A11103 Qfisms

CO Q« NBS SPECIAL PUBLICATION 260-61

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

tandard Reference Materials:

THE CHARACTERIZATION

OF LINEAR POLYETHYLENE

SRM's 1482, 1483, AND 1484

X.2
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The

Bureau's overall goal is to strengthen and advance the Nation's science and technology and

facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory,

and the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

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and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

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THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal Agencies in the selection,

acquisition, application, and use of computer technology to improve effectiveness and

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The National Bureau of Standards was reorganized, effective April 9, 1978.
Standard Reference Materials:

THE CHARACTERIZATION

OF LINEAR POLYETHYLENE

SRM's 1482, 1483, AND 1484

Edited by:

Peter H. Verdier

Herman L. Wagner

Center for Materials Science

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

Reprinted from the National Bureau of Standards

Journal of Research, Vol. 83, No. 2, March/ April 1978. (The original page numbers of each paper have been

retained for citation purposes.)

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued December 1978
Library of Congress Catalog Card Number 78-600148

National Bureau of Standards Special Publication 260-61

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-61, 41 pages (Dec. 1978)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1978

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-02006-1 Price $1.70

(Add 25 percent additional for other than U.S. mailing).
PREFACE

Standard Reference Materials (SRM's) as defined by the

National Bureau of Standards are " wel 1- cha ra c t e r 1 z ed materials, produced In quantity, that calibrate a measurement

system to assure compatibility of measurement In the nation."

SRM's are widely used as primary standards In many diverse

fields In science, Industry, and technology, both within the

United States and throughout the world. In many Industries

traceablllty of their quality control process to the national

measurement system Is carried out through the mechanism and

use of SRM's. For many of the nation's scientists and technologists It Is therefore of more than passing Interest to

know the details of the measurements made at NBS In arriving

at the certified values of the SRM's produced. An NBS series

of papers, of which this publication Is a member, called the

NBS Special Publication - 260 Series Is reserved for this

purpose.

This 260 Series Is dedicated to the dissemination of

Information on all phases of the preparation, measurement,

and certification of NBS-SRM's. In general, much more detail will be found In these papers than Is generally allowed,

or desirable. In scientific journal articles." This enables

the user to assess the validity and accuracy of the measurement processes employed, to judge the statistical analysis,

and to learn details of techniques and methods utilized for

work entailing the greatest care and accuracy. It Is also

hoped that these papers will provide sufficient additional

Information not found on the certificate so that new applications In diverse fields not foreseen at the time the SRM

was originally Issued will be sought and found.

Inquiries concerning the technical content of this

paper should be directed to the author(s). Other questions

concerned with the availability, delivery, price, and so

forth will receive prompt attention from:

Office of Standard Reference Materials

National Bureau of Standards

Washington, D.C. 20234

J. Paul Call, Chief

Office of Standard Preference Material
OTHER NBS PUBLICATIONS IN THIS SERIES

Catalog of NBS Standard Reference Materials

(1975-76 edition), R. W. Seward, ed., NBS

Spec. Publ. 260 (June 1975). $1.50* SN003-O03-

01445-1

Michaelis, R. E., and Wyman, L. L., Standard

Reference Materials: Preparation of White Cast

Iron Spectrochemical Standards, NBS Misc.

Publ. 260-1 (June 1964). COM74-1 1061**

Michaelis, R. E., Wyman, L. L., and Flitsch, R.,

Standard Reference Materials: Preparation of

NBS Copper-Base Spectrochemical Standards,

NBS Misc. Publ. 260-2 (October 1964). COM74-

11063**

Michaelis, R. E., Yakowitz, H., and Moore, G. A.,

Standard Reference Materials: Metallographic

Characterization of an NBS Spectrometric LowAlloy Steel Standard, NBS Misc. Publ. 260-3

(October 1964). COM74-1 1060**

Hague, J. L., Mears, T. W., and Michaelis, R. E.,

Standard Reference Materials: Sources of

Information, NBS Misc. Publ. 260-4 (February

1965). COM74-11059

Alvarez, R., and Flitsch, R., Standard Reference

Materials: Accuracy of Solution X-Ray Spectrometric Analysis of Copper-Base Alloys, NBS

Misc. Publ. 260-5 (March 1965). PB168068**

Shultz, J. I., Standard Reference Materials:

Methods for the Chemical Analysis of White

Cast Iron Standards, NBS Misc. Publ. 260-6

(July 1975). COM74-11068**

Bell, R. K., Standard Reference Materials:

Methods for the Chemical Analysis of NBS

Copper-Base Spectrochemical Standards, NBS

Misc. Publ. 260-7 (October 1965). COM74-

11067**

Richmond, M. S., Standard Reference Materials:

Analysis of Uranium Concentrates at the

National Bureau of Standards, NBS Misc. Publ.

260-8 (December 1965). COM74-1 1066**

Anspach, S. C, Cavallo, L. M., Garfinkel, S. B.,

Hutchinson, J. M. R., and Smith, C. N., Standard Reference Materials: Half Lives of Materials

Used in the Preparation of Standard Reference

Materials of Nineteen Radioactive Nuclides

Issued by the National Bureau of Standards,

NBS Misc. Publ. 260-9 (November 1965).

COM74-1 1065**

Yakowitz, H., Vieth, D. L., Heinrich, K. F. J., and

MichaeUs, R. E., Standard Reference Materials:

Homogeneity Characterization on NBS Spectrometric Standards II: Cartridge Brass and LowAlloy Steel, NBS Misc. Publ. 260-10 (December

1965). COM74-11064**

Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of Standard

Lead-Silica Glass, NBS Misc. Publ. 260-11

(November 1966). NBS Misc. Publ. 260-11**

Yakowitz, H., Vieth, D. L., and Michaelis, R. E.,

Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards III: White Cast Iron and Stainless Steel

Powder Compact, NBS Misc. Publ. 260-12

(September 1966). NBS Misc. Publ. 260-12**

Spijkerman, J. I., Snediker, D. K., Ruegg, F. C,

and DeVoe, J. R., Standard Reference Materials: Mossbauer Spectroscopy Standard for the

Chemical Shift of Iron Compounds, NBS Misc.

Publ. 260-13 (July 1967). NBS Misc. Publ.

260-13**

Menis, O., and Sterling, J. T., Standard Reference

Materials: Determination of Oxygen in Ferrous

Materials - SRM 1090, 1091, and 1092, NBS

Misc. Publ. 260-14 (September 1966). NBS Misc.

Publ. 260-14**

Passaglia, E., and Shouse, P. J., Standard Refer- ence Materials: Recommended Method of Use

of Standard Light-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for

Colorfastness to Light, NBS Misc. Publ. 260-15

(June 1967). (Replaced by NBS Spec. Publ.

260-41.)

Yakowitz, H., Michaelis, R. E., and Vieth, D. L.,

Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards IV: Preparation and Microprobe Characterization of W-20% MO Alloy Fabricated by

Powder Metallurgical Methods, NBS Spec.

Publ. 260-16 (January 1969). COM74-1 1062**

Catanzaro, E. J., Champion, C. E., Gamer, E. L.,

Marinenko, G., Sappenfield, K. M.,and Shields,

W. R., Standard Reference Materials: Boric

Acid; Isotopic and Assay Standard Reference

Materials, NBS Spec. Publ. 260-17 (February

1970). Out of Print

IV
Geller, S. B., Mantek, P. A., and Cleveland, N.

G., Standard Reference Materials: Calibra

tion of NBS Secondary Standard Magnetic Tape

(Computer Amplitude Reference) Using the

Reference Tape Amplitude Measurement

"Process A," NBS Spec. Publ. 260-18 (November

1969). (See NBS Spec. Publ. 260-29.)

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold (Certification of Standard Reference Material 745), NBS

Spec. Publ. 260-19 (January 1970). PB190071**

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressures of Cadmium and

Silver, NBS Spec. Publ. 260-21 (January 1971).

COM74-11359**

Yakowitz, H., Fiori, C. E., and MichaeHs, R. E.,

Standard Reference Materials: Homogeneity

Characterization of Fe-3 Si Alloy, NBS Spec.

Publ. 260-22 (February 1971). COM74-1 1357**

Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of a Standard

Borosilicate Glass, NBS Spec. Publ. 260-23

(December 1970). COM71-00157**

Sappenfield, K. M., Marineko, G., and Hague, J.

L., Standard Reference Materials: Comparison

of Redox Standards, NBS Spec. Publ. 260-24

(January 1972). COM 72-50058**

Hicho, G. E., Yakowitz, H., Rasberry, S. D., and

Michaelis, R. E., Standard Reference Materials:

A Standard Reference Material Containing

Nominally Four Percent Austenite, NBS Spec.

Publ. 260-25 (February 1971). COM 74-1 1356**

Martin, J. F., Standard Reference Materials:

National Bureau of Standards-US Steel Corportion Joint Program for Determining Oxygen and

Nitrogen in Steel, NBS Spec. Publ. 260-26

(February 1971). 85 cents* SN003-O03-O0786-2

Garner, E. L., Machlan, L. A., and Shields, W. R.,

Standard Reference Materials: Uranium

Isotopic Standard Reference Materials, NBS

Spec. Publ. 260-27 (April 1971). COM74-

11358**

Heinrich, K. F. J., Myklebust, R. L., Rasberry, S. D., and Michaelis, R. E., Standard Reference

Materials: Preparation and Evaluation of

SRM's 481 and 482 Gold-Silver and GoldCopper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM7 1-50365**

Geller, S. B., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic

Tape (Computer Amphtude Reference) Using

the Reference Tape Amplitude Measurement

"Process A-Model 2," NBS Spec. Publ. 260-29

(June 1971). COM7 1-50282**

Gorozhanina, R. S., Freedman, A. Y., and

Shaievitch, A. B. (translated by M. C. Selby),

Standard Reference Materials: Standard

Samples Issued in the USSR (A Translation

from the Russian), NBS Spec. Publ. 260-30 (June

1971). COM71-50283**

Hust, J. G., and Sparks, L. L., Standard Reference

Materials: Thermal Conductivity of Electrolytic

Iron SRM 734 from 4 to 300 K, NBS Spec. Publ.

260-31 (November 1971). COM71-50563**

Mavrodineanu, R., and Lazar, J. W., Standard

Reference Materials: Standard Quartz Cuvettes,

for High Accuracy Spectrophotometry, NBS

Spec. Publ. 260-32 (December 1973). 55 cents*

SN003-003-01213-1

Wagner, H. L., Standard Reference Materials:

Comparison of Original and Supplemental

SRM 705, Narrow Molecular Weight Distribution Polystyrene, NBS Spec. Publ. 260-33

(May 1972). COM72-50526**

Sparks, L. L., and Hust, J. G., Standard Reference

Materials: Thermoelectric Voltage, NBS Spec.

Publ. 260-34, (April 1972). COM72-50371**

Sparks, L. L., and Hust, J. G., Standard Reference Materials: Thermal Conductivity of

Austenitic Stainless Steel, SRM 735 from 5

to 280 K, NBS Spec. Publ. 260-35 (April 1972.)

35 cents* COM72-50368**

CaH, J. P., Mandel, J., Moore, L. J., and Young, D.

S., Standard Reference Materials: A Referee

Method for the Determination of Calcium in

Serum, NBS SRM 915, NBS Spec. Publ. 260-36

(May 1972). COM72-50527**

Shultz, J. I., Bell, R. K., Rains, T. C, and Menis,

O., Standard Reference Materials: Methods of

Analysis of NBS Clay Standards, NBS Spec.

Publ. 260-37 (June 1972). COM72-50692**

Richmond, J. C, and Hsia, J. J., Standard Refer- ence Materials: Preparation and Calibration of

Standards of Spectral Specular Reflectance,

NBS Spec. Publ. 260-38 (May 1972). COM72-

50528**

Clark, A. F., Denson, V. A., Hust, J. G., and

Powell, R. L., Standard Reference Materials:

The Eddy Current Decay Method for Resistivity

Characterization of High-Purity Metals, NBS

Spec. Publ. 260-39 (May 1972). COM72-50529**
McAdie, H. G., Garn, P. D., and Menis, O., Standard Reference Materials: Selection of Thermal

Analysis Temperature Standards Through a Cooperative Study (SRM 758, 759, 760), NBS

Spec. Publ. 260-40 (August 1972.) COM-72

50776**

Wood, L. A., and Shouse, P. J., Standard

Reference Materials: Use of Standard LightSinsitive Paper for Calibrating Carbon Arcs

Used in Testing Textiles for Colorfastness to

Light, NBS Spec. Publ. 260-41 (August 1972)

COM72-50775**

Wagner, H. L., and Verdier, P. H., eds., Standard

Reference Materials: The Characterization of

Linear Polyethylene, SRM 1475, NBS Spec.

Publ. 260-42 (September 1972). COM72-

50944**

Yakowitz, H., Ruff, A. W., and Michaelis, R. E.,

Standard Reference Materials: Preparation and

Homogeneity Characterization of an Austenitic

Iron-Chromium-Nickel Alloy, NBS Spec. Publ.

260-43 (November 1972). COM73-50760**

Schooley, J. F., Soulen, R. J., Jr., and Evans, G. A.,

Jr., Standard Reference Materials: Preparation

and Use of Superconductive Fixed Point

Devices, SRM 767, NBS Spec. Publ. 260-44

(December 1972). COM73-50037**

Greifer, B., Maienthal, E. J., Rains, T. C, and

Rasberry, S. D., Standard Reference Materials:

Powdered Lead-Based Paint, SRM 1579, NBS

Spec. Publ. 260-45 (March 1973). COM73-

50226**

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and

Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 K, NBS Spec. Publ. 260-46

(March 1975). SN003-003-0 1278-5

Hust, J. G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797,

and Austenitic Stainless Steel, SRM 798, from 5

to 280 K, NBS Spec. Publ. 260-47 (February

1974). COM74-50176**

Mangum, B. W., and Wise, J. A., Standard Refer- ence Materials: Description and Use of Precision

Thermometers for the Clinical Laboratory,

SRM 933 and SRM 934, NBS Spec. Publ. 260-48

(May 1974). 60 cents* SN003-003-0 1278-5

Carpenter, B. S., and Reimer, G. M., Standard

Reference Materials: Calibrated Glass Standards for Fission Track Use, NBS Spec. Publ.

260-49 (November 1974). SN003-003-0 1344-7

V i

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRM's 734 and 797 from 4 to 1000 K, NBS Spec. Publ. 260-50 (June 1975).

1.00* SN003-003-0 1425-7

Mavrodineanu, R., and Baldwin, J. R., Standard

Reference Materials: Glass Filters As a Standard

Reference Material for Spectrophotometry;

Selection; Preparation; Certification; Use -SRM

930, NBS Spec. Publ. 260-51 (November 1975).

$1.90* SN003-003-01481-8

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials

730 and 799, from 4 to 3000 K, NBS Spec. Publ.

260-52 (September 1975). $1.05* SN003-003-

01464-8

Durst, R. A., Standard Reference Materials:

Standardization of pH Measurements, NBS

Spec. Publ. 260-53 (December 1975, Revised).

$1.05* SN003-003-01551-2

Burke, R. W., and Mavrodineanu, R., Standard

Reference Materials: Certification and Use of

Acidic Potassium Dichromate Solutions as an

Ultraviolet Absorbance Standard, NBS Spec.

Publ. 260-54 (August 1977). $3.00* SN003-003-

01828-7

Ditmars, D. A., Cezairliyan, A., Ishihara, S., and

Douglas, T. B., Standard Reference Materials:

Enthalpy and Heat Capacity; Molybdenum

SRM 781, From 273 to 2800 K, NBS Spec. Publ.

260-55 (September 1977). $2.20* SN003003-

01836-8

Powell, R. L., Sparks, L. L., and Hust, J. G.,

Standard Reference Materials: Standard

Thermocouple Material, Pt.-67: SRM1967, NBS

Spec. Publ. 260-56 (February 1978). $2.20*

SN003-003-0 18864

Cali, J. P. and Plebanski, T., Guide to United

States Reference Materials, NBS Spec. Publ.

260-57 (February 1978). $2.20* SN003-003-

01883-0

Barnes, J. D. and Martin, G. M., Standard Refer- ence Materials: Polyester Film for Oxygen Gas

Transmission Measurements. SRM 1470, NBS

Spec. Publ. 260-58 (in press).

Chang, T. and Kahn, A. H., Standard Reference

Materials: Electron Paramagnetic Resonance

Intensity Standard: SRM 2601, NBS Spec.

Publ. 260-59 (in press).
Velapoldi, R. A., Paule, R. C, Schaffer, R.,

Mandel, Jr., and moody, J. R., Standard Refer- ence Materials: A Reference Method for the

Determination of Sodium in Serum, NBS Spec.

Publ. 260-60 (in press).

Verdier, P. H. and Wagner, H. L., Standard Refer- ence Materials: The Characterization of Linear

Polyethylene (SRM 1482, 1483, 1484), NBS

Spec. Publ. 260-61 (in press).

* Send order with remittance to: Superintendent

of Documents, US Government Printing

Office, Washington, DC 20402. Remittance

from foreign countries should include an

additional one-fourth of the purchase price for

postage.

** May be ordered from: National Technical

Information Services (NTIS), Springfield,

Virginia 22151.

vi i
CONTENTS

THE CHARACTERIZATION OF LINEAR POLYETHYLENE SRM'S 1482, 1483,

AND 1484:

PAGE

I. INTRODUCTION, Peter H. Verdier and Herman L. Wagner .... 169

II. NUMBER-AVERAGE MOLECULAR WEIGHTS BY MEMBRANE

OSMOMETRY, Herman L. Wagner and Peter H. Verdier 179

III. WEIGHT-AVERAGE MOLECULAR WEIGHTS BY LIGHT SCATTERING,

Charles C. Han, Peter H. Verdier, and

Herman L. Wagner 185

IV. LIMITING VISCOSITY NUMBERS BY CAPILLARY VISCOMETRY,

Herman L. Wagner and Peter H. Verdier 195

viii
The Characterization of Linear Polyethylene SRM's 1482,

1483, and 1484

Peter H. Verdier

and

Herman L. Wagner, Editors

Center for Materials Science

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

The National Bureau of Standards has issued a new series of three

linear polyethylene Standard Reference Materials, SRM 1482, 1483, and

1484. These polyethylenes have molecular weights of the order of

10,000, 30,000, and 100,000 g/mol, respectively, and ratios M /M of

w n

weight- to number -average molecular weight of the order 1.2. Their

number -average molecular weights (by membrane osmometry) , weight -average

molecular weights (by light scattering) , and limiting viscosity numbers

in two solvents (by capillary viscometry) are certified; the procedures

employed are described in these collected papers previously published

"n the Journal of Research of the National Bureau of Standards.

Key Words: Capillary viscometry; fraction; light scattering; limiting

viscosity number; membrane osmometry; narrow molecular weight distribution;

number -average molecular weight; polyethylene; Standard Reference Material;

weight -average molecular weight.

ix

JOURNAL OF RESEARCH of the National Bureau of Standards

Volume 83, No. 2 March-April 1978

The Characterization of Linear Polyethylene SRM's 1482, 1483,

and 1484. I. Introduction

Peter H. Verdier and Herman L. Wagner

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

(October 19, 1977)

The National Bureau of Standards ha,s issued a series of three linear polyethylene Standard Reference

Materials, SRM 1482, 1483, and 1484. These polyethylenes have molecular weights of the order of 10,000,

30,000, and 100,000 g/inol, respectively, and ratios M^j/Mn of weight- to number-average molecular weight of the order of 1.2. Their number-average molecular weights (by membrane osmometry), weight-average molecular

weights (by light scattering), and limiting viscosity numbers in two solvents (by capillary viscomelry) are certified; the procedures employed are described in subsequent papers in this series. In the present paper, we describe the preparation of the materials and some of iheir general properties.

Key words: Fraction; limiting viscosity number; narrow molecular weight distribution; number-average molecular

weight; polyethylene; Standard Reference Material; weight-average molecular weight.

1 . Purpose

The National Bureau of Standards has issued a series of

three linear polyethylene Standard Reference Materials,

.SRM 1482, SRM 1483, and SRM 1484.* These polyethylenes have molecular weights of the order of 10,000, 30,000

and 100,000 g/mol, respectively, and ratios /l/«,//W„ of

weight- to number-average molecular weight of the order of

1.2. Their number-average molecular weights (by membrane

osmometry), weight-average molecular weights (by light scattering), and limiting viscosity numbers in two solvents (by

capillary viscomelry) are certified; the certificates are reproduced at the end of this paper. They are intended for the

calibration and checking of instruinents used in polymer

technology and science for the determination of properties

related to molecular weight and distribution in molecular

weight, such as light scattering photometers and gel permeation chromatographs. They should also prove useful as

characterized samples for measurements of other physical

properties of linear polyethylene.

Succeeding papers of this series describe the experimental

methods and data analysis techniques employed to obtain the

certificate values of number-average molecular weight [la],'

weight-average molecular weight [lb], and limiting viscosity

number [Ic] of SRM's 1^2, 1483, and 1484. In the present

paper, we describe the preparation and treatment of these

materials, and the results of various semiquantitative measurements employed to estimate such uncertified properties

as distribution in molecular weight, impurity content, etc.

2. Description of Materials

Standard Reference Materials 1482, 1483, and 1484 were

prepared from fractions produced by Waters Associates,

* Available through the Office of Standard Reference Materials, National Bureau of Standards,

Washington, D. C. 20234.

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

Inc., Milford, Mass.^ by large-scale gel permeation fractionation of a linear polyethylene from the same stock as Standard Reference Material 1473 (Linear Polyethylene

Whole Polymer),* and with physical properties essentially

identical with those of SRM 1475. As reported elsewhere [2,

3], SRM 1475 has a degree of branching undetectable by

infrared spectroscopy and limiting viscosity number, and an

ash content of 0.002 percent. We believe that the fractions

will have the same characteristics. In other respects, however, the three fractions have different histories and are discussed separately in the following sections. Gel permeation chromatography of all three Standard Reference Materials shows a single symtnetrical peak, without noticeable

shoulders and of a width consistent with a ratio Mw/M„ of

weight- to number-average molecular weight, estimated as described elsewhere [2], of the order of 1.2.

2.1. SRM 1483

According to the producer, the material for SRM 1483 was made by blending and reprecipitation (from xylene by cooling) of about 600 nine-gram "cuts" obtained by gel permeation fractionation, in Styragel coluirins, of the parent material

in xylene with antioxidant at 135 °C. After the final reprecipitation, the material was washed with acetone and air-dried.

Upon delivery to the National Bureau of Standards, the entire

stock (about 5.5 kg) was blended in a two-cone porcelainlined mixer, packed in 46 quart jars and stored under dry

nitrogen at reduced pressure.

As a check on homogeneity, two samples were taken from

each of five jars chosen at random. Viscosity numbers at five concentrations in 1,2,4-trichlorobenzene were determined as described elsewhere [Ic] for each sample. The results showed

no statistically significant variation within jars or between

jars.

^ Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimenttd procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply thai the material or equipment

identified is necessarily the best available for the purpose.

169
Trace-metal analyses (by emission spectroscopy on ^/2 g

samples) showed iron and magnesium not exceeding 1 ppm.

Total volatiles detected by mass spectrometry upon heating

the material to 300 °C did not exceed 0.1 percent. Carbonhydrogen analyses agreed with the values expected for (CH2)n

to within 0.1 percent.

2.2 SRM 1482

The gel permeation fractionations which produced the

material for SRM 1483 as described above also yielded

"cuts" at higher and lower molecular weights. Five batches

of the lower molecular weight materials were found to be

suitable for a Standard Reference Material with a molecular

weight of the order of 10,000. The batches ranged in weight

from 100 to 400 g each. Their M^/M„ ratios, estimated by

gel permeation chromatography, were in the range 1.1 to 1.2. The batches were individually reprecipitated as described below, then blended to make the final product.

Reprecipitation was carried out in 1,2,4-trichlorobenzene

containing 500 ppm of an antioxidant, 2,6-di-ieri-butyl-4-

methylphenol. For each batch, sufficient solvent to make a

solution of concentration 0.5-1 percent (by weight) was first heated to 130 °C under nitrogen, and the polyethylene added

to the hot solvent while stirring. The material dissolved in 5-10 min. The solution was allowed to cool, over a period of

several hours, to 45-65 °C with gentle stirring. During the

cooling the polyethylene precipitated, forming a floating

slurry, and the bulk of the liquid phase was pumped out. The individual slurries were blended by mixing and

vigorous stirring for V2-I hr. The blended slurry was

strained through a 40 mesh screen, filtered on filter paper,

and washed three times with acetone. It was then air-dried at room temperature until the acetone content was about

10 percent by weight, dried in a vacuum oven for 13 hrs at 50 °C, and bottled under di^ nitrogen at reduced pressure.

Residual 1,2,4-trichlorobenzene content was estimated

spectrophotometrically. Four samples of SRM 1482 were

dissolved in cyclohexane (at 140 °C under pressure) to give

solutions with concentrations from 30 to 160 g/L. The

polyethylene was then reprecipitated by cooling to room

temperature and removed by filtration. The concentration of

1,2,4-trichlorobenzene in the filtrate was estimated by comparing its optical density at a wavelength of 286 nm with that of solutions of known amounts of 1,2,4-trichlorobenzene in

cyclohexane. The 1,2,4-trichlorobenzene content estimated

by this method was 0.053, 0.058, 0.059, and 0.065 percent

for the four samples. Based on these values, we estimate an upper limit of 0. 1 percent residual 1,2,4-trichlorobenzene in SRM 1482.

Total volatile content was estimated by measuring the

weight lost by three 0.5 g samples and a blank after heating

to 50 °C for one h at a pressure of about 10 Pa. During this period, the blank decreased in weight by 0.1 mg, and the

samples decreased by 0.2, 0.3, and 0.4 mg. No further

weight loss was observed in either blank or samples after 2^/2 additional hours of drying under the same conditions.

Based on these values, we estimate total volatiles in this material to be 0.1 percent or less.

2.3 SRM 1484

Six batches of the polyethylene "cuts" described in the

preceding section were chosen as starting materials for SRM

1484. The batches consisted of 100 to 300 g each. Their gel

permeation chromatograms showed major peaks at molecular

weights in the vicinity of 100,000, with ratios A/u,/A/„ in the

range 1.1-1.2, and minor peaks, amounting to a few percent

of the total material, in the molecular-weight range 600-

3600. In order to remove the low molecular-weight components, the individual batches were fractionally reprecipitated

as described below.

Fractional reprecipitations were carried out in 1,2,4-trichlorobenzene containing .500 ppm 2,6-di-^er^-butyl-4-methylphenol. The solvent was preheated and the solutions pre- pared as described above for SRM 1482, except that the

higher molecular-weight material required V2 to 1 h to dissolve. The hot solution was then cooled under nitrogen at a rate of 5-6 °C/h to 80 °C with gentle stirring. During the

cooling, most of the higher molecular-weight components

precipitated, forming a slurry. The stirring and the nitrogen cover were then discontinued, and the system was left unstirred at 80 °C until the precipitate had all floated to the

surface of the liquid. The underlying liquid, containing the

low molecular-weight contaminant, was pumped out. Fresh

1,2,4-trichlorobenzene preheated to 82-85 °C was added,

and the precipitate was washed by stirring under nitrogen for several minutes, then left unstirred for a minimum of 3 h at 80 °C. The liquid underlying the precipitate was again

pumped out and the remaining slurry cooled to room temperature. Gel permeation chromatograms of the resulting precipitates showed no sign of the low molecular-weight contaminant. The individual slurries were blended by mixing and

vigorous stirring for two hours. The blended slurry was

filtered on filter paper and washed three times with ethanol

and once with acetone. It was then air-dried at room

temperature for a week, further dried in a vacuum oven at 50

°C for 8 h, and bottled under dry nitrogen at reduced

pressure.

Residual 1,2,4-trichlorobenzene content of SRM 1484 was

estimated spectrophotometrically by the method described in section 2.2 for SRM 1482. Measurements on two solutions,

of initial SRM 1484 concentrations about 100 g/L, yielded

estimates of 1,2,4-trichlorobenzene content of 0.057 and

0.063 percent. From these values, we estimate an upper

limit of 0.1 percent residual 1,2,4-trichlorobenzene in SRM

1484. n

Total volatile content was estimated by measuring the

weight lost by four 0.5 g samples and two blanks after heating to 60 °C for 2 h at a pressure of 10-100 Pa. During

this period, the blanks decreased in weight by 0.03 and 0.07

mg, and the samples decreased by 0.11, 0.11, 0.13, and

0.14 mg. No further weight loss was observed in either blank; or samples after 2^ additional hours of drying under the same

conditions. These values appear to imply a volatile content

of about 0.02 percent, which is inconsistent with the observed residual 1,2,4-trichlorobenzene content. We conclude

that the drying procedure employed was incapable of remov-1

ing all the residual 1,2,4-trichlorobenzene. As a result of the^ fractional reprecipitation of SRM 1484, we believe thai 1,2,4-trichlorobenzene is the only likely volatile contami^

170
lanl, and that our estimated upper limit of 0.1 percent

esidual 1,2,4-trichIorobenzene is also a safe upper limit for

otal volatiles in SRM 1484.

Note: The word liter is abbreviated lowercase "1" in these

Certificates. The approved abbreviation for liter is capital

'L".

3. References

1] The Characterization of Linear Polyethylene SRM's 1482, 1483, and

1484:

(a) Wagner, H. L., and Verdier, P. H., II. Number-Average Molecular Weights by Membrane Osmometry, J. Res. Nat Bur. Stand,

(U.S.) 83, No. 2 (Mar.-Apr. 1978).

(b) Han, C. C, Verdier, P. H., and Wagner, H. L., III. WeightAverage Molecular Weights by Light Scattering, J. Res. Nat. Bur. Stand. (U.S.) 83, No. 2 (Mar.-Apr. 1978).

(c) Wagner, H. L. , and Verdier, P. H., IV. Limiting Viscosity

Numbers by Capillary Viscometry, J. Res. Nat. Bur. Stand.

(U.S.) 83, No. 2 (Mar.-Apr. 1978).

[2] Hoeve, C. A. J., et al.. The Characterization of Linear Polyethylene

SRM 1475 (a series of ten papers), J. Res. Nat. Bur. Stand. (U.S.) 76A, No. 2, 137-170 (Mar.-Apr. 1972); also available as Wagner, H.

L., and Verdier, P. H. Eds., The Characterization of Linear Polyethylene SRM 1475, Nat. Bur. Stand. (U.S.). Spec. Publ 260-42, 39

pages (Sept. 1972).

[3] Wagner, H. L. and Hoeve, C. A. J., The Mark-Houwink Equation and

Chain Dimensions of Linear Polyethylene in Theta Solvents, J. Polym.

Sci., Symposium No. 54, 327-339 (1976).

171
U.S. Department of Commerce

Elliot L. Richardson,

Secretary

National Burrau of Standards

Ernest Ambler, Acting DirectorRational ^ureau af ^tanrfarrfg

(HtxixVxtnit

Standard Reference Material 1482

Linear Polyethylene

(Narrow Molecular Weight Distribution)

p. H. Verdier and H. L. Wagner

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

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

use as a characterized sample for measurements of other physical properties of linear polyethylene.

Property Value

Sample standard

deviation of

value, percent

Number of

degrees of

freedom

Expected limit of

systematic error, percent

Number-average

molecular weight,

M„, g/mol' 11,400 0.7 18 2"

Weight-average

molecular weight,

Mw, g/mol' 13,600 1.0 6

11"'"

Limiting viscosity

number, ml/g:

at 130 °C in 1,2,4-trichlorobenzene 40.2 0.33 28 1

at 130 °C in 1-chloronaphthalene 36.4 0.31 24 1

a. Determined by membrane osmometry in l-chloronaphthaiene at 126 °C.

b. The expected limits of systematic error for the number- and weight-average molecular weights are based on analyses of the osmometry

and light-scattering determinations, respectively, without taking account of the necessity of M« exceeding M„.

c. Determined by light scattering in l-chloronaphthalene at 135 °C based on a value of 1 7.8 X 10 " cm ' for the Rayleigh ratio for the

vertically polarized scattering of vertically polarized light, of wavelength 546 nm in vacuum, from benzene at 23 °C. This value was

derived from published values of the unpolarized Rayleigh ratio and the depolarization ratio for unpolarized light [D. J. Coumou.

J. Colloid Sci. 15, 408 (I960) ]. The differential refractive index of this polyethylene in l-chloronaphthalene at 135 ^ C, also required

for the calculation of molecular weight, was found to be -0. 195 ml g at wavelength 546 nm in vacuum, based on the value of 0. 1429 ml g for the differential refractive index of sucrose in aqueous solution at 25 °C [Norberg and Sundelof, Makromol. Chem. 77, 77

(1964) ].

d. The expected limit of systematic error from all sources c\\ e/>i the vertically polarized Rayleigh ratio for benzene is 4 percent.

Measurements leading to the certification of this Standard Reference Material were performed by J. E. Brown,

R. G. Christensen, C. C. Han, J. R. Maurey, P. H. Verdierand H. L. Wagnerinthe Polymers Division, Institute for Materials Research.

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

October 18, 1976 Office of Standard Reference Materials

172
This sample of linear polyethylene was prepared by recrystallization from 1,2,4-trichlorobenzene and subsequent blending of fractions produced by Waters Associates, Inc. of Milford, Mass., by large-scale gel

permeation chromatography, from a linear polyethylene substantially identical with Standard Reference

Material 1475 (Linear Polyethylene, Whole Polymer). Both total volatiles, estimated gravimetrically, and

residual 1,2,4-trichlorobenzene content, estimated spectrophotometrically, do not exceed 0.1 percent.

The maximum rate of shear in the Ubbelohde capillary viscometers employed for the determination of limiting

viscosity numbers was 3000 sec ' for 1,2,4-trichlorobenzene and 2000 sec"' for l-chloronaphthalene. The

maximum specific viscosities were 0.4 in both solvents. A report describing the investigations required for this and related polyethylene Standard Reference Materials

will be published as an NBS Special Publication.

173
U.S. Department of Commerce

Elliot L. Richardson,

Secretary

National Bureau of StandaidH

Ernest Ambler, Acting DirectorRational ^ur^au of ^taiutards

Standard Reference Material 1483

Linear Polyethylene

(Narrow Molecular Weight Distribution)

H. L. Wagner and P. H. Verdier

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

technology and science for the determination of molecular weight and molecular weight distribution, and for use as a characterized sample for measurements of other physical properties of linear polyethylene.

Property Value

Sample standard

deviation of

value, percent

Number of

degrees of

freedom

Expected limit of

systematic error, percent

Number-average

molecular weight,

Mn, g/mor 28,900 1.5 22 2"

Weight-average

molecular weight,

Mw, g/mol' 32,100 2.3 4

,,b,d

Limiting viscosity

number, ml/g:

at 130 °C in 1,2,4-trichlorobenzene 79.4 0.39 24 1

at 130 °C in 1-chloronaphthalene 70.6 0.39 17 I

a. Determined by membrane osmometry in 1-chloronaphthalene at 129 °C.

b. The expected limits of systematic error for the number- and weight-average molecular weights are based on analyses of the osmometry

and light-scattering determinations, respectively, without taking account of the neccs^,ity of M. exceeding Vl„.

c. Determined by light scattering m l-chloronaphthalene at 135 °C based on a value of 17.8 x |0" cm"' for the Rayleigh ratio forthe

vertically polarized scattering of vertically polarized light, of wavelength 546 nm in vacuum, from benzene at 23 °C. This value was

derivedXrom published values of the unpolarized Rayleigh ratio and the depolarization ratio for unpolarized light [D. J. Coumou,

J. Colloid Sci. 15,408(1960)]. The differential refractive index of this polyethylene in l-chloronaphthalene at 135 °C, also required

for the calculation of molecular weight, was found to be -0. 193 ml/gat wavelength 546 nm in vacuum, based on the value of 0. 1429 ml/g for the differential refractive index of sucrose in aqueous solution at 25 °C [Norberg and Sundelbf, Makromol. Chem. 77,77

(1964) ].

d. The expected limit of systematic error from all sources except the vertically polarized Rayleigh ratio for benzene is 4 percent.

Measurements leading to the certification of this Standard Reference Material were performed by J. E. Brown,

R. G. Christensen, J. R. Maurey and H. L. Wagner in the Polymers Division, Institute for Materials Research.

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

March 9, 1976 Office of Standard Reference Materials

174
This sample of linear polyethylene was prepared by Waters Associates, Inc. of Milford, Mass., by large-scale

gel permeation chromatography, from a linear polyethylene substantially identical with Standard Reference

Material 1475 (Linear Polyethylene, Whole Polymer). Volatiles detected by mass spectrometric analysis upon

heating the material to 300 °C did not exceed 0. 1 percent. Viscosity numbers of samples chosen at random from

different parts of the material showed no statistically significant sample-to-sample variation.

The maximum rate of shear in the Ubbelohde capillary viscometer employed for the determination of limiting

viscosity numbers was 3000 sec"' for 1,2,4-trichlorobenzene and 2000 sec ' for 1-chloronaphthalene. The

maximum specific viscosities were 0.4 in both solvents.

A report describing the investigations required for this and related polyethylene Standard Reference Materials

will be published as an NBS Special Publication.

175
U.S. Department of Commerce

Elliot L. Richardson,

Secretary

National Bureau of Standards

Ernest Ambler, Acting Director Rational ^ur^au of ^tantlarrfft

(Etttxixtntt

Standard Reference Material 1484

Linear Polyethylene

(Narrow Molecular Weight Distribution)

p. H. Verdier and H. L. Wagner

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

technology and science for the determination of molecular weight and molecular weight distribution, and for use as a characterized sample for measurements of other physical properties of linear polyethylene.

Property Value

Sample standard

deviation of

value, percent

Number of

degrees of

freedom

Expected limit of

systematic error, percent

Number-average

molecular weight,

Mn, g/mor 100,500 3.7 34 4"

Weight-average

molecular weight,

Mw, g/mor 119,600 1.8 5

Limiting viscosity

number, ml/g:

at 130 °C in 1,2,4-trichlorobenzene 197.9 0.30 22 1

at 130°C in 1-chloronaphthalene 169.4 0.35 22 1

a. Determined by membrane osmometry in l-chloronaphtlialene at 130 °C.

b. The expected limits of systematic error for the number-and weight-average molecular weights are based on analyses of the osmometry

and light-scattering determinations, respectively, without taking account of the necessity of M. exceeding M„.

c. Determined by light scattering in l-chloronaphthalene at 135 °C based on a value of 1 7.8 x 10 ' cm ' for the Rayleigh ratio for the

vertically polarized scattering of vertically polarized light, of wavelength 546 nm in vacuum, from benzene at 23 °C. This value was

derived from published values of the unpolarized Rayleigh ratio and the depolarization ratio for unpolarized light [D. J. Coumou,

J. Colloid Sci. 15, 408 (I960) ]. The differential refractive index of this polyethylene in l-chloronaphthalene at 135 °C, also required

for the calculation of molecular weight, was found to be —0. 191 ml/g at wavelength 546 nm in vacuum, based on the value of 0. 1429 ml/g for the differential refractive index of sucrose in aqueous solution at 25 °C [Norberg and Sundelbf. Makromol. Chem. 77, 77

(1964) ].

d. The expected limit of systematic error from all sources except the vertically polarized Rayleigh ratio for benzene is 4 percent.

Measurements leading to the certification of this Standard Reference Material were performed by J. E. Brown,

R. G. Christensen, C. C. Han, J. R. Maurey, P. H. Verdier and H. L. Wagner in the Polymers Division, Institute for Materials Research.

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

October 18, 1976 Office of Standard Reference Materials

176
This sample of linear polyethylene was prepared by fractional recrystallization from 1 ,2,4-trichlorobenzene and

subsequent blending of fractions produced by Waters Associates, Inc. of Milford, Mass., by large-scale gel

permeation chromatography, from a linear polyethylene substantially identical with Standard Reference

Material 1475 (Linear Polyethylene, Whole Polymer). The fractions as received contained several percent by

weight of polyethylene components with molecular weights in the range 1,000-4,000. The amount of this material remaining after the fractional recrystallization is less than 0.5 percent. Both total volatiles, estimated

gravimetrically, and residual 1,2,4-trichlorobenzene content, estimated spectrophotometrically, do not exceed

0.1 percent.

The maximum rate of shear in the Ubbelohde capillary viscometers employed for the determination of limiting

viscosity numbers was 3,000 sec ' for 1,2,4-trichlorobenzene and 2,000 sec ' for 1-chloronaphthalene. The

maximum specific viscosities were 0.4 in both solvents. A report describing the investigations required for this and related polyethylene Standard Reference Materials

will be published as an NBS Special Publication.

177

JOURNAL OF RESEARCH of the National Bureau of Standards

Volume 83, No. 2 March-April 1978

The Characterization of Linear Polyethylene SRM's 1482, 1483,

and 1484. II. Number-Average Molecular Weights by

Membrane Osmometry

Herman L. Wagner and Peter H. Verdier

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

(October 1 9, 1 977)

Linear polyethylene Standard Reference Materials SRM 1482, 1483, and 1484 are certified for numberaverage molecular weight M„. In this paper the experimental procedures employed for the determination of /W„ for these materials by membrane osmometry are described, and the techniques used to analyze the data and to estimate limits of systematic error are discussed.

Key words: Fraction; limiting viscosity number; membrane osmometry; narrow molecular weight distribution; number-average molecular weight; polyethylene; Standard Reference Material; weight-average molecular weight.

1 . Introduction

Standard Reference Materials 1482, 1483, and 1484 are

linear polyethylenes with relatively narrow distributions in molecular weight, issued by the National Bureau of Standards. Their general characteristics are described in the first paper of this series [1].' In the present paper, we describe

the determination of their certificate values of numberaverage molecular weight by membrane osmometry. This

well-established [2, 3] technique consists of measuring the

equilibrium hydrostatic pressure difference between a solution and pure solvent separated by a membrane permeable to solvent alone, as a function of solution concentration.

2. Experimental

Osmotic pressure measurements were made with a Model

502 Hewlett-Packard Mechrolab Membrane Osmometer.^

This instrument, which has been described elsewhere [3],

adjusts the hydrostatic pressure on the solvent side of the

semipermeable membrane to achieve zero net liquid transfer

across the membrane. The pressure is adjusted by varying

the solvent level, which is measured with a resolution of 0.01

cm, corresponding to a pressure difference of about 1 Pa for water or typical organic solvents. Gel cellophane membranes,

type 450D, obtained from ArRo Labortories, Inc., were

employed. Before use, they were conditioned to 1-chloronaphthalene, the solvent in which ineasurements were made,

by a successive solvent-exchange procedure given in detail

previously [4]. Solution temperatures at the membrane surface, which

were in the range 125-130 °C, could not be ineasured

directly without risk of damage to the metnbrane. Temperatures were therefore monitored during osmotic pressure

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

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

measurements by a copper-constantan thermocouple springloaded against the stainless steel membrane clamps. In separate experiments, the temperature difference between

this thermocouple and the membrane surface was determined

by inserting a second thermocouple at the membrane surface.

Osmotic pressure differences were ineasured for solutions

whose concentrations ranged from 0.7 to 3 g/L for SRM

1482, 1 to 10 g/L for SRM 1483, and 0.5 to 1.4 g/L for SRM

1484. All solutions were made up directly by weight, without

employing successive dilution techniques. Concentrations were calculated using values of solvent density and partial

specific volume determined pycnometrically in this laboratory. The 1-chloronaphthalene was obtained from commercial

material by distillation at reduced pressure after removal of

residual naphthalene by sublimation, also at reduced pressure. Solutions were made up without adding antioxidant,

since preliminary experiments suggested that its use led to erratic results, possibly due to the formation of gaseous

decomposition products in the osmometer. No evidence of

degradation was found in the course of this work. Reference

readings, with solvent on both sides of the membrane, were

taken before and after each solution reading, to take account

of slow drifts due to changes in ambient pressure, etc.

3. Results

Number-average molecular weight M„ may be obtained

from the variation of osmotic pressure tt with solution

concentration by means of the familiar virial expansion,

expressed in one of the two equivalent forms:

77 = RT{M-'c + A^c^ + Agc^ + • • • ) = {RT/Mrd{c + Y^^ + Y^c^ + ---),

^

where c is solution concentration (weight per unit volume), R

and T are the gas constant and the absolute temperature,

respectively, and the /4's and F's are the usual virial coefficients. In practice, the quantity actually measured is

179
the difference h in liquid level between solvent and solution,

related to the osmotic pressure by TT = pgh, where p is solvent density and g is the acceleration due to gravity.

Thus, Mn niay be determined from the coefficient of the first power of concentration in a fit of osmotic pressure (or h) to a polynomial in solution concentration with no constant term. Since the concentrations chosen and the number of terms in eq (1) employed differ for the three Standard Reference

Materials, we discuss them separately in the remainder of

this section.

3.1 SRM 1483

Five subsets of measurements were made on SRM 1483.

Each subset consisted of measurements on five solutions,

with concentrations of approximately 1, 2, 3.5, 5.5, and 10

g/L, at a temperature of 128.6 °C. The measured values of h,

which ranged from 1 to 15 cm, were fitted by unweighted

least squares to a polynomial in the first, second, and third

powers of solution concentration, and eq (1) was used to calculate A2, and /I3 from the coefficients so obtained.

The standard deviation in h obtained from the least-squares

analysis was 0.055 cm, only slightly larger than the repeatability of the measurements. The values of M„ and/42 obtained

are shown in table 1, together with their standard deviations

inferred from the least-squares fit. The value oi A2 is consistent with literature values for linear polyethylenes in 1-chloronaphthalene [4-7], and is in reasonable agreement

with the value of 4 2 obtained for SRM 1483 by light

scattering cited in paper III of this series [8]. The value

found (or is 0.011 mol cm*'/g'', with a standard deviation

of 0.012 mol cm'Vg''- Thus, over the range of concentrations

employed and to the precision of our measurements, we were

unable to obtain a value for the third virial coefficient

statistically significantly different from zero. This is hardly

surprising, since at the highest concentrations employed, the

contribution to the right-hand side of eq (1) from the second

and higher virial coefficients is only about 40 percent of the

term linear in c, and the contribution to the height difference

h from the third virial term is less than 0.4 cm. Curiously,

however, the ratio r3/r2^ = A^KMnAt') has the value 0.3,

remarkably close to the often-employed estimate of V4 for

this ratio [2, 9].

3.2. SRM 1482

Five subsets of measurements were made on SRM 1482.

Each subset consisted of measurements on four solutions,

with concentrations of approximately 0.7, 1, 2, and 3 g/L, at a temperature of 126.3 °C, and observed height differences

h ranging from 2 to 9 cm. Preliminary analyses indicated a molecular weight of about 10** g/mol and a second virial coefficient roughly the same as that found for SRM 1483.

tion As/iMnA' V4 gives us an estimate of 3 X 10"

mol cmVg^ for A3. Using these estimates, we find that at concentration of 10 g/L, the maximum employed for SRR

1483, the expected contributions to the measured heigh

difference from the three terms on the right-hand side of e(

(1) are 2.9 cm, 3.2 cm, and 0.9 cm, in that order. Thus, tht second term is actually larger than the first, and it seem

more than likely that the fourth and higher terms wil contribute significantly. Since the primary purpose of thii work is the determination of Mn, we restrict ourselves t< measurements at and below a concentration Cmax of 1.4 g/L

rather than include additional terms in eq (1). At Cmaxi th« expected contributions to the measured height difference wil

be about 0.4 cm, 0.07 cm, and 0.003 cm. The third term i well below the 0.01 cm resolution of the osmometer, anc since the size of the terms is decreasing rapidly as we go t( successively higher-order terms in concentration, we can b< reasonably certain that the higher-order terms may be safel? neglected.

Given the maximum concentration Cmax to be used and th( functional form to be fitted (eq (1) with the last term omitted),

the expected precision with which M„ may be estimated by £ series of measurements of height difference h at various

concentrations not exceeding Cmax is a function of the concentrations chosen. It can be shown [10] that for the present case, maximum precision in an estimate of M„ is achieved by taking about one-sixth the measurements at CmaK and the other five-sixths at a concentration roughly one-thirc

Cmax- At this lower concentration, the predicted height

difference is only about 0. 14 cm, much lower than is usuall)

measured, and considerable replication is needed to obtain

laluf

Using these values and the approximate relation r.j/r2^ -

*/4 previously cited, we can readily show that at the highes

concentration measured, the contribution of the third viri& term amounts to a height difference of only 0.002 cm, we*

below the measuring capability of our equipment. Accorc

ingly, for the analysis of the data the terms in A3 and T3 on the right-hand sides of eq (1) were ignored, and the measure*

values of h were fitted by unweighted least squares to polynomial in the first and second powers of concentration

The standard deviation in h obtained from the fitting wa

0.046 cm, an acceptable value. The resulting values of Mv

and A2 are given in table 1, together with their standarl

deviations inferred from the least-squares fit.

'

3.3. SRM 1484

The experimental design for measurements on SRM 148< ,|| was substantially different from that used for SRM's 1481 Bte and 1483. If we take a nominal value of 10^ g/mol for M\ ppHi and take the value of found for SRM 148.3 as a rougi

estimate of A2 for SRM 1484, then the approximate rela

Table 1. Molecular parameters obtained by membrane osmometry on solutions of linear polyethylene Standard Reference Materials 1482, 1483, and 1484^

in 1-chloronaphthalene

Standard deviations are obtained from least-squares analyses of the data as described in the text.

Sample

Measurement

temperature,

°c.

Number-average molecular weight, M„, g/molStandard deviation in M„, g/molSecond virial coeffi- cient. A-i, mol cm''/g^Standard deviation in

/1 2. mol cm'/g^

Number of degrees of freedom SRM 1482 126.3 1.1397 X 10^ 0.0080 X 10^ 1.34 X 10"' 0.22 X 10"^ 18 SRM 1483 128.6 2.895 X 10< .045 X lO-* 1.12 X 10"' .17 X 10^' 22 SRM 1484 129.7 1.005 X 10^ .037 X 10^ 1.49 X 10 3 .32 X 10"^ 34

180
satisfactoi-y precision in the final estimate of M^. Accordingly, 30 measurements were made at a concentration of

about 0.5 g/L, and 6 measurements at a concentration of

about 1.4 g/L.

The measured values of h were fitted to a polynomial in the first and second powers of concentration. The standard

deviation in h obtained from the fitting was 0.018 cm. The

values of Af„ and obtained are given in table 1, together

with their standard deviations inferred from the least-squares

fit.

4. Systematic Errors

We now list the likeliest sources of systematic enor in the

estimates of number-average molecular weight described in

Ithe preceding section, and attempt to set upper limits on

their magnitudes. Individual sources of error are discussed

in the following subsections; the resulting error-limit esti- mates are summarized in table 2, expressed as percent errors applied to /!/„.

Table 2. Percent errors in M„ intruduced by measured quantities

and approximations

Source of error

I 4.

5.

I 6.

7.8.

10.

II

Measurement temperature

Solvent density in hydrostatic

column

Solvent density at membrane

temperature

Solute weights

Solvent height scale Change in volume of solvent system with solvent height Bubble compression

Penneation of solute through

membrane

Change in solution density with concentration

Cutoff of virial expansion

1. Sum of positive errors

12. Sum of negative errors

13. Maximum magnitude of error from the signed errors combined

Root-sum-square of the above maximum magnitude of error and the unsigned errors

Expected limit of systematic er- rors from all sources, including sources not identified and

treated here

Error in M„, percent

SRM 1482

0.3 0.27

0.3

0.60 0.56 -0.06

-0.34 + 0.5

-0.06

+ 0.03 + 0.53 -0.46

0.53

1.10

2%

SRM 1483

0.1 0.27

0.25

0.85 0.99 -0.06

-0.34 + 0.2

-0.16

+ 0.10 + 0.3 -0.56

0..56

1.47

2%

SRM 1484

0.1 0.27

0.25

0.19

3.04 -0.06

-0..34

-0.56

+ 0.25 + 0.25 -0.96

0.96

3.22

4%

In practice, M„ is calculated froiri the relation:

M„ = RT/ip^P), (2)

jvhere ^ is the gas constant;

r is the absolute temperature of the solution;

\ is the solvent density in the liquid column whose height

differences h measure the osmotic pressure;

i!' is the acceleration due to gravity; and

P is the coefficient of concentration c in a fit of the height

differences h to a polynomial in c of the form:

h = Pc + Qc^ + Rc^ + (3)

Of the quantities other than P on the right-hand side of eq

(2), only T and pn can be in enor by amounts sufficient to affect the final value of M„ noticeably. Errors from these sources are discussed in sections 4.1 and 4.2. Since P is the

limit, as f approaches zero, of the ratio /i/c, systematic errors

in c and in h will give rise to errors in P and therefore in /W„.

Systematic errors from these sources are discussed in sections 4.3 and 4.4. Errors may also be introduced by the

retention of too few terins on the right-hand side of eq (.3) for the concentration range employed; errors from this source are discussed in section 4..5. Finally, the error limits from all the

foregoing sources are combined and summarized in section

4.6.

4.1 . Errors in Measurement Temperature

As described in section 2, measurement temperatures were monitored by a thermocouple in contact with the clamps

which support the membrane. The thermocouple itself is calibrated to 0.1 °C; for SRM's 1483 and 1484 the principal

error in measurement teinperatures is due to the uncertainty

in the temperature difference of about 1 °C between the

monitoring thermocouple and the surface of the membrane.

We believe that this uncertainty does not exceed 0.5 °C. The

resulting relative error in M„, at a measurement temperature

of about 400 K, is seen from eq (2) to be 0.5/400, or 0.1

percent for SRM's 1483 and 1484. The temperature control

systein was not working properly when measurements were made on SRM 1482, and the- temperature varied over several

degrees. We believe that the uncertainty in the effective

average temperature for all the data is no greater than 1 °C,

which would result in a relative error in M„ of 1/400, or 0..3 percent.

4.2. Errors in Solvent Density

Errors in solvent density affect the value of M„ in two

ways. First, the density p/, of solvent in the hydrostatic head

which balances the osmotic pressure difference between

solvent and solution enters directly into the calculation of M„

as shown by eq (2). Second, since solutions were made up by

weight, rather than by voluine, the value of Po of the solvent

density at the measurement temperature affects the calculated values of solution concentrations and thus affects the

calculated value of P in eqs (2) and (3). The effect of errors

in P(, and M„ is discussed in the following section. We

believe that our tneasured values of p/, are accurate to 0.2

percent at a given temperature. However, tlie temperature of

the liquid column is uncontrolled, and is essentially room

temperature. During this work, the fluctuations in room

temperature were such as to make the effective average

temperature uncertain by about 1 °C. Measureinents of the

variation of the density of 1-chloronaphthalene with temperature in the vicinity of room teinperature give a value of

about 0.07 percent per °C. Thus, the uncertainty in the

teinperature of the liquid column adds another 0.07 percent

to the uncertainty in p/,. The total expected error in p/, is therefore 0.27 percent, which by eq (2) leads to a possible

error of 0.27 percent in M„, for all three SRM's.

181
4.3. Errors in Solution Concentration

As stated in section 2, solutions were made up by weight,

and concentrations c were calculated from the relation:

c = wpo/[l - w(l - Pow)], (4)

where w and v are the weight fraction and partial specific

volume, respectively, of solute in the solution. Thus, ierrors in c can arise from errors in w, po, and v. However, the value

of P, and therefore of M„, is unaffected by errors in w. To see

this, we observe that P is the limit, as c approaches zero, of

the ratio h/c. However, c may also be written as the product

of w and the solution density p. As c approaches zero, p of course approaches Po, and P can be re-expressed as Po'

times the zero-concentration limit of h/w, and is therefore

independent of v and inversely proportional to Po- The

relative error in M„ is therefore independent of the error in v and equal in magnitude to the relative error in po- We

believe that the accuracy of our measurement of po is 0.2

percent at a given temperature. However, as with p/,, the

uncertainties in measurement temperature discussed in section 4. 1 increase this figure by 0. 1 percent for SRM 1482

and by 0.05 percent for SRM's 1483 and 1484. Therefore, our final estimates for errors in M„ arising from errors in po

are: 0.3 percent for SRM 1482, 0.25 percent for SRM's 1483

and 1484.

Solute and solution weights were measured on semimicro

balances accurate to 0. 1 mg. The balance used to measure

solute weights for SRM 1484 was checked at the values of

solute weight actually employed and was found to be accurate

to 0.1 percent at those values. In order to estimate the effect of these weighing uncertainties on the values of M„, a series

of comparison calculations was carried out. For each SRM,

a reference subset of typical data points was chosen, one at each concentration measured, and a "reference" value of M„

was calculated from this set of points. The value of each

solute weight in turn was then increased by its assumed limit

of error, and the value of M„ recalculated. The resulting

percent changes in the reference values of M„ are shown in table 3, together with the sum of the absolute values of the

individual changes, their algebraic sum, and the square root of the sum of their squares (root-sum-square). The sum of the

absolute values represents the error in the case where every

weighing is in error by the maximum amount possible and in the direction which maximizes the resulting error in M„. We

reject this estimate as overly pessimistic. The algebraic sum

would be the appropriate measure if all the weighings were

in error by the same amount, and the root-sum-square woulc

be appropriate if the individual errors were of random sign

Since both these possibilities seem physically plausible, we

select as our error estimate the larger of the absolute value o

the algebraic sum and the root-sum-square. This turns out to be the algebraic sum for SRM's 1482 and 1483, and the root sum-square for SRM 1484; the corresponding values are shown in line 4 of table 2.

4.4. Errors in Solvent Heights

Errors in the scale used to measure the solvent heights h

will of course cause errors in P and therefore in M„. The

scale was therefore spot-checked with a cathetometer over its entire range. The largest discrepancy found was 0.012 cm

This value was therefore used to obtain error estimates for SRM's 1482 and 1483. However, for SRM 1484, with much

smaller measured height differences than the other two, a more precise error limit was needed. The scale was therefore

rechecked every 0.01 cm over the region in which height

differences were measured for SRM 1484. Over this very

limited region of the scale, the largest discrepancy found was 0.0031 cm, and this value was used to obtain error estimates

for SRM 1484. The errors in M„ resulting from the assumec

errors in h were obtained by the same kind of comparison

calculation described in section 4.3 for errors in solute

weight; the results are shown in table 3. Again, we reject the

sum of the absolute values of the individual changes as being

too pessimistic and choose the larger of the absolute value o; the algebraic sum of the individual changes and their root sum-square. As with the errors due to solute weights, this turns out to be the absolute value of the algebraic sum for SRM's 1482 and 1483, and the root-sum-square for SRM

1484; the corresponding values are given in line 5 of table 2

Table 3. Percent errors in number-average molecular weight M„ introduced by assumed errors in solute weight and and in solvent heights

SRM 1482 SRM 1483 SRM 1484

Number of solutions in reference subset 4 5 2

Percent changes in M„ from assumed errors in solute weight

0.23, -0.16,

0.29, 0.24

0.34, 0.44,

0.37, -0.34,

0.04

0.17,

-0.08

Algebraic sum of above 0.60 0.85

•> 0.09

Sum of absolute values of above 0.92 1.53 0.25

Root-sum-square of above 0.47 0.75 0.19

Percent changes in M„ from assumed errors in solvent height-0.23, 0.15,

-0.29, -0.19

-0.40, -0.48,

-0.38, 0.29,

-0.02

-3.01,

0.46

Sum of absolute values of above 0.86 1.57 3.47

Algebraic sum of above -0.56 -0.99 -2.55

Root-sum-square of above 0.44 0.79 3.04

ill

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182
Errors in solvent height can also arise from changes in the

I volume of the solvent reservoir system with height. The

quantity actually measured is not strictly the liquid level of

solvent, but rather the position of a reservoir of solvent

connected to the osmometer by flexible tubing. If the volume

of the tubing changes slightly with changes in the height of

the reservoir, the liquid level within the reservoir will change, and the true height difference between solvent and

solution will be the difference in scale reading plus the

change in solvent level within the reservoir at the two

heights. This error was estimated by comparing the difference

in solvent meniscus level at two positions near the top and

bottom of the total range of 40 cm, measured directly with a cathetometer, with the difference in osmometer scale readings at the two positions. The difference in the scale readings was found to be 0.022 cm larger than the difference measured

with the cathetometer. This amounts to a scaling error in h of

0.022/40 or 0.06 percent, and a corresponding error in of —0.06 percent, shown in line 6 of table 2. Changes in the length of the control bubble whose motion

is used to sense liquid flow give rise to a third source of error

in solvent height. When the solvent level changes in response

to changes in solution concentration, the hydrostatic pressure

I on the control bubble changes and the bubble expands or

contracts. Treating the bubble as a perfect gas, which is adequate for our present purpose, we can easily show that

the relative error in h is given by bp/ig/Po, where b is the

length of the bubble and Po is atmospheric pressure. Assuming a maximum bubble length of 3 cm (a very safe upper

llimit), we find an error in h from this source of 0.34 percent.

The control bubble is located directly underneath the membrane. Its expansion when the concentration of solution in

I the osmometer is increased therefore gives rise to an apparent

increase in h, or a decrease in the apparent value of M„. The

Iresulting error in M„ of —0.34 percent is shown in line 7 of

table 2. Measured values of h will be too low if the membrane is

not completely impermeable to solute. Although experience

suggests that permeation should be negligible for the memjranes and solutes employed in this work, limits of error

roni this source were estimated for SRM's 1482 and 1483 as iescribed below.

Membrane permeation effects were estimated for SRM

1482 by comparing the values of h obtained for a solution of

SRM 1482 using the 450D membranes normally employed in his work with the values obtained for the same solution with

m appreciably thicker membrane (ArRo 600D). The measured value of h was about 13 cm, and the value obtained

NiXh the thicker membrane was larger than that obtained with

he normal membrane by 0.03 ± 0.04 cm. Taking the worst

;ase, we have a maximum difference of 0.07 cm, which

mplies a maximum relative error in M„ of 0.07/13, or +0.5

)erc^nt. Errors from membrane permeation were estimated for SRM

483 by looking for a slow decrease in h with time resulting rem such leakage. No such drifts were observed for a

olution which gave a value of h of about 13 cm. We estimate

hat we could have observed a drift of 0.01 cm, and that such

I drift might imply a total decrease of 0.02 cm, allowing

or instrumental response time. We therefore estimate the

imit of error from membrane permeation for SRM 1483 as

).02/13, or +0.2 percent.

Finally, the difference in density between solvent and

solution gives rise to an error in h. In practice, h is measured

as the change in reading when solution in the sample side of

the osmometer is replaced by solvent. The sample tube is

filled to the same height in both cases. If the densities of

solvent and solution are different, as is usually the case, replacing solution by solvent will give rise to a purely

hydrostatic pressure change, and the observed value of h will be the sum of this change and the change arising from the

osmotic pressure difference across the membrane. The

change in hydrostatic pressure is just ag(p — po), where a is the height above the membrane surface to which the sample

tube is filled and p is the solution density. The resulting

change in the measured h is then a(po ~ P)/Ph- The

difference Po — p is given by c(P(P — 1), so the error in h is just ac(P(p — \)lph- Using eqs (2) and (3), we find that the

resulting relative error in M„ is given by:

Mn ag{\ - Pov)/{RT).

For our osmometer and operating conditions, this error is — 0.06 percent, —0.16 percent, and —0.5.5 percent for SRM's 1482, 1483, and 1484, respectively, as shown in line

9 of table 2.

4.5. Errors due to Cutoff of Virial Expansion

As discussed in section 3, only the first two terms on the

right-hand side of eq (1) were employed for the analysis of

the data for SRM's 1482 and 1484. Although contributions

from the third and higher virial coefficients are smaller than

the resolution of the osmometer, their neglect nevertheless

constitutes a source of systematic error. In order to estimate

the magnitude of the error involved, we estimate the third

term on the right-hand side of eq (1) by making the

assumption = r2^/4. As discussed in section 3, the data

obtained for SRM 1483 are at least not inconsistent with this assumption. This allows us to estimate the contribution to h

of the third term on the right-hand side of eq (3). Its neglect

in the analysis may be treated as an error in the measured h

at each concentration measured; the resulting error in M„

may then be obtained by making use of the estimates of the

effect of errors in h on M„ obtained by comparison calculations as described in section 4.4. In this case, since the "errors" in h are of the same sign for all the measured

solutions, we take the algebraic sum of the individual

changes in M„ given in table 3, each scaled by the ratio of

the third virial term in h to the error in h assumed in table 3. The resulting errors of +0.03 percent and +0.25 percent for SRM's 1482, and 1484, respectively, are shown in line 10 of

table 2. For SRM 1483, contributions from the third virial coefficient are already included in the analysis. In this case, we

wish to set bounds on the possible contributions from the

fourth and higher virial coefficients. In the absence of any means of estimating the fourth virial coefficient theoretically, we resort to the expedient of examining the relative sizes of

the three terms in the right-hand side of eq (1) at the highest

concentration measured. They turn out to be in the ratio

1:0.324:0.026. Thus, the third virial term is only about 8

percent of the second, and the second is about 32 percent

of the first. It seems adequately cautious to assume that as a

183
maximum, the fourth term will be to the third as the second

is to the first. Then we have as a maximum estimate:

r4 - r,T,.

Treating the contribution to h from a hypothetical fourth

virial coefficient of this magnitude as an error in h, in a manner analogus to that described above for the third virial terms for SRM's 1482 and 1484, we obtain an estimated

error in M„ for SRM 1483 of +0.10 percent, as shown in line 10 to table 2.

4.6. Summary

Estimates of the contributions of individual sources to the

overall systematic error in M„ are summarized in table 2. Errors which may be in either direction are shown unsigned;

errors which can only be in one direction are shown with the

appropriate signs. We believe that for errors which can be

either positive or negative, the sum of the absolute values of

the individual contributions gives an overly pessimistic

estimate of total error. In addition, the total error from all the

signed sources together cannot exceed the greater of the sum

of all the positive errors, shown in line 11 of table 2, and the

negative of the sum of all the negative errors, shown in line

12. This quantity, the maximum possible error arising from

the signed error sources, is shown in line 13. In order to combine its effects with those of the unsigned error estimates, we form the root-sum-square, shown in line 14. Finally, to take account of any sources of error not explicitly considered

here, we round each of the estimates so obtained upward to

the next whole percent. The resulting estimates of limits of

systematic error, shown on line 15 of table 2, are those given on the certificates for SRM's 1482, 1483, and 1484.

5. References

[1] Verdier, P. H., and Wagner, H. L., The Characterization of Linear

Polyethylene SRM's 1482, 1483, and 1484. I. Introduction., J. Res. Nat. Bur. Stand. (U.S.), 83, No. 2, (Mar.-Apr. 1978).

[2] See, for example, Flory, P. J., Principles of Polymer Chemistry

(Cornell University Press, 1953).

[3] 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).

[4] Brown, J. E., and Verdier, P. H., The Characterization of Linear

Polyethylene SRM 1475. IX. Number Average Molecular Weight of Fractions by Membrane Osmometry, J. Res. Nat. Bur. Stand. (U.S.) 76A, No. 2, 161-163 (Mar.-Apr. 1972).

[5] Kokle, v., Billmeyer, F. W., Jr., Muus, L. T., and Newitt, E. J., The

Molecular Structure of Polyethylene. XI. Weight- and NumberAverage Molecular Weights of Selected Samples, J. Polvm. Sci. 62,251-261(1962).

[6] Chiang, R., Intrinsic Viscosity-Molecular Weight Relationship for Fractions of Linear Polyethylene, J. Phys. Chem. 69, 1645-1653

(1965).

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

Characterization of Linear Polyethylene SRM 1475. VIII. LightScattering Studies on Polyethylenes in 1-Chloronaphthalene, J. Res. Nat. Bur. Stand. (U.S.) 76A, No. 2, 156-160 (Mar.-Apr.

1972).

[8] Han, C. C, Verdier, P. H., and Wagner, H. L. , The Characterization

of Linear Polyethylene SRM's 1482, 1483, and 1484. III. WeightAverage Molecular Weights by Light Scattering, J. Res. Nat. Bur. Stand. (U.S.) 83, No. 2 (Mar.-Apr. 1978).

[9] See, for example, Morswetz, H.. Macromolecules in Solution (Intersci- ence, 1965), p. 174.

[10] Verdier, P. H., to be published.

I

184
JOURNAL OF RESEARCH of the National Bureau of Standards

Volume 83, No. 2, March-April 1978

The Characterization of Linear Polyethylene SRM's 1482, 1483,

and 1484

. Weight-Average Molecular Weights by Light Scattering

Charles C. Han, Peter H. Verdier, and Herman L. Wagner

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

(October 13, 1977)

Linear polyethylene Standard Reference Materials SRM 1482, 1483, and 1484 are certified for weight- average molecular weight Mui- In this paper the experimental procedures employed for the determination of for these materials by light scattering are described, and the techniques used to analyze the data and to estimate

limits of systematic error are discussed.

Key words: Fraction; light scattering; limiting viscosity number; narrow molecular weight distribution; numberaverage molecular weight; polyethylene; Standard Reference Material; weight-average molecular weight.

1 . Introduction

Standard Reference Materials SRM 1482, 1483, and 1484

are linear polyethylenes with relatively narrow distributions

in molecular weight, issued by the National Bureau of

Standards. Their general characteristics are described in the

first paper of this series [1].' In the present paper, we

describe the determination of their certificate values of

weight-average molecular weight M^, from measurements

jf the scattering of light by solutions of the SRM's in 1-chloronaphthalene at 135°C.

The use of light scattering to determine the molecular

weight and size of macromolecules in dilute solution is well

established [2]. The usual practice is to ineasure the scattering from the macromolecules in solution relative to that from

a material of known scattering power. The measurements

reported in this paper, and consequently the certificate

values of M^,' are referred to values published by Coumou [3]

for the scattering of light of wavelength 546 nm from benzene

at 23 °C.

The value of the differential refractive index dn/dc is needed to obtain weight-average molecular weights from light

scattering data. The differential refractometer employed for

this purpose was calibrated with aqueous solutions of sucrose

at 25 °C, using values for tl^ differential refractive index for

ithis system published by Norberg and Sundelof [4].

2. Experimental

2.1. Light Scattering

a. Apparatus

A "SOFICA 42,000 Photo Gonio Diffusometer" light

scattering photometer was used for scattering measurements.^

' Figures in brackets indicate lileralure references al tlie end of ttiis paper.

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

identified is necessarily the best available for the purpose.

Light of nominal wavelength 546 nm was used, polarized

with the electric vector of the incident beam normal to the

plane containing the incident and scattered wave vectors

(vertical polarization). A green filter and a vertical polarizer were placed in the paths of both the incident and the

scattered beam. Measurements were made at 135 °C with the

scattering cells immersed in a vat of silicone oil which had

been filtered through a glass frit before use. A glass rod supplied by the photometer manufacturer was

used as a working standard. Its scattering relative to that of

benzene was ineasured at room temperature at a scattering

angle of 90°, at the wavelength and polarization used for measurements on polyethylene solutions. During the course

of the measurements, the optical alignment of the photometer was checked periodically by comparing the scattering signals

from solvent at scattering angles of 45 and 135°. The signals were found to differ by less than 1 percent in all cases. The

effects of alignment errors of this size on the values obtained

for the mean-square radius and the weight-average molecular

weight are discussed in sections 3.2 and 4.9, respectively.

The benzene used for calibrating the photometer was

prepared from Certified A.C.S. grade benzene. The starting

material was first extracted eight times with concentrated

H2SO4, four times with a 5 percent aqueous solution of

NaOH, and four times with distilled water. It was then dried

by mixing with anhydrous CaCl2, and fractionally distilled in glass over sodium metal. Finally, it was passed through a column of silica gel and adsorption alumina to adsorb any

remaining fluorescent impurities.

b. Preparation of Solutions

Commercial grade 1-chloronaphthalene was distilled at reduced pressure after removal of residual naphthalene by

sublimation, also at reduced pressure. Immediately before

use, dissolved air was swept out of the solvent by bubbling

oxygen-free nitrogen gas (The Matheson Co., "prepurified

grade") through it at room temperature for at least 1 h. Polyethylene solutions were made up by weight, and their

185
concentrations were calculated using values of solvent density and partial specific volume at 135 °C determined

pycnometrically in this laboratory. The polyethylene samples were dissolved at 135 °C with gentle stirring. They were then

filtered, as described in section 2.1.3, directly into the lightscattering cells and the scattering recorded. In preliminary

experiments, the filters employed showed discoloration and

signs of disintegration after 2 h exposure to 1-chloronaphthalene at 140 °C. Evidence of degradation (discoloration, increased and erratic small-angle scattering) was also

found when filtered solutions were kept at 135 °C for more

than 2 h, but no such evidence was found in less than 2 h. The final measurements were therefore scheduled so that the

total exposure time of the filters to hot 1-chloronaphthalene was less than ^/a h in all cases, and so that no more than 2 h

elapsed between the beginning of heating and completion of

the measurements of each solution.

c. Measurement Procedure

Before each use, xylene vapor was allowed to condense on

the inside surfaces of the inverted light scattering cells, to remove dust. Polyethylene solutions or solvent were filtered

directly into the cells through a hypodermic syringe heated

to 135 °C and fitted with a "Swinney Adapter" filter holder

(Millipore Corp., Bedford, Mass.). For measurements on SRM's 1483 and 1484 and their associated solvent readings,

solutions and solvents were filtered through 0.22 /xm MF

Millipore filters (No. GSWPO 2500) made of mixed esters of

cellulose. No external pressure was applied during the

filtration. The scattering from SRM 1482 was much smaller than that from the other two polyethylenes, and noise from dirt and

dust was a more serious problem. For measurements on this material, the final de-dusting of the scattering cells by

condensed xylene vapor was preceded by boiling in xylene,

soaking in hot chromic acid, and successive rinsing in tap

water, distilled water, and ethanol. Two stacked 0.22 fim

Millipore filters were used to filter SRM 1482 solutions and

solvent into the scattering cells. External pressure of about

0.5 psi* was applied during filtration and adjusted to give a flow rate of about V2 mL/min., in order to make the total exposure time of the filter to hot 1-chloronaphthalene less than V2 h. For all three SRM's, the filter was first rinsed with the

preheated material to be measured (solvent or solution), to remove detergent added during the filter manufacturing

process and surface dust. Three rinses of about 2 ml each were then filtered into the scattering cell and discarded.

Finally, 8 to 10 ml were filtered into the cell for measurement, and the cell was placed in the photometer and allowed

to reach thermal equilibrium.

Measurements of scattered intensity were made at scatter- ing angles from 45 to 135° in 15° steps. The scattering signal

at 90° from the glass rod used as a working standard was measured after each solution or solvent measuremenf. For

measurements on SRM 1483, solvent measurements were made in three of the five scattering cells used. The three sets of solvent measurements were averaged, and the average

readings used for the analysis of the measurements on all the

solutions. For measurements on SRM's 1482 and 1484,

solvent measurements were taken in every cell used for

* 1 psi equals approximately 7 x 10^ Pa.

solution measurements, and the solvent scattering intensities

obtained for each cell were used for the analysis of measure- ments on solutions taken with that cell. In addition, each

cell was always placed in the photometer with the same

angular orientation to minimize the effects of imperfections

in the cells. Seven sets of measurements were made on SRM 1482, five sets on SRM 1483, and six sets on SRM 1484. Each set consisted of measurements on solutions with nominal concentration of: 3, 4, 5, 6.5, 8, 10, and 12 g/L for SRM 1482; 2,

3, 4.5, 6, and 10 g/L for SRM 1483; 0.6, 0.8, 1, 1.3, 1.8,

2.3, and 3 g/L for SRM 1484. For SRM 1483, each set contained one solution at each of the nominal concentrations; some sets for SRM's 1482 and 1484 omitted at most one ofi the nominal concentrations. Thus, the sets of measurements

on SRM 1483 are equivalent, and those for SRM's 1482 and

1484 are nearly so.

2.2. Differential Refractive Index

The differential refractometer employed for measurements

on SRM's 1482, 1483, and 1484 has been described

elsewhere [5]. For the present work, it was modified slightly

by the addition of a condensing lens between the mercury

lamp source and the slit. The instrument was calibrated with

7 solutions of sucrose, with concentrations from 6..3 to 26 g/L, at 25 °C. The sucrose solutions were made up by

weight, and their concentrations were calculated using the

density tables of Schneider et al.[6]. Otherwise, the equipment'

and measurement techniques employed in this work were

identical with those described in [5].

3. Results

3.1. Differential Refractive Index

The experimental determination of the differential refractive index dn/dc described in detail in [5] consists essentially

of the measurement of the displacement d of an optical slit image resulting from the substitution of a solution of concentration c for solvent in one side of a measuring cell. For

dilute solutions, d is proportional to c; the ratio k = d/c is proportional to dn/dc. In practice, k is determined by

measuring displacement for several concentrations and fitting

the observed displacements {o d = kc. Calibration is accomplished by determining the value /cq for a material of known

differential refractive index {dn/dc)^; then for substance i we

have:

m

Is

ill

{dn/dc)i = {dn/dc)Qki/kt). (1

Displacements were measured as a function of concentration for SRM's 1482, 1483, and 1484 at 135 °C inj

1-chloronaphthalene, and for aqueous solutions of sucrose atJ 25 °C. Table 1 shows the resulting values ki (in arbitrary!

units), together with the estimates Si[d) and s{ki) of standard!

deviation in d and k, respectively, and the number of degreesf

of freedom Fi, equal in each case to one less than the numberH

of concentrations measured. The values of Si{d) for the four||

materials are consistent with the physically plausible as-^ sumption that they are all estimates of the same quantity,!

i.e., the inherent imprecision of the measurement of d is independent of the sample. We therefore form a pooled

186
Table 1. Results ofdifferential refractive index measurements at wavelength in vacuum 546 nm.

In tht* headings, ki is the result of fitting the observed displacements d (in arbitrary units) obtained with solutions of substance i of c<)ncentrations r to the form d = kc by least squares; si{d) and s{ki} are the

.standard deviations in d and ki, respectively, obtained from ihe least-squares analysis; is the number of degrees of ireedom asso<'iated with Si{d} and s{ki); .s'(ki) is the standard deviation in k obtained by

jsing a pooled value ktr s(d) as described in the text; dn/dr and s(dn/d<)/\dn/di \ are the differential refractive index and its relative standard deviation, respectively, calculated as described in the text.

Substance

Range of concentration g/L

Si(d} s(ki) S'(ki)

s'{ki)/\ kil

percent

dn/dc\ mL/g

s(dn/dc)

1 dnjdc 1 percent

Sucrose ^ 6.3 to 26 167.46 0.00386 0.08 6 0.15 0.09 0. 1429"

SRM 1482"^ 6.3 to 15 -228.4 0.00878 0.38 7 0.32 0.14 -0.1949 0.17

SRM 1483*^ 5.6 to 13 -225.6 0.00477 0.22 5 0.34 0.15 -0.1925 0.17

SRM 1484<^ 5.6 to 13 -224.4 0.00987 0.43 6 0.32 0.14 -0.1920 0.17

Pooled 0.00744 24

^ Aqueous solutions at 25 °C.

*" Value from [4], used for calibration.

' At 135 °C in 1-chloronaphthalene.

estimate of the variance v(d) = s'^(d) as the average of the

individual estimates of variance, weighted by the number of

degrees of freedom associated with each estimate:

s{d) = [v{d)]^ = [F-'Y.FM']'^

(2)

i

where F — ^F, and the index i is summed over the four

i samples. We then use this pooled value to form improved

estimates s'(/c,) = s{ki)s{d)/si{d). Values of s'{ki) and the

associated relative standard deviations s'(/i:,)/|/ci| are shown

in table 1. We then obtain the relative standard deviation in the ratios ki/ko, where the subscript zero denotes the measurements on sucrose solutions, as:

sikjk,)/\kjk,\ = {[s Ud/kf + [s 'iko)/kof }\ (3)

Finally, we observe that by eq (1), the relative standard

deviation s{dn/dc)/\dn/dc\ in dn/dc is just s{ki/k())/\ki/ko\.

Values of dn/dc calculated from the /c's and the literature

value for dn/dc of sucrose by eq (1) are shown in table 1 for SRM's 1482, 1483, and 1484, together with the associated

lvalues of s{dn/dc)/\dn/dc\.

3.2. Light Scattering

In principle [2], light scattering data from polymer solutions of concentrations c at scattering angles 6 may be

analyzed by fitting cg/Ic to a power series in c and sin^(0/2),

where g is unity for vertical polarization (and cos^d for horizontal polarization), Ic = sm0[I(d, c) — I{0,O)]/Ig, Iq is the scattering signal from the glass working standard at 9 =

90°, and 1(6, c) is the scattering signal from a solution of

concentration c at scattering angle 0:

cg//c = SC;,cWW2). (4)

,'l

In order to use eq (4) for the estimation of molecular

parameters, we must first decide how many terms on the

right-hand side must be included to provide an adequate fit

to the experimental data. The dependence of cg/Ic upon c and upon sin^(0/2) reflects solute-solute interactions and

solute size, respectively. Since both effects increase with

increasing molecular weight, we expect the highest molecular-weight material to provide the most sensitive test of

adequacy of fit. Accordingly, preliminary scattering data for SRM 1484, with the highest molecular weight of the three

SRM's, were first plotted as c/Ic versus sin^(0/2) at constant concentration and versus c at constant scattering angle, to see whether a linear expansion (i.e., retaining only Cqo, Cqi,

and Cio) would provide an adequate fit. The plots revealed

that the linear approximation was clearly inadequate in this case; in particular, the constant-angle plots versus c showed

distinct curvature. The effect of including second-order terms

in eq (4) (C02, Cn, and C20) was therefore investigated by a

series of least-squares analyses of the data. Inclusion of C20 was found to reduce the residual standard deviation in c/lc

by 55 percent, while inclusion of Cn resulted in a reduction

of only 4 to 10 percent and inclusion of C02 increased the

residual standard deviations slightly. The number and range

of concentrations were not sufficient for inclusion of higher

terms in c (C3(), etc.) to be sensible. The final analyses on all three SRM's were therefore carried out including C20 but not the other second-order terms:

c/Ic = Coo + Coism^{d/2) + Cio c + C^o c\ (5)

The coefficients in eq (5) are related to the weight-average

molecular weight M^, moleculai' mean-square radius Rg^,

and second and third virial coefficients A2 and A3 by [2, 7]:

— (K'Coo) ^ (6)

Rg' - 3[Xo/(47rn)]2Coi/Coo (7)

A2 = yzK'Cio, (8)

= yaK'C^o, (9)

K' = ^7TVidn/dc)y{ko*N^V,''S), (10)

where:

A.0 is the wavelength in vacuum of the scattered light, set at 546 nm in this work,

n and ng are the indices of refraction of the solvent and

benzene, taken as 1.586 [8] and 1.503 [3], respectively.

187
dn/dc is the differential refractive index of the solution,

measured as described in 3.1,

/V^ is Avogadro's number, taken as 6.022 X 10^'' mol~',

is the Rayleigh ratio for the vertically polarized scattering

of vertically polarized light f rom benzene, used for calibration and obtained as described in the following paragraph,

and

S is the measured ratio Iq/Ib of the scattering signal obtained

from the glass working standard to that obtained from

benzene.

The "vertical-vertical" Rayleigh ratio is related to the

Rayleigh ratio Uu for the unpolarized scattering of unpolarized light and the depolarization ratio Pu for unpolarized light

by:

V, = Uu{2 - pj/(l + pu).

Using the published [3] values for benzene

Uu = 15.8 X 10-« cm->

and Pu = 0.41, we obtain

(11)

B — 17.8 X 10"*^ cm"

The uncertainty in Muj introduced by the use of this derived

Rayleigh ratio is discussed in section 4.4.

As described in section 2. Ic, from five to seven sets of

measurements were made on each SRM. Each set consisted

of scattering measurements on from five to seven solutions,

together with solvent measurements, at seven scattering

angles. The sets for each SRM are equivalent or nearly so. The data in each set were fitted by least squares to eq (5), and the resulting values of Coo, Cqi, Cio, and C20 were used

to calculate M^, Rq^, A2, and using eq (6)-(10). The

estimates obtained from each set were then averaged. The

resulting mean values and sample standard deviations of the

mean are given in table 2, together with values of the

molecular radius of gyration the ratio A3/{Mu)A2^),

and the number of degrees of freedom (equal in each case to one less than the number of sets).

The values of My^ in table 2 may be compared with the

number-average molecular weights A/„ determined by membrane osmometry and reported in paper II of this series [9].

It will be seen that My^ is slightly greater than M„ for all three SRM's, yielding estimates of the ratio Mu,/M„ in the

range 1.1 to 1.2, consistent with estimates obtained by gel

permeation chromatography [1]. The values obtained for the

second virial coefficient are in crude but satisfactory agreement with those obtained by membrane osmometry [9] and

with literature values for linear polyethylenes in 1-chloronaphthalene [7, 10-12]. In addition, the ratios /43/(M^/l2^)

are consistent with the often-cited estimate [13] of V4. On

the other hand, the values obtained for Rq^ are clearly

absurd, since they indicate that SRM 1482 in solution is more than half again as large as SRM 1483, which has a molecular weight 2V2 times as large as SRM 1482. The

obviously large errors in Rq^ are almost certainly due to a combination of instrumental misalignment and incomplete

removal of dust from the solute. For SRM's 1482 and 1483,

the intensity at 0 = 45° is only 2-3 percent greater than that

at 6 = 135 . Consequently an error from either source of 1 percent in the scattering at 45° relative to that at 135° would

result in errors of 35-100 percent in Rq'^. Clearly, these

values for Rq^ must be treated as no more than very rough

estimates.

4. Systematic Errors

We now list the likeliest sources of systematic error in the

estimates of weight-average molecular weight described in the preceding section, and attempt to set upper limits on

their magnitudes. Individual sources of error are discussed

in the following subsections; the resulting error-limit esti- mates are summarized in table 3, expressed as percent errors applied to M^).

According to eq (6), M„, is the reciprocal of the product

A^'Coo, where K' is given by eq (10). The effects of errors in the quantities that enter into K' are discussed in sections

4.1-4.5. The coefficient Coo may be written as the zero- angle, zero-concentration limit of the quantity

eg cscd/[SG{e, c) - SaiOM, f

where Sg(0, c) is the ratio of the signal obtained at scattering

angle 6 from a solution of concentration c to that obtained

from the glass working standard at the same instrumental

gain. Because of the non-ideality of the polarizers placed in the path of the incident and scattered light, the geometric

factor g is not strictly unity; the resulting error is discussed

in section 4.6. It is clear that systematic errors in 5g(^,c)

and c will affect the value of Coo and therefore of My^; errors from these sources are discussed in sections 4.7 and 4.8

The assumptions implicit in the use of eq (5), (6) and (10)

introduce several possible sources of error; these are dis- cussed in sections 4.9-4.14. Finally, the error limits from

all the foregoing sources are combined and summarized in section 4. 15.

IBIE

4.1 . Index of Refraction of Benzene

I

The index of refraction of benzene at 546 nm and 23 °C is given in [3] as 1.503. We believe that this value should be

good as stated, i.e., to 1 part in 1500. Since riB appears in K' as the square, the resulting relative error in M„ is 2/1500

or 0. 1 percent.

4.2. Differential Refractive Index

I

Errors in our values for the differential refractive index of the SRM's arise both from possible errors in the literature value for the differential refractive index of sucrose solutions,

used for calibration, and from the imprecision of our measurements. We believe that the value of dn/dc for sucrose in

[4] is accurate to 1 percent. The relative standard deviation

of our own measurements, shown in table 1, is 0.17 percent

for each of the SRM's. We choose the 95 percent confidence,

limit corresponding to this value as a reasonable error limit.i The Student t factor [14] for 24 degrees of freedom and 95|

percent confidence limits is 2.064; the 95 percent confidence;

limit is therefore 2.064 X 0.17 percent, or 0.35 percent.

Finally, since dn/dc appears in K' as the square, the resulting errors in My, from the literature sucrose value and

our own measurements are 2 percent and 0.7 percentj

respectively. ,

'mtt

188
Table 2. Molecular parameters obtained by light scattering on solutions of linear polyethylene

Standard Reference Materials 1482, 1483, and 1484 in 1 -chloronaphthalene at 135 °C.

Numbers in parentheses are sample standard deviations of the mean.

Sample

Weight-average

moleciilar weight,"

Mu,, g/mol

Molecular

mean-scjuare

radius,''

Molecular

radius of

gyration,'' y^G f > A

Second virial PORlIlflRnt A,, mol cm'/g^

Third virial

pn#^ffir* if^ fit ''

mol cmVg3

A3 Number of degrees of

1 x't^f^fA i\ in

SRM 1482 13.63 X 10^ 1.79 X 10-'2 133.7 1.59 X 10-3 1.28 X 10-2 0.35 6

(0.13 X 10^) (0.16 X 10-'2 (6.0) (0.08 X 10-3) (0.37 X 10-2) (0.19)

SRM 1483 32.1 X 10^ 6.75 X 10-'3 82.2 1.09 X 10-3 1.34 X 10-2 0.63 4

(1.6 X 10-'') (0.53 X 10 '') (3.2) (0.10 X 10-3) (0.60 X 10-2) (0.37)

SRM 1484 119.6 X 4.75 X 10"'^ 217.9 1.03 X 10-3 2.8 X 10-2 0.40 5

(2.2 X 10^) (0.10 X 10-'^ (2.4) (0.10 X 10-3) (1.7 X 10-2) (0.20)

^ Systematic errors in weight-average molecular weight are discusssd in section 4 of the text and summarized in table 3.

'' As discussed in section 3.2 of the text, there is reason to believe that these values are subject to large systematic errors. We have not attempted to estimate systematic errors in these quantities.

ABLE 3. Percent errors in introduced by assumed errors in measured

quantities and approximations

Source of Error

Error in M^, percent

SRM

1482

SRM

1483

SRM

1484

1. Index of refraction of benzene 0.1 0.1 0.1

2. Literature value of differential refractive index of sucrose

2.0 2.0 2.0

3. Measured value of differential refractive index of SRM's relative to that of sucrose0.7 0.7 0.7

4. Wavelength of radiation 0.5 0.5 0.5

5. Rayleigh ratio for benzene, derived from literature values of Uu and

10. 10. 10.

6. Measured ratios IgIIb 0.4 0.4 0.4

7. Polarizer errors 0.0 0.0 0.0

8. Measured ratios Sg(6, c) 0.3 0.3 0.3

•9. Solvent density 0.2 0.2 0.2

0. Solute weights 0.3 0.4 1.2

1. Reflection correction 0.0 0.0 0.0

2. Instrumental misalignment 0.7 0.7 0.7

3. Refraction correction 0.4 0.4 0.4

4. Anisotropy of polyethylene 0.1 0.1 0.0

5. Temperature dependence of scattering of glass working standard

0.4 0.4 0.4

;6. Cutoff of virial expansion 0.7 1.4 0.9

7. Sum of all the above except (5) 6.8 7.6 7.8

8. Root-sum-square of all the above ex- cept (5)

2.5 2.8 2.8

9. Expected limit of systematic errors from all sources except (5), including sources not identified and treated here

4.0 4.0 4.0

0. Root-sum-square of (5) and (19) 11. 11. 11.

i

4.3. Wavelength of Light

The light-scattering photometer employed for this work

uses a mercury lamp in conjunction with a green filter in the

incident beam which selectively transmits the so-called

"mercury green line," and a similar filter in the scattered

beam to remove any possible fluorescence from the solution.

However, at the relatively high operating pressure of the

mercury lamp, the green-line radiation is appreciably broadened. The light-scattering experiment senses the inverse

fourth power average of the wavelength, as may be seen from

eqs (5)-(10). Broadening of the radiation therefore produces an apparent shift in the effective wavelength. In addition, at sufficiently high pressures the center of the "green line"

spectrum may shift. In order to estimate the size of the errors introduced into A/^ by these effects, we measured the

combined optical transmission cun e of the two green filters placed in the incident and scattered light paths. Using this transmission curve and a plot of the spectral distribution of

lamp output supplied by the lamp manufacturer, we calculated the inverse-fourth power average wavelength of the

scattered light reaching the detector, obtaining a result of

549.6 nm, 3.5 nm larger than the nominal value of 546.1 nm

for the mercury green line. If the actual value of the inversefourth power average wavelength could be determined with

sufficient accuracy, it could be used instead of the nominal

value. However, the data on the spectral distribution of the

lamp output are given to a resolution of only 5 nm, and in addition are merely representative data for the type of lamp

employed, rather than measured values for the lamps actually

used. Direct measurement of the spectral distribution of the

lamps used in this work was impractical, partly because of

the relatively short lifetime of individual lamps, which

resulted in several different lamps being used in the course

of the measurements. We have therefore used the nominal

value of the wavelength in our calculations, and have treated

the deviation of 3.5 nm as a systematic error. In order to ascertain the effect of an error in wavelength of this size upon

Myj, we first note from eqs (6) and (10) that the strongly

wavelength-dependent quantities which appear in the calculation of My; are Xq itself and the index of refraction and

Rayleigh ratio for benzene. From eq (10) and (11), the

wavelength dependence of the calculated My, is that of the

189
expression (A^o''f/u/"B^) (2 — Pu)l{^ + Pu)- Using the values

reported by Coumou [3] for (/„, ns, and p„ at wavelengths of

436 nm and 546 nni, we find that with increasing wavelength,

f/u decreases more strongly than Xo^? while nn and p„

remain essentially constant. As a result, the combined

expression increases by only 13 percent as the wavelength

decreases from 546 nm to 436 nm. Assuming a roughly

linear dependence of the expression on wavelength, we find

that a change of 3.5 nm corresponds to an error of 0.42

percent in M^,. Allowing for some nonlinearity and for the

neglect of the wavelength dependence of dn/dc, we believe

that 0.5 percent is a safe upper limit for systematic errors in arising from uncertainty in the wavelength of the light

used.

4.4 Rayleigh Ratio of Benzene

As described in section 3.2, the value of the "verticalvertical" Rayleigh ratio for benzene was calculated from

published [3] values of Uu and py, using eq (11). However,

the quantities directly measured were not Uu and Pu, but

rather Uu and U^,, the unpolarized scattering from vertically

polarized light. Now K|, is simply expressed in terms of Uu

and f/t, as:

V, = 3/2 Uy - Uu, (12)

and the standard deviation in resulting from known

standard deviations in (independent) measurements of Uy

and Uu may be estimated as the square root of the sum of the

squares of the standard deviations in Uu and the quantity

U^. The standard deviations in Uu and U are given by

Coumou as 3 percent and "better than 2 percent," respectively. In order to convert the relative standard deviation in Uy to an absolute standard deviation, we use eq (12) to backcalculate Uy from the published value of Uu and the value

of Vy calculated from eq (11), obtaining finally an implied

standard deviation in of 0.82 X 10"*^ cm~\ or 4.6

percent. From this estimate of standard deviation and the

account of experimental techniques given in [3], we believe

that 10 percent is a reasonable upper limit for systematic

error in the value of for benzene, and therefore for errors

in our values of Mu, from this source.

4.5. The Ratio Xdh

Seven replicate meajrdrements were made of the ratio IgIJb

of the scattering signal obtained with the glass working

standard to that obtained with benzene, at a scattering angle

of 90°. The resulting standard deviation of the mean value of

the ratio was 0.11 percent. Using the Student t factor for 6

degrees of freedom, we obtain 95 percent confidence limits

of 0.3 percent. The value of the ratio for the glass rod

employed was about 2.5, close enough to unity that both

signals could be measured without changing gain settings.

Thus the only further source of error in the ratio is in the

non-linearity of the detection system. If we allow 0.3 percent

for error from this source, then we obtain our combined

estimate for errors in IqIIb and Mu, from both sources as the

square root of the sum of the squares of the individual error estimates, or 0.4 percent.

4.6. Polarizer Errors

The geometric factor g in eq (4) is unity only if tht vertically oriented polarizers in the incident and scattered

beams transmit no horizontally polarized light at all. In th» general case, we must consider both components of polari;

zation in both the incident and scattered beams. Let t,i be th* ratio of the transmission coefficients for horizontally ano

vertically polarized light for the polarizer in the inciden

beam, and let C,s be the corresponding ratio for the polarizein the scattered beam. Then the observed scattering signai

will be proportional to Vy + t,sHy + l,iVh + CiCMh, where l\ and H denote the vertically and horizontally polarized coma

ponents, respectively, of the scattered radiation, and th« subscripts v and h denote the vertically and horizontally

polarized components, respectively, of the incident radiation]

The ratio Hy/Vy = Vhl^v 's the depolarization ratio py foi vertically polarized light, related to Pu by p„ = Pu/(2 — p„)|

By considering the geometry of the scattering system, we fine [15] that the ///, component of the scattering observed at ai angle 6 is the sum of two components, one independent 0] depolarization and proportional to cos^O, the other arisinj]

from depolarized scattering and proportional to py&m^d. Th(J

observed scattering signal is then proportional to

|

1 + + is)pv + CiUcos'O + Pysin'O).

The measured values of and £,g for the polarizers in ouj

instrument are 0.9 X 10"'^ and 1.0 X 10~^, respectively]

therefore the term in ^,^5 is negligible. The estimated optical

anisotropics of polyethylenes discussed in section 4. 12 impl|

values of Py less than 0.8 X 10"^, so the term (^, + is)p\ can also be neglected for the polyethylene measurements!

Finally, for the calibrating measurements on benzene wij

have Pu = 0.41, which gives py — 0.26. The error in thij benzene measurements is therefore (0.9 + 1.0) X 0.26 >|

10~^, which is zero to the nearest 0.1 percent, and is sil entered on line 7 of table 3. I

4.7. The Ratios Sdd.c)

j

The measured values Sg(0,c) of the scattering from polyl

ethylene solutions and solvent relative to the scattering fronl the glass working standard are subject to errors arising fronl non-linearity of the detection system. However, scatterinl

from solvent and from the most dilute solutions, to which thl

value of Mu) is most sensitive, were measured at the saml

gain settings as the glass working standard. Therefore, wl

believe that the estimated eiror of 0.3 percent used in sectioil

4.5 is also adequate as an estimate of systematic error ill SG(d,c).

I

4.8. Solution Concentration |l

As stated in section 2.1b, solutions were made up bl

weight. Concentrations c were calculated from the relation!

c = wp = wpo/[l - w(l - pov)], Om

where w, p, Po, and v are weight fraction, solution densit)«

solvent density, and partial specific volume, respectively^

Thus, errors in c can arise from errors in w, po, and vm However, the value of is unaffected by errors in v. ThiB

can be seen by observing that the coefficient Cqo in eq (5)B

from which Mu, is calculated by eq (6), is the zero-angleB

zero-concentration limit of the product of c and a quantitS

190
:aii

ihich is a function/ of the scattering angle and measured

mattering signals. As c approaches zero, p approaches

l| lie limiting value p^, so that using the left-hand equality of

q (13), we can rewrite Cqo as Po times the zero-angle, zero- oncentration limit of the product wf. Thus errors in v will

ot affect the final value of M^; errors in po will produce

ilative errors of the same size in M^^. We believe that our

ilue for solvent density is accurate to 0.2 percent, as shown

n line 9 of table 3. Solute and solvent weights were measured on semimicro

^

jalances accurate to 0. 1 mg. The resulting errors in solvent

' eights are of the order of a few parts per million, and can

neglected. In order to estimate the effect of errors in

)lute weights on the values of M„, obtained, a series of

ijmparison calculations was carried out. For each SRM, one

the sets of measurements described in section 2.1c was

losen, and the value of obtained from this set was taken

) a "reference" value. The value for each solute weight in

SRM 1482 SRM 1483 SRM 1484

lumber of solutions in reference subset 7 5 7

ercent changes in from assumed changes in solute -0.30, -0.09, 0.38, 0.10, -1.06, -0.49,

eight 0.00, 0.06, -0.06, -0.08, -0.11, 0.19,

0.04, 0.02 0.03 -0.22, 0.21,

-0.04 -0.08

jm of absolute values of above 0.55 0.65 2.36

Igebraic sum of above -0.31 0.37 -1.12

oot-sum-square of above 0.32 0.41 1.23

turn was then increased by 0.1 mg and the value of M„,

recalculated. The resulting percent changes in the reference

values of My, are shown in table 4, together with the sum of

the absolute values of the individual changes, their algebraic

sum, and the square root of the sum of their squares (rootsum-square). The sum of the absolute values represents the

error if every weighing is in error by the maximum amount

possible and in the direction which maximizes the resulting

error in My,. We reject this estimate as overly pessimistic.

The absolute value of the algebraic sum would be the

appropriate measure if all the weighings were in error by the same amount, and the root-sum-square would be appropriate

if the individual errors were of random sign. Since both these

possibilities seem physically plausible, we select as our error estimate the larger of the absolute value of the algebraic sum

and the root-sum-square. As shown in table 4, this turns out

to be the root-sum-square in all three cases. The corresponding values are shown on line 10 of table 3.

Table 4. Percent errors in weight-average molecular weight My, introduced by assumed errors of 0.1 mg in solute weights

4.9. Reflection Correction

As a result of the reflection of light from the surface of the

altering cell, the signal observed at a scattering angle 6

ill include a component due to light scattered through an

ngle TT -\- 0. Several expressions have been given [2b, 7,

6] for the magnitude of this effect, which depends upon the

fstem geometry and upon the indices of refraction of the

pattering solution, the scattering cell, and the surrounding

edium. When the effect is large, for example when the

irrounding medium is air, explicit coiTcction must be made

the observed scattering signals. For the work reported

ere, the surrounding medium was a silicone oil with an

ilidex of refraction of about 1.5, so that all three media have

30ut the same index of refraction. In this case, the correcon will be very small, and it will suffice to set an upper

mit on the error introduced by its neglect.

The fraction fr of light reflected at a perpendicular

terface between regions with index of refraction «i and ^2

given by Fresnel's formula as fr — {{iii — ni)l(ni + n2)Y'-

i the present case, all the indices of refraction involved are

iout 1.5; the maximum difference between them is about

T, giving a value of fr about 0.001. The fraction of

fdiation scattered through tt + 6 appearing in the output at Ottering angle 6 is approximately [7] 2/i-, or about 0.002.

appose we wish to estimate an intercept a in the equation = a — bx, where y is inversely proportional to the intensity

af the scattering signal andx = sin^(0/2), but the intensities

Jserved (denoted by primes) are linear combinations of the rue" intensities at 6 and tt + 6:

/i' = (1 - S)/i + 8/2;

h' = 8/1 + (1 - 8)/2,

(14)

where the subscripts 1 and 2 denote scattering angles d and

TT + 6, respectively. We wish to find the error in the

intercept a, determined from measurements at two points

(xi,yi) and {x2,y2), where j; = 1//,-, due to the use of// and

1

2' instead of /i and 1 2- Clearly the size of the error depends

upon the relative sizes of /j and 12; if / 1 is equal to /2 no amount of mixing will produce an enor in the intercept. Here we are interested in the case where /2 is only slightly smaller

than 1 1, and we write:

// = /2'(l + e). (15)

Solving for the apparent intercept in terms of (xi,yi') and

(x2-,y2') and using eqs (14) and (15) as appropriate, we find

after some manipulation that to second order in 8 and e, the

relative error in the intercept is given by

8e(:»;2 + ^i)/(^2 ~ Xi).

Taking the maximum and minimum scattering angles used

for X2 and x^, we have {x2 + Xi)/{x2 ~ Xi) = ^J2. For SRM

1484, with the strongest angle-dependence of the three

SRM's, the observed scattering signal at 135° was about 6

percent larger than that at 45°. Then we have e = 0.06, and

the relative enor in My, from neglect of the reflection

correction is 0.002 X 0.06 X ^2, or about 0.02 percent for SRM 1484 and even less for the other two SRM's. To the

nearest 0.1 percent, this is zero, and is so entered on line 11

of table 3.

191
4.10. Instrumental Misalignment 4.12. Anisotropy of Polyethylene

As described in section 2.1a, the optical alignment of the

photometer was checked by observing that the scattering

signals obtained from solvent at angles of 45 and 135

differed by less than 1 percent. From consideration of the

instrument geometry and the alignment procedure, it appears

that the likeliest misalignment is a constant offset in the

scattering angle. For the vertically polarized scattering of

vertically polarized light from solvent, the signal observed at scattering angle d should be proportional to esc 6. It can

easily be shown that in this case, a difference in scattering

signal at 45 and 135° of 1 percent could be produced by an

offset in the scattering angle of only 0.3°, which is consistent

with our estimate of the accuracy of the alignment. Using the

notation of section 4.9, we find that the relative error in the

intercept a, and therefore in M^,, arising from equal and

opposite relative errors 8/2 in ji and j2 is given by

{xi + X2 + 2xiX2b/a)(8/2)/(x2 - xj.

For Xi and X2 corresponding to scattering angles of 45

and 135° respectively, this reduces to the simpler form

8(1 + i6/a)V2.

Thus the error increases with b/a, which is proportional

to the mean-square radius. However, even for SMR 1484,

the term ^ b/a is only about 0.05, and the error given by

the above expression for 8 = 0.01 is 0.7 percent for all three

SRM's.

4.11. Refraction Correction

The observed scattering signal is proportional to both the

scattering volume "seen" by the detector and the angular

aperture of the detector optics. In general, both these

quantities are functions of the index of refraction of the

scattering liquid and of the system geometry. Equation (10)

is written for the special case where the size and uniformity

of the incident light beam are such that the incident intensity

is constant over the region "seen" by the detector. For the

instrument employed in this work, this condition is only

approximately satisfied and eq (10) is not strictly valid. In principle, the factor n^^ in eq (10) should be replaced by a function of rig, the index of refraction ng of the solutions

being measured, the system geometry, and integrals of

intensity over various parts of the beam profile. However, for our present purpose it is neither practical nor necessary t obtain the exact expression. It is shown elsewhere [17] that

in the special case where the incident beam dimension is much smaller than the region "seen" by the detector, the

shape of the beam profile is irrelevant and the correct expression is obtained by replacing ng^ in eq (10) by

ngnBiriB + z)/i^s ^)'> where z is a function of system

geometry equal to about 1/9 for our instrument. The correction factor to be applied to eq (10) in this case would then be

just ins/n.B){nB ^)/('*s + 2). This represents the limiting case; in our instrument the beam and the detector aperture

are roughly the same size. The correction will then be

smaller, and we can use the small-beam expression as an upper limit on the error in eq (10) from refraction effects. Taking rig = 1.503 and ns = 1.586, we find a correction

factor of 1.004, or a limiting error of 0.4 percent.

Equations (6) and (10) are derived on the assumption that the light scattered by the solute is not depolarized. When the solute is optically anisotropic, in eq (6) should be

replaced by My,{l + ^), where the correction term ^ is given

[18] by:

^ = {l/45){l/M)i(y^)/M)[47rnsNjidn/dc)f, (16)

where (y^) is the mean-square optical anisotropy of the solute

molecules. For polyethylene, (y^) is given approximated

[19] as 267 X lO"^" cm^ per CH2 group. The ratio {y^)/M is just 1/14 of this, or 1.91 X 10"^^ cm^/g. Using this value,

and values already cited for the other quantities in eq (16), we find values for ^ of 0.001, 0.0005, and 0.0001 for SRM .s 1482, 1483, and 1484, respectively. The corresponding

error estimates are shown on line 14 of table 3, rounded to the nearest 0. 1 percent.

4.1 3. Temperature Dependence of Scattering of Glass

Since the glass rod used as a working standard was compared with benzene at 23 °C and with the polyethylene

solutions at 135 °C, any temperature dependence in the

scattering from the glass rod will give rise to errors in our values of Mu,. It appears [20] that for the type of glass used

for the working standard, the temperature-dependent scatter- ing should amount to no more than 1 percent of the total scattering, and the temperature dependence of this part

should be no stronger than the first power of the absolute

temperature. The resulting maximum error, for comparisons

between 23 and 135 °C, is 0.4 percent.

4.14. Cutoff of Virial Expansion

As described in section 3.2, virial coefficients beyond the third were not included in the analysis of the light-scattering

data. At the solution concentrations employed in this work,

their contribution should be negligible. Nevertheless, theii neglect constitutes a source of systematic error, upon whicli

we now attempt to set a limit. We first examine the relative; sizes of the terms Cno, Ciqc, and Czqc^ in eq (5) at the maximum concentrations at which measurements were taker

for each of the three SRM's. The relative sizes turn out to be 1.00 : 0.52 : 0.08 for SRM 1482, 1.00 : 0.70 : 0.15 foji SRM 1483, and 1.00 : 0.74 : 0.09 for SRM 1484. The' series all appear to be converging at a satisfactory rate. Iri addition, in each case the ratio of the third term to the! second is appreciably smaller than the ratio of the seconcj

term to the first. Lacking any means of estimating the size o: the fourth virial coefficient directly, it seems sufficiently

cautious to suppose that the ratio of the fourth term to thej third will be no larger than the ratio of the second term to tht].

first, i.e., C30 ^ CioC2o/Coo- In terms of the virial coeffij

cients, this amounts to the assumption /1 4 < ^/i M„,/l2'43

using the relation ^4 = ^K'C^o, the analogue of eqs. (8) anc

(9) for the fourth virial coefficient. The effect of a value o C30 of this maximum size upon the value of My, was found b; a technique similar to the method described in 4.8 fo estimating the effects of errors in solute weights. For eacl

192
SRM, a typical set of measurements was chosen as a reference set, and the corresponding value of taken as the reference value. An "error" term Csoc', with C30 determined as described above, was then subtracted from each

value of c/Ic in the set, and the value of M^, recalculated.

The resulting changes of 0.7 percent, 1.4 percent, and 0.9

percent for SRM 1482, 1483, and 1484, respectively, are shown on line 16 of table 3.

4.15. Summary

Estimates of the contributions oi individual sources to the

overall systematic error in Mjj, are summarized in table 3. It will be seen that the uncertainty in the Rayleigh ratio for benzene, shown on line 5 of table 3, completely ovei-whelms

all the other uncertainties. Furthermore, it is based on

literature values, which may be subject to future revision.

Therefore, we first consider all the listed sources of error except the Rayleigh ratio of benzene. The sums and root-sumsquares of these are also shown in table 3. As discussed in

4.8, we believe that the simple sum is an overly pessimistic

estimate of error, and that the root-sum-square is more

realistic. However, both to temper this judgment and to allow

for other sources of error not considered here explicitly, we

form our final, "best" estimates by increasing the root-sumsquares values of 2.5 to .3 percent in line 18 to 4 percent, as shown on line 19. Finally, we form the root-sum-square of

this value with the uncertainty in the Rayleigh ratio for benzene to obtain final estimates for systematic enors from

all sources of 11 percent, as shown on line 20 of table 3 and

on the certificates for SRM's 1482, 1483, and 1484.

5. References

[1] Verdier, P. H., and Wagner, H. L., The characterization of linear polyethvlene SRM's 1482, 1483, and 1484. I. Introduction, J. Res.

Nat. Bur. Stand. (U.S.) 83, No. 2. (Mar.-Apr. 1978).

[2] See, for example: (a) Kerl<er, M., The Scattering of Light (Academic

Press, New York, 1969); (b) Yamakawa, H., Modern Theory of Polymer Solutions (Harper & Row, New York, 1971); (c) Utiyama,

H., Calibration and Correction Factors, Chapter 4 in Light Scatter- ing from Polymer Solutions. Ed. M. B. Huglin, pp. 61-88 (Academic Press, New York, 1972).

[3] Coumou, D. J., Apparatus for the measurement of light scattering in

liquids; measurement of the Rayleigh factor of benzene and of some

other pure liquids, J. Colloid Sci. 15, 408-417 (1960).

[4] Norberg, P. H., and Sundelof, L. A., A study of the purity of some

polystyrene samples by means of refractive index increment measurements, together with a calibration of a differential refractometer, Makromol. Chem. 77, 77-89 (1964).

[.5] Wagner, H, L., The characterization of linear polyethylene SRM

1475. VII. Differential refractive index of polyethvlene solutions, J. Res. Nat. Bur. Stand. (U.S.) 76A, 151-155 (Mar.-Apr. 1972).

[6] Schneider, F., Schliephake, D., and Klimmek. A., Dichtetabelle fiir wassrige Saccharolosung, Zucher 16, 17 (1963), Sonderbeilage pp. 1-19.

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

characterization of linear polyethylene SRM 1475. VIII. Light

scattering studies on polyethylenes in 1-Chloronaphthalene, J. Res.

Nat. Bur. Stand. (U.S.) 76A, 1.56-160 (Mar.-Apr. 1972).

[8] Wagner, H. L., and Hoeve, C. A. J., Effect of molecular weight on

the refractive increment of polyethylene and n-Alkanes, j. Polvmer

Sci. Part A-2 9, 1763-1776 (1971).

[9] Wagner, H. L., and Verdier, P. H., The characterization of linear polyethylene SRM's 1482, 1483, and 1484. II. Number-average

molecular weights by membrane osmometrv, J. Res. Nat. Bur. Stand. (U.S.) 83, No. 2, (Mar.-Apr. 1978).

'

[10] Brown, J. E., and Verdier, P. H., The characterization of linear polyethylene SRM 1475. IX. Number average molecular weight of

fractions by membrane osmometry, J. Res. Nat. Bur. Stand. (U.S.) 76A, 161-163 (Mar.-Apr. 1972).

[11] Kokle, v., Billmeyer, F. W., Jr., Muus, L. T., and Newitt, E. J., The

molecular structure of polyethylene. XI. Weight- and numberaverage molecular weights ol selected samples, J. Polymer Sci. 62,

251-261 (1962).

[12] Chiang, R., Intrinsic viscositv-molecular weight relationship for frac- tions of linear polyethylene, J. Phys. Chem. 69, 1645-1653

(1965).

[13] See, for example, Florv, P. J., Principles of Polymer Chemistry,

(Cornell University Press, Ithaca, New York, 195.3); Morawetz, H., Macromolecules in Solution (Interscience Publishers, New York

1965).

[14] See, for example. Handbook of Mathematical Functions, M. Abramowitz, and I. A. Stegun. Ed., Nat. Bur. Stand. (U.S.), Appl. Math.

Ser. 55 (1964).

[15] Reference 2a, Chapter 10. [16] Kratohvil, J. P., Calibration of light-scattering instruments. IV. Corrections for reflection effects, J. Coll. Interface Sci. 21, 498-

512 (1966).

[17] Verdier, P. H., to be published.

[18] Utiyama, H., and Tsunashiina, Y., Measurements of anisotropic light scattering and thermal transition in optical anisotropy of pol\-amethylstyrene, J. Chem, Phys. 56, 1626-1633 (1972).

[19] Jernigan, R. L. , and Flory, P. J., Optical anisotropy of chain

molecules. Theory of depolarization of scattered light with application to n-Alkanes, J. Chem. Phys. 47, 1999-2007 (1967).

[20] Macedo, P. B., private communication.

193

JOURNAL OF RESEARCH of the National Bureau of Standards

Volunne 83, No. 2, March-April 1978

The Characterization of Linear Polyethylene SRM's 1482, 1483,

and 1484. IV. Limiting Viscosity Numbers by

Capillary Viscometry

Herman L. Wagner and Peter H. Verdier

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

(October 19, 1978)

Linear polyethylene Standard Reference Materials SRM 1482, 1483, and 1484 are certified for limiting

viscosity number in 1,2,4-trichlorobenzene and 1-chloronaphthalene at 130 °C. In this paper the experimental

procedures employed for the determination of limiting viscosity numbers for these materials by capillary viscometry

are described, and the techniques used to analyze the data and to estimate limits of systematic error are discussed.

Key words: Capillary viscometry; fraction; limiting viscosity number; narrow molecular weight distribution; number-average molecular weight; polyethylene; Standard Reference Material; weight-average molecular weight.

1 . Introduction

Standard Reference Materials 1482, 1483, and 1484 are

linear polyethylenes with relatively narrow distributions in molecular weight, which are issued by the National Bureau

of Standards. Their general characteristics are described in the first paper of this series [1].* In the present paper, we

describe the determination of their certificate values of

limiting viscosity number at 130 °C in 1,2,4-trichlorobenzene

(TCB) and in 1-chloronaphthalene (ICN). The determination

of limiting viscosity number by capillary viscometry is relatively simple. Although the relationship between limiting

viscosity number and molecular weight remains analytically

intractable, it has been well established empirically for linear polyethylene in the solvents and at the temperature

cited above [2].

2. Experimental

Viscosity measurements were made with a Cannon-Ubbelohde filter stick viscometer (Cannon Instrument Co., State College, Pa.,^ size 75) immersed in a constant-temperature

bath. Flow times in the viscometer were measured with a Hewlett-Packard Autoviscometer, Model 5901 B. Flow limes were measured in both solvents for solutions

whose concentrations ranged from 2 to 9 g/L for SRM 1482,

1 to 5 g/L for SRM 1483, and 0.3 to 2 g/L for SRM 1484.

All solutions were made up directly by weight, without

employing successive dilution techniques. Concentrations were calculated using values of solvent density and partial

specific volume determined pycnometrically in this labora-

'tory. The ICN was obtained from commercial material by

distillation at reduced pressure after removal of residual

naphthalene by sublimation, also at reduced pressure. Several sources of TCB were used, without apparent effect on

' Figures in brackets indicate 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 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.

the results obtained. From 0.05 to 0.1 percent of the

antioxidant 2,6-di-ierf-butyl-4-methylphenol was added to

all solvents. The polyethylenes were dissolved by heating the

solvent to 130-140 °C with occasional stirring, and the

solutions were then tranferred to the viscometer through a

sintered glass frit, as described in ASTM D 1601-61.^ A few

minutes were allowed for thermal equilibration, then flow

times were measured repeatedly until a value stable to 10 ms

or so was obtained. The flow times measured in this way

ranged from 70 to 100 s in TCB, and from 100 to 150 s in ICN.

3. Results

The solution viscosity T7(c) may be expanded as a power

series in solution concentration c:

Tj(c) = P' + Q'c + R'<^ + . (!)

The viscosity number, defined as [17(0) — i7(0)]/[7j(0)c], is then:

Mc) - 7,(0)]/[r,(0)c] = Q'/P' + {R'/P')c + .

The limiting viscosity number, for which we shall employ the

symbol A in this paper,* is just the zero-concentration limit

of the viscosity number [3], and is given by the ralio Q' /P' of

the coefficients in eq (1). The zero-concentration derivative

of viscosity number with respect to concentration is usually

expressed as A^/c', where k' is called the Huggins coefficient

[3] and is given in terms of the coefficients in eq (1) by

P'R'/Q'^

For a properly designed capillary viscometer, the solution

viscosity is almost proportional to the product of solution

density and measured flow time [4]. The departure from

Available from the American Society for Testing and Materials, 1916 Race Street, Philadelphia,

Pa. 19103.

^ The symbols LVN and [rj] are often used to denote this quantity; here we prefer a symbol which

is not an acronym and is free of punctuation marks.

195
proportionality is due to a combination of kinetic energy

effects and hydrodynamic effects at the ends of the capillary.

For the viscometer design and Reynolds numbers used in this work, the relationship between viscosity and flow time is given approximately [5] by:

17/p = Cu - Et-\ (2)

where p is the density of the liquid, tm is the measured flow

time through the capillary, and C and E are constants of the

viscometer, determined experimentally. Since only ratios of

viscosities are needed for the determination of limiting

viscosity number and Huggins coefficient, it is convenient to introduce a "corrected" flow time /, defined by:

t = tjl- Kt-^), (3)

with K — E/C. In terms of t, eq (2) becomes rf/p — Ct, and

using eq (1), we can write the product pt as a polynomial in concentration:

p{c)t{c) = P + Qc + Rc^ + • • , (4)

where P, Q, and R are equal to the corresponding primed

quantities in eq (1) divided by the viscometer constant C,

and we have A = (>/P, k' = PRIQ"".

In the remainder of this section, we discuss first the

method used to obtain the constant for the viscometer

employed in this work, then the procedures used to obtain

limiting viscosity numbers and Huggins coefficients for SRM's 1482, 1483, and 1484 from the "corrected" flow

times, and finally the procedures employed to estimate the

effect of shear rate upon the results.

3.1 . Correction for Kinetic Energy and End Effects

The correction factor K in eq (3) was determined by

measuring flow times for two certified viscosity standards

(Cannon Instrument Co., State College, Pa.), of known

viscosity and density. One (N4) of these was chosen to give

a flow time close to that obtained with 1,2,4-trichloroben- zene, the less viscous of the solvents in which limiting

viscosity numbers are reported. The other (S3) was chosen to have a v.ery long flow time, giving a "correction" Kt^ of

about 3 X 10~^. Six measurements were made with N4 and

four with S3. A measurement consisted of charging the

viscometer with liquid and measuring flow time repeatedly

until a constant flow time was reached. The resulting mean

flow times were used in eq (2) to determine A. Letting the

subscripts A' and S refer to measurements made on N4 and

S3, respectively, we write eq (2) for each mean flow time and

solve the resulting pair^f equations for E/C , obtaining:

K^E/C= (rt^ - ts)/{rt],' - ts^l (5)

where r = VsPiv/iTq^Ps)-

The standard deviations of the mean flow times amounted

to about 0.01 percent for both liquids. Using Student t factors [6] for 5 and 3 degrees of freedom, we obtain 95

percent confidence limits of 0.02 percent and 0.03 percent

for flow time measurements on N4 and S3, respectively. The

effects of these uncertainties upon the value of A, and

ultimately upon the values of A, are discussed in section

4.3.

3.2. Limiting Viscosity Numbers

Limiting viscosity numbers were determined, for each

SRM and each solvent, by measuring flow times for solvent

and for solutions of several different concentrations. The

measured flow times were first converted to "corrected" flow

times, using eq (3). The corrected flow times were then

multiplied by solution densities calculated from measured

values of solvent density and partial specific volume. In preliminary studies, it was found that for concentrations c such that the ratios p{c)t{c)/[p{0)t{0)] were less than 1.4,

plots of {p(c}t(c)/[p{0)t(0)] — l}/c versus c appeared linear,

in accordance with eq (4). The certification measurements

were therefore carried out in this concentration range, and

the products p{c)t{c) were fitted by least squares to secondorder polynomials in solution concentration c, as shown in eq

(4). The limiting viscosity numbers A and Huggins coefficients k' were then obtained as the ratios Q/P and PR/Q^ of

the coefficients in eq (4). In principle, the flow time for a given viscometer, solvent,

and temperature ought to be constant in time. In practice,

however, solvent flow times appeared to be materially more

reproducible within a single day than over longer periods.

Standard deviations of solvent flow times measured within a single day were typically about 16 ms; standard deviations of

flow times measured on different days were about twice this value. Measurements on each SRM and in each solvent were

therefore grouped into subsets, each consisting of one or two

values of solvent flow time and values of flow time for several

solutions. All the measurements in each subset were made

on the same day. The flow times in each subset were fitted separately by least squares to eq (4). For each SRM and each

solvent, several subsets of data were obtained, leading to several estimates of A and k' . In some cases, the subsets were far from equivalent, some subsets containing twice as many measurements as others. The structure of the subsets

and data analysis techniques employed are discussed separately for each of the three SRM's in the following subsections.

a. SRM 1482

Five subsets of measurements on SRM 1482 were made in each solvent. Each subset consists of from six to twelve flow

time measurements, including solvent flow times. The solutions had nominal concentrations of 2, 3, 4.5, 7, and 9 g/L. • Some nominal concentrations were omitted from some of the

subsets; other subsets contain more than one solution of the same nominal concentration. Consequently, the estimates of

A and k' obtained from the separate subsets differ appreciably in precision. The final estimates of A and k' in each

solvent were therefore taken as weighted averages of the

estimates from the individual subsets, obtained as described

in the following paragraph.

Let the number of flow time measurements (of both solvent

and solutions) in the ith subset be A',. The least squares

analysis for the fth subset yields an estimate A, of limiting

viscosity number, together with an estimate Vi(t) of the

variance in flow time inferred from the mean-square differ- ences between observed and calculated (from eq (4)) flow

times, and an estimate v{Ai) of the variance in A,-. Each

estimate z'(Ai) is the product of Vi{t) and a factor obtained

from the covariance matrix for the ith subset by standard

196
techniques [6]. The scatter in the values v{A.i) therefore

reflects both the differences between the covariance matrices

for the subsets and the scatter in the individual estimates

Vi(t). We now make the assumption that all the Vi(t) for a given solvent are estimates of the same quantity v(t). Since

three parameters are fitted in each subset analysis, the

number jpj of degrees of freedom associated with Vi(t) is just — 3. Our best estimate of v(t) is given by the average of

the Vi{t) over all the subsets, weighted by the Fj, i.e.,

v{t) = 2 FivM,

i

here F = the summations are taken over all the

subsets for a given solvent. We can then obtain improved

stimates i''(A,) of the variance in A,-, which are free of the

scatter in the individual estimates i',- (t), as

v'iAd = v(AMt)/vM.

inally, we obtain our overall estimate of A as the average of

he A,-, weighted inversely by the v'{Ai}, i.e..

A= ^v'iAi)-'

i

with variance v{A) given by

lv'{Ad-'K, (6)

v{A) iv'iAr' (7)

with F degrees of freedom. Finally, the standard deviation

i(A) in A is obtained as s(A) = [i)(A)]"^. Overall estimates

jf /c' and s(k') are obtained by an exactly analogous procedure. The results are given in table 1.

b. SRM 1483

Five subsets of measurements on SRM 1483 were made in rCB. Each subset contains five solution flow times, for solutions with nominal concentrations of 1, 2, 3, 4, and

> g/L, and two solvent flow times. Since the subsets are

issentially equivalent, we obtain our final values for A and

:' as the unweighted averages of the estimates from the

ndividual subsets. Three parameters are determined for ;ach subset, so four degrees of freedom are associated with

he estimates of the variance in A and k' from each subset.

Additional estimates of the variance in A and k\ also

associated with foiu' degrees of freedom, are obtained from

the set of five individual subset estimates of A and A'. Our

final estimates of the variance in the subset values of A and

k' are then formed as the unweighted average of the six

individual estimates, one from each subset analysis and one

from the set of subset values of A and A', and are associated

with a total of 24 degrees of freedom. The estimated

variances ^(A^) and v(km') of the final mean values of A and

A-' are then of course just ^/s the estimated variances v{A]

and v(k') of the individual values.

The estimated variance v{t) and standard deviation s(t) in flow time are not used directly in the calculation of A, A

' and

their variances. They may be obtained by obsei"ving that for equivalent subsets, the ratio v{t)/v{A) of the variance of a single measurement of flow time to the variance of a single

subset determination of A is constant. Choosing the quantity

Vi{t)/'^i f(A,) to estimate this ratio, we have

v{t) = s'{t) = v{A) ^vM/J^viAd

i i = 5viAJ S^.-W/IKA,-),

(8)

where i'(Aj) and Vi{t) are the estimated variances in A and in

t, respectively, obtained from the ;th subset analysis.

Four subsets of measurements on SRM 1483 were made in ICN. Three of these were identical in structure with the

subsets in TCB. The fourth subset differed from the other

three only in the omission of one of the solvent flow time

measurements. We shall refer to this subset as the six-point

subset, and to the others as the seven-point subsets. We first obtain estimates of A, A', f(A), v{k'), and v(t) from the three

equivalent seven-point subsets, in a way analogous to the

method employed for the measurements on SRM 1483 in TCB. The variances so obtained are associated with 14

degrees of freedom, four from each subset and two from the

subset-to-subset variation. We then combine these estimates

with those from the six-point subset, associated with three

degrees of freedom, in the way described in section 3.2a,

obtaining the final values given in table 1, with a total of 17

degrees of freedom.

c. SRM 1484

Five subsets of measurements on SRM 1484 were made in each solvent. Each subset contains one or two flow times for

Table 1. Limiting viscosity numbers and Muggins coefficients for solutions of linear polyethylene Standard Reference Materials 1482, 1483, and 1484 in

1 ,2,4-trichlorobenzenf (TCB) and 1 -chloronaphthalene ( ICN) at 130 °C, obtained by capillary viscometry

Slatidard devialiuns s(0 in viscometer fluw limes are also shown, as an indiealion of ihe overall precision of llie ineasureineiits.

Solvent Material s(t) seconds

Limiting viscosity number, A,

mL/g

Standard deviation in A,

mL/g

Muggins coeffi- cient, A'Standard deviation in A"

Number of de- grees of free- dom

TCB SRM 1482 0.052 40. IS 0.13 0.399 0.011 28

SRM 1483 .0.56 79.40 .31 .419 .013 24

SRM 1484 .0.39 197.93 .60 .462 .010 22

ICN SRM 1482 .064 .36.36 ,11 .446 .011 24

SRM 1483 .064 70..56 .28 .461 .016 17

SRM 1484 .064 169.38 .60 .526 .014 22

197
solvent, flow times for two solutions with nominal concentrations of 0.6 g/L, and one flow time each for solutions with

nominal concentrations of 0.4, 0.8, 1.2, and 1.8 g/L. Since

the number of solvent flow times is not the same in every

subset, the subsets are not ecjuivalent. They were therefore

analyzed by the same technique employed for SRM 1482 and

described in section 3.2a. The results are shown in table 1.

3.3 Shear Rate Dependence

At low rates of shear, the viscosity of a solution of flexible

macromolecules is independent of shear rate. At higher rates of shear, however, solution viscosity decreases with increasing shear rate. The possibility of dependence of our.measured

viscosities upon shear rate was investigated by a series of

comparison measurements in two capillary viscometers with

different shear rates. Since shear-rate dependence increases

with increasing molecular weight, measurements were made

on solutions of SRM 1484, the highest in molecular weight of

the three SRM's.

The maximum shear rate in a capillary viscometer is given

[7] in tenns of the flow time t and the bulb volume V and

capillary radius a of the viscometer by the expression

4V/(7ra''i). For the viscometer employed for the measure- ments described in section 3.2, hereafter referred to as the

reference viscometer, this gives a maximum shear rate of

about 3 X lO'' s~' for measurements in TCB at 130 °C. The

viscometer employed for comparison had a maximum shear

rate of about 6 X 10'^ s~' for the same solvent and

temperature.

Flow times for solvent and for a solution of SRM 1484 with a nominal concentration c of 1 g/L were measured in both

viscometers. The kinetic energy and end effect correction

factor A^, determined as described in section 3. 1, was applied

to the flow times measured with the reference viscometer.

The corresponding correction for the comparison viscometer was found to be negligible from the manufacturer's calibration measurements. The ratios t(c)/t(0) of solution flow time

to solvent flow time were 1.219 for the reference viscometer

and 1.221 for the comparison viscometer. The difference

between them is consistent with our estimated precision of

0.001 in the ratio, and is in the opposite direction from the

expected effect of shear-rate dependence, which would lead

to a smaller ratio at higher shear rates. Thus we are unable to detect any shear-rate dependence in our results.

4. Systematic Errors

We now list the likeliest sources of systematic error in the

estimates of limiting viscosity number described in the

preceding section, and attempt to set upper limits on their

magnitudes. Individual sources of error are discussed in the

following subsections; the resulting error-limit estimates are summarized in table 2, expressed as percent errors applied

to A.

In this work, A is calculated as the ratio Q/P of coefficients in eq (4), which are obtained by fitting the product

p{c)t{c) to a second-order polynomial in solution concentra- , tion cby least squares. Here p{c) is solution density and t(c) is related to the measured flow time tm{c) in the viscometer by

eq (3). The correction factor K in eq (3) is obtained as described in section 3.1. The concentration is given by the

product wp(c), where w is the weight fraction of solute in the

solution, and p(c) is given in terms of the solvent densit)

p(0) and the partial specific volume v by:

pic) = p(0)/[l - wil - p(0)il

Systematic errors in p(0), v, K, w, and im(t) will therefore

affect the calculated values of A directly. The effects o

errors in the first three of these quantities can be exhibitec

explicitly. For this purpose, we first write, using eq (4):

Til.

iowi

A =^{[p{c)t{c) - p{om]/[p(0)t(oy]}, (10:

where we use the symbol if{ } to mean the zero-concentra

tion limit of the quantity within the curly brackets. "We ther use eq (3) and (9) to re-express the limit in eq (10) in terms

of a limit which involves only the directly measured quanti

ties w and tmic). After some rearrangement, and making use of the fact that the limit of a product is the product of the limits of the factors when all the limits involved exist, we

find:

A = p(0)-> [ [1 4 2Ktm{0r']/[l - Ktm(OrT

X ^{ [t„,(c) - tmiO)] I [wtM } + 1 ] -

(11 k

from which the effects of errors in p(0), K, and v upon A ma)

be obtained directly.

Table 2. Percent errors in limiting viscosity numbers introduced by

measured quantities

llivi

l'H|

ilylii

siglil

laiK

Jer

ijert

Vi

mifi

>el

icer

iglil

mr, I

Source of error Error in limiting viscosity number, percent,

Solvent

1,2,4-trichloroben- zene

1-chloronaphthalene

Material SRM

1482

SRM

1483

SRM

1484

SRM

1482

SRM

1483

SRM

1484

Solvent density 0.20 0.20 0.20 0.20 0.20 0.20

Partial specific vol ume .10 .05 .02 .11 .06 .02

Solute weights .19 .14 .38 .18 .15 .36

Timer .19 .19 .20 .13 .14 .15

Flow time correction factor .28 .28 .28 .08 .08 .08

Measurement temperature .10 .10 .10 .10 .10 .16

Root-sum-square of the above .46 .43 .56 .34 .32 .46

Sum of the individual error estimates1.06 .96 1.18 .80 .73 .91

Expected limit of systematic

errors from all sources, in- cluding sources not identified and treated here

1 1 1 1 1 1

In the following subsections, the effects of errors ii solution concentration and density, errors in measured flov swm time, and errors in A are discussed in sections 4. 1, 4.2, am

4.3, respectively. Since A is in general temperature-depend

ent, errors in the measurement temperature will give rise tt implicit errors in A; these are discussed in section 4.4

Finally, the error limits from all sources are combined an( ^ti summarized in section 4.5.

.tmr

in

Kills

198
Bit) 4.1 Errors in Solution Concentration and Density

The effects of errors in solution density resulting from

rrors in solvent density and partial specific volume are hown by eq (11). We believe that for both solvents, our leasurements of p(0) are accurate to 0.2 percent, and that ur values of j; are accurate to about 3 percent, or 0.04 mL/g.

>y eq (11), a 0.2 percent relative error in p(0) will lead to 0.2 percent relative error in A, and an absolute error of

.04 mL/g in v will lead to an absolute error of the same size

1 A, leading to the relative errors in A shown in table 2. The most direct source of possible systematic errors in alution concentrations is the balances used to weigh solute

nd solvent. Solute weights for SRM 1482 and solvent

eights for all three SRM's were measured on semimicroalances accurate to 0.1 mg. Solute weights for SRM 1483

nd SRM 1484 were measured on an electrobalance accurate

I 0.04 mg. The resulting errors in solvent weights are of the

rder of a few parts per million, and can be neglected. In

rder to estimate the effect of errors in the solute weights on

le values of A, a series of comparison calculations was

arried out. For each SRM and each solvent, a reference

iibset of typical data points was chosen, one at each

oncentration measured, and a "reference" value of A was

cul^ted from this set of points. The value for each solute

nil eight in turn was then increased by its assumed limit of

Tor, and the value of A recalculated. The resulting percent

langes in the reference values of A are shown in table 3,

gether with the sum of the absolute values of the individual

langes, their algebraic sum, and the square root of the sum

= their squares (root-sum-square). The sum of the absolute

dues represents the error in the case where every weighing

in error by the maximum amount possible and in the

rection which maximizes the resulting error in A. We

— iject this estimate as overly pessimistic. The algebraic sum

ould be the appropriate measure if all the weighings were

_ error by the same amount, and the root-sum-square would

; appropriate if the individual errors were of random sign, nee both these possibilities seem physically plausible, we

fleet as our error estimate the larger of the absolute value of

;e algebraic sum and the root-sum-square. This turns out to

r the absolute value of the algebraic sum for all three SRM's

in TCB and for SRM 1482 in ICN, and the root-sum-square

for SRM's 1483 and 1484 in ICN. The corresponding values

are shown in table 2. A second possible source of systematic error in solution

concentrations would arise if buoyancy corrections were not applied to solute and solvent weighings. Buoyancy corrections were applied to all measured solute and solvent

weighings for SRM 1484, but not for SRM's 1482 and 1483.

From the definition of weight fraction and the usual expression for the buoyancy correction, it is easily seen that as the

concentration tends to zero, the correction factor /(c) by

which the "apparent" weight fraction (i.e., with uncorrected

weighings) should be multiplied to give the true weight

fraction approaches the limiting value

/(O) = (1 - Pa/P.)/(1 - Pa/P»),

where pa, Pui and Pf, are the densities of air, solute, and

solvent, respectively. It is clear from the form of the limit

expression in eq (11) that the limit is converted to its "corrected" value by dividing it by /(O). Although this correction amounts to only about 0.03 percent for polyethyl- ene in TCB and ICN, it affects the last digit in the values of

A given in table 1, and was therefore applied to the data for SRM's 1482 and 1483.

4.2. Timer Errors

Viscometer flow times are measured to 0.001s. Spot

checking suggests that they are accurate to at least 0.01s.

The errors in A resulting from assumed errors in flow time of

0.01s were obtained by the same kind of comparison calculation described in 4. 1 for errors in solute weight; the results are shown in table 4. Again, we reject the sum of the

absolute values of the individual changes as being too pessimistic, and choose the larger of the absolute value of

the algebraic sum of the individual changes and their root- sum-square. Since the viscosity number is essentially measured by the difference between solvent and solution flow

times, it is not surprising that the algebraic sum of the

individual changes including solvent is nearly zero. We

therefore choose the root-sum-square as our error estimate,

as shown in table 2.

Table 3. Percent errors in limiting viscosity number A introduced by assumed errors in solute weights

''V

Material SRM 1482 SRM 1483 SRM 1484

easurements in TCB: Percent changes in -.04, -.07, -.02, -.07 -.01, -.20,

.VIH A from assumed errors in solute weight -.09, -.07, -.08, -.04, -.17, -.14, + .08 + .07 + .14 m of absolute values of above 0.35 0.26 0.66

gebraic sum of above -0.19 -0.14 -0.38

1

iot-sum-square of above 0.16 0.13 0.33

easurements in ICN: Percent changes in -.03, -.06, + .004, -.08, + .03, -.17,

A from assumed errors in solute weight -.10, -.08, -.10, -.03, -.19, -.19, + .09 + .07 + .17 M m of absolute values of above 0.36 0.28 0.75 1

ll gebraic sum of above -0.18 -0.14 -0.35

Wt-sum-square of above 0.17 0.15 0.36

199
Table 4. Percent errors in limiting viscosity number A introduced by assumed errors in measuredflow limes

Material SRM 1482 SRM 1483 SRM 1484

Measurements in TCB: Percent changes in A from assumed changes in: Solution

flow times

+ .03, +.05, + .06, +.05,

-.05

+ .02, +.07, + .07, +.03,

-.06

+ .01, +.08, + .06, +.05,

-.04

Solvent flow time -.16 -.15 -.16

Sum of absolute values of above 0.40 0.40 0.40

Algebraic sum ol above -0.02 -0.02 0.00

Root-sum-square of above 0.19 0.19 0.20

Measurements in ICN: Percent changes in A from assumed changes in: Solution

flow times

+ .02, +.03, + .05, + .04, -.04-.002, +.05, + .065, +.018,

-.04

-.01, +.05, + .05, +.05,

-.04

Solvent flow time -.10 -.10 -.11

Sum of absolute values of above 0.28 0.28 0.31

Algebraic sum of above 0.00 -0.01 -0.01

Root-sum-square of above 0.13 0.14 0.15

4.3. Errors in K

As described in section 3.1, the correction factor was

determined from the flow times fjv and ts of two calibrating

liquids of known viscosity and density. Equation (5) gives K

in terms of tf/, ts, and the ratio r of the viscosities and

densities of the calibrating liquids. The ratio r is equivalent

to the ratio of flow times measured in special viscometers

used for calibration. We believe that r is accurate to 0.

percent. As stated in section 3.1, 95 percent confidence

limits of 0.02 percent and 0.03 percent can be assigned to our measured values of Z^' ^nd tg, respectively. Using the

numerical values for these quantities in eq (5), we find that

changes of these amounts in r, /^y and ts produce changes in K of 10 percent, 2 percent, and 3 percent respectively. The

root-sum-square of the three error limits is 1 1 percent in A'. The products A/^IO)"^ which occur in eq (11) are equal to 0.0088 for TCB and 0.0025 for ICN. From eq (11), errors of 11 percent in these products result in errors in A of 0.28

percent and 0.08 percent for measurements in TCB and

ICN, respectively, shown in table 2.

4.4. Errors in Measurement Temperature

It is clear from eq (11) that so long as we have

Ktjor^

1

and V « A, the temperature dependence of A will be

essentially that of the product of p(0)~' and the limit

^{[tmic) - tJO)]/[wtmiO)}.

The decrease in solvent density with temperature is roughly

0.1 percent per °C for both TCB and ICN, which would lead

to an increase in A of about the same size. Estimates of the

temperature dependence of the limit quantity are not available. However, Chiang [8] has reported a decrease in A of

0.2 percent per °C for linear polvethylenes in six theta

solvents, consisting of aromatic hydrocarbons, ethers, and

alcohols, and Flory, Ciferri and Chiang [9] report a decreasi

of 0. 1 percent per °C for linear polyethylenes in three n

alkanes. Since the temperature dependence of p(0) wil

always contribute an increase in A with increasing tempera

ture, typically of about 0.1 percent per °C, it appears tha the limit quantity must decrease with temperature at two o three times this rate. Lacking more directly applicable data we choose 1 percent per °C as a safe upper limit for th change in A with temperature in the solvents employed i this work. We believe that our measurements of the viscom

eter bath temperature are accurate to 0.1 °C. The corre sponding uncertainty in A of 0. 1 percent is shown in table 2

4.5. Summary

Estimates of the contributions of individual sources to th possible systematic errors in A are summarized in table 2 together with their sums and root-sum-squares. As previous!

discussed, we believe that the sum of the absolute values c the individual errors is an unduly pessimistic estimate of th error from all the sources discussed here, and that the root sum-squares constitute a more reasonable estimate. To tak

account of sources of error not considered explicitly here, vn round each of the root-sum-square estimates, which rang

from 0.32 percent to 0.56 percent, upward to 1 percent in a

cases. Finally, we note that our final error estimates of

percent are exceeded by the sum of the absolute values c individual error estimates in only two out of the six cases and that the largest sum of absolute values, for SRM 1484 i TCB. is only 1.18 percent. We therefore believe that on

arbitrary limits of 1 percent for systematic errors from al sources are quite likely to be realistic. These estimates ar those given on the certificates for SRM's 1482, 1483, ani 1484.

5. References

|

[1] Verdier. P. H.. and Wagner. H. L., The characterization of lines polvethvlene SRM's 1482, 1483. and 1484. I. Introduction, J. Res

Nat. Bur. Stand. (U.S.) 83, No. 2, (Mar. -Apr. 1978).

200

it-
Wagner, H. L. , and Hoeve, C. A. J., Mark-Houwink relations for linear polvethvlene in I-ehloronaphthalene and 1 ,2,4-lrichlorobenzene, J. Polvmer Sci. (Polymer PInsics Ed.) 11, 1189-1200

(1973). See, for example, Yamakawa, H., Modern Theon of Polvmer Solutions Ch. VI (Harper & Row, 1971). See, for example. Hardy, R. C, NBS viscometer calibrating liiiuids and capiUan tube viscometers, Nat. Bur. Stand. (U.S.), Monogr.

55, 22 pages (Dec. 1962). Cannon, M. R., Manning, R. E., and Bell, J. D.. Viscosity measurement: the kinetic energy correction and a new viscometer. Anal. Chem. 32, 35.5-358 (1960). See, for example. Statistical Methods in Research and Production,

Davies, 0. L. Ed. (Hafner Publishing Co., .New York, 1961); Bennett, C. A. and Franklin, N. L., Statistical Analysis in Chemistry and the Chemical Industry (John W ile\ & Sons, Inc., New York, 19.54).

[7] See, for example, Onyon, P. F., Viscometry, Ch. 6 in Techniques of Polymer Characterization, P. W. Allen, Ed. (Butterworths Publications Ltd, London, 1959).

[8] Chiang, R., Temperature coefficient of the unperturbed dimension of

linear polyethylene from intrinsic viscosity measurements in 0

solvents, J. Phys. Chem. 70, 2348-2352 (1966).

[9] Flory, P. J., Ciferri, A., and Chiang, R., Temperature coefficient of the polyethylene chain conformation from intrinsic viscosity measurements, J. Am. Chem. Soc. 83, 1023-1026 (1961).

T^U.S.GOVERNf^ENT PRINTING OFFICE: 1978 0—281-067 (332)

I

201
hNBS-114A (REV. n-77)

J.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUHLICATION OK REPORT NO.

NBS SP 260-61

2, Gov't Acccs.sion No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Standard Reference Materials:

The Characterization of Linear Polyethylene SRM's 1482,

14;]3, and 1484

5. Publication Date December 1978

6. Performing Organization Code

7. AUTHOR(S)

Peter H. Verdier and Herman L. Wagner - Editors

8. Performing Organ. Report No.

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 Complete Address (Street, City, State, ZIP) 13. Type of Report & Period

Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 78-600148

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 new series of three linear

polyethylene Standard Reference Materials, SRM 1482, 1483, and 1484. These

polyethylenes have molecular weights of the order of 10,000, 30,000, and

100,000 g/mol, respectively, and ratios M /M of weight- to number -average

molecular weight of the order 1.2. Their number -average molecular weights

(by membrane osmometry), weight -average molecular weights (by light scattering),

and limiting viscosity numbers in two solvents (by capillary viscometry) are

certified; the procedures employed are described in these collected papers

previously published in the Journal of Research of the National Bureau of

Standards

Iiio

lie

lli y

Mlk\

its

Msg

tioU

imoDi

tit

lii)

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Capillary viscomotry; fraction; light scattering; limiting

viscosity number; membrane osmometry; narrow molecular v;eigur distriburion;

number -average molecular weight; polyethylene; Standard Reference Material;

weight -average molecular weight.

iiiii

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