2] studies were carried out with

these samples. The final results are tabulated in paper

X of this series [2].

3. References

[1] Hoeve, C. A. J., Wagner, H. L., and Verdier, P. H., J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.), No. 2, 137-140

(Mar.-Apr. 1972). Paper I of this series.

[2] Ross, G. S., and Frolen, L. J., J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.) No. 2, 163-170 (Mar.-Apr. 1972). Paper X of this series.

[3] Hoeve, C. A. J., and Wagner, H. L., to be published.

[4] Desreux, V., Rec. Trav. Chim. 68, 789 (1949).

[5] Chiang, R., J. Polymer. 36, 91 (1959).

[6] Frolen, L. J., Ross, G. S., Wims, A. M., and Verdier, P. H.,

J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.),

No. 2, 156-160 (Mar.-Apr. 1972). Paper VIII of this series.

[7] Brown, J. E., and Verdier, P. H., J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.), No. 2, 161-163 (Mar.-Apr. 1972). Paper IX of this series. (Paper 76A2-711)

150
The Characterization of Linear Polyethylene SRM 1475. VII

Differential Refractive Index of Polyethylene Solutions

Herman L. Wagner

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

The value of dnidc for polyethylene in 1-chloronaphthalene at 135 °C, required for the deter- mination of molecular weight by light scattering, was found to vary with molecular weight. Similar changes were found in 1,2,4-trichlorobenzene, the gel permeation chromatograph solvent. The absolute value of dnjdc decreases by about 2 percent as the polymer molecular weight increases from

12,000 to 110,000. Key words: 1-chloronaphthalene; dnjdc; differential refractive index; refractometer; refractive index;

1 2,4-trichlorobenzene.

1. Introduction

Since the change of refractive index with concentration, dnjdc (differential refractive index), enters as a squared term in the light scattering equation, its ac- curacy is of considerable importance for obtaining

reliable values of molecular weight of polymers.

The first determination of dnjdc of polyethylene in 1-chloronaphthalene (table 1) found in the literature was by Nichols and was reported by Billmeyer [1].* It was measured at 90 °C and 125 °C using a divided

cell technique, giving values of —0.199 ml/g and — 0.191 ml/g respectively. The latter value is the one most often quoted. Kobayashi, Chitale, and Frank [2], using an interferometer technique, obtained a somewhat lower value at 90°, namely —0.183. Nicholas

[3] found a very low value (— 0.257 at 125 °C) using a Rayleigh differential refractometer at concentrations

of 0.15 to 0.7 g/100 ml. This result seems to be completely out of line with the other values reported and

may be due to the greater errors incurred working at low concentrations. The use of such low concentrations

would appear to be unnecessary inasmuch as dnjdc

is found to be constant at the concentrations used in

this work, which range from 0.5 g/100 ml to 4 g/100 ml» Most of the other literature values fall in the range

of -0.188 to-0.199|4,5,6]. The recent data are those of Drott and Mendelson [7], Chiang and Rhodes [8] and

Benoit et al. [9]. Drott and Mendelson provide considerable detail about their procedure, which appears to

Table 1. Literature values of dn/dc for polyethylene in I -chloronaphthalene

dnjdc in ml/g

Refs. 1 2 3 6 22 7 8 9

Temp. °C

90 -0.199 -0.183 -0.198

99.5 -0.1924

104.5 -.1927

105 -0.188

109 -.1934

114 -.1927 -0.1957

120 -.1917

125 -.191 -0.257 -.195 -0.195 -.1911

127 -.1967

128 -.1955

135 -.190

139 -.1956

140 -.191 -.1961

145 -.1967

' Figures in brackets indicate the literature references al the end of this paper.

151
be thorough and careful, and obtained a value of— 0.191

at 140 °C and -0.195 at 125 °C. Chiang believes his values for a low molecular weight branched sample of — 0.195 at 80 °C [10] are consistent with his values

for higher molecular weights which range from—0.193

at 100 °C to -0.190 at 135 °C. Benoit et al. measured

dnidc between 141 °C and 150 °C finding values about

2i percent higher than those of Chiang and BiUmeyer. The change in dnjdc with temperature is insig- nificant in this temperature range. In view of the uncertainties described above and the

importance of accurate values of dnIdc, it appeared

necessary to make as accurate a determination as possible for the Standard Reference Materials Pro- gram. It soon became evident that dnjdc was to some

extent a function of molecular weight. This may ac- count for some of the discrepancies in the literature but these could not be readily resolved because in most cases no characterization is provided for the

polyethylene used in the dn/dc measurement. It was

a^so necessary to measure the variation with molecular

V ;ight in 1,2,4-trichlorobenzene since this solvent is used in gel permeation chromatography with the

assumption that dnIdc is constant.

2. Experimental Procedure

The determination of the change of refractive index

with concentration is most conveniently accomplished

by a differential refractometer. The instrument employed here was the image displacement type, in which

light passes through a cell consisting of two adjacent

prismatic compartments, one containing solvent, the

other dilute solution. It may be easily shown that in the limit as the difference Are between the refractive

index of solution and of solvent becomes small, the

displacement A,d of the imaged light source from its position with pure solvent in both compartments of the

cell becomes proportional to An, i.e.,

where k is the proportionality constant and is deter- mined by calibration with a substance of known

refractive index.

2.1. Optical System

The optical system, consisting of the elements

shown in figure 1, is mounted on an optical bench 125

cm long. Light from an air cooled mercury lamp passes

L| CELL Lj lERCURY FILTER SLIT COLLIMAT- AND IMAGING MICROMETER LAMP ING THERMO- LENS MICROSCOPE

LENS STAT

Figure 1. Optical system, schematic.

through a combination of filters which transmits

green monochromatic light at 5460 A. This light enters a slit, passes through the coUimating lens, Li,

then through the cell, where the deviation due to the refractive index difference takes place. The dis- placed slit, imaged by the lens, L2, is observed with a micrometer eyepiece having a 10 mm scale and a drum divided to 0.01 mm. The entire optical system

is carefully aligned so that the coUimated beam is normal to the face of the cell. The system was stable

in that once the optical components were fixed the

reading did not change over a period of several days

with a given solvent in both compartments of the cell.

2.2. Glass Cell The sample cell, supplied commercially [11] '^ is a

sinter fused Pyrex optical cell 15 mm square with

plane parallel windows. The partition is set at such an

angle that the light beam forms an angle of incidence of

approximately 69° with the normal to the surface

of the partition. This cell is provided with a fused top

with openings which are closed by Teflon stoppers,

thus ehminating the problem of evaporation which in the past has caused troublesome temperature gradients

at high temperatures.

2.3. Cell Holder

In order to achieve temperature stability over long

periods of time and to keep the temperature difference

between the two compartments of the cell down to a few hundredths of a degree, considerable care was

necessary in the design of the cell holder. As in the

apparatus discussed by Benoit et al. [9], the cell is set into a rectangular opening in the center of a cylindrical

aluminum block, 4 in in diameter and 5 in high (fig. 2) containing a f in hole for passage of the light beam.

Aluminum 1100 was used because of its superior heat

conductivity. The aluminum block is positioned by

three bakelite pins inside a ^ in thick brass shell of 5 in diameter, leaving a half inch air space to minimize heat loss. Both the aluminum block and the brass

shell are heated by coils of wire embedded in silicone rubber. Additional heat is supplied by means of four

rod heaters inserted into holes in the block and by

another coil heater, also embedded in silicone rubber,

underneath the brass shell. The temperature of the cell holder is maintained by a thermistor temperature controller. The entire assembly is insulated by a laminate

composed of eight layers of balsa wood alternating with

aluminum foil. Short term temperature fluctuations of the aluminum block were of the order of 0.001 °C.

Drift during a set of measurements was no greater

than 0.01 °C. Brice [12] recommends that the temperature dif- ference between solvent and solution should be no

greater than 0.01 °C. Attempts to measure this dif- ference by simply inserting thermocouples into each

^ Certain commercial equipment, instruments, or materials are identified in this paper

in order to adequately specify the experimental procedure. In no case does such identifica- tion imply recommendation or endorsement by the National Bureau of Standards, nor does

it imply that the material or equipment identified is necessarily the best available for the purpose. 152
Figure 2. Heating blockfor cell.

(1) Divided cell, (2) aluminum cylinder, (3) cartridge heaters, (4) brass shell, (5) balsa wood- aluminum foil laminate, (6) opening for light path, (7) heaters embedded in silicone rubber,

(8) balsa wood cap, (9) air space, (10) bakelite positioning pins, (11) thermistor. compartment were unsuccessful, probably because of

heat loss through the openings for the thermocouple

leads and through the leads themselves. In view of the

construction described above it is doubtful that a significant difference existed. In any case the effect of such a difference would be cancelled since measurements

were made first with solution on one side and solvent on

the other and again with solution and solvent reversed.

3. Materials

3.1. Solvents

Reagent grade 1-chloronaphthalene was double

distilled, center cuts being taken each time. Observable impurities were less than 0.05 percent by gas hquid chromatography. The 1,2,4-trichlorobenzene,

technical grade, was not further purified and 0.05

percent lonol (2,6-di-ferf.-butyl-4-methylphenol) was

added as an antioxidant in order to use the same

material used in the gel permeation apparatus [13]. Gas liquid chromatography revealed only a single major

peak containing at least 99 percent of the material.

3.2. Polymers

Measurements of dn/dc were made on several polyethylenes. They are: (1) SRM 1475, the linear polyethylene standard reference material described pre- viously [14]; (2) fractions of SRM 1475 obtained by

column extraction of this polyethylene [15]; (3) SRM

1476, the branched polyethylene standard reference

material. The available data are provided in the

certificate for this material. Additional details will be given in a forthcoming publication; (4) fraction

R 1201-7 is a hnear polyethylene supplied by the

Monsanto Chemical Company; (5) AC-6 is a polyethylene wax obtained from the Allied Chemical

Corporation.

The number average molecular weights of these

materials were obtained in various ways, as indicated

in tables 2 and 3. Some were obtained by direct meas- urement by osmometry [16]; others were determined by

gel permeation chromatography (G.P.C.) [13]. The

number average molecular weights of fractions 12x and

7y were estimated from molecular weight measure- ments made on other fractions prepared by the same

process. For three of the samples (AC-6, R 1201-7, and

SRM 1476), the values supplied by the manufacturer were used.

4. Procedure

For each concentration two readings of the dis- placement of the light beam were made. The first was

taken with the solvent on one side and solution on

the other and another reading was taken with these

reversed. One-half the difference between the two

readings multiplied by the calibration constant gave the

value of the refractive index difference An. This is similar to the procedure of Brice and Halwer [12] ex- Table 2. dn/dc of Polyethylenes in l-Chloronaphthalene at 135 °C

dnidc. Stand, dev. No. of Sample Mn ml/g of dn/dc," points " ml/g

SRM 1475 " 18,310 -0.1932 0.00016 5 SRM 1476 " 25,200 -.1916 .00028 5 Fraction R 1201-7 " 12,300 -.1931 .00042 3 Fraction PE 15 ' 13,500 -.1929 .00035 3 Fraction 12x " 110,000 -.1883 .00088 2 Fraction PE 120 c 112,200 -.1879 .00059 4

^ Value obtained from Gel Permeation Chromatography [13]. Value provided by manufacturer.

*^ Determined by osmometry [16]. Estimated as described in text.

* The estimated standard deviation of the slope, calculated by linear regression of the refractive index difference, An. on the concentration c, assuming a zero intercept. The number

of points in each regression line is shown in column 5. For convenience all standard deviations are given to two significant figures, with no implication that such precision is warranted. 153
Table 3. dn/dc of Polyethylenes in 1,2,4-Trichlorobenzene at 135 °C

aniac. Stand, dev. INo. 01 Sample ml/g of dnldc," points

ml/g

AC-6 " 2,000 -0.1085 0.00028 3 SRM 1475 " 18.310 -.1085 .00015 5

a OA o(\(\ -UUUIV o

Fraction 7y 77,000 -.1073 .00038 3 Fraction 12x <= 110,000 -.1063 .00014 4

* Value obtained from Gel Permeation Chromatography [13]. Approximate value, supplied by manufacturer.

^ Estimated as described in text.

** The estimated standard deviation of the slope, calculated by linear regression of the refractive index difference. An, on the concentration c, assuming a zero intercept. The number

of points in each regression line is shown in column 5. For convenience all standard deviations are given to two significant figures, with no implication that such precision is warranted.

cept that since it is not possible, as in their apparatus,

to rotate our cell housing because of its large bulk,

the cell is kept fixed and the contents reversed. Readings with solvent on both sides were made occasionaUy to make certain that the beam's position through

the center of the cell had not shifted. Solutions were made up by weight, and concentrations were calculated from measurements of solvent

densities and partial specific volumes. The densities

at 135 °C of 1-chloronaphthalene and 1,2,4-trichlorobenzene were found to be 1.095 g/ml and 1.315 g/ml

respectively. The partial specific volumes were approximated from measurements of the change in density on

dissolving the polymer to specified concentrations. The

values obtained were 1.29 ml/g in 1-chloronaphthalene

at a concentration of 0.03 g/ml and 1.30 ml/g in 1,2,4- trichlorobenzene at a concentration of 0.01 g/ml. It was assumed that at the low concentrations employed here

the partial specific volume is constant, so that the

volume increase on dissolving polymer is equal to the

weight of the polymer multiplied by this approximate

partial specific volume. The polymer was dissolved in the solvent at 140 °C and about 1.5 ml was transferred

by a heated hypodermic syringe to the cell. The compartment was not cleaned and dried when its content was changed but was thoroughly rinsed beforehand

with solvent and solution of the new concentration. A

period of at least 15 min was allowed after transfer for temperature equilibration before readings were taken.

The standard error (15 readings) was about 2 X 10"^ in An or about 0.2 percent. The least square slopes computed from these data show a standard deviation of the

slope of from 0.1 to 0.5 percent, as shown in tables 2 and 3. The standard deviation of the slope for the standard reference sample is about 0.1 percent.

No refractive index data at 135 °C are available for calibration of differential refractometers. We therefore calibrated our instrument with aqueous solutions

of NBS sucrose at 25 °C and assumed the calibration

did not change with temperature. The most likely cause for a change in calibration would be a change in the angle of the glass partition of the cell. Measurements in a cell similar to ours by Benoit et al. [9] of sodium chloride solutions up to 70 °C did not reveal

any changes with temperature.

The partial specific volume of sucrose in water was

taken as 0.618 ml/g at 25 °C [19]. The value of 0.1429

ml/g for dn/dc at 5460 A at 25 °C, obtained by Norberg

and Sundeloff [18], was employed in the calibration of

the apparatus. This value agrees very well with the

results of other authors [19-21]. Bodmann [21] has

shown that dn/dc is constant up to concentrations of

at least 0.025 g/ml. We found that the displacement

Ac? of the light beam is linear with concentration for concentrations as high as 0.04 g/ml and displacements

up to 5 mm, the limit of our instrument scale. The

calibration constant k for our instrument was found to be 1.1417x10"^ refractive index units per mm

deflection, with a standard deviation of 0.1 percent.

5. Results and Discussion

The values of dn/dc for various polyethylenes in 1- chloronaphthalene are listed in table 2. The value for the linear sample, SRM 1475 at 135 °C is -0.193 ml/g

and for the branched sample, SRM 1476, is —0.192.

The numbers fall into two groups: values of — 0.192 to — 0.193 for low number average molecular weights

(11,000-25,000) and a decidedly higher value, -0.188

for the higher molecular weights. In order to obtain

a better idea of the molecular weight dependence and

to determine whether gel permeation chromatography

intensities need to be corrected for molecular weight,

dn/dc was measured in 1,2,4-trichlorobenzene over a range of molecular weights. These are enumerated in table 3 and a plot of these values against 1/M„ is shown

in figure 3. The change in dn/dc in going from an Mn

of 12,000 to 110,000 is about the same in both solvents, a decrease of about 2 percent in absolute value. Several

dn/dc

-.106 - ^ O

-.108 - O

o

-.110 - 12 3 4 5 l/M X 10^

Figure 3. Differential refractive index in 1 ,2,4-trichlorobenzene.

154
factors contribute to the belief that this is a real change.

It is outside the limits of error of the determination,

for which the standard deviation is of the order of

0.5 percent. Different fractions of the same molecular

weight, such as 12x and PE 120 in one case, and R

1201-7 and PE 15 for another, the latter two coming

from different starting polymers, have the same values

of dn/dc. The infrared spectra of the whole polymer

SRM 1475 and a high molecular weight fraction, showing a smaller dn/dc, are similar, indicating the absence

of some chemical group which might account for the

difference in dn/dc.

Unfortunately it was not possible to measure

dn/dc for fractions of A/„ greater than 110,000 because

of the difficulties of handling the extremely high vis- cosities of these fractions at the concentrations needed

to give meaningful results. For most determinations

concentrations ran between 0.5 to 4 g/100 ml but were limited to no greater than 2 g/100 ml for the high

molecular weight samples.

6. Conclusion

Because dn/dc changes with molecular weight, it is necessary to use the correct value of dn/dc in

light scattering work, as is done in Paper VIII of this series [23]. Although 1-chloronaphthalene measure- ments were not made for the intermediate molecular

weight range, the measurements in trichlorobenzene

are extensive enough to show that dn/dc changes

continually so that interpolation should provide

sufficiently precise values for the former solvent. No

data are available, however, at number averages

greater than 110,000, and since it can not be assumed

that the absolute value of dn/dc decreases without

limit, the value at high molecular weights is taken,

for the present, as constant at —0.188 ml/g in 1-chloronaphthalene.

7. References

[1] BUlmeyer, F., J. Am. Chem. Soc. 75, 6118 (1953).

[2] Kobayashi, T., Chitale, A., and Frank, H.'P.', j: Polymer Sci. 24,

156(1957).

'

[3] Nicolas, L., J. Polymer Sci. 29, 191 (1958).

[4] Chiang, R., J. Polymer Sci. 36, 91 (1959).

[5] Duch, E. and Kuchler, L., Z. Electrochem. 60, 218 (1956).

[6] Trementozzi, Q. A.. J. Polymer Sci. 36, 113 (1959).

[7] Drott, E. E. and Mendelson, R. A., Polymer Letters 2, 187

(1964).

[8] Chiang, R. and Rhodes, J. H., Polymer Handbook, Editors J. Brandrup and E. D., Immergut, p. 14-282, (Interscience,

1966).

[9] Ehl, J., Louchaux, C, Reiss, C, and Benoit, H., Makromol. Chem. 75,35 (1%4).

[10] Chiang, R., J. Polymer Sci. 08, 295 (1965).

[11] Phoenix-Precision OpticeJ Company, Philadelphia, Pa.

[12] Brice, B. A., and Halwer, M., J. Optical Soc. of America 41,

1033(1951).

'

[13] Ross, G. S. and Frolen, L. J., J. Res. Nat. Bur. Stand (U.S.)., 76A, (Phys. and Chem.), No. 2, 163-170 (Mar.-Apr. 1972). Paper X of this series.

[14] Hoeve, C. A. J., Wagner, H. L., and Verdier, P. H., J. Res.

Nat. Bur. Stand. (U.S.)., 76A, (Phys. and Chem.), No. 2, 137-140 (Mar.-Apr. 1972). Paper I of this series.

[15] Christensen, R. G., J. Res. Nat. Bur. Stand. (U.S.)., 76A,

(Phys. and Chem.), No. 2, 149-150 (Mar.-Apr. 1972). Paper

VI of this series.

[16] Brown, J. E. and Verdier, P. H., J. Res. Nat. Bur. Stand.

(U.S.), 76A, (Phys. and Chem.), No. 2, 161-163 (Mar.-Apr.

1972). Paper IX of this series.

[17] Bates, F. J., et al., NBS Circular C440 (May 1, 1942).

[18] Norberg, P. H. and Sundelof, L. A., Makromol. Chem. 77,

77(1964).

[19], Costing, L. J. and Morris, M. S., J. Am. Chem. Soc. 71, 1998

(1949). [201 Maron, S. H. and Lou, R. L. H., J. Phys. Chem. 59, 231 (1955).

[21]' Bodmann, O., Chemie-Ing.-Tech. 29, 468 (1957).

[22] Tung, L. H., J. Polymer Sci. 36, 287 (1959).

[23]' Frblen, L. J., Ross, G. S., Wims, A. M., and Verdier, P. H.,

J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.),

No. 2, 156-160 (Mar.-Apr. 1972). Paper VIII of this series.

(Paper 76A2-712)

155
The Characterization of Linear Polyethylene SRM 1475

VIII. Light-Scattering Studies on Polyethylenes in

1 -Chloronaphthalene

Lois J. Frolen, Gaylon S. Ross, Andrew M. Wims*, and Peter H. Verdier

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

Light-scattering measurements have been made on a series of linear polyethylene fractions and a

linear polyethylene standard reference material (SRM 1475). All measurements were made in 1- chloronaphthalene at 135 °C, and over an angular range from 45° to 135°. The data were analyzed to obtain the weight average molecular weights, second virial coefficients and root-mean square end-to- end distances. Key words: End-to-end distance; light scattering; linear polyethylene; polyethylene fractions; My,; second virial coefficient; solution properties.

1 . Introduction

Several investigators [1, 2]^ have used the technique

of Hght scattering to obtain weight-average molecular

weights, second virial coefficients and radii of gyration

for polyethylene in dilute solutions. In this paper, we

report the results of light scattering studies on a series

of linear polyethylene fractions with molecular weight

ranging from about 1.9X10^ to about 6.9 XlO^. The

weight-average molecular weights reported here were employed in the calibration of a gel permeation

chromatograph used [3] to obtain the molecular weight

distribution of Standard Reference Material 1475,

Linear Polyethylene. We also report the direct deter- mination of weight-average molecular weight for SRM

1475 by light scattering.

2. Experimental Procedure

2.1 Apparatus

The hght scattering photometer described by

Mclntyre and Doderer [4] was used for most of the

studies reported here. However, a few measurements

were made on a modified Brice-Phoenix Photometer

(Phoenix Precision Instrument Company, Philadelphia,

Pa.). 2 Consistent results were obtained from the two

instruments, and data from both instruments are included in the analysis of results.

* Present address: General Motors Research Laboratory. Warren. Michigan 48092

' Figures in brackets indicate the literature references at the end of this paper

^Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental procedure. In no case does such identifica- tion imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.

All measurements on polyethylene solutions were made at 135 °C, using a heated cell holder [5] designed

and constructed in this laboratory. A schematic drawing of the cell holder is shown in figure 1. It consists of

two concentric cyhnders wrapped with heating wire,

insulated with alternating layers of balsa wood and

aluminum foil bonded together with silicone rubber

adhesive. A slot, not shown in the figure, extends

slightly more than halfway around the oven at the

height of the sample ceU to provide paths for the inFigure 1. Schematic drawing of high temperature oven for light scattering cells.

a. Insulation, b. outer cylinder, c. inner cylinder, d. heating wire, e. light scattering cell,

f. stirring bar, g. rotatable magnet. 156
cident, transmitted and scattered light. A small

rotatable magnet under the sample cell permits stirring

when desired. The scattering cells used with the oven are clear Pyrex cylindrical cells fitted with capillary necks and Teflon stoppers to minimize contamination by dust. Measurements on polyethylene were made with the outer cylinder heated to 130 °C and the temperature of

the inner cylinder controlled to maintain the sample

at 135 °C. No attempt was made to monitor the temperature of the solutions in the light scattering cell while measurements were being taken. However, in preliminary tests, the temperature at various points in the stirred solvent was monitored with thermocouples.

The liquid attained a steady temperature of 135 ° in 15 minutes and thereafter showed temperature varia- tions of less than ± 0.05 °C during a period of one hour.

A solution of polystyrene in toluene was used as a working standard to calibrate the instrument. Measurements of absolute scattering on the working standard were made at room temperature (about 25 °C) in a semi-octagonal sample cell with a clear (unblackened)

back surface. The temperature control employed for the higher-temperature measurements on polyethylene was felt to be unnecessary for the room-temperature

reference measurements. The oven and cell holder

described above were therefore not used for the

reference measurements.

2.2. Preparation of Samples

The preparation of the linear polyethylene fractions

is described in paper VI of this series [6]. The solvent

employed was Fisher Reagent Grade 1-chloronaphthalene which was passed through activated 28-200 mesh

silica gel before use. Gas chromatographic analysis of the solvent showed less than 0.1 percent observable

impurity. Before being filled with solution, the light

scattering cells were cleaned with hot chromic acid,

rinsed with distilled water, dried in a dust-free atmosphere, and rinsed from three to five times with filtered 1-chloronaphthalene.

Each sample was prepared by adding approximately

10 cm'' of solvent to a weighed amount of polyethylene,

stirring at 130-135 °C until the polyethylene dissolved

(usually 1 to IV2 h) and weighing the resulting solution. The sample was then filtered as described below into a weighed scattering cell. After light scattering measure- ments had been taken, second and third concentrations were prepared for measurement by adding

approximately 5 cm^ increments of filtered solvent,

weighing the scattering cell before and after each addition. Weight per unit volume concentrations were cal- culated from the weights of solvent and solute, solvent

density, and partial specific volume [7] of polyethylene

in 1-chloronaphthalene. For some representative

samples, the final concentration was checked by

evaporating 10 cm^ of the solution and weighing

the residue. In all cases, the concentration so ob- tained agreed with that calculated from the known

dilutions to within 1 percent.

The samples were filtered with a heated 40 cm-'

hypodermic syringe fitted with a "Swinney Adapter"

fiher holder (Millipore Corp., Bedford, Mass. 01730).

A ball joint sealed to the top of the syringe allowed the

rate of filtration to be controlled with nitrogen gas under pressure. The nitrogen pressure was adjusted to give a flow rate of approximately 1 drop per second. Faster flow rates resulted in less clean samples as determined by their erratic scattering at low angles.

Two Metricel type, Alpha-6 filter discs with a nominal

pore size of 0.4 (xm (Gelman Instrument Co., Ann

Arbor, Mich. 48106) were used for each filtration. These discs had been found to be resistant to 1- chloronaphthalene and could be used at temperatures

up to 150 °C without apparent damage. They were

rinsed with the material to be filtered before use, and were changed after each filtration. During filtration, the syringe was heated by placing

it in a glass tube wrapped with heating wire and

maintained at 135-140 °C. The needle of the syringe was inserted into the capillary neck of the lightscattering cell, and the filtration was carried out in a stagnant air box to minimize contamination by dust.

2.3. Scattering Measurements

Scattered intensities were measured at eleven

scattering angles ranging from 45° to 135°. Measurements on SRM 1475 were made at 25 concentrations,

in the range from 1.7X10-'' to 20.8x10--' g/cm'l

Measurements on each of the seven fractions listed in table 1 were- made at six concentrations. The concentrations chosen varied with the molecular weights of

the fractions, from a range of 1.8 X 10"- to 5.7 X 10 - g/cm-' for PE 15 to a range of 0.7 X 10 ' to 2.6 X 10~-' g/cm-^ for PE 600. Measurements were also made on pure solvent. The incident illumination in all cases was

the mercury green line of wavelength 5461 A, planepolarized with its electric vector perpendicular to the

scattering plane.

As mentioned previously, a solution of polystyrene in toluene was used as a working standard. The absolute

scattering of the working standard at 90° was first determined. As each polyethylene solution was

measured, the scattered intensity from the working

standard at 90° was also recorded. Thus, the quantity

actually obtained was the ratio of the scattering from

the solution (or solvent) at each angle to that of the

working standard at 90°.

3. Treatment of the Data

The use of light scattering to determine molecular

weight and size parameters of macromolecules in dilute solution is well established [8]. At sufficiently low

concentrations and small scattering angles, the ratio of solution concentration to scattered light intensity may

be expanded in a Taylor series in concentration and

in the sine of half the scattering angle. For planepolarized monochromatic light scattered through an

angle 6, the result for a solution of monodisperse

157
material may be expressed in the form [9J: Kc_ 1 h^l

Re~ 3M +2^2^+- • "

(j)

with:

K= {^7r-'n'l)^NA)idnldc)Hl-cos'ijjsm^e), (2)

Re=r'[nd,c)-l{d,0)]livlo), (3)

and

h= (47r/\)sin(0/2) = (47r/i/\o)sin(0/2)

,

(4)

where

c is solution concentration (weight per unit volume),

M is the molecular weight of the solute,

Rc is the radius of gyration of the solute,

A2 is the second virial coefficient of the solution, Xo is the wavelength in vacuo of the radiation, n is the index of refraction of the solvent at wavelength Xo, X=koln is the wavelength of the radiation in the solvent,

A'^^ is Avogadro's number,

dnidc, the so-called differential refractive index, is the

derivative (at constant temperature and pressure and

in the limit of zero concentration) of solution refractive index with respect to concentration,

6 is the angle between the incident and scattered wave

vectors,

1// is the angle between the electric vector of the

incident radiation and the plane containing the in- cident and scattered wave vectors,

lo is the intensity of the incident radiation,

I{d,c) is the scattered intensity at angle 6 for a solution

of concentration c, r is the distance from the scattering center to the point

at which the scattered intensity is observed, and

v=v{n,B) is the volume of solution from which the

scattered radiation is observed.

For the special cases «//=7r/2 and i//=0 (so-called

vertical and horizontal polarization), the last factor in eq (2) becomes unity and cos^0, respectively. (The

usually-quoted result for unpolarized incident radiation is obtained by averaging over all possible vcdues of

i//, in which case the factor becomes (1 -f cos^0)/2.)

For a solution of polydisperse material, it can be

shown [10, 11] that eq (1) still holds at sufficiently small

scattering angle and low concentration, provided M

is replaced by M^, the weight-average molecular

weight, Rl is replaced by its z-average, {Rc.)z [12], and

A2 is replaced by an "effective" value without simple

interpretation [11]. In order to use eqs (l)-(4) to relate observed scat- tering to molecular parameters, it is necessary to know the functional dependence of the scattering

volume, V, upon n and 6. For the geometry of our instru- ment, the scattering volume is inversely proportional

to the square of the index of refraction of the material

in the scattering cell [13,14]. A simple geometrical

argument suggests that for scattering angles not too

close to 0° or 180°, the scattering volume should vary as the cosecant of the scattering angle. (The validity of

the approximation was estabhshed for the present

work, in the course of checking the alignment of the

instrument, by measurements on fluorescein solutions.) Thus we can write

v{n,d) =Von~^csc6. (5)

Finally, the observed intensities must be corrected

for the effects of reflections at the entrances and exits of the scattering cells, as discussed by Kratohvil [15]. When light impinges perpendicularly upon an interface

between two regions with indices of refraction ni

and 7i2, the fraction / reflected is given by Fresnel's

formula: /= [(rai— n2)/(n] +^2)]^- In the light-scattering experiment, such interfaces occur at both the inside

and the outside surfaces of the walls of the scattering

cells. If we make the usual assumption that the differ- ence between the index of refraction of the solution

inside the scattering cell and the index of the glass in the cell walls is so small as to cause negligible re- flection, we are left with only the interfaces between

the cell walls and the air outside the cell to consider.

By counting up the various possible paths resulting

from multiple reflections of the incident and scattered

beams, we can readily show that for a circularly

cylindrical scattering cell, the observed intensity

rid,c) is related to the "true" intensity I{d,c) (i. e., that which would be observed in the absence of reflec- tions) by

/(M = (l-/)-'[(l+/')/'(M-2//'(7r-0,c)], (6)

where [(/ig— 1)/ (ng+ 1)]^, and Ug is the index of

refraction of the cell wall glass. Equation (6) is in agree- ment, to first order in /, with the approximate result obtained by Kratohvil [15] for this case. For the semioctagonal cell used to determine

absolute scattering by the working standard, only

the intensity of the beam scattered through an angle

0 = 77/2 and the intensity /o of the incident (unscattered) beam need be considered. For right-angle

scattering, the light paths for this cell are identical

with those for a circularly cylindrical cell, and the

special case / = /' obtained from eq (6) for d = Trl2 also applies to this cell. For the incident beam, ob- served after passage through the semioctagonal cell,

it can easily be shown that

/o=/ai+/)/(i-/). (7)

For the present work, the quantity Rni2,s=r^IslivIo),

where we denote by h the intensity of right-angle

scattering from the working standard, was first de- termined as described by Mclntyre [13]. The intensity

ratio Islh was measured with the use of a set of cali- brated filters, and was corrected for reflections as described above. For the semioctagonal cell employed,

the quantities r and vo were obtainable from the

158
instrument geometry, and the scattering volume

V was obtained from eq (5). For measurements made on the working standard

at 90° in the circularly cylindrical scattering cells, we can use the definition of Rni2,s and eq (5) to write

VoIolr^-IsnllRni2,s, (8)

where rig is the index of refraction of the working standard. With the use of eqs (2)-(6), the left-hand side of

eq (1) can be rewritten in the form

/i:c_ 47r''nfc(l-cos^i/;sin^ 6>) esc djdnldcy

Re A.0-^/l/?7r/2,s

^ {i{d, c)-ne,o))-

Thus, measurement of the scattering of the solution

relative to that of the working standard (the last factor on the right-hand side of eq (9)), together with

the value of dn/dc for the solution, yields Kc/ReEquation (1) may then be used to determine Mw,

{Ra)z, and A2 from the dependence of KcjRe upon

c and 6. In order to extract molecular parameters from ex- perimental values of Kc/Re, we employ the well-known

Zimm method [16]. If we plot Kc/Re as a function of

sin^{d/2)+ kc, where A: is a constant chosen for con- venience, we obtain an array of points through which

lines of constant concentration and lines of constant

angle can be drawn, as exemplified in figure 2. Extrapolation of each of the constant-concentration lines

to zero angle gives a set of points which constitute a

plot ofKc/Ro versus kc. According to eq (1), such a plot

intersects the Kc/Re-a.\is at l/M^, with a hmiting slope

of QAi/k. In the same way, extrapolation of each of the

constant-angle lines to zero concentration yields a

plot of hm c-^o [Kc/Re] versus sm^{dl2). Combining eqs

(1) and (4), we find: hm ^[Kc/Re] = + (16/3)7r2\-2</?2) ,smHd/2) ]

.

The intercept is therefore again l/Mw, and the hmiting

slope is a measure of {R(;)z. In the special case of a

linear random-coil chain one can estimate the meansquare distance, (L^) , between the ends of the chain

by using the relation [17] (D) =6 {R%), although this

sin»f kC

Figure 2. Typical Zimm plot (Kc/Ra versus sinH6l2) +kc) obtained

for linear polyethylene in 1-chloronaphthalene at 135 °C.

The concentration c is expressed in g/cm^; the arbitrary constant k was chosen to have a vaJue of 10 cm-^/g. The other symbols are explained in the text. The circles are experi- mental values; the squares are extrapolations to zero angle at constant concentration and to zero concentration at constant angle.

relation has been established only for chains with

Gaussian random-flight statistics.

4. Results

The results obtained for the hnear polyethylene

fractions and for SRM 1475 are summarized in table 1, together with the values of dnjdc used in calculating

Kc/Re. For SRM 1475 and the fractions with Mu, less than 200,000, measured values [7] of dn/dc were used.

For fractions with greater than 200,000, measured

values of dn/dc were not available, but measurements

on the lower-molecular-weight fractions appeared to suggest that by this point, dn/dc had reached a constant value of —0.188 ml/g independent of molecular

weight. This value of dn/dc was therefore used in calculating Kc/Re for the fractions of Mw above

200,000.

Values of Kc/Re for each fraction and for SRM 1475 were analyzed by the Zimm technique, as described

in the preceding section. In all cases, plots of Kc/Re

versus sin^ {6/2) + kc were found to be linear throughout the entire angular range. A typical plot, obtained

for SRM 1475, is shown in figure 2. For clarity, the plot

Table 1. Weight-average molecular weights My,, second virial coefficients A2, and rms end-to-end lengths {U)'l'^,for linear polyethylenes

in 1-chloronaphthalene at 135 °C.

The uncertainties shown are estimates of the standard deviations obtained from Unear least squares analyses of the corrected experimental scattering intensities, as described in the text.

Sample dn/dc, ml/g Mw X 10-3, g/n,oi A2 X 103, njoi . cm^jgi <Z,2>>/2XlO-3, A

PE 15 -0.193 19.1 ± 2.4 1.9 0.4 PE40 -.191 49.4± 2.0 1.6 .6 PE 60 -.190 82.2 ± 7.1 1.6 .6 PE 120 -.188 170 ±16 1.4 .7 PE 180 -.188 210 ±30 1.2 .9 PE 350 -.188 520 ±42 1.3 1.4 PE 600 -.188 688 ±67| 1.2 2.1 SRM 1475 -.193 52.0± 2.0

159
shows the data for only six of the 25 concentrations

actually employed. The lack of downward curvature in the plots suggests that the samples were adequately

cleaned [18]. The linear extrapolations necessary to obtain Mw,

{Rl)z, and A-z were carried out by unweighted linear

least-squares analyses. The results are given in table

1, together with estimates of the standard deviation in Ma- inferred from the least-squares analyses. The

values of the rms end-to-end length, (L^)''^, given in table 1 were obtained from the values found for {Ra)z by use of the approximate relation (L'^) = 6

(R'a) • as described in the preceding section. It is clear from the lack of smoothness in the variation of A2 and

(L-)^'2 with molecular weight that they are to be

regarded as no more than crude estimates. Estimates

of the standard deviations in {Rc)z and A-z from the

least-squares analyses were unrealistically low

(typically, about 5 per cent for A2 and 50-100 A for

(L-)''-), and are therefore not shown in the table. Values of (R'f; )z and At were not calculated for SRM 1475.

5. References

[1] DeLaCusta, M. O.. and BiUmeyer, F. W.. Jr., J. Polymer Sci. Al, 1721 (1963). [2] Chiang. R., J. Phys. Chem. 69, 1645 (1965). [3] Ross, G. S., and Frolen. L. J.. J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 2, 163-170 (Mar.-Apr. 1972). Paper X of this series.

[4] Mclntyre, D., and Doderer, G. C, J. Res. Nat. Bur. Stand.

(U.S.), 62, 153 (1959). [5] Wims. A., and Ross, G. S., unpublished work.

[6] Christensen. R. G., J. Res. Nat. Bur. Stand. (U.S.), 76A,

(Phys. and Chem.). No. 2, 149-150 (Mar.-Apr. 1972). Paper VI of this series. [71 Wagner. H. L., J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.), No. 2, 151-155 (Mar.-Apr. 1972). Paper VII

of this series. [8] See, for example, Kerker, M., The Scattering of Light (Ac- ademic Press. New York, 1969); Tanford, C, Physical

Chemistry of Macromolecules, John Wiley and Sons, New

York. 1961; Flory. P. J., Principles of Polymer Chemistry

(Cornell University Press, Ithaca, New York, 1953).

[9] The notation used here is essentially that used by Kerker

(op. cit., Ch. 8), but is written for plane-polarized incident

radiation rather than for unpolarized radiation. [10] Kerker. op. cit., Ch. 8. [11] Fujita, H.. Mathematical Theory of Sedimentation Analysis,

p. 268 {. (Academic Press, New York, 1962). [12] We define the 2-average of the square of the radius of gyration

of a polydisperse material as

where n,- is the number of molecules of the i-th component,

of molecular weight A/, and radius of gyration

[13] Mclntyre. D., J. Res. Nat. Bur. Stand. (U.S.), 68A, (Phys. and Chem.) 87 (1964). [14] Herman. J. J. and Levinson. S., J. Opt. Soc. Am. 41, 460

(1951). [15] Kratohvil, J. P., J. Colloid and Interface Science 21, 498

(1966). [16] Zimm, B. H., J. Chem. Phys. 16, 1099 (1948). [17] See. for example. Flory, P. J., od. cit. [18] Muus, L. T.. and Billmeyer, F. W.. Jr., J. Am. Chem. Soc. 79, 5079 (1957). (Paper 76A2-713)

160
The Characterization of Linear Polyethylene SRM 1475.

IX. Number Average Molecular Weight of Fractions by

Membrane Osmometry

James E. Brown and Peter H. Verdier

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

The number average molecular weights of a series of fractions of linear polyethylene have been

determined using a high speed membrane osmometer. The M,, values of the fractions, which were

prepared by an elution technique, were used in GPC calibration and subsequent characterization of

linear polyethylene SRM 1475. The molecular weights, measurement techniques, and the precision

of the measurements are presented.

Key words: Concentration dependence; linear polyethylene; membrane; number average molecular

weight; osmometer; osmotic pressure; virial coefficient.

1. Introduction

In the course of the characterization of the linear

polyethylene Standard Reference Material 1475

described in this series of papers [1],' the molecular

weight distribution was determined [2] by gel permeation chromatography. The gel permeation chromatograph was calibrated with linear polyethylene fractions

obtained [3] by a column elution technique. These

fractions were characterized for use in the calibration

procedure by determining their number- and weightaverage molecular weights. Determination of the

weight-average molecular weights from light-scattering

studies is described elsewhere [4]. In the present paper, we report the determination of the number-average

molecular weights, A/„, ranging from about 8,000 to about 350,000, from osmotic pressure measurements.

2. Experimental Procedure

2.1. Apparatus

Osmotic pressure measurements were made with

a Hewlett-Packard Mechrolab Membrane Osmometer,

Model 502^. This instrument, which has been de- scribed elsewhere [5], consists essentially of a photocell for detecting liquid flow across a semipermeable

membrane, monitored by the motion of a bubble in a

capillary tube, and a servomechanism for balancing

the osmotic pressure by varying the liquid level on

the solvent side of the membrane. It is characterized

' Figures in brackets indicate the literature references at the end of this paper.

^ Certain commercial equipment, instruments, or materials are identified in this paper

in order to adequately specify the experimental procedure. In no case does such identifi- cation imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available

for the purpose.

by rapid response time (of the order of a few minutes

with a suitable membrane), negligible solvent transfer across the membrane [6], and small sample volume

(about 0.3 ml).

2.2. Membranes

The semipermeable membranes employed were

gel cellophane membranes, type 450D, obtained from

Arro Laboratories, Inc. When received, they were

swollen in an isopropanol-water solution. The follow- ing procedure was used to condition them to 1-chloro- naphthalene, the solvent used in this work: 24 hours in 50 percent ethanol solution; rinsing with etbanol; 48

hours in ethanol; 24 hours in a 1 : 1 mixture of ethanol

and acetone; 24 hours in a 1:1 mixture of acetone

and toluene; rinsing with toluene; 24 hours in toluene;

rinsing with 1-chloronaphthalene; heating (with an

infrared lamp) in 1-chloronaphthalene under reduced

pressure for a minimum of 1 hour, to drive off dis- solved gases.

2.3. Procedure

Polyethylene solutions were made up by weight in

distilled Fisher reagent grade 1-chloronaphthalene,

in concentrations ranging from 0.3 to 12 g/1. Osmotic

pressure measurements were made by first placing

pure solvent in both sides of the osmometer and

recording the level on the solvent side, then flushing out and filling the sample side with one of the solu- tions and recording the new solvent level. Several

measurements were made for each solution. The

reference solvent height was checked between solu- tions by flushing and refilling the sample side with

pure solvent. The osmotic pressure for each solution

is then given directly as the hydrostatic pressure

161
difference between solvent and solution. AU measure- ments were made at a temperature of 130 °C.

3. Results and Discussion

In order to obtain values of Mn from the variation

of osmotic pressure with solution concentration, we

start with the familiar virial expansion, expressed in one of the two equivalent forms:

ttIc^RT

1 Mn

+ A2C + A3C^.

= (7r/c)o[l + r2C+r3C^+. . . ] , (1)

where tt is the osmotic pressure of a solution of concentration c (weight per unit volume), relative to that of pure solvent, R and T are the gas constant and

absolute temperature, respectively, the /4's and

r's are the virial coefficients, and the subscript zero denotes the limit of zero concentration.

According to eq (1), Mn is obtained directly from

the zero-concentration intercept of a plot of tt/c versus

c. Such plots are shown in figure 1 for three typical

fractions, PE 7, PE 120, and PE 350. Ahhough the

plot for PE 7, the lowest molecular-weight fraction, is essentially linear, the plots for the higher molecularweight fractions show distinct curvature, and extra- polation to zero concentration presents a problem. In

principle, the extrapolation may be performed by

fitting tt/c to a polynomial in c, thus determining some

of the virial coefficients higher than the second. In the present case, however, the precision of the data

and the concentration range spanned do not appear

to warrant the determination of more than two parameters. We therefore resort to the approximate rela- tionship r3 = i r|, which is frequently found to give

Figure 1. Plots of tt/c versus c, where n is osmotic pressure and

c 15 concentration, for solutions of three fractions of linear polyethylene, PE 7 (A), PE 120 (), and PE 350 (O), in 1-chloro- naphthalene.

The solid lines are the results of linear least-squares fits of ir/c versus c; the dashed lines are the results of linear least-squares fits of (tt/c) ''^ versus c.

satisfactory results for polymer solutions in good

solvents at sufficiently low concentrations [5, 7]. With

the aid of this relation, and neglecting terms beyond

the third virial coefficient, eq (1) may be rewritten in the form:

(tt/c) -(7r/c)i/2(l+ir2c), (2)

To the extent that the approximations implied in obtaining eq (2) are justified, a plot of (Tr/c)'/^ versus

c should yield a straight hne with a zero-concentration

intercept of (RTIMnV' and a slope of {RTIMnY'^Yill.

Figure 2 shows the data of figure 1 replotted as {ttIcY^^ versus c. The plot is clearly much more nearly Unear

than that of figure 1. We have therefore used a linear

least-squares analysis to fit (Tr/c)^/^ to a linear function

of concentration, according to eq (2). The dashed lines

in figure 1 are plots of eq (2), using the parameters

obtained from the least-squares analysis. It is clear

that for the higher molecular-weight fractions, use

of a simple linear plot would introduce significant errors into the limiting zero-concentration value of

tt/c, and therefore of MnThe results of the least-squares analyses are shown

in table 1. The standard deviations for the values of

Mn range from about 0.1 percent for PE 7 to 2-4

percent for the higher molecular-weight fractions. For the lower molecular-weight fractions, accuracy

is limited by the diffusion of solute through the membrane, as discussed by Staverman et al. [8, 9] and

by Tung [10]. From observation of the drift in hydrostatic pressure over periods of an hour or more, we

conclude that errors arising from this source are much

smaller than the reproducibility of the measurements,

even for the lowest molecular-weight fractions re- ported here. The accuracy of the Mn values for the

high molecular-weight fractions is limited primarily

by uncertainties arising from the use of the approximate eq (2) to fit the data. In the absence of information on the behavior of the higher virial coefficients,

it is very difficult to estimate the uncertainty introduced

by the use of eq (2). It is our feeling, however, that for

all the fractions, the errors in Mn from cdl sources are

unlikely to exceed 10 percent.

AO 10.0 1 1.0 12.0 CONC. g/l

Figure 2. The data of figure I, replotted as (tt/c)"'' versus c. The solid lines are the results of linear least-squares fits of the data in this form, and are equivalent to the dashed lines in figure 1. 162
Table 1. Values of number-average molecular weight, M„, and

second virial coefficient, A2, for solutions of polyethylene in 1- chloronaphthalene at 130 °C, inferred from measurements of

osmotic pressure, it, versus concentration, c, by linear least- squares fit of the data to the form (tt/c) "2= (RT/Mn) (1 +

MnAj c/2), where R and T are the gas constant per mole and the absolute temperature, respectively.

Number in parentheses following the Afn values are the standard deviations in M„ obtained from the linear least-squares analyses. The last column shows the number of solution concentrations at which each sample was measured.

Ai X lo^ Number of Sample M„ mol cm^/g^ concentrations PE 7 7,730(10) 15.78 4 PE 15 13,500(60) 11.48 5 PE 20 20,700(240) 11.16 4 PE 40 49,700(1,350) 10.29 5 PE 60 61,000(2,400) 9.00 5 PE 120 , 112,200(1,900) 8.74 5 PE 180 142,800(3,400) 8.44 5 PE 200 200,600(5,800) 8.44 4 PE 350 241,400(8,300) 7.05 4 PE 600 355,300(1,400) 6.46 5

Values of the second virial coefficient, A2, obtained

in the least-squares analyses are also shown in table

1. Because of the uncertainties introduced by the use

of eq (2) and by the precision of the experimental

data, they should be regarded only as rough estimates

of A2 for these systems.

4. References

[1] Hoeve, C. A. J., Wagner, H. L., and Verdier, P. H., J. Res.

Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.), No. 2, 137-140, (Mar.-Apr. 1972). Paper I of this series.

[2] Ross, G. S., and Frolen, L. J., J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.), No. 2, 163-170, (Mar.-Apr. 1972). Paper X of this series.

[3] Christensen, R. G., J. Res. Nat. Bur. Stand. (U.S.), 76A,

(Phys. and Chem.), No. 2, 149-150, (Mar.-Apr. 1972). Paper

VI of this series.

[4] Frolen, L. J., Ross, G. S., Wims, A. M., and Verdier, P. H.,

J. Res. Nat. Bur. Stand. (U.S.), 76A, (Phys. and Chem.)

No. 2, 156-160 (1972). Paper VIII of this series.

[5] See, for example. Coll, H. and Stross, F. H., Determination

of Molecular Weights by Equilibrium Osmotic-Pressure Measurements, in Characterization of Macromolecular

Structure (Publication 1573, National Academy of Sciences,

Washington, D.C., 1968).

[6] Steele, R. E., Walker, W. E., Burge, D. E., and Ehrmantraut,

H. C, Paper presented at the Pittsburgh Conference on

Analytical Chemistry and Applied Spectroscopy, March,

1963.

[7] Flory, P. J., Principles of Polymer Chemistry, p. 533ff. (Cornell University Press, 1953).

[8] Staverman, A. J., Rec. Trav. Chim. 70, 344 (1951).

[9] Staverman, A. J., Pals, D. T. F., and Kruissink, C. A., J. Polymer

Sci. 23,57 (1957).

[10] Tung, L. H., J. Polymer Sci. 32, 477 (1958).

(Paper 76A2-714)

The Characterization of Linear Polyethylene SRM 1475.

X. Gel Permeation Chromatography

Gaylon Ross and Lois Frolen

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(December 15, 1971)

The determination of the integral molecular weight distribution {MWD) of the linear polyethylene

sample (SRM 1475) by means of gel permeation chromatography (GPC) is described. Both the experi- mental and mathematical details of column calibration and sample analysis are included.

Key words: Gel permeation chromatography (GPC); linear polyethylene; molecular weight distribution (MWD); number average; weight average.

1. Introduction

Heretofore the molecular weight characterization

of polymer samples issued by the National Bureau

of Standards has been primarily limited to the reporting

of the number average molecular weight, Mn, and the

weight average molecular weight, Mw This paper

describes the determination of the integral molecular

weight distribution {MWD) of the linear polyethylene

sample (SRM 1475) using the technique of gel permeation chromatography (GPC).

Prior to 1964 the determination of the MWD of a polymer was a tedious, time-consuming task. The

first step was to fractionate the polymer using either

batch fractionation or elution chromatographic techniques, both of which take advantage of changes in solution properties as a function of molecular weight.

Then Mn and Mw measurements were made on each

fraction, and, by knowing the weight percent of each

fraction and by making certain simplifying assumptions

about the molecular weight distribution of each fraction, the MWD was constructed.

In 1964, J. C. Moore first published his work on

a process which he called gel permeation chromatography [1].' In GPC a dissolved sample of polymer

' Figures in brackets indicate the literature references at the end of this paper.

163
is carried into and through a packed column by an

appropriate solvent stream. The packing is such that the polymer is separated by molecular size, the larger

molecules eluting first. By using the appropriate

sensing devices, a function of the quantity of each

molecular species is graphically displayed on a stripchart recorder against the volume of solution emerging

from the column (elution volume).

Thus, providing the system has been calibrated, one can determine the MWD for a given polymer

sample in a very short time (usually less than one day). In the past, for each polymer system, the calibration

procedure has required the use of well-characterized

fractions of the polymer. This paper describes the

techniques for the use of such fractions to provide a cahbration curve, as well as the methods used to determine the MWD of our linear polyethylene whole

polymer (SRM 1475). This Standard Reference Material, with its certified MWD, may then be used

to calibrate other gel permeation chromatographs

without requiring the use of fractions.

2. Description of Apparatus

The particular gel permeation chromatographic

apparatus used was the Waters Model 200 (analytical

scale) GPC.--^ This instrument is designed to analyze

samples in the milligram range. The range of molecular

weights which can be analyzed is dependent upon

column selection. The pertinent features of the apparatus include, in order of flow: (1) a solvent reservoir,

(2) a solvent degasser and preheaters, and (3) a precision metering pump with an adjustable pumping rate. The solvent flow emerging from the pump is split, one portion going into a set of columns being used for sample injection, and the other portion flowing through

a second set of columns (reference set). Multi-port

valving is used to inject the dissolved sample into the

appropriate set of columns for analysis. The materials

emerging from the two sets of columns pass through the

two sides of a differential refractometer cell. The re- fractometer is stated by the manufacturer to be capable

of detecting a difference of 10"^ in refractive index.

The electronic output from the refractometer is recorded on a chart recorder, providing a continuous

record of the difference in refractive index between

the two streams. From the refractometer the samplesolvent mixture flows directly into a dump-syphon

(5 ml capacity). When the syphon empties a spike

is displayed on the recorder trace. In GPC language

each spike or pip is referred to as a "count," and the

sample injection is timed to coincide with a count,

labeled the zeroth one. Temperature controls are pro- vided for regulating the temperature throughout the

column, detector, and syphon system. The one modification made to the Model 200 GPC was to provide

a Teflon cover for the top of the syphon, to minimize

solvent evaporation.

^ Certain commercial materials and equipment are identified in this paper in order to specify adequately the experimental procedures. In no case does such indentification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply

that the material or equipment is necessarily the best available for the purpose.

^ Waters Associates, 61 Fountain Street, Framingham, Mass. 01701

In the Model 200 GPC, each column is a 4-foot long, thin (3/8 in diameter) stainless steel tube packed

with beads of a rigid, crossHnked polystyrene gel.

The gel was prepared, characterized, and packed in the columns by Waters Associates, Inc. Five such

columns were connected in series to form the column

set used for the analysis. The columns had nominal

exclusion hmits of 1 X 10^ 1 X 10^, 1 X 10^, 1 X \0\

and 1 X lO'^ angstroms. This particular nomenclature

[1] describes the minimal length in angstroms of a polystyrene molecule which will be excluded from

permeation into the pores of the particular bead

packing. The reference column set was a five column

set having similar nominal exclusion limits.

3. Column Broadening Effects

From the cursory information in the introduction one might assume that a sample of monodisperse

material injected into the GPC column would emerge

from the column without change in concentration,

producing a rectangular area as a recorder trace,

having a base length equal to the volume of the

sample injected. However, as is well known [2], in any chromatographic procedure the elution profile

is broadened due to longitudinal diffusion in the

column, producing, in the case of a single component,

a beU-shaped curve. Therefore, in the case of a polydisperse polymer the height of the chromatogram at any point is due to the cumulative effect of the pres- ence of many neighboring molecular weights. The

amount of broadening observed is a function of the

molecular weight, becoming larger as the molecular

weight increases. The observed width is due to: (1) the actual MWD, (2) the spreading which occurs

during flow through connecting tubing, (3) the effect due to spreading in the interstitial volume of the

column packing, (4) the dilfusional spreading within

the pores, and (5) the effects of any adsorption within

the system. The combined result may be not only

spreading or broadening, but also skewing of the

chromatogram.

Attempts to obtain analytical and numerical corrections for column broadening have been made by Tung

and others [3-5] , and the general state-of-the-art of GPC correction of broadening and skewing has been

discussed by Hamielec [6, 7]. Fortunately, these

effects tend to cancel out when the molecular weight

distribution of a relatively broad material is obtained on a GPC column calibrated with much narrower

fractions of the same material. Since the work reported

here meets this condition, throughout this paper we

assume that column broadening effects can be

neglected. The vahdity of this assumption is discussed

in section 9.

4. The Molecular Weight Distribution

In this section we describe the method used to calibrate the GPC. As stated in the preceding section, we assume that column broadening effects are not

164
significant. In the notation of Frank [8J, the caUbration curve and the elution chromatogram are respectively:

m = m{v)

Z{m)=N{v).

(1)

(2)

In (1) the molecular weight, m, is a function of the

elution volume, v. Z{m) is the number of molecules in the particular sample having molecular weights which

are greater than m; conversely N{v) is the number

of molecules in the sample which elute at volumes

which are less than or equal to v. We define z{m)dm

as the number of molecules having molecular weights

between m and m + dm, such that: — z{m) — dZ{m)ldm= (dN/dv) (dvldm) = illm')(dNldv), (3)

where m' is the slope of the calibration curve, m(v)

versus v. For this development we assume that the height,

h, of the chromatogram from the base line results

solely from the presence of molecules all having the same molecular weight, m, for each corresponding

elution volume, v. In particular it is assumed that the detector responds linearly to the mass of the

sample. Thus:

mdN{v)ldv = kh{v)

Combining (3) with (4), we obtain:

z(m) = — kh/mm'

(4)

(5)

Here k is an unknown instrumental scaling factor. The number-, weight-, and z-average molecular

weights Mn, Mw, and Mz are given by:

Mn

j

mz{m)dm

J" {hjm')dm

j

z{m)dm j {hi mm') dm

/

h{v)dv

/

(6)

\^h{v)lm{v)^dv

j

m'^z{m)dm j (mhlm')dm

j

mz(m)dm

J

{h/m')dm

m{v)h{v)dv

(7)

h{v)dv

m'-{v)hiv)dv

j

m{v)h{v

(8)

}dv

The integral MWD is obtained in the following

fashion. We define a function w{m) by

w{m) = kh (v) (9)

Then the cumulative weight percent, i.e., the weight

percent of polymer of molecular weight less than M,

is given by

100 j w{m)dm

I

^ w{m)dm.

The integral MWD is usually given as cumulative

weight percent versus log molecular weight.

5. The Calibration Curve

In this section we will presuppose that the column

selection has been made such that log m is a nearly

linear function of v in the molecular weight range of

interest. Further, we will assume that we already have

a calibration curve for polystyrene using the same

column set. The development of the calibration curve for any

particular polymer usually starts from the preparation

and characterization of narrow molecular weight

fractions. The molecular weight range covered by

the fractions should at least encompass the expected

distribution of any samples to be subsequently analyzed. By classical characterization methods such as osmometry and light scattering, the average molecular

weights M„ and Mw are determined for each fraction. One of two general methods is then used in pro- ducing a reliable calibration. In the first method we

define Mo as being that molecular weight species

which elutes at the peak of a chromatogram, and we

assume that a reasonable value of A/o can be assigned

by knowing both Mn and Mw In the second method we assume that, for each fraction, we know the general form of the calibration curve, eq (1).

A. Method One

In this development we assume that the peak

molecular weight. Mo, can be approximated by:

(M„ + M,,)/2 = Mo. (11)

This assumption would appear reasonable to a

first approximation providing that the polydispersity,

Mxv/Mn, is sufficiently close to unity, and that the

chromatogram is symmetrical and single-peaked.

From the individual chromatograms of the frac- tions we can determine the elution volume fo cor- responding to Mo.

165
A prelimirikry calibration curve is constructed using

the pairs of Ma and vo values, and a least-squares

fitting routine is employed to determine whether the

points can be best described by a first, a second,

or a third degree polynomial. Comparison of this preliminary calibration curve vyrith the polystyrene

calibration curve obtained with the same column set, should show qualitative similarity, i.e., the inflection points and general curvature at all elution volumes

should be similar. Next equations (6) and (7), in conjunction with the prehminary calibration curve,

are used to calculate M„'s and A/u,'s from the GPC

chromatograms of the individual fractions, and from

the preliminary calibration curve we determine the

corresponding elution volumes. We now use the values

of Mn and My, (classically determined) together with

the elution volumes (GPC determined) and plot these

points on the preliminary calibration curve. This type

of plot should reveal that most of the calculated points

fall on or near the calibration curve. However, if all the

number-average molecular weight points lie on one

side of the curve and all of the weight-average molecular weight points lie on the other side, this is usually an indication of extreme broadening and skewness of

the chromatograms resulting from poor column selection or poorly chosen operational parameters.

Assuming that this latter possibility did not arise, we now refit the data, using only the classically de- termined MnS and Mm;'s and their calculated elution

volumes (GPC), and at this point we consider that the

best fit has been obtained.

B. The Second Calibration Method

In this method we assume that for our narrow dis- tribution fractions (MwlM„ from 1.1 to 1.7) the portion

of the caHbration curve for each fraction will be

adequately represented by the relationship:

m{v) = exp (a — bv). (12)

Of course we do not assume that the parameters a and b are the same for all fractions. Again following the

development by Frank [8], we incorporate eq (12) into eqs (6) and (7). By using eq (12) in the denominator

of (6) and in the numerator of (7), we obtain two ex- pressions for the parameter a:

a„=lnM„ + ln e'"'h{v)dv-ln \ h{v)dv (13) Jo Jo and

at„ = lnM,„+ln h{v)dv-\n \ e-'>^h{v)dv. (14)

Jo Jo

After equating a„ with Ow, simultaneous solution

of eqs (13) and (14) yields unique values for the pa- rameters a and b. If this were done for each fraction, a plot using eq (12) over the particular molecular

weight range involved should result in a collection

of straight lines which define the calibration curve

exactly.

Both the first and second methods herein described

have the disadvantage that Mn and Mw have to be

known for each fraction; further, an error in either

Mn or Mw seriously affects the calculation. A modification of the second method allows calibrational in- formation to be obtained when only M„ or only Mw

is known for a fraction, and, in addition, may provide

insight into the question of whether or not error

exists in Mn or Mw as determined classically.

Rather than solving eqs (13) and (14) simultaneously

to obtain a unique pair of values for the parameters a and b, we can, by treating each equation separately,

obtain the functional dependence of a„ and aw on b over the range of values for which b may be expected

to lie. Either equation (13) or equation (14) imphes

a functional relationship between a and 6, i.e., a= a{b). The calibration curve (or rather, our estimate

of it based on one determination of Mn or Mw) is then one of the family of curves.

In m{v)^a{b)-bv. (15)

and must therefore be tangent to the envelope of the

family at some point. The envelope is easily obtained,

in the usual way, as the simultaneous solution of eq

(15) and the result of partial differentiation of eq (15)

with respect to b at constant m and v, i.e., v^daldb. (16)

For each point (v, m{v)) on the calibration curve,

the abscissa v is given by eq (16) and the ordinate

m{v) by eq (15). A calibration curve may then be esti- mated from measurements of M„ and/or Mw on a

series of fractions by plotting the envelope obtained

for each measurement and requiring that the calibra- tion curve be tangent or nearly so to each envelope

at some point. Since this technique uses each ex- perimental value of Mn and Mw independently, it can be useful in identifying individual molecular

weight measurements which may be in error.

6. Experimental Procedures

AH samples were dissolved in nitrogen-saturated,

1,2,4-trichlorobenzene (TCB) (filtered technical

grade) at 135 °C using magnetic stirring. They were

then filtered under nitrogen pressure through re- generated cellulose filters having an average pore

size of 0.45 microns. The GPC column oven was

operated at approximately 135 °C, and nitrogensaturated TCB was used. Five hundredths of one

percent by weight of 2,6-c?i-terf.-butyl-4-methylphenol was added to the TCB as an antioxidant.

We assumed that the calibration curve for polyethylene would be similar to that for polystyrene and

hence selected the column combinations used herein

because they produced a nearly linear polystyrene

calibration curve. The degree of replication which can be achieved in successive chromatograms resulting from a series of

166
identical experiments appears to be almost totally

dependent upon base-line stability. Of the various

factors affecting this stability, we found that the

constancy of both fluid flow and temperature was the

most important. We were fortunate in that our GPC

was in an area in which both the air temperature and

air circulation were well controlled, and this, coupled

with stable line voltages, gave good temperature

stability throughout the system. We found that the

constancy of solvent flow could be improved upon by

keeping both of the column throttle valves in their

open position, regulating solvent flow solely by adjustment of the pumping stroke. Under these conditions a point by point comparison of the heights of the

chromatograms resulting from supposedly identical

experiments showed maximum deviations of approximately ± 1 percent, and a comparison of the areas

of the chromatograms showed a maximum deviation of

less than ± 2 percent. Uncertainties of this magnitude

could be explained almost completely by the ob- served base-line instability.

A change in operating parameters may result in a change of the chromatogram obtained with gel permeation chromatography. Ideally, perhaps, one would

like to use samples of very small size and of vanishing

concentration together with very small flow rates, but, practically, one compromises by using samples

whose size and concentration are such that good

detector response is obtained, and a flow rate such

that the experiment can be run in a reasonable amount

of time. A large number of experiments were run, varying each of the operating parameters in turn. We found that between the extremes of 0.2 and 2.0 ml/minute no discernible change occurred in the

chromatograms resulting from replicate experiments.

We therefore chose to use 0.5 ml/ minute as the flow

rate which would be used. With the whole polymer

(SRM 1475) a change in the concentration from 0.02

to 0.2 weight percent caused no observable change

in the calculated weight versus elution volume dis- tribution. We therefore chose to use a 0.1 weight per- cent concentration for the whole polymer. The

acceptable range of concentration varied for each

fraction, but we found that the use of concentrations

such that the resulting viscosities were similar to that of the 0.1 weight percent of the whole polymer was

a good workable rule. The detector response was such

that for a 0.1 weight percent concentration of whole

polymer, an injection time of two minutes was required

to produce a 1/2 to 2/3 full scale deflection of the

recorder pen at the peak elution, and this injection

time was used throughout.

For the final calibration, three independently pre- pared concentrations of each calibrating matericd were used. For each material, the three concentrations were such as to cause peak heights of nearly full scale,

one-half of full scale, or one-quarter of full scale. When any two chromatograms within each triplicate set were compared in respect to height ratio at each

elution volume, or in respect to area ratios, these were,

within the precision of the experiment, identical to the ratios of the known concentrations. Therefore,

within the limits of our sensitivity, we believe that

there was no dnjdc (refractive index change in respect

to concentration) dependence with molecular weight.

This observation is not in conflict with paper VII of

this series [9], wherein, when greater sensitivity and

precision was used, there indeed was shown to be a dn/dc dependence with molecular weight.

The integration of the chromatograms was performed

numerically using Simpson's one-third rule, using an

elution increment of 0.2 count.

7. Determination of the Calibration Curve

We used both polyethylene fractions and linear

hydrocarbon samples in the determination of the cali- bration curve. Zone-refined samples of n-C36H74 and

n-C94Hi9o were used. The values assigned to the hydrocarbon samples were the calculated molecular weights,

and these calculated molecular weights were assigned

to the peak elution volumes. Table 1 lists these materials together with the Mn and Mw values associated

with each. These were determined by membrane os- mometry and light scattering experiments. For details of the fractionation and of the determination of the

molecular weights see papers VI, VIII and IX of this series [10-12]. Included also in table 1 are the GPC

determined moments using the final calibration curve. The calibration curve used in this work was deter- mined by the use of method 1. For the preliminary

determination of the calibration curve the chromatograms of the hydrocarbon samples and those of the

fractions for which both yi^„ and Mw had been deter- mined were used. As can be seen from table 1, the

diff"erences between the classical and GPC values of

Mw for PE 350 and PE 60 do not appear consistent

with those for the other fractions. The same discrepancies are shown when method 2 is employed (see

fig. 2), and as a result we did not use the Mu> values for these two fractions in the final determination of the

calibration curve. In addition the Mw values for PE 200

and PE 20 were not available and only Mn values were

employed. A plot of the final calibration curve is shown

in figure 1, together with the points corresponding to Mo, Mn, and Mw for the fractions and the hydrocarbons.

The best least squares fit, using Method 1, was

found to be a quadratic of the form (log M=a+ bv

+ cv'^), having the following coefficients and standard

deviations:

a= 7.4 ±1.2

6= 0.106 ±0.07

c = - 0.0051 ±0.0009

The standard deviation of the molecular weight was ± 0.047 log M units. The volume v is in units of count. Method 2 was also investigated. Figure 2 shows the

calibration curve as derived by method 1, together with

the envelope plots for each material used in the

calibration. Figure 3 shows the same calibration curve, superimposed on which are the individual line seg- ments cedculated for the individual calibrating materials. The unusual behavior associated with the two

167
Table 1. Classic versus gel permeation chromatographic analysis of polyethylene fractions used in calibration procedure

bample M,i X 10 ^ Mw X 10 ^ Mu-IM„

GPC analysis'^ Mn X 10-^ M„. X 10"^

rboUU 35.5 68.8 1 A

1.9 39 67 1.7 PE350 24.1 52.0 2.2 26 40 1.5 r n,zOU 20.1 21 32 1.5 PE180 14.3 21.0 1.5 14.0 21 1.5 PE120 11.2 17.0 1.5 12.2 16 1.3 PE60 6.1 8.22 1.3 6 6.9 1.2 PE40 4.97 4.94 1.0 4.6 5.2 1.1 PE20 2.07 2.2 2.5 1.1 PE15 1.35 1.91 1.4 1.4 1.6 1.1 C94 Calc M= 0.132x 10-* (1.00) 0.146 0.154 1.05 C36 Calc M= 0.0506x 10^ (1.00) .047 .049 1.04

^ = results from membrane osmometry.

'' = results from light scattering.

results of using the samples to calibrate the GPC, then analyzing the samples using

calibration curve. Not employed in construction of calibration curve. See text.

calculated

hydrocarbon samples results from using their cal- culated molecular weight to describe both M„ and

M„, in eqs (13) and (14), and the slopes of these hues

probably reflect the column dispersion. While the

calibration curve was determined solely by method 1,

it is obvious from figures 2 and 3 that method 2 would

have produced a nearly identical curve.

It was interesting to note that the polyethylene cahbration curve remained unchanged for approximately

a year of continuous running. Immediately after start- ing up there would be an apparent shift of caHbration,

but the columns would return to their previous state

after approximately 48 hours of running time. During

this year the solvent and the general operational parameters were not changed.

8. Analysis of SRM 1475

The data in table 2 result from the analysis of twelve

samples of SRM 1475, Hsted as samples 1 through 12. Each of the twelve samples was prepared from 25-75

pellets as described in section 6. The mean values and

sample standard deviations of the mean for M„, Mw,

ELUTION COUNT

Figure 1. The calibration curve derived by use of Method One, showing all calibration points.

^PE60 PD90' PEIJO X.PE40

30 35 ELLTTION COUNT

Figure 2. The calibration curve derived by use of Method One

(dotted line) together with the calculated envelopes for each

calibration sample.

ELUTION COUNT Figure 3. The calibration curve derived by use of Method One

(dotted line) together with the calculated line segments for each

calibration sample for which both M„ and My, are known. 168
and Mz are those shown on the certificate for SRM

1475.

Table 2. Gel permeation chromatographic analysis of SRM 1475

Sample number M„ X 10--" M„ X 10-"

* M, X 10-^

1 1.833 5.503 1.518

2 1.789 5.309 1.490

3 1.681 5.013 1.291 4 1.726 5.247 1.369

5 1.921 5.451 1.351 5 2.019 5.149 1.200

7 2'068 5.400 1.243 8 1.820 5.065 1.220

9 1.883 5.538 1.534

10 1.789 5.310 1.489

11 1.657 5.032 1.277

12 1.789 5.669 1.583 Mean 1.831 5.307 1.380 Estimated standard deviation 0.125 0.214 0.127 Estimated standard deviation

of mean .036 .062 .037

Samples 1 through 4 were also subjected to a modified treatment, in order to check the effects of the

handling procedure. After the solutions had been made

up as described in section 6, and aliquots taken for the original chromatograms, the remaining portions of

the solutions were allowed to cool to room temperature, precipitating the polymer, reheated and stirred as before to redissolve the material, and fresh aliquots rerun on the GPC column. The results obtained for the original and rerun materials are shown in table 3. If degradation or other modification of the sample

occurred in the handling procedure, one might expect

to find trends in the results for the original and rerun

materials. No such trends are apparent, and the dif- ferences between original and rerun values are not inconsistent with the sample-to-sample spreads implied by the sample standard deviations given in table

2. We conclude that the effects of our sample handling procedure are not observable.

Table 3. Effect of rerunning SRM 1475 samples

Sample Number Mn X 10-" Mu< X 10-" M, X 10-^

1 1.833 5.503 1.518

1.852 5.374 1.363

2 1.789 5.309 1.490

2, rerun 1.741 5.296 1.469

3 1.681 5.013 1.291

3, rerun 1.674 5.196 1.410

4 1.726 5.247 1.369

1.745 5.276 1.395

The integral MWD was obtained by summing the

chromatograms for samples 1 through 12. In view of

the lack of trend in the reruns of samples 1 through 4

described above, the rerun chromatograms were included in the final sums. The resulting molecular

weight distribution is given in table 4 and on the certificate for SRM 1475. Since this distribution is based

on an "average" chromatogram, the values of Mn,

Mw, and Mz obtained from it wiU not necessarily

agree precisely with those quoted in table 2, which

are obtained by averaging molecular weights from

the individual chromatograms. From the MWD, we

obtain values of 17,900, 52,900, and 139,000 respectively for Mn, Mw, and Mz. These may be compared

with the values 18,310, 53,070, and 138,000, respectively, shown in table 2.

Table 4. Cumulative molecular weight distribution of SRM (1475) by gel permeation chromatography

log M Wt. log M log M log M Wt.

percent percent percent

2.800 0.0 4.014 15.2 5.065 90.7

2.865 .005 4.070 18.1 5.113 92.2

2.929 .020 4.126 21.5 5.161 93.7 2.992 .052 4.182 25.2 5.209 94.8

3.056 .105 4.237 29.3 5.256 95.8

3.119 .185 4.292 33.7 5.303 96.6

3.181 .343 4.346 38.5 5.349 97.3 3.243 .475 4.400 43.4 5.395 97.9 3.305 .706 4.454 48.5 5.440 98.4 3.366 .999 4.507 53.5 5.485 98.7

3.427 1.38 4.560 58.3 5.530 99.1 3.488 1.88 4.612 62.9 5.574 99.3 3.548 2.51 4.664 67.3 5.618 99.5 3.607 3.30 4.715 71.4 5.662 99.7 3.667 4.28 4.776 75.1 5.705 99.8

3.725 5.46 4.817 78.5 5.789 99.9 3.784 6.87 4.868 81.6 5.87 100.0 3.842 8.56 4.918 84.4 3.900 10.50 4.967 86.7 3.957 12.7 5.016 88.9

9. Discussion and Conclusion

For both calibration and analysis, no corrections

have been applied to take into account the effects of

column broadening in the GPC system. While such

effects are obviously present, it would appear that in

this particular case, they do not significantly affect the

validity of the analysis. Evidence to this effect may be

found in the general agreement between values of

MwIMn obtained from the chromatograms of the

individual fractions and the classically determined

ratios. Since SRM 1475 is substantially broader than

the individual fractions, we conclude that column

broadening effects are not likely to introduce serious

errors into the molecular weight distribution obtained

for SRM 1475. The internal consistency of the experiment was

checked by comparing chromatograms obtained from

sixteen fractions of a sample of SRM 1475 with the

chromatogram of the whole polymer. The polymer was

fractionated into sixteen fractions using a conventional

column elution technique [10]. The fractions were

analyzed using GPC, and the areas under the result- 169
ing chromatograms were normalized to the weight of

the respective fraction. These normahzed curves were summed. When this reconstructed "whole

polymer" was analyzed, the number- and weightaverage molecular weights were calculated to be 17,400

and 53,300 respectively, whereas the best GPC

values for the whole polymer were calculated as 18,300 and 53,100.

The results given herein reflect primarily on the

precision of the measurement. A statement as to the

absolute accuracy is impossible at this time; however,

it is our opinion that the errors reflected in the uncertainty of the GPC analysis are largely those asso- ciated with the light scattering and membrane

osmometry analyses of the calibrating samples.

Individual credit has not been given to some of the

specific experimental and analytical details used

herein. In many instances original credit is not known,

but a great many of these details are to be found in references [8, 13, and 14].

10. References

[1] Moore, J. C, J. Polymer Sci. A 2 , 835 (1964).

[2] Determan, H., Gel Chromatography, Chap. 3 (SpringerVerlag, New York, N.Y. 1968).

[3] Tung, L. H., J. Appl. Polymer Sci. 10,375 (1966). [4] Tung, L. H., Moore, J. C. and Knight, G. W., J. Appl. Polymer

Sci. 10, 1261 (1966). [5] Hess, M., and Kratz, R., J. Polymer Sci. A 2 , 4 , 731 (1966). [6] Hamielec, A., Proceedings of the 6th International GPC

Seminar, Miami Beach, Fla. (1968).

[71 Duerksen, J. H., and Hamielec, A. C. J. Polymer Sci. C 21,83

(1968). [8] Frank, F. O., Ward, I. M., and Williams, T., Proceedings of the 5lh International GPC Seminar, London (1968). [9] Wagner, H. L., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and

Chem.), No. 2, 151-155 (Mar.-Apr. 1972). Paper VII of this scncs

[10] Christeiisen, R. G., J. Res. Nat. Bur. Stand. (U.S.), 76A,

(Phys. and Chem.), No. 2, 149-150 (Mar.-Apr. 1972). Paper

VI of this series. [11] Frolen, L. J., Ross, G. S., Wims, A., and Verdier, P. H., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 2, 156-160 (Mar.-Apr. 1972). Paper VIH of this series. [12] Brown, J. E. and Verdier, P. H., J. Res. Nat. Bur. Stand.

(U.S.), 76A (Phys. and Chem.), No. 2, 161-163 (Mar.-

Apr. 1972). Paper IX of this series. [13] Moore, J. C, Proceedings of the 4th International GPC

Seminar, Miami Beach, Fla. (1967). [14] Yau, W. W., Suchan, H. L., Malone, C. P., and Fleming, S. W.,

Proceedings of the 5th International GPC Seminar, London

(1968). (Paper 76A2-715)

170
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS SP 260-42

2. Gov't Accession No.3. Recipient's Accession No. ,

4. TITLE AND SUBTITLE

Standard Reference Materials:

The Characterization of Linear Polyethylene SRM 1475

5. Publication Date September 1972

6. Performing Organization Code

7. AUTHOR(S)

Herman L. Wagner and Peter H. Verdier - Editors

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as 9

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The National Bureau of Standards has issued a linear polyethylene standard reference

material, SRM 1475. This material is certified for weight average molecular weight

(M^) , number average molecular weight 0^)) Z average molecular weight (M^) , molecular

weight distribution, limiting viscosity numbers in several solvents, melt flow rate,

and density. The experimental details of the determination and certification of these

properties are given in these collected papers previously published in the Journal of

Research of the National Bureau of Standards.

Key words, continued:

index; standard reference material; viscosity; weight average molecular weight;

Z average molecular weight.

17, KEY WORDS (Alphabetical order, separated by semicolons) Density; differential refractive index; gel

permeation chromatography (GPC) ; light scattering; linear polyethylene; melt flow rate;

molecular weight distribution; number average molecular weight; osmometry; refractive

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