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1971

Intrinsic viscosities of linear polyethylene Intrinsic viscosities of linear polyethylene

Joseph Shing Chiang

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Recommended Citation Recommended Citation Chiang, Joseph Shing, "Intrinsic viscosities of linear polyethylene" (1971). Masters Theses. 7209. https://scholarsmine.mst.edu/masters_theses/7209

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INTRINSIC VISCOSITIES OF LINEAR POLYETHYLENE

BY

JOSEPH SHING CHIANG, 1944-

A THESIS

Presented to the Faculty of the Graduate School of the

UNIVERSITY OF MISSOURI-ROLLA

In Partial Fulfillment of the Requirements for the Degree

MASTER OF SCIENCE IN CHEMICAL ENGINEERING

1971

Approved by

.. /

T2552 ~~r 76 pages

:194278

ABSTRACT

Intrinsic viscosity measurements were performed on

linear polyethylene (Marlex 6009) in decalin at 135°C and in

diphenyl ether at 163.9°C. Molecular weights ranging from

3xl0 3 to 35xl0 4 were studied. It was found that for linear

polyethylene of molecular weight up to 35xl04 , the tedious

i

intrinsic viscosity measurement could be replaced by inherent

viscosity measurement at a concentration of 0.1 grams per

deciliter.

The effect of shear on viscosities measured in decalin

increased as the molecular weight of the sample increased.

The shear rate effects on intrinsic viscosities were

negligible. On the other hand, the shear rate effect on the

Huggins' constant was surprisingly high considering the small

shear rate effect on viscosities but still negligible.

The validity of the Huggins equation was tested. It

was found that the equation holds to [n]c~o.75or nrel<l .9

for all polyethylene samples except the highest molecular

weight sample (3Sxl0 4). For samples of Mw=6,200 to 145,000,

the Huggins' constants were sensitive to the molecular

weight of the sample in poor solvents.

The Mark-Houwink expression for the linear polyethylene

samples (0.62<Mwxl0- 4 <35.0) in decalin at 135°C was:

[n]=S.72xl0- 4Mw0 · 70 . In diphenyl ether at 163.9°C, a theta -4 0 5 solvent, (n] 6=26.lxl0 Mw · was observed for samples

(0.62<M xl0 4<S.8). w

The dimensionless ratio (r~)/n1 2 calculated from the

intrinsic viscosity of samples in the e solvent was 6.06,

and a value 1.03xlo-16 for (r~)/M was obtained for all the

samples. The values are close to the values obtained by

Chiang 10 and support the theoretical calculation done by

Hoover~ 5 and Nagai.~ 6

ii

iii

ACKNOWLEDGEMENT

The author wishes to express his thanks to his advisor,

Dr. K. G. Mayhan and his co-advisor, Dr. J. L. Zakin and

to Dr. G. L. Bertrand for their advice and suggestions in

this work.

Special thanks are extended to the Graduate Center for

Materials Research for providing financial support for this

work.

iv

TABLE OF CONTENTS

Page

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

ACKNOWLEDGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X

LIST OF TABLES ....................................... . xii

I. INTRODUCTION ................................... . 1

2

2

3

I I. LITERATURE REVIEW ...........•..................•

I II.

A.

B.

c.

Intrinsic Viscosity ........................ .

Huggins' Constant .......................... .

The Effect of Shear Rate on Intrinsic

Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

D. The Effect of Molecular Weight on Intrinsic

Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

E. The Unperturbed Root Mean Square End to End

Distance of Linear Polyethylene ............ .

EXPERIMENTAL ................................... .

10

15

A. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

B.

1 0

2.

Polymers

So1vent.s

................................

. .............................. . 15

15

3. Antioxidants ............................ 15

4. Heat Transfer Fluid ..................... 15

Apparatus .................................. .

1 0

2 0

Constant Temperature Bath .............. .

Thermometer ............................ .

18

18

18

v

Page

3. Thermometer Calibration Equipment ....... 18

4. Viscometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5. Density Measurement Equipment ........... 20

C. Experimental Procedure ...................... 20

IV. RESULTS AND DISCUSSION ......•..•..........•..... 23

A. Experimental Difficulties ................... 23

B. Intrinsic Viscosities and the Huggins'

Constants.................................... 24

1. Intrinsic Viscosities of Linear

Polyethylene Solutions .................. 24

2. The Effect of Solvent on the Huggins'

Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7

3. The Effect of Molecular Weight on the

Huggins' Constant of Polymer in Good

Solvent and Poor Solvent ................ 29

C. The Effect of Molecular Weight on

Intrinsic Viscosity ........................ . 30

D. The Unperturbed Root Mean Square End-to-End

Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

E. Effect of Concentration on Viscosity of

Polyethylene in Good Solvent ................ 38

V. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

VITA .................................................. 47

APPEND I X . . . . . . . . . . . . • . . . . . . . . . . . . • . . . . . • . . . . . . . . . . . . . . 4 8

A. EXPERIMENTAL DATA

B. EXPERIMENTAL DATA CORRECTED FOR SHEAR

vi

Page

49

EFFECTS ..................................... 55

NOMENCLATURE

a = exponent of the Mark-Houwink equation

A2 = second virial coefficient

B = proportionality constant in Eq. (4)

C = concentration; grams/deciliter

d = radius of gyration used by Gillespie

vii

K = proportionality constant of the Mark-Houwink equation

k = 0.28xlo 24 or 0.29xlo 24 in Eq. (4)

k' = Huggins' constant

k" = 0.5-k'

9., = the length between two base units

9., = the length of the c-c bond, em or ~

M = molecular weight

Mo = mer weight

Mn = number average molecular weight

Mw = weight average molecular weight

Mv = viscosity average molecular weight

n = the number of bonds

p = the number of unit mers

q = heterogeneity correction factor

rate of shear, sec. -1 r =

r = the radius of the hydrodynamic sphere of the unit mer

in Eq. (4)

~ = mean square end to end distance

~ = unperturbed mean square end to end distance 0

R = radius of the hydrodynamic equivalent sphere of a e polymer molecule

r = the radius of the capillary of the viscometer in

Eq. (3)

-z rz = z average mean square end to end distance

;z = number average mean square end to end distance n

s = radius of gyration

t = time, seconds

T = temperature, °K

viii

UVN = ultimate viscosity number; in the second Newtonian

region [n] 2=lim UVN c-+o

V = bulb volume (E) of the viscometer, cm3 (Fig. 1)

v = slope in the equation from Ref. 24

Subscripts

0 = at zero shear rate

1 = solvent

2 = solution

Greek Symbols

a. = expansion factor

6 = the overlap distance of doublets

p = density, grams/cm3

~ = constant in Flory-Fox equation

e = theta temperature

n = viscosity

no = viscosity at zero shear rate

nrel ... relative viscosity

ix

nsp = specific viscosity

[n] = intrinsic viscosity, deciliters/gram

[n] 2 = intrinsic viscosity, in the second Newtonian region

Angles

~ = the internal equivalent angle of free rotation

a = the angle between adjacent segment vectors; bond angle

LIST OF FIGURES

FIGURE Page

1 Viscometer and the Closed System ............. 19

2 Plot of [n]d versus [n] 9 (10) for Poly­

ethylene Samples (2 to 6) in Decalin at

135°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Plot of [n] versus Mw of the Linear

Polyethylene Solutions in Decalin at 135°C 32

4 Plot of [n] 9 versus Mw for Polyethylene

Samples in Diphenyl Ether at 163.9°C ......... 34

5 Plot of nsp/C[n] versus k'[n]C for

Polyethylene Samples (0.3<Mwxl0- 4<35.0)

6

7

in Decalin at 0 13 5 c ......................... .

Plot of nsp/C and ~nnrel/C versus C for

Polyethylene Samples (1 to 5) in Decalin at

0 13 5 c ....................................... .

Plot of n /C and ~nn 11c versus C for sp re Polyethylene Samples (6 to 9) in Decalin

39

50

at 135°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

8 Plot of nsp/C and ~nnrel/C versus C for

Polyethylene Samples in Diphenyl Ether at

163.9°C ...................................... 52

9 Plot of nsp/C and nsp,r=o/C versus C for

Polyethylene Samples (1 to 5) in Decalin

at 135°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

X

FIGURE

10

xi

Page

Plot of n /C and n • /C versus C for sp sp,r=o

Polyethylene Samples (6 to 9) in Decalin

at 135°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

TABLE

I

LIST OF TABLES

INTRINSIC VISCOSITY-MOLECULAR WEIGHT

RELATIONSHIPS FOR LINEAR POLYETHYLENE IN

GOOD SOLVENTS

II INTRINSIC VISCOSITY-MOLECULAR WEIGHT

RELATIONSHIPS FOR LINEAR POLYETHYLENE IN

POOR SOLVENTS

III MOLECULAR WEIGHTS OF LINEAR POLYETHYLENE

FRACTIONS .................................... IV PHYSICAL .PROPERTIES OF SOLVENTS USED IN

THIS WORK

V INTRINSIC VISCOSITIES AND INHERENT

VISCOSITIES AT 0.1 g/dt OF THE POLYETHYLENE

SOLUTIONS IN DECALIN AT 0 13 5 c ............... .

VI INTRINSIC VISCOSITIES AND HUGGINS' CONSTANTS

FOR POLYETHYLENE IN DIPHENYL ETHER

0 (163.9 C) ••••••••••••••••••••••••••••••••••••

VII HUGGINS' CONSTANTS FOR POLYETHYLENE IN

DECALIN AT 135°C ............................. VIII UNPERTURBED ROOT MEAN SQUARE END-TO-END

DISTANCES OF LINEAR POLYETHYLENE SAMPLES IN

xii

Page

11

12

16

17

25

26

28

DIPHENYL ETHER AT 163.9°C .................... 37

IX VISCOSITY DATA FOR POLYETHYLENE IN DECALIN

AT 135°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

TABLE

X VISCOSITY DATA FOR POLYETHYLENE IN DIPHENYL

ETHER AT 0 163.9 c ............................ .

XI HUGGINS' CONSTANTS CORRECTED FOR RATE OF

SHEAR EFFECTS FOR POLYETHYLENE IN DECALIN

0 AT 135 C .................................... .

XII SHEAR RATE EFFECTS ON INTRINSIC VISCOSITIES

OF POLYETHYLENE SOLUTIONS IN DECALIN AT

xiii

Page

54

60

135°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

XIII THE EFFECT OF RATE OF SHEAR ON SPECIFIC

VISCOSITIES OF POLYETHYLENE IN DECALIN AT

0 13 5 c ....................................... . 62

I. INTRODUCTION

The purpose of this investigation was to study the

behavior of linear polyethylene molecules in good and in

poor solvents and to compare laboratory experimental data

with existing correlations. In particular, the following

parameters were considered: (1) the effect of shear rate

on intrinsic viscosity and on Huggins' constant; (2) the

effect of molecular weight on Huggins' constant and on

intrinsic viscosity; (3) the effect of solvency on

intrinsic viscosity; (4) the relationship between the

unperturbed root mean square end to end distance and

intrinsic viscosity; and (5) comparison of the results of

this investigation to generalized viscosity-concentration

correlations for linear polymer molecules in good solvents.

1

II. LITERATURE REVIEW

A. Intrinsic Viscosity

Viscosities of polymer solutions depend on the

structure, stereo-specificity, polarity, saturation,

molecular weight and concentration of polymer molecules

and on polymer-solvent interaction. Viscosity

measurements can be used to determine molecular weight

as well as molecular size in solution and in some cases

can give information about the shape of long chain

molecules in solution.

At very dilute concentrations, the individual

molecules are far apart from one another and each of

them functions independently. Intrinsic viscosity

measurements, therefore, provide a measure of the size

and shape of isolated polymer molecules in solution and

provide information on polymer-solvent interactions.

Tung 1 suggested that for low molecular weight

polyethylene, inherent viscosity measurements at con­

centration 0.1 g/dt can be substituted for intrinsic

viscosity. He reported that {n}c=O.l had the same

2

values as [n] for polyethylene samples whose molecular

weights ranged from 1,770 to 13,900 in tetralin at 130°C.

Billmeyer 2 also pointed out that the inherent viscosities

at 0.5 g/dt can be used as an approximation of [n] for

linear polymers.

B. Huggins' Constant

Huggins 3 proposed an equation for the calculation

of the intrinsic viscosity by a linear extrapolation of

nsp/C to zero concentration

(1)

Here k', the Huggins' constant, was taken as constant

for a given polymer-solvent system at a given temper­

ature. Flory and Fox~ confirmed these observations.

Chou and Zakin 5 found that the lfuggins' equation holds

to [n]·C~l or to nrel values of about 2.4.

More recent data 5 - 9 on linear polymer molecules

show that k' depends slightly on molecular weight. In

3

good solvents, k' will decrease with increasing molecular

weight; whereas, in poor solvents, the molecular weight

dependency is complex.

Chiang 10 reported that k' values varied only from

0.39 to 0.41 for linear polyethylene of Mw from 2.10x10 4

to 1.035xl06 in decalin at 135°C. Trementozzi 11 observed

a k' value of 0.71 for linear polyethylene of Mw=ll,ZOO

in p-xylene at 81°C and 0.69 for Mw=l60,000. Neither of

them observed any significant dependency of k' on M . w

Gillespie 12 concluded from a theoretical analysis

and experimental data on polystyrene solutions that for

linear polymers with molecular weight of about 10 5 , the

Huggins' prediction that k' should be constant is sound.

4

However, at low molecular weight, he showed that k' will

increase with decreasing molecular weight. This is

similar to Berry's 1 ' observations that k' should be

independent of M for Mw>SO,OOO. Harris 14 found that

for branched polyethylene in xylene at 75°C, k' is

sensitive to the degree of branching of the polymer

and he observed that k' increased from 0.58 to 1.02 as

molecular weight increased from 1.3xl03 to 76xl03 .

However, this may have been due to variations in the

degree of branching.

It was pointed out by Berry, et al. 7 that the

relationship between nsp/C and C in poor solvent may be

parabolic when it falls in the range of C[n] values of

0.2 to 0.5. A linear fit could then possibly lead to

low values of [n] and high values of k'.

C. The Effect of Shear Rate on Intrinsic Viscosity

Even dilute solutions of crystalline olefin polymer

of broad molecular weight distributions may not be

Newtonian. At dilute concentrations Wesslar 15 found

that in most capillary viscometers, where the shear

rate at the wall is 1,000 sec.-lor greater, the solu­

tion viscosity of unfractionated linear polyethylene

is sensitive to shear rate at any concentration, even

with intrinsic viscosities as low as 2.1 dt/g.

On the other hand, Tung 16 observed that when the

rate of shear is less than 200 sec.- 1 , the viscosities

5

of dilute polymer solutions are independent of the shear

rate, even for intrinsic viscosities as high as 5.71.

Chiang 10 reported that for fractionated polyethylene

solutions in decalin at 135°C, if [n] is higher than

3.8 dt/g the shear rate correction should apply (shear

rate range not mentioned).

The extrapolation of the shear-rate-sensitive

viscosities to infinite dilution does not eliminate the

effect of a dependence on shear rate. For polyethylene

in decalin solutions, Francis, et al. 17 mentioned that

even for solution concentration as low as 0.1 g/dt

shear rate corrections are still needed. He suggested

an equation for a zero shear rate correction

nsp,r=o = n [1+(1.5xlo- 4 )(n )]r sp sp (2)

• 3 r = 4V/r tn (3)

where r is the nominal rate of shear at the wall of the

capillary of the viscometer, V is the volume of the

efflux bulb, t is measured flow time and r is the

radius of the capillary. Thus, in order to obtain the

true value of intrinsic viscosity, it is necessary to

make a shear rate correction for each viscosity reading

by extrapolating to zero shear rate, or we must use the

high-shear ultimate viscosity numbers [n] 2=lim UVN in c~o

the second Newtonian region. 18

Billmeyer 2 predicted that for polymer solutions, the

ratio of [n] to its value [n] 0 at zero shear rate is a

function of the product of the shear gradient at the

wall and the quantity M·n 1 ·[n] 0 /RT, where n1 is solvent

viscosity. He also mentioned that the apparent visco­

sity will decrease with increasing shear rate, until at

a sufficiently high rate of shear (10 5 sec.- 1), the

viscosity again becomes constant in the upper Newtonian

region. For samples with sufficiently high molecular

weight, the reduced viscosity (n 1=n /C) calculated re sp from data obtained in the upper Newtonian region may be

almost independent of polymer concentration. Ram and

Siegman 18 suggested that for polyisobutylene in toluene

at 30°C the high-shear ultimate viscosity number (UVN)

can be used and extrapolated to zero concentration in

order to evaluate [n] 2 for high molecular weight

samples (l.lxl06 to 6.6xl0 6).

D. The Effect of Molecular Weight on Intrinsic Viscosity

In the treatment of the properties of dilute

6

polymer solution, it is convenient to have all of the

elements or segments of the molecules represented as a

statistical distribution about the center of the gravity.

This is confirmed by the theories of Debye and Bueche, 19

Kirkwood and Risemen~ 0 and Brinkman. 21 They showed that

for sufficiently large chain length, the effective

hydrodynamic radius Re must vary directly with a

7

parameter of the Gaussian distribution which charac­

terizes the polymer solution. Therefore, a random

kinked (or coiled) chain model with segments of Gaussian

distribution is the most acceptable model for linear

flexible polymers in the dilute solution range.

For solutions of kinked-chain molecules, Huggins 22

proposed an expression of [n]-M for high molecular

weights:

(4)

where B depends on the bond angle, B=(l-cose)/(l+cose),

constant k=0.29xlo 24 for strong Brownian motion and

0.28xlo 24 for weak Brownian motion, M is the molecular

weight, P is the number of unit mers and M0 is the

corresponding "mer weight", r stands for the length

between two base units and r is the radius of the hydro­

dynamic sphere of the unit mer. J. J. Hermans, 23 Kuhn

and Kuhn, 2 ~ Kramers, 25 Debye, 26 Flory, 27 and Kirkwood

and Riseman 20 all have reported similar relationships

between [n] and M.

The following equation, proposed by Mark 28 and

Houwink 29 has been found to be a reliable guide for

linear polymer chains in solution.

[n] = KMa v (5)

Here K and a are characteristics of the given solvent-

solute system. M v is the viscosity average molecular

weight. For the sake of conven.i,ence, Mv is often

replaced by Mw. Patrick 3 0 reported that for a poly-

ethylene sample with Mw/Mn=20, a fairly wide fraction

sample, its Mw/Mv is 1.5. For the same polymer with a

Mw/Mn=2, its Mw/Mv is 1.1. Therefore, even for broad

molecular weight distributions, this substitution

introduces only a moderate error.

Usually K and a are determined directly from a

log[n]-logMw plot. However, Chiang 10 proposed a useful

expression for the direct evaluation of the slope, a,

of the Mark-Houwink equation from two sets of intrinsic

viscosity values, provided that the relationship 1

[n] 9 =K 9M~ holds for one of them. The equation is:

log[n] = 2alog[n] 9 + log(K/K~a) (6)

Huggins 31 found that for flexible polymer solutions

having small heats of mixing, the exponent a is usually

between 0.6 and 0.7. In most solutions of cellulose

8

derivatives a values are 0.8 to 1.0, indicating that the

molecular chains are more extended than for a random

kinked model.

Flory and Fox 32 proposed a similar expression for

long chain polymers in solution:

[n] 1, 3 = KM'Za. (7)

where K, a constant, depends on the structure of the

polymer, on the solvent and on the temperature. At the

theta temperature where a;l, Eq. (7) reduces to

9

k [n] = KM 2 (8) e

where K=(~)(;;) 31 2;M and~ ranges from 1.9Sxlo 21 to

2.65xlo 21 with a weighted mean value of 2.1x1o 21 if

[n] is in di/g. Since a 3 varies as M to the 0 to 0.3

power, Eq. (7) predicts a valuesof 0.5 to 0.8.

Trementozzi 33 has taken heterogeneity into account

by using

(9)

and

(10)

in place of [n]

and obtained ~ values from 0.88xlo 21 to 1.89xlo 21 for

linear polyethylene of Mw varying from 1.25xl0 5 to

4.6Sxl0 5 where ~ depends slightly on molecular weight

and reaches the usual asymptotic value at M -Sxl0 5 • w

Chiang 34 obtained values of ~=1.7xlo 21 for unfraction-

ated polyethylene. He also stated that after ~ is

corrected for the residual heterogeneity, it becomes

21 2.2xl0 . Neglecting q, the effect of heterogeneity,

Patrick 30 observed ~=2.0xlo 21 independent of molecular

weight for linear polyethylene in a-chloronaphthalene.

10

Many molecular weight-intrinsic viscosity

relationships have been reported for linear polyethylene

in good solvents and these are condensed and summarized

in Table I. Discrepancies between the equations in

Table I are caused by samples of different molecular

weight distributions, by small amounts of branching in

some of the samples, by different solvents and by

different molecular weight determining methods and by

variations in the viscosity measuring techniques. The

latest equation reported by Chiang 10 is considered to

be of good accuracy and reliability by Nakajima. 35

Some intrinsic viscosity-molecular weight rela-

tionships of polyethylene in poor solvents are summarized

in Table II.

E. The Unperturbed Root Mean Square End to End Distance of

Linear Polyethylene

The relationship for calculating the unperturbed

root mean-square end-to-end distance (~)~ of the chain

is:

(11)

When M is large, ~ should attain a constant (limiting)

value. However, in the low molecular weight range [n] will

decrease with decreasing M. For polymer chains

TABLE I

INTRINSIC VISCOSITY-MOLECULAR WEIGHT RELATIONSHIPS FOR LINEAR POLYETHYLENE IN GOOD SOLVENTS

Solvent for [n]

tetralin

decal in tetralin decal in decal in decal in decal in p-xylene p-xylene tetralin tetralin a-CN decal in

104K

5.10

5.86 4.60 5.30 4.60 6.80 6.20 1.65 1. 76 2.36 1. 62 4.30 3.90

F = fractions

a

0.725

0.725 0.725 0.725 0.73 0.67 0.70 0.83 0.83 0.78 0.83 0.67 0.74

U = whole polymer 0 = osmometry E = ebuliometry

Method of Solvent for M Detn. M Detn.

O,E o-xylene and methyl cyclo-hexane

0 o-xylene L.S. a-CN L.S. a-CN L.S. a-CN L.S. a-CN L.S. a-CN L.S. tetralin 0 p-xylene L.S. tetralin L.S. tetralin L.S. a-CN L.S. a-CN

L.S. = light scattering a-CN = a-chloronaphthalene

Molecular Wt. Temp.

Range for Ref. ( n] (°C)

3,750-lOO,OOO(F) 130 so

3,750-lOO,OOO(F) 135 1 121,000-62S,OOO(F) 130 16 121,000-62S,OOO(F) 135 •16

25,000-640,000(F) 135 30 100,000-200,000(U) 135 34

63,000-338,000(F) 135 10 125,000-46S,OOO(F) 105 33

10,000-180,000(F) 105 11,33 50,000-1,500,000(U) 120 so

125,000-465,00g(F) 105 33 48,000-5.6xl0 (U) 125 49 25,000-640,000(F) 135 52

.....

......

Solvent for

(n) a

Diphenyl

Diphenyl methane

Diphenyl ether

Diphenyl ether

TABLE II

INTRINSIC VISCOSITY-MOLECULAR WEIGHT RELATIONSHIPS FOR LINEAR POLYETHYLENE IN POOR SOLVENTS

104K Method of Solvent for Molecular Wt. Temp. for

a M Detn. M Detn. Range (n)a(oC) e -

33.0 0.5 Viscosity* Decal in 50,900-442,100(F) 127.5 Measurement

32.2 0.5 Viscosity Decal in 21,300-136,800(F) 142.2 Measurement

30.9 0.5 Viscosity Decal in 14,300-204,900(F) 163.9 Measurement

29.5 0.5 L. s. a-Chloro- 21,900-1,035,000(F) 161.4 naphthalene

* Molecular weights were determined by using the relationship

(n)decalin, 135°C = 6.2xlo- 4~ O.?O w

F = fractions

Ref.

35

35

35

10

I-" N

consisting of more than a few segments, ;z/M is both a 0

13

constant and a characteristic of a given chain structure.

For polyethylene o~ Mw>lO,OOO in diphenyl ether at

163.9°C, Nakajima 35 obtained Ke3.09xl0- 3 independent of

molecular weight, and a value of ~=2.5xlo 21 which was

adopted by Chiang 10 for random coils in the theta

solvent.

For restricted rotation around the valence angle,

e, the mean-square end-to-end distance is

-z 2 /( ) -- --ro = nt (1-cose) l+cose ·(l+cos~)/(1-cos~)

where ~ is the angle of rotation, and cos~ is the average

value of cos~ over the gauche and trans states.

Thus, Eq. (11) becomes

If K, ~' t, e and M0 are known, ~ can be calculated.

Bianchi 37 indicated that at very low molecular

weights, (;z)/nt 2 will decrease with molecular weight 0

with a power greater than 1 and consequently [n] will

show a stronger dependence on Mw.

Chiang 10 obtained (~)/M=l.l2xl0- 16 cm 2 and

(~)/nt 2 =6.67 for polyethylene (21,900<Mw<l,035,000) in

diphenyl ether at 161.4°C. Later, Nakajima 35 obtained a

similar result, (~)/nt2=6.80, for polyethylene

(14,300<Mw<442,100) in

Trementozzi 33 reported

and 3.61xlo- 16 cm 2 for

diphenyl ether at 163.9°C.

(r0 2 /Mw)~=3.68xl0- 16 , 4.62xlo- 16 w

three linear polyethylene

fractions of Mwxl0- 5=1.25, 2.69 and 4.63, respectively,

in tetralin at 105°C based on angular light scattering

measurements. This gave r~/nt 2=22.0, 27.6 and 21.6.

All of these values are about three times larger than

those of Chiang 10 and Nakajima. 35

14

15

III. EXPERIMENTAL

A. Materials

(1) Polymers

For this study nine fractionated linear

polyethylene samples of Marlex 6009 were furnished

by Gulf Oil Company. Samples were fractionated

and characterized by U. S. Industrial Chemical

Company. Characteristics of the samples are

listed in Table III.

(2) Solvents

Decahydronaphthalene (decalin; furnished by

Fisher) was used as a thermodynamically good solvent

while diphenyl ether (by Kodak) was used as a poor

solvent for polyethylene. Both solvents were of

good chromatograph quality. Their densities are

listed in Table IV.

(3) Antioxidants

Phenyl-a-naphthylamine was chosen as an

oxidation inhibitor for the polyethylene in

solution at high temperatures.

(4) Heat Transfer Fluid

A constant high temperature bath was con­

structed using DC-200 silicone oil as the heat

transfer medium.

16

TABLE III

MOLECULAR WEIGHTS OF LINEAR POLYETHYLENE* FRACTIONS

Fraction No. Mw x 10- 4 M /M w n

1 0.300

2 0.620 1.30

3 1.160 to

4 1.950 1.54

5 2.950

6 5.800 --7 10.000 2.00

8 14.500 to

9 35.000 3.50

* All samples contain approximately 20 ethyl side chains per

thousand carbon atoms and contain less than one double

bond per thousand carbon atoms (38).

TABLE IV

PHYSICAL PROPERTIES OF SOLVENTS USED IN THIS WORK

Decal in

Diphenyl Ether

Density measured at 25°C (g/cm3)

0.8701

1. 0611

Density measured at operating tem­

perature (g/cm3)

0.7973 (135°C)

0.9492 (163.9°C)

* cis-decalin density is reported at 18°C

Density reported (39) at 20°C (g/cm3)

0.8720 (trans) 0.895 (cis)*

1. 0730

Refractive index measured at 25°C

1.4743

~

"

B. Apparatus

(1) Constant Temperature Bath

A constant temperature bath capable of

maintaining temperatures within ±0.03°C was

employed.

(2) Thermometer

A calibrated 0.1°C thermometer was used for

checking the temperature of the bath.

(3) Thermometer Calibration Equipment

18

A platinum resistance thermometer calibrated

by the National Bureau of Standards, a model 1551-E

Mueller Bridge made by Honeywell, a null detector

and a galvanometer were used as the thermometer

calibration equipment.

(4) Viscometer

A modified Cannon-Ubbelohde dilution viscometer

size 50 (Fig. 1) was used to make all of the

viscosity measurements. A closed system was

designed to prevent the entry of atmospheric gases

and foreign particles into the viscometer and to

minimize the evaporation of solvent.

To remove the dust from the solutions before

running the samples through the viscometer, a

coarse fritted filter was mounted in the viscometer.

Another medium filter was used for screening any

MANOMETER AIR

I

C---H

8-----t

VACCUM FILTER

1----D 1----£

----A

FIGURE 1. Viscometer and the Closed System.

19

solid particles from the inert purging gases.

(5) Density Measurement Equipment

A 25 milliliter pycnometer was used for the

density measurements.

20

C. Experimental Procedure

Polymer solutions were prepared by weighing the

desired quantities of polymer on a glassine weighing

sheet and the solvent in a weighing buret. The polymer

and then the solvent were directly transferred into the

reservoir of the viscometer through tube B (Fig. 1).

The proper amount of phenyl-a-naphthylamine (0.01% for

the good solvent, 0.04% for the poor solvent) was added.

Subsequently, inlet 4 was closed and all the stopcocks

(1, 2 and 3) were opened to the system. After evacuating

and filling with helium several times to assure thorough

removal of air (no oxygen) from the system, the

viscometer was placed in the constant temperature bath

and agitated occasionally until a state of apparent

dissolution was observed.

Up to this point, the whole system was filled with

helium. In order to fill the delivery bulb (D) with

solution, stopcock 2 was closed and stopcock 3 was

opened to the atmosphere. The helium pressure then was

increased to force the solution upward to the delivery

bulb (D) through the sintered glass filter and the

capillary (A). After the delivery bulb was filled,

21

stopcock 2 was opened and stopcock 3 was switched back

to the closed system from atmosphere. The solution was

allowed to discharge through the capillary under the

force of gravity. Gas pressure was equalized above the

bulb and at the suspended level. Flow times were

recorded to ±0.1 seconds. Several readings of flow time

were obtained by the same procedure, until three

successive readings fell within the limit of experimental

error (±0.1 seconds) indicating that thermal equilibrium

had been reached.

All of the experiments were carried out at relative

viscosities less than two. The solution of highest

concentration was always prepared first. After its

flow time was satisfactorily measured, the viscometer

was removed from the oil bath and was cooled to room

temperature. The gas delivery valve was closed and a

measured amount of solvent was added to the viscometer.

Measurements at the next lower concentration were

carried out as described above. Measurements were made

at four or five concentrations based on equal volumes

of added solvent.

Both nsp/C and tn(nrel)/C data were extrapolated

linearly to C=O to obtain the intrinsic viscosities

[n] (see Appendix I) and values of k' and k". The

intersections of the two extrapolations were set at

C=O.

With the exception of Sample 1, all measurements

were made on duplicate samples in order to determine

reproducibility of the technique. The quantities of

Sample 1 available limited the number of measurements

to one. Therefore, the data for Sample 1 are less

reliable than those for the other samples.

The equation for zero shear rate correction

reported by Francis 18 was used here,

• r =

where V=3.1 cm 3 and r•0.044 em as reported by the

viscometer manufacturer.

22

(2)

(3)

23

IV. RESULTS AND DISCUSSION

A. Experimental Difficulties

There are many experimental problems involved in

measuring the properties of polyethylene in solution at

high temperature. The most serious of these are:

(1) There are difficulties in the clarification of

solutions. Billmeyer 40 and others have reported

clogging of filters while clarifying solutions. Muss

and Billmeyer 41 also pointed out that polyethylene

solutions frequently contain an insoluble component

which cannot be· removed by filtration. Kobayashi 42

mentioned that insoluble swollen gels may exist. In a

poor solvent, it is difficult to dissolve polyethylene

and the swollen gels are clearly visible. Special care

was taken in the preparation and the filtration of the

solutions studied here and no swollen gel particles

were visible.

(2) Polymer oxidation and degradation can occur

after prolonged exposure to high temperature. This

problem was minimized by the use of a good antioxidant,

an inert atmosphere, a closed system and high purity

solvents.

(3) From the refractive index results on the

decalin used, it appears that the decalin consists of a

mixture of trans (1.4828) and cis (1.46994) isomers or

small amounts of even a third component, tetralin (1.4614)

24

which is difficult to separate from decalin. The effects

of solvent purity were not investigated in this study.

B. Intrinsic Viscosities and the Huggins' Constants

(1) Intrinsic Viscosities of Linear Polyethylene

Solutions

Intrinsic viscosities were obtained by

extrapolating nsp/C versus C and tnnrel/C versus

C plots to zero concentration (Appendix I). For

nine fractionated linear polyethylene samples

(0.3<Mxl0- 4<35.0) in decalin at 135°C, intrinsic

viscosities vary from 0.148 to 4.86 dt/g (Table V).

The intrinsic viscosities of some of the same

samples (0.62<Mxl0- 4<5.80) in diphenyl ether at

163.9°C are lower than in decalin ranging from

0.156 to 0.732 dt/g (Table VI). Corrections for

the effect of shear rate on intrinsic viscosity

were negligible (see Appendix II).

Viscosity measurements of the type reported

here are tedious to make. Several hours are

required to make one intrinsic viscosity

determination. The inherent viscosity of 0.1 g/dt

is often fairly close to the intrinsic viscosity.

Since it is much easier to determine the inherent

viscosity {n} 0 _1 rather than spend hours doing the

tedious intrinsic viscosity measurement work, most

of the intrinsic viscosity values reported in the

25

TABLE V

INTRINSIC VISCOSITIES AND INHERENT VISCOSITIES AT 0.1 g/d.t

OF THE POLYETHYLENE SOLUTIONS IN DECALIN AT 135°C

Sample No. Mwx10- 4 [n] {n}c=0.1 100([n]-{n}c=0. 1)/[n],% ---·---------- ---- ----·- -·-·---

1 0.300 0.148 0.140 5

2 0.620 0.194 0.194 0

3 1.160 0.321 0.306 5

4 1.950 0.462 0.450 3

5 2.950 0.603 0.612 2

6 5.800 1.269 1.260 1

7 10.000 1.930 1. 880 3

8 14.500 2.571 2.470 4

9 35.000 4.858 4.588 6

TABLE VI

INTRINSIC VISCOSITIES AND HUGGINS' CONSTANTS FOR POLYETHYLENE IN DIPHENYL ETHER (163.9°C)

Sample No. :.twxlO -4 [n]e k' k" k'+k" 0.5-(k6+k6) 3

a e e e O.S x100,% a - -

2 0.620 0.156 0.41 0.09 0.50 0 1.2

3 1.160 0.275 0.44 0.10 0.54 8 1.2

4 1.950 0.353 0.53 0.00 0.53 6 1.3

5 2.950 0.467 0.53 0.00 0.53 6 1.3

6 5.800 0.732 0.54 0.00 0.54 8 1.7

Due to the limited amounts of the polymers, only five samples could be measured in this solvent.

N 0\

literature are actually inherent viscosities at a

concentration of 0.1 g/d£.

Table V summarized the intrinsic viscosities

and the inherent viscosities at C=O.l g/d! found

in this work for linear polyethylene in decalin

(135°C). The percent deviation does not exceed

6% for any sample. Thus, for linear polyethylene

samples of molecular weight up to 0.35xl0 6 , the

observed deviations between [n] and {n}c=O.l are

within the experimental error range for [n], and

the replacement of [n] by {n}c=O.l is acceptable.

(2) The Effect of Solvent on the Huggins' Constant

In good solvents polymers have expanded

27

conformations, and the resulting k' values are lower

than in poor solvents. De La Cuesta and Billmeyer 43

obtained a k' of 0.44 for an unfractionated linear

polyethylene sample in decalin at 135°C, 0.47 for

the same sample in tetralin at 125°C and 0.48 in

a-chloronaphthalene at 125°C. The k' values

measured here (Table VI and VII) are significantly

lower for the good solvent (decalin) than the k's

of the same samples in a poor solvent (diphenyl

ether at 163.9°C). Corrections for the effect of

shear rate on k' were considerably larger than

those for [n] but are not significant (see

Appendix II and Table XI).

28

TABLE VII

HUGGINS' CONSTANTS FOR POLYETHYLENE IN DECALIN AT 135°C

Sample No. Mwx10- 4 k' k" k'+k" 0.5-{k'+k") 100 % 0.5 X '

1 0.300 0.24 0.23 0.47 6

2 0.620 0.37 0.15 0.52 4

3 1.160 0.31 0.17 0.48 4

4 1.950 0.39 0.13 0.52 4

5 2.950 0.35 0.15 0.50 0

6 5.800 0.34 0.16 0.50 0

7 10.000 0.34 0.16 0.50 0

8 14.500 0.32 0.17 0.49 2

9 35.000 0.40 0.14 0.54 8

29

(3) The Effect of Molecular Weight on the Huggins'

Constant of Polymer in Good Solvent and Poor Solvent

Small molecules are rather compact in

comparison to the large ones. From the equation

derived by Gillespie 12

o/d = ~ - k'/3 (13)

the degree of entanglement (o/d) will increase as

the molecular weight increases, which results in a

decrease ink'. This has been observed experi­

mentally in polystyrene 6 ' 9 ' 44 (l.S<M xl0 4 <101) and w

in polyisobutylene 5 ' 45 (1.27<Mwxl0 4 <101) solutions

in good solvents. Gillespie 12 pointed out that

when molecular weight is large, the ratio of the

overlap distance to the radius of gyration d (or s)

reaches a constant and both quantities increase at

a constant rate with no change in the o/d ratio

giving no change in k'.

The good solvent data reported in Table VII

show no significant variation in k' with molecular

weight from 6,200 to 350,000. The 3000 molecular

weight sample gave an unusually low value, the

reason for which is not understood.

The results in Table VI show that k' increases

with increasing molecular weight (6,200 to 58,000)

in poor solvent. This may be due to increased

aggregation as the precipitation temperature is

30

approached at high molecular weights.

Simha and Zakin~ 9 Berry, et al.~ 7 Chou~ 5 and

Luh~~ found that except for low molecular weights,

k' values for linear polymers in good solvents are

below 0.5 while for linear polymers in poor sol­

vents they are near 0.5 or above. The data

reported here are consistent with these observations.

k'+k'' for all the samples in decalin •t 135°C

are between 0.47 and 0.54 (Table VII). All values

are less than 8% off from 0.5, the theoretical

value. k'+k'' for samples in diphenyl ether at

163.9°C are between 0.5 and 0.54 and are less than

8% above 0.5. These deviations are due to a

combination of errors in measurement and shear rate

effects.

C. The Effect of Molecular Weight on Intrinsic Viscosity

Equation (6) can be used to evaluate the exponent

a of the Mark-Houwink equation without considering the

heterogeneity corrections, and still give an accuracy

of ±1%. 10 Using this equation, a value of a=0.70 was

obtained for all the linear polyethylene samples in the

good solvent, decalin (135°C) (Fig. 2). The value 0.70

is close to what is directly read from the log[n]-log Mw

plot (Fig. 3) which gives a=0.72. (The lowest molecular

weight sample is not included in the slope estimate.)

The scatter of data points is attributed to experimental

I 0

/.0

a -a7o

0

I 0

0.1

FIGURE 2. Plot of [n]d versus [n] 9 (10) for Polyethylene Samples (2 to 6) in Decalin at 135°C.

31

o/o

a- 0.72 ·

0

.... o .. ...

/04 Mw

FIGURE 3. Plot of [n] versus Mw of the Linear Polyethylene Solutions in Decalin at 135°C.

o"

~ N

difficulties in obtaining intrinsic viscosity data at

elevated temperature. For a=0.70, an average K was

calculated to be 5.72xl0-4 . The [n]-Mw relationship

for sample 2 to sample 9 in good solvent is:

33

[n] = 5.72xl0- 4 M0 · 70 w (14)

Chiang 10 obtained the relationship [n]=6.20xl0- 4

M~· 70 . The slight difference between the two expressions

may be due to different molecular weight distributions

and experimental techniques.

-4 An average value K6=26.lxl0 of the samples (2 to

6) in poor solvent (diphenyl ether at 163.9°C) was also

calculated with an assumed slope of a=0.5. This is

close to K6 =30.9xl0- 4 reported by Nakajima 35 for the

same system. Thus, the expression for these linear

polyethylene samples in diphenyl ether at 163.9°C is

(15)

However, Fig. 4 shows that the slope a is approximately

0.57 instead of the expected 0.50. This indicates that

under our experimental conditions either the second

virial coefficient in the light scattering equation, A2 ,

is not zero, the experimental difficulties in measuring

viscosity at such a high temperature gave rise to

significant errors in [n] or polymer degradation may

have occurred particularly in the low molecular weight

[11Je h-

0.//03 /04

Mw ·c---) lines are drawn according to the relationship:

0

/ /

/

[n] =K M 0.5 a a w

/

/ /

FIGURE 4. Plot of [n] 6 versus Mw for Polyethylene Samples in Diphenyl Ether at 163.9°C. (..N

.+:>.

35

samples.

The slope a of the Mark-Houwink plot in good solvent

(Fig. 3) decreases at low molecular weight. This may be

due to experimental error, but it seems reasonable to

expect that the linear relationships between [n] and Mw

discussed above which are based on statistical treatment

of the chain conformation will not hold for short chain 3

lengths~° From the ratio of Eqs. 7 to 8, values of a

are ~ , a 3 values for five of the samples are listed LnJa in Table VI. There is little change in a from 6,200 to

29,500 but the value at 58,000 is much larger.

behavior has been observed previously. 10 ' 35

Similar

D. The_~~perturbed Root Mean S9uare End-to-End Distance

As mentioned in the Literature Review, for molecules

of sufficiently large chain length, the effective hydro-

dynamic radius, Re, must vary directly with a parameter

of the Gaussian distribution characterizing the polymer

in solution. The most convenient linear parameters for

this purpose are the root-mean-square end-to-end

distance (;z)~ or the radius of gyration (;z)~.

For polymers in a poor solvent (a-solvent) the

excluded volume effect is balanced by the polymer­

polymer attractions and a random flight chain model

(with corrections for bond angles and restricted

rotation) can describe the molecular conformation. In

a a-solvent, the net thermodynamic interaction between

segments and solvent is zero. (;z)~, the unperturbed 0

root-mean-square end-to-end distance, can be obtained

from the equation

36

(16)

where ~ is the universal constant and its numerical

value should be the same for all polymers regardless of

the solvent and temperature. For each polymer-solvent

system, each K8 is a constant so that (;z/nM ) 312 is 0 0

also a constant provided that the chain length is above

a certain limit. Since ~ is a universal constant, the

difference in the K's for various polymers should

reflect the differences in (~/M) 3 1 2 . Fox and Flory 46

mentioned that K for any given polymer will be determined

solely by M0 , the molecular weight of the unit mer, and

the degree of extension of the chain ;z/n in the absence 0

of thermodynamic interaction. If K8 is a function of

the extension of the chain, then K8 also will be a

function of the temperature, since temperature changes

the effect of hindrance to rotation.

The unperturbed dimension of linear polyethylene,

(;z)~, calculated from K =26.lxl0- 4 and ~=2.5xlo 21 is 0

from 0.79xl0- 6 to 2.44xl0- 6 em (Table VIII) for samples 2

to 6. The average value for (r~)/M is 1.03xlo- 16 cm 2 .

This value is close to the values that Chiang 10

(1.12xlo- 16 at 161.4°C) and Nakajima 35 (l.lSxl0- 16 at

(5) The effect of the rate of shear on the Huggins'

constant is more pronounced than its effect on intrinsic

viscosity. Deviations between k' and k'r=O ranged from 0

to 7%, but are not significant.

42

(6) A Mark-Houwink type expression for eight linear

polyethylene samples in decalin at 135°C was observed to be:

[n] = 5.7xl0- 4 ~· 70 w

The Mark-Houwink type expression for five of these samples

in diphenyl ether at 163.9°C (a theta solvent) is:

(7) A constant value of 6.06 for the dimensionless

ratio (r 2 )/nt2 was obtained from these viscosity experi-o

ments for polyethylene in diphenyl ether at 163.9°C. This

is close to the value 6.67 obtained by Chiang 10 experi­

mentally, and the values of 6.75 and 8.0 calculated

theoretically by Hoover 47 and Nagai. 48

(8) The plot of nsp/[n]C versus k'[n]C as suggested

by Chou and Zakin indicates that the linearity between

n /[n]C and k'[n]C in good solvent holds to at least sp

(n]C=0.75 or n /C[n]=l.3 for samples of molecular weight sp below 145,000. Thus, the lfuggins' equation holds up to

n 1 of at least 1.9. re

43

BIBLIOGRAPHY

1. L. H. Tung, J. Polymer Sci., 26, 333 (1957).

2. F. W. Billmeyer, Textbook of Polymer Science (New York: Interscience, 1962) 81, 82.

3. M. L. Huggins, J. Am. Chern. Soc., 64, 2716 (1942).

4. T. G. Fox, Jr. and P. S. Flory, J. Am. Chern. Soc., 73, 1915 (1951).

5. L. Y. Chou and J. L. Zakin, J. of Colloid & Interface Sci., 25, 547 (1967).

6. H. W. McCormick, J. Colloid Sci., 16, 635 (1961).

7. G. C. Berry, H. Nomura and K. G. Mayhan, J. Polymer Sci.,~' 1 (1967).

8. T. A. Orofino and J. W. Mickey, Jr., J. Chern. Phys., l!, 2512 (1963).

9. R. Simha and J. L. Zakin, J. of Colloid Sci., 17, 270 (1962).

10. R. Chiang, J. of Phys. Chern., 69, 1645 (1965).

11. Q. A. Trementozzi, J. Polymer Sci.,~' 887 (1957).

12. T. Gillespie, J. Polymer Sci., Symposia l-3c, 31 (1963).

13. Berry, G. C., "The Intrinsic Viscosity of Linear Polymers in Interacting and In Non-interaction Media," work done at Mellon Institute, Pittsburgh, Pa., from Ref. 44.

14. I. Harris, J. Polymer Sci.,!, 353 (1952).

15. H. Wesslarm, Makromol Chern., 26, 102 (1958), from Ref. 10.

16. L. H. Tung, J. Polymer Sci., 36, 287 (1959).

17. P. S. Francis, R. C. Cooke, Jr. and J. H. Elliott (Actual work done by J. Boylan unpublished), J. Polymer Sci., 31, 453 (1958).

18. A. Ram and A. Siegman, J. Appl. Polymer Sci., 12, 5Q (1968).

19. P. Debye and A.M. Bueche, J. Chern. Phys., 16, 573 (1948).

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

J. G. Kirkwood and J. Riseman~ J. Chern. Phys., 16~ 565 (1948).

H. C. Brinkman~ Appl. Sci. Research, Al, 27 (1947).

M. L. Huggins, J. Phys. Chern.~ 42, 911 (1938); 43, 439 (1939).

J. H. Hermans, Physica, 10, 737 (1943) from Ref. 31.

W. Kuhn and H. Kuhn~ Helv. Chim., Acta., 26, 1324 (1934); [n]=KMw~ from Ref. 31. --

H. A. Kramers~ J. Chern. Phys., 14, 415 (1946).

P. Debye, J. Chern. Phys.~ 14, 636 (1946); [n]=[(3/2·a(~)]/M0 . --

P. J. Flory, J. Chern. Phys., 13, 453 (1945).

H. Mark, Der Peste Korper, Leipzig, 103 (1938), from Ref. 31.

R. Houwink, J. Prakt. Chern., 155, 241 (1940), from Ref. 31.

H. M. Patrick, J. Polymer Sci., 36, 91 (1959).

44

M. L. Huggins, Phys. Chern. of High Polymers, (New York: John Wiley & Sons, Inc., 1958).

T. G. Fox, Jr., J. C. Fox and P. J. Flory, J. Phys. Chern., 53, 197 (1949); J. Polymer Sci.,~~ 745 (1950).

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

R. Chiang~ J. Polymer Sci., 36, 91 (1959).

A. Nakajima and F. Hamada, J. Polymer Sci., Part C, No. 15~ 285 (1966).

P. Flory, Princi~les of Polymer Chemistry (New York: Cornell Press, 1 53) 545.

U. Bianchi and A. Peterlin, J. Polymer Sci., Part A2, No. 6, 10 (1968).

Personal communication, Dr. Leslie Wild, U. S. Industrial Chemicals Company.

Data are from International Critical Tables and Lange's Handbook of Chemistry, 9th Ed., 1277 (1956).

45

40. F. W. Billmeyer, Jr., J. Am. Chern. Coc., 75 6123 (1953). _,

41. L. T. Muus and F. W. Billmeyer, Abst. Paints and Varnish Div., Am. Chern. Soc. Meeting, Dallas, April 1967.

42. T. Kobayashi, A. Chitale and H. P. Frank, J. Polymer Sci., 24,156 (1957).

43. M. 0. De La Cuesta and F. W. Billmeyer, Jr., J. Polymer Sci., Part A,!, 1721 (1963).

44. H. Luh, Master's Thesis, University of Missouri-Rolla, Rolla, Missouri (1968).

45. L. Y. Chou, Master's Thesis, University of Missouri­Rolla, Rolla, Missouri (1966).

46. T. G. Fox, Jr. and P. J. Flory, J. Am. Chern. Soc., Zl, 1909 (1951).

47. C. A. Hoover, J. Chern. Phys., 35, 1266 (1961).

48. K. Nagai and T. Ishikawa, J. Chern. Phys., ~' 496 (1961).

49. J. T. Atkins, L. T. Muus, C. W. Smith and E. T. Pieski, J. Am. Chern. Soc.,~~ 5089 (1957).

SO. E. Duch. L. Kuchler, Z. Elektrochem., 60, 218 (1956), from Gen. Ref. 7 (Table I).

51. L. T. Tung, J. Polymer Sci.,~' 333 (1957).

52. F. W. Billmeyer, J. Polymer Sci., Al, 1721 (1963).

General References

1. H. Tompa, Polymer Solutions (New York: Academic Press, 1956).

2 .

3.

4 .

5 •

Ott, Spurlin, High Polymers, Vol. V, Cellulose Part III (New York: Interscience Publishers, 1955).

A. J. Barry, High Polymer Ph~sics, A Symposium (New York: Remsen Chemicalublishing Co., Inc., 1948).

P. J. Flory, Princi}les of Polymer Chemistry (New York: Cornell Press, 1953 .

F. W. Billmeyer, Textbook of Polymer Science (New York: Interscience, 1962).

6.

7 .

8.

9.

M. L. Huggins, Phys. Chern. of High Polymers (New York: John Wiley & Sons, Inc., 1958).

Q. A. Trementozzi, High Poll1ers, Vol. XX, Chap. 9, Crystalline Olefine Polymer New York: Interscience, 1961).

J. K. Stille, Introduction to Polymer Chemistry (New York: John Wiley & Sons, Inc., 1967).

H. Morawetz, Macromolecules in Solutions (New York: Interscience, 1962).

46

47

VITA

Joseph Shing Chiang was born on March 2, 1944 in

Shanghai, China. He received his high school education in

Taiwan and his Bachelor's degree in Chemical Engineering

from Chung Yuan Christian College of Science and Engineering,

Taiwan in 1965.

After one year of service in the Chinese Armed Forces,

he worked as the Head of the Publication Department and

was in charge of the general Chemistry Laboratory at

Chinese Overseas Student University. At the same time, he

was on the research staff of the Chemistry Service of the

Chinese Army.

He enrolled in the Graduate School of the University of

Missouri-Rolla in September 1967.

48

APPENDIX

49

A. EXPERIMENTAL DATA

1.0,...

.!lse c

AND

fn1Jce~ c

...

1-

~ 0

rv--5 1- 0- ---1 __.--0-- --0 loC-o-o_o_oo __

0-­o--k:--::::::.,_o-o 0

4

-0-

~ c r

1-

-o 0

~o 0 o- ~ J

~---o o

8 ---0 ·O 2 ==9

O.IQ

o o o--1 ===8 8 o-• I I

20 40

FIGURE 6.

C IN GRAMS/DECILITER

Plot of nsp/C and tnnrel/C versus C !or Polyethylene Samples (1 to 5) in Decalin at 135 C.

VI 0

7.0

5.0 'T)sp c AND

Jn'f}reJ c

3.0 0---­----o-o---o 8 O-o- -o-----o.=--o

o- --o--o--- 7 ~~====o---o----o------o ____ __

0 0 0 0 0 0

1.00 Q3 c IN GRAMSIDECILITER

51

o-6

0-

0.5

FIGURE 7. Plot of n 5 p/C and ~nnrel/C versus C for Polyethylene Samples (6 to 9) in Decalin at 135°C.

1.0-~ ~0~ ~~~ 6 0----·

~ --o_?E--C 05 o-o----o l!!rJmt 5

AND · o-o o 0 ---r--.%....---------o-O 0 4 0

0 0-0 0 0 '"(!"' t -

0 0 0 0 0 0 0

1-

B 0 g 8 0

~

I I J

0 1.0 C IN GRANS/D£CILIT£R

FIGURE 8. Plot of nsp/C and innrel/C versus- C-~or Polyethylene Samples in Diphenyl Ether at 163.9 C.

J

2

I

2.0

(1"1

N

53

TABLE IX

VISCOSITY DATA FOR POLYETHYLENE IN DECALIN AT 13S°C

Polymer c g/dR. Solution Flow nsp/C R.nnre1/C Sample Time, sec. nre1

1 3.8680 303.5 1.640 0.165 0.128 2.1002 246.7 1.333 0.158 0.137 1.4746 227.6 1.230 0.156 0.140 1.0985 216.5 1.170 0.154 0.143

2 2.5433 303.4 1.583 0.229 0.180 1.7109 263.2 1.373 0.218 0.185 1.2126 240.7 1.256 0.211 0.188 0.8335 224.8 1.173 0.207 0.191

3 2.2738 362.5 1.891 0.392 0.280 1.5070 298.3 1.556 0.369 0.293 1.0853 265.6 1.386 0.355 0.300 0.7361 240.3 1.254 0.344 0.307

4 1.4512 355.1 1.852 0.587 0.425 0.9940 296.2 1.545 0.548 0.488 0.7176 263.8 1.376 0.524 0.445 0.4907 239.6 1.250 0.509 0.454

5 1.0564 341.1 1.779 0.738 0.546 0.6900 283.6 1.479 0.695 0.568 0.4905 254.3 1.327 0.666 0.576 0.3342 233.1 1.216 0.646 0.585

6 0.4871 335.2 1.779 0.738 0.545 0.3239 281.4 1.479 0.695 0.568 0.2301 253.2 1.326 0.666 0.576 0.1580 232.8 1.216 0.646 0.585

7 0.2914 320.0 1.669 2.296 1.758 0.2021 276.5 1.442 2.188 1. 812 0.1424 249.3 1.300 2.109 1.844 0.0951 229.4 1.197 2.069 1.889

8 0.2478 338.5 1.766 3.090 2.294 0.1696 286.8 1.496 2.925 2.375 0.1194 256.4 1.338 2.827 2.436 0.0794 234.1 1.221 2.786 2.516

9 0.1412 360.7 1.882 6.244 4.477 0.0946 296.3 1.546 5.768 4.603 0.0715 267.6 1.396 5.537 4.665 0.0545 247.4 1.291 5.331 4.680

The solvent flow time of decal in at 135°C was 191.7 sec.

54

TABLE X

VISCOSITY DATA FOR POLYETHYLENE IN DIPHENYL ETHER AT 163.9°C

Polymer c g/dR. Solution Flow nsp/C R.nnrel/C Sample Time, sec. nrel --

2 1.3700 189.0 1.233 0.170 0.153 0.8930 176.0 1.148 0.166 0.155 0.6548 169.7 1.107 0.163 0.155 0.4367 164.1 1.070 0.161 0.156 0.3209 161.1 1.051 0.159 0.155

3 1.6771 238.3 1.553 0.330 0.262 1.0948 205.5 1.339 0.310 0.267 0.8044 190.6 1.242 0.301 0.270 0.6492 183.0 1.193 0.297 0.271

4 1.0506 221.1 1.442 0.421 0.349 0.7018 196.4 1.281 0.401 0.353 0.5098 183.6 1.198 0.388 0.354 0.3434 173.1 1.129 0.376 0.354

5 0.8770 229.6 1.497 0.566 0.460 0.5955 202.9 1.322 0.541 0.469 0.4173 186.5 1.215 0.516 0.467 0.3315 179.2 1.167 0.505 0.467

6 0.5462 228.7 1.490 0.898 0.731 0.3597 199.6 1.301 0.836 0.731 0.2656 186.3 1.214 0.806 0.730 0.2099 178.9 1.166 0.790 0.731

The solvent flow time of dipheny1 ether at 163.9°C was 153.4 sec.

55

B. EXPERIMENTAL DATA CORRECTED FOR SHEAR EFFECTS

The non-Newtonian behavior of polymer solutions has

generally been ignored in the evaluation of intrinsic

viscosity data. It is usually assumed that the effect of

56

shear rate on dilute polymer solution viscosity is small and

vanishes as the polymer concentration decreases to zero.

However, when the molecular weight is large such a correction

is required. 10 ' 15 ~ 17 ' 18

Shear rates of polyethylene in decalin at 135°C were

estimated and shear corrections were applied to all the

viscosity measurements (Eq. 2). Results are listed in

Tables XI, XII and XIII. The nominal wall shear rate in

all the measurements is within the limits of 402<r<672 sec- 1 .

After the correction for shear rate, the intrinsic visco-

sities of samples 4 to 9 changed by only 0.2% to 0.4% from

their original values. Therefore, the shear rate correction

for intrinsic viscosity is not significant, even for these

relatively high intrinsic viscosity values, and no correc­

tions were made for the poor solvent (diphenyl ether) data

where intrinsic viscosities were lower.

After the rate of shear correction, the Huggins'

equation is

n • /C - [n] + k'[nJ 2 c 2 sp,r=O -

(17)

Values of k' calculated from this equation differed from

the values before shear rate corrections were applied and

are listed in Table XII. Deviations of k' values up to

7.0% were obtained. The effect of shear rate on k' values

is much larger than the effect of values of [n] or on

individual viscosity measurements but are not significant.

57

1.0 o - BEFaiE r CCRR£CT/ON

~a~ ..,P'w~~~

+ - AFTER f CORRECTION

~ c Q5 ·-•""""""~~~

J

~------·- -·- . ·--------~~-

r-----·- • • " 2 Q/0 + • •-------- I ·-

2.0 C IN GRA/tfSAJECILITER 4.0

FIGURE 9. Plot of n /C and n • /C versus C for Polyethylene sp sp,r=o Samples (1 to 5) in Decalin at 135°C.

V1 00

7.0

fJSP c 4.0

I

1.00

.~~ ~~

~~P

-~ ·-·-- =e-

... • $

• • ~ -- ---- -- -

02 C IN G~/LITER

0 - BEFORE f CXRReCTION

+ - AFTER f CORRECT"ION

8

7 • 5~

Q4

FIGURE 10. Plot of n /C and n • /C versus C for Polyethylene sp sp,r=o Samples (6 to 9) in Decalin at 135°C. tl1

~

TABLE XI

HUGGINS' CONSTANTS CORRECTED FOR RATE OF SHEAR EFFECTS FOR

POLYETHYLENE IN DECALIN AT 135°C

k I • -k I Sample No. k' k I • k"• r=O xlOO,% (k'+k")· r=O r=O k I •

r=O r=O

1 0.24 0.24 0.23 0 0.47

2 0.37 0.37 0.15 0 0.52

3 0.31 0.31 0.17 0 0.48

4 0.39 0.41 0.12 3.5 0.52

5 0.35 0.37 0.14 5.4 0.51

6 0.34 0.36 0.14 5.6 0.50

7 0.34 0.36 0.15 5.6 0.51

8 0.32 0.34 0.16 5.9 0.50

9 0.40 0.43 0.10 7.0 0.53

60

TABLE XII

SHEAR RATE EFFECTS ON INTRINSIC VISCOSITIES OF

POLYETHYLENE SOLUTIONS IN DECALIN AT 135°C

Sample No. [n] dt/g

1 0.148

2 0.194

3 0.321

4 0.462

5 0.603

6 1.269

7 1.930

8 2.571

9 4.858

[nl;.=o dt/g

0.148

0.194

0.321

0.464

0.605

1.272

1.940

2.580

4.869

[n]·-[n] [~]· ~100,%

r

0

0

0

0.4

0.3

0.2

0.3

0.4

0.2

61

62

TABLE XIII

THE EFFECT OF RATE OF SHEAR ON SPECIFIC VISCOSITIES OF POLYETHYLENE IN DECALIN AT 135°C

Polymer Cone. Shear Rate Measured Corre<;ted g/d.R. Sec. -1

nsp n 5 p,r=O

1 3.8680 479.5 0.6396 0.6490 1.1002 589.9 0.3328 0.3359 1.4746 639.4 0.2296 0.2312 1.0985 672.2 0.1696 0.1706

2 2.5433 479.7 0.5827 0.5905 1.7109 553.0 0.3730 0.3766 1.2126 604.6 0.2556 0.2575 0.8335 647.4 0.1727 0.1736

3 2.2738 401.5 0.8910 0.9062 1.5070 487.9 0.5561 0.5633 1.0853 548.0 0.3855 0.3894 0.7361 605.7 0.2535 0.2554

4 1.4512 409.9 0.8524 0.8666 0.9940 491.4 0.5451 0.5521 0.7176 551.7 0.3761 0.3798 0.4907 607.4 0.2499 0.2517

5 1.0564 426.7 0.7793 0.7917 0.6900 513.2 0.4794 0.4850 0.4905 572.3 0.3266 0.3295 0.3342 624.4 0.2160 0.2176

6 0.4871 431.0 0.7488 0.7604 0.3239 513.4 0.4682 0.4735 0.2301 570.7 0.3206 0.3234 0.1580 620.6 0.2144 0.2158

7 0.2914 451.6 0.6691 0.6787 0.2021 522.6 0.4422 0.4471 0.1424 579.6 0.3004 0.3029 0.0951 517.7 0.1968 0.1980

8 0.2478 430.0 0.7658 0.7778 0.1696 507.5 0.4901 0.5021 0.1194 567.6 0.3375 0.3406 0.0794 621.7 0.2212 0.2226

9 0.1412 426.7 0.8816 0.8966 0.0946 513.2 0.5456 0.5526 0.0715 572.3 0.3959 0.4000

"··- 0.0545 624.4 0.2906 0.2929