Intrinsic viscosity and axial extension ratio of random coiling macromolecules in a hydrodynamic shear field

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ARCH I EF

INTRINSIC VISCOSITY AND AXIAL EXTENSION RATIO OF RANDOM!-COILING. MACROMOLECULES

IN A HYDRODYNAMIC SHEAR. FIELD

F.R. Cottrell, E.W. Merrill, and K.A. Smith

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Contract Nonr 3963 (10)

Task NR 062-333 (1970)

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JOURNAL OF POLYMER SCIENCE: PART A-2 VOL. 8, .289-294 (1970)

Intrinsic Viscosity and Axial Extension Ratio of

Random-Coiling Macromolecules in a Hydrodynamic

Shear Field

F. R. COTTRELL, E. W. MERRILL, and K. A. SMITH, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge,

Massachusetts 02139

Synopsis

The shear dependence of the intrinsic viscosity and the conformation of high molecular

weight polyisobutylene in dilute solutions of decahydronaphthalene under shear were

determined simultaneously. Experimental variables investigated were the shear rate

(0 to 2 X 10' sec'), the molecular weight (1.0 X 107 to 1.7 X 107) and the

poly-mer concentration (1.8 X 10 to 8.4 X 10 g/cc). Correlations allowing

concen-tration and shear rate norma]ization for any one sample are described.

Conforma-tional extention ratios along the orientation direction of the deformed molecule to 1.42 and intrinsic viscosity ratios (sheared to zero shear) to 0 5 were observed.

The shear dependence of the intrinsic viscosity has been previously in-vestigated'6 for a variety of macromolecules in a number of different so)-vents.

Numerous theoretical relationships6" have also been proposed,

but to date, gross discrepancies generally exist between theory and experi-mental data. These discrepancies have been unresolvable, in part, because of the complete lack of experimental information concerning the conforma-tion of the macromolecule under shear.

To elucidate the nature of this

phenomenon, we have simultaneously determined both the shear depen-dence of the intrinsic viscosity and the conformation of high molecular weight polyisobutylene in dilute solutions of decahydronaphthalene under shear.

TABLE I

Sample Characterization Data

First-Newtonian

(zero-shear) M,X 10-6 Sample intrinsic viscosity (from light number []o, dl/g scattering)

LS-4 18.9 10.5

LS-3 25.0 16.8

LS-9 23.9 15.0

From high-angle light-scattering data.

289

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290 COTI'RELL, MERRILL, AND SMITH

Q

(Flow Direction)

30 '85°

a :1.425 b:094 20

2B2°

a:1.29, b=0.96

2:1.15, b0.98

: 10. 80°

Fig. 1. Statistical shape of deformed macromolecular coil. a and b are major and minor axis extension ratios, respectively.

For these studies, two samples of polyisobutylene (Vistanex L250 and L300, Enjay Corp.) were fractionated by fractional precipitation from dilute solutions of benzene by the addition of the nonsolvent acetone. Pertinent

characterization data are summarized in Table I and described in more

detail elsewhere.'3"4

The conformation of the macromolecule under shear was experimentally

determined by a new technique based on light-scattering measurements

taken from dilute polymer solutions in a Couette flow field. The results of this experiment have been previously described13"4 and are summarized in Figure 1, which ifiustrates the statistical shape of the deformed

macro-molecules. *

Viscosity measurements of the dilute polymer solutions were taken on a

Couette-type viscometer'5 at low shear rates (0.1-100 sec') and on a

pressurized Ubbelohde viscometer at higher shear rates (200-2000 sec'). Viscosities from the Couette viscometer measurements were calculated in the usual manner, assuming a Newtonian fluid. Shear rate corrections for non-Newtonian behavior were negligible. Viscosities from the Ubbelohde viscometer were calculated'4"6 from the wall shear stress and calculated values of the wall shear rate which were obtained from the measured flow * Statistical shape is defined as the locus of points of equal probability of finding the terminal segment with the first segment fixed at the origin and calculated by assuming a Gaussian distribution of distances separating the chain ends.

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and 10.0

V0

0.1 0.1 4& 1.0 x.

Fig. 2. Shear thinning behavior of sample LS-9 at various concentrations.

times by assuming a power-law viscosity relationship; the exponent of the power law equation was experimentally determined and was alwaysfound

to lie in the range from 0.87 to 1.0.

Kinetic energy corrections of the Ubbelohde were negligible.

All measurements were carried out at 25.0

0.1°C. No polymer degradation was observed and all measurements could be reproduced within experimental error.

It was found that concentration normalization of the shear-thinning data could be realized by plotting values of ( - '7o)/('7O _{- '70)} versus/3', where'7

is the solution viscosity under shear, '70 is the first-Newtonian (zero shear) solution viscosity, and ?7 is the solvent viscosity.

The parameter

/3' is

defined by therelation:

/3' =

(0/c)0 il?n0/RT

(1)

where ('730/c)o is the first-Newtonian (zero shear) reduced viscosity, .2iTW is the weight-average molecular weight, and the other symbols take on their usual meanings. These variables are related to the more familiar quantities

['l/

[]o

and /3 by the relation

10 40

['71

=lim

(/c)

lim

[(ti -

o)1 ₍₂₎

['710

(/c)0

c.O ('7O_ '70)] j3 = lim13' (3) FIB - DECALIN Sample LS -9 £ C1 .0839 g/dl C4=.040 1 Viscosity at C2=07 C3=0534

1Newtonion Viscosity _C5O267

Solvent Viscosity _CO178

(5)

292 COTTRELL, MERRILL, AND SMITH

Figure 2 illustrates the normalization afforded by these coordinates to

copious data taken with sample LS-9 over a range of dilutions.

The normalization is a valuable experimental tool in that it eliminates the need of' extrapolating the data to zero concentration.

Figure 3 illustrates the same method applied to data taken on three frac-tionated samples at a series of polymer concentrations ranging from 0.01 g/dl to 0.09 g/dl. Similar curves were obtained for urifractionated samples,

10.0 1.0 PIB - DECALIN Symbol Sample LS-9 LS-4 LS- 3 LS-9 01

III

'I

II Illil

I 111111 01 10 10 40

Fig. 3.. Shear thinning behavior of three fractionated samples .at various concentrations.

and a theoretical polydispersity analysis'4 illustrated a nearly negligible

effect of polydispersity on the curves illustrated in Figures 2 and 3. In addition,, the viscosity data for each sample concentration was fitted to a power law relation of the form:

gh

Y1<Y<72

(4)

where T is the wall shear stress, is the wall shear rate, g and h are con-stants, and , and 2 determine the range of validity of the equation.

Ex-perimental data illustrated that the concentration dependeuce of g and h

could be given by the forms:

g = ,(1 + A,c + A,c2 +

(5)

(6)

1.0

'7 0.1

RANDOM-COILING MACROMOLECULES 293

where A1, A2, K1, and K2 are positive constants for any one sample. Ma-nipulation of eqs. (4), (5), and (6) yields the expression:

[fl = A1 - K1 1n

71<'Y<72

(7) where values of A1 and K1 can be determined experimentally from the

extrapolation to infinite dilution of values of (g/o 1)/c versus c and (1

-h)/c versus c, respectively. The solid lines of Figure 3 represent values of

LS-9 LS-3 A LS-4 0.01 I I I I I I I I 0.1 1.0 2.0 j

'l-Fig. 4. Major axis fractional extension vs. versus excess vicosity ratio.

['11/ ['710 calculated from eq. (7) with experimental values of A1 and K1 for each sample.

As illustrated by this figure, excellent agreement of both

methods of plotting the experimental data is observed.

Figure 4 illustrates a plot of the quantity 1 - a versus

('1 '7o)/('7°

-170), where a is the major axis extension ratio of the macromolecule along

the direction of orientation in the flow field. Inspection of Figure 4 illus-trates the normalization of the data for all three fractionated samples to a single curve, the equation of which is:

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294 COTTRELL, MERRILL, AND SMITH

The conformation of random coiling rnacrbmolecules under shear can be

correlated with some success" to the recent theoretical results of Cerf'T

which predict a conformation dependence on both and an effective rigidity factor, n.. Assuming a unique relationship between the coil conformation

and the intrinsic 'viscosity, one can speculate that eq. (8) is valid for a

specific effective rigidity factor and is not in general a universal relationship. Further indication of the nonuniversal character of this result is provided by the shear dependence of the intrinsic viscosity under conditions where a large macromolecular expansion is suspected.

This work was supported by the Office of Naval Research under Contract NONR

3963(10).

References

T. E. Fox, Jr., J. C. Fox, and P. J. Flory, J. Amer. Chem. Soc., 73, 1901 (1951). L. J Sharman, R. H. Sones, and L. H. Cragg, J. Appl. Phys., 24, 703 (1953). M. A. Golub, J. Phys. Chem., 60,431(1956).

M. Copic, J. Chim. Phys., 54, 348 (1957).

S. P. Burow, A. Peterlin, and D. T. Turner, Polymer, 6, 35 (1965). R. Cerf and C. Wolff, Eur. Polyin. J., 4,317 (1968).

7 A. Peterlin and M. Copic, J. Appl. Phys., 27,434 (1956).

Y. H. Pao, J. Chem. Phys., 25, 1294 (1956). R. Cerf, J. Phys..Radium, 19, 122 (1958). A. Peterlin, J. Chem. Phys., 33, 1799 (1960).

J. A. Subirana, in Macromolecular Chemistry Prague 1965 (J. Pólym. Sci. C, 16), 0. Wichterleand B. Sedlàek, Eds., Interscience, New York, 1967, p. 1423.

A. Peterlin, in U. S.-Japan Seminar in Polymer Physics (J. Polym. Sci. C, 15),

R. S. Stein and S. Onogi Eds., Interscience, New York, 1966, p. 337.

F.R. Cottrell, E. W. Merrifi, and K. A. Smith, J. Polym. Sci., A-2, 7, 1415 (1969). F. R. Cottrell, Sc.D. Thesis, Massachusetts Institute of Technology, August

1968.

P. J. Gilinson, C. R. Dauwalter, and E. W. Merrifi, Trans. Soc. Rheol., 7, 319

(1963).

W. Phillipoff and F. H. Gaskins, Trans. Soc. Rhcol., 2, 265 (1958). B. Cell, C. R. Acad. Sci. (Paris), C267, 1112 (1968).

Received April 2, 1969 Revised July 29, 1969

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Dr. Q Kuhn

National Bureau of Standards

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Department of the Arnr

Coastal Engineering Research Center

5201 Little Falls Road, NW. Washington, D.C. 20011 Code 521

Naval Ship Research arid

Development Center

Washington, D.C. ₂₀₀₀₇

Code

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Chief of Naval Research Department of the.Navy

Washington, D.C. ₂₀₃₉₀

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Commander

Naval Ordnance Systems Command Code OR])

₀₃₅

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Division of Ship Design

.ritime Administration 11141 G. Street, NW. Washington, D.C. ₂₀₂₃₅ HQ tJSAF (.AFRS'TD) Room ID 377 The Pentagon Washington, D.C. ₂₀₃₃₀ Commander

Naval Ship Ssts Command

Code 66LJC

Code.525

Washington, D.C. ₂₀₀₀₇ Dr. A. Powell (Code 01)

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Washingtn_n, D.C. ₂₀₀₀₇ Director of Research Coda ER

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Commander

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Naval Ordnance Systems Command

(16)

-8--AIR S3o1

Naval. Air Syste. Command

Deprttnent of the Navy

Washington, D.C.

20360

AIR 6oL.

Naval Air Systens Command

Departnent of the Navy

Washington, D.C.

_20360.

Dr. John Craven (PM 111)0)

Deep

ibtnergence Systems

Proj ect

Deprtmeit of the Navy

Waaington, D.C.

20360

Code S22

Naval Ship Research and

Development C enter

Washington, D.C.

20007 Commander

Naval. Oceanographic Qffice

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Chief of Research & Devel.opment

Office. of Chief of Staff

Department of the A1*

The Pentagon, Washington, D.C..

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Code 63IaA

..

Naval Ship Systexm

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Department of the.Navy

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Code 1..68 .

Chief of Naval Research

Departhient of the Navy

Washington, D.C...

₂₀₃₆₀

Director

. -U

S. Naval Resarch

.

aboratozy

Code 6170

.

Washington, D.C.

_20390.

Code 1473

Chief of Naval Reeeajch.

Departanent of the Navy

Washington, D.C.

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Naval Ship. Engineering Center

Department of the Navy

Washington, D.C.

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-9-Nr Ralph Lacey (Code 61114)

Naval. Sdp Engineering. Center

Depar1nent of. the Navy

Waàbingten, D.C.

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Dr. A. S. .ibel1, President

Genera]. Technical Serviàes, Inc.

bS].

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Dr. H. Cohen

IBM Research. Center

P. 0. Boi 218

(17)

Security Classification

DOCUMENT CONTROL DATA - R & D

(Security classification of title, body of abstract and indexing annotation must be entered when the overall report Is classIfied)

ORIGINS TING ACTIvITY (Corporate author)

Massachusetts Institute of. Technology

2a. REPORT SECURITY CLASSIFICATION

UNCLASSIFIED

2b. GROUP

3 REPORT TITLE

Intrinsic. Vlscosity.:and Axial... Extension Ratio..of. Randorn-Col.iing Macromolecules in. a Hydrodynam.ic. Shear Field

4. DESCRIPTIVE NOTES (Type of report and.Iz,clusjve dates)

Technical Report

5. AL) THOR(S) (First name, middle Initial, laetnañw)

F.R.Cottrèil, .E..W...Merrl.l.l,. and .JCA. Smith

6. REPORT DATE May., 1970

7a. TOTAL NO. OF PAGES 6

7b. NO. OF REFS 17 Ba. CONTRACT OR GRANr NO.

Nonr 3963 (10)

b. PROJECT NO.

Task NR 062-333

C.

d.

ea. ORIGINATORS REPORT NUMBER(S)

Sb. OTHER REPORT NO(S) (Any other numbers that_{this report)} may bèassigned

'tO. DISTRIBUTION STATEMENT .

-II. SUPPLEMENTARY NOTES _{(2. SPONSORING MILITARY ACTIVITY}

Office of Nava? Research

13. ABSTRACT . .

-The shear. dependence. of. the..in,trjnsjc viscosity, and the conformation, _{of high}

molecular weight polyisobuty-lene. in _{dilute solutions of decahydronaphtha.lene. under} shear were determined, simultaneously. _{Experimental, variables investigated}

were the. shear rate (0 to .2..X io. sec'), _{the molecular. weih.t (1.0 x io}

to 1.7.X l0) and the polymer concentration (1.8 X 10' to 8.4 X .10- g/cc). Correlations.

allowing concentration.. and. shear _{rate normalization. forany. one sample. are-described.}

Conformational extent.ion.ratios. along _{the orientation direction of the. deformed} molecule to 1.42. and. intrinsic viscosity

ratios...(sheared. to zero. shear.)..to 0.5 were. observed.

I IIflM .

--

._ -

--I NOV 6!

(18)

Security Classification

14.

KEY WORDS LINK *

RO L.E W-T

LINK B

ROLE

LIN ROLE

DDFORM

I NOV 68 I