ARCHIEF
IN DILUTE SOLUTION
SUBJECTED TO A HYDRODYNAMIC. SHEAR FIELD
F.R. Cottrell, EW. Merrill, and K.A. Smith
Technica.l Report Prepared For
Office of Naval Research Contract Nonr 3963 (10)
Task NR 062-333 (1970)
This document. has been. approved for. public release and. sale; its distribution is unlimited.
Lab. v. Scheepsbo.uwkuncle
Technische Hogeschool
Deift
) DOCUMEHTATIE-d
eelc van de Onderafdeling d ouwkurn3eConformation of Polyisobutylene in Dilute
Solution Subjected to a Hydrodynaznic Shear Field*
F. II. COTTRELL, E. W. MERRILL, and K. A. SMITH, Department of Chemical EngineerIng, Massachusetts Institute of Technology, Cambridge,Massachusetts 02139
Synopsis
A new light-scattering experiment which allows a direct determination of the
con-formation of macromolecules deformed in flow is descnbed. Light-scattering
relation-ships based on the interference function are developed, and results of an experimental
study are detailed The deformed conformation of high molecular weight
polyiso-butylene was determined in a Couette-type shear field. Decalin was the solvent.
Vari-ables investigated were the shear rate (0 to 600 sec'), the polymer molecUlar weight
(1.0 X 10 to 1.6 X l0), and the polymer concentration (2.0 X lO' to 8.0 X l0
g/cc). Conformation variables determined were the orientation of the molecule in the shear field and its maximum and minimum extension ratios in the plane defined by the
direction of flow and the direction of the shear rate. The deformation of the molecule was found to be markedly discrepant when compared to the dynamic
macro-molecular models which assume complete coil flexibility, and more closely in agreement
with the recent theories of Cerf, developed for nonfree-draining coils which exhibit a
finite internal viscosity.
INTRODUCTION
The conformation of random coiling polymer molecules subjected to a hydrodynamic shear stress in dilute solution has been the subject of con-siderable interest for the past three decades. Several theoretical relation-ships exist in the literature'5 which account for the statistical shape of a series of macromolecular models in terms of the statistical distñbuti6n of distances separating the chain ends. Other relationships exist from models of the coil as an elastic sphere.6
Both categories qualitatively agree as to the nature of the coil
conforma-tion under flow condiconforma-tions. The originally spherical statistical shape of the random coil takes on an effipsoidal shape when subjected to a simple shear field. Deformation occurs in the plane defined by the flow and shear rate directions where motion of the segments can best be described as a tank tread rotation. Thai is, the time-averaged conformation of the macro-molecule rern.ins fixed while the segments rotate in an ellipsoidal path
This paper was presented in part at the International Symposium on Macromolecular Chemistry, Toronto, Canada, 1968.
416 corrilELL, MERRILL, AND SMITH
Fig. 1. Theoretical rnacromolecular statistical shape in a simple shear field. around the center of mass of the macromolecule. An illustrative example
of this behavior is shown in Figure 1.
Experimental evidence of the magnitude of the coil deformation has never been unequivocally determined. Birefringence measurements have allowed the determination of the orientation of the deformed coil but an absolute measure of the extent of coil deformation has, until now, been de-pendent upon theoretical estimates. Accordlingly, we have developed an experimental technique, based on the theories of light scattering, which allows the direct determination of the deformed macromolecular
conforma-tion under flow condiconforma-tions.
To further elucidate the nature of the deformed macronaolecular con-formation, the shear dependence of the intrinsic viscosity was also
deter-mined The results of these measurements will be published in another
paper.
LIGHT SCATTERING
It has been recognized for some time that light. scattering would allow a direct determination of the deformed conformation of the random coiling macromolecule in flow.
Relationships exist in the literature9 which
describe the theoretical interference of the light which would be scattered from macromolecules deformed according to the dumbbell model and theRouse model. It is also shown here that light-scattering experiments will
allow a direct determination of the flow deformed macromolecular
con-formation independent of any macromolecular model.
The parameter from which conformation information is determined is the inverse of the interference functiOn, P1, which can be written as:
= 1.0 + 167r2 sin2(O/2)p/X2 +
...
(1)where is the observation angle, A is the wavelength in the scattering me-dium, and p32 is the mean-squared radius of gyration of the intramolecular distances projected in the s direction. This direction is defined by a unit vector A along the direction of the incident beam and a unit vector B along the direction of observation such that:
The projected mean-squared radius of gyration, p2, is defined by the
rela-tionship:
-
1NN
2N282 (r11S)2 (3)
where N is the total number of segments in the polymer chain, S is the magnitude of the vector S, and r, is the position vector from segment i to segment j and the bar represents the time average. Random-coiling macromolecules in solutions at rest adhere to the relationship:
p02 = p02/3 (4)
where the subscript s refers to a projected gyration radius and zero refers
to the zero shear state.
Equation (1) treats the intramolecular interference of the scattered light according to the Debye method,'° which presupposes the existence of
opti-cally isotropic polymer segments which exhibit small excess polarizabilities
with respect to the solvent. Both presuppositions are generally justified in studies of macromolecular solutions at rest. However, under conditions of flow, slight modification to eq. (1) may be required in the case of large deformations and orientations of the random coils. Stevenson" and Rein-hold'2 have treated this problem theoretically using the macromolecular
dumbbell arid Rouse models, respectively. However, no attempt has been made in this study to account for depolarization effects since extremely
small macromolecular deformations were encountered
The properties of the interference function [eq. (1)] are such as to allow a direct determination of both the orientation of a deformed macromolecule
in a shear field as well as the magnitude of the deformation. In the present experiment, apparatus design dictated that the plane containing S [eq. (2)] coincide with the plane deflied by the shear rate and flow directions.
Thus, conformation information was determined only in this plane.
As an indicator of the orientation of the light-scattering coordinate system and the flow coordinate systems, a new angle f", is defined as the angle which the S direction makes with respect to the positive shear rate
direction. Because the square of the radius of gyration of the projected intramolecular distances is measured in light scattering, the sign of S is not important. Thus, ' is defined only in the half plane formed by the
shear rate axis in the positive direction of flow.
The orientation angle x can be directly determined through the use of the interference function. This angle is defined here as the angle between the positive shear rate direction and the major axis of the macromolecule (see Fig. 1). Study of eq. (1) shows that when S corresponds to the major
axis of the macromolecule (" = x),
takes on a maximum value and0_1 becomes a maximum. That is, when the major axis of the macro-molecule corresponds to the direction of 5, one experimentally observes maximum destructive interference or, in other words, a minimum of the scattered intensity for a given value of the observation angle The
con-1418 CorI'RELL, MERRILL, AND SMITH
verse is true for the superposition of S with the minor axis (f' = x ± 900) where p3' takes on a minimum va1ue Thus, experimental values of Pr1
taken as a function of fi' at constant observation angIe 0 and shear rate will allow a direct determination of the orientation angle of the deformed
macromolecule.
Once the orientation angle is determined, meaningful values of the pro-jected radii of gyration, (p32)
',
can be directly obtained through the use ofeq (1) In this experiment, values of Pr' are experimentally observed for given values of ' and and decreasing values of the observation angle 0. The use of these data and Equation (1) allows a direct -determination of
values ofPa2.
The projected radii of gyration are reported as a ratio to the values ex hibited by the zero shear state. An extension ratio, (1'), is defined as:
-[/2] 1/2
(5)where the subscript zero refers tO the zero shear state and the subscript s
refers to a projected radius of gyration
Because projections of the intramolecular dimension are measured in the plane containing s, only two extension ratios are independent. The
rela-tionship between the extension ratios is :8,13
(si/s)2a2 + (s2/s)2b2 (6)
where s, is the magnitude of the projection of s onto the major axis, s2
is the magnitude of the projection of s onto the minor axis, s is the
magni-tude of s, a is the major axis extension ratio defined as:
a =
= x)
(7)and b is the miuor.axis extension ratio defined as:
-b = (' = X + 90°)
- (8)MACROMOLECULAR CONFORMATION CRITERIA
Complete light-scattering conformation information would yisld values of
the orientation of the macromolecule in the shear field as well as projected gyration radii along the major (extended), minor (compressed), and per-pendicular directions of the deformed macromolecule Since the pro-jected root-mean-squared radius of gyration is related to the propro-jected root-mean-squared end-to-end distance along the same direction by a
constant factor, the extension, ratio may also be written as:
(9)
where is the mean-squared end-to-end distance of the flow deformed polymer coil along, the direction of x and tije subscript zerp refers to the zero shear state. - -Assigning the three orthogonal directions x, y, aid z to the major, minor, and perpendicular directions, respectively, a
r2 = x2 ± y2 + z2 =
2xo2 + y2Yo2 ± Ez2Zo2 (10) or, sinceby previousdefinition,= a, = = c, and = 1702 eq. (10) becomes:
= {(a2 + b2 + c2)/3} (11)
where the subscript zero refers to the undefOrmed end-to-end distance.
Assuming that the distribution of the projected end-to-end distances around the mean remains Gaussian in form along the three orthogonal directions x, y, and z; the joint probability function w(x,y,z) of finding the terminal bead at coordinates x to x + dx, y to y + dy, and z to z + dz
where the first segment is fixed at the origin can be written as:
w(x,y,z) = (3/22)½(1/abc)'2exp - (3/2) [x2/a2)
+ (y2/b2) + z2/c2)J} (12) Equation (12) dictates that the locus of points of equal probability of find-ing the terminal segment must satisfy the equation:
(x2/a2) + (y2/b2) ± z2/c2) = constant (13)
Thus, ivith the Gaussian assumption, the statistical shape of the deformed
macromolecule is that of an ellipsoid.
MATERIALS
The solvent decahydronaphthalene (Fischer Chemical Co., purified grade) was used throughout this study. Its selection was based on its refractive index which could be vaned by appropnate nuxing of its cis and trans isomers to match the refractive index of the glass shear cell used. Pertinent physical properties of the mixture at 25°C are: refractive index n0 = 1.476; viscosityo = 2.48cp.
The polymer polyisobutylene (Enjay Chemical Co., L250 and L300) was fractionated by fractional precipitation from a dilute solution of ben-zene by addition of the nonsolvent acetone. Seven fractions were
col-lected from each master sample.
APPARATUS
Light-scattering measurements were taken of polymer solutions which were subjected to a Couette-type shear field in the annulus of a coaxial cylinder shear cell. Through the use of a constant speed motor with a suitable gear reduction unit, the inner cylinder could be rotated at a series of incremental rotational speeds (12, 30, 60, 120, 300, 600 rpm) while the outer cylinder was held stationary. The drive, mechanism of the inner cylinder was designed. after that used in the GDM viscometer.14 With this apparatus, eccentricities of revolution at the extreme rotor end were
1420 COTERELL, MERRILL, AND SMITH
Two sets of inner and outer cylinder pairs fabricated from Corning 7740 glass were used. The dimensions of the sets as well as the ratio of the shear rate to the rotational speed are given in Table I.
TABLE I
Shear Cell Dimensions
Heights of the cups and bobs were approximately 3.0 inches. b Calculated for the mean radial position of the annular area.
The use of the cell fabrication material, Corning 7740 glass, was dictated by refractive index considerations. By selection of the mixture of ci (n1 = 1.483) and trans (n = 1.470) decalin, which was usedas the solvent,
it was possible to match the refractive index of the glass parts (n = 1.474) Unfortunately, the 7740 glass is not of optical quality, and careful selection of the raw material is required to obtain acceptable parts. All glass
sur-faces of the shear cell were optically polished.
The fluid flow within the annular volume is subject to both vortex
generation and end effects. Flow visualization experiments with the use of aluminum flakes (Reynolds Metal Co., Paste No. 13) iii 1,1,2,2 tetrabrorno-ethane illustrated the absence of any appreciable flow-perturbing end effects prior to the onset of vortex flow, and theoretical calculations on the basis of the Taylor instability criteria'5 dictated the complete absence of vortex flow at rotational speeds below 300 rpm, while rotational speeds of 600 rpm were possible for polymer solutions exhibiting relative viscosities greater than 2.6.
The light-scattering apparatus used throUghout this experimentation was a modification of the Sofica light-scattering photometer (manufactured by Société Francaise d'Instruments de Contrôle et d'Analyse). Major modifications consisted of: (1) substitution of the shear cell in the place of the standard sample cell (accomplished by constructing the shear cell above the rotating bath plate) and (2) modification of the incident beam so that it could be shifted parallel to its ongmal propagation direction in the plane perpendicular to the axis of rotation of the shear cell Displacement of the incident beam to 0.43 in. of the centerline of the shear cell could be obtained. Reproducible adjustment of the incident beam to 0.004 in.
was possible. Incremental source apertures were also available to modify the dimensions of the incident beam. (3) There was modification of the secondary beam-defining optics so that it could be oriented to observe any predetermined pOint in the annular area of the shear cell. Incremental beam-defining apertures were also available for this apparatus. (4) An amplification system was introduced to allow accurate determinations of
Description Seti Set2
Outer cylinder ID, in. 0.997 1.030
Ijiner cylinder D, in. 0.892 0.912
VAT WALL (CONTAINING DECALIN) FIXED PRISM MOVEABLE PRISM WI N DOW ROTATABLE CYLINDER SCATTERED BEAM DEFINING OPTICS STATIONARY VOLUME CYLINDER ELEMENT LIGHT T RAP TOP VIEW
Fig. 2. Optical diagram of modified Sofica apparatus.
both the secondary intensity under zerO shear conditions and differential
intensity readings upon shearing the polymer solution.
An optical diagram of the modified Sofica instrument is shown in Figure
2. The experimental optical settings illustrated in Figure 2 are: the angle
defining the position of the incident beam, the angle 6 defining the position
of the secondary beam defining optics, and the observation angle 0. In terms of these settings, the angle I" dictating the mutual orientation of the light-scattering vector S and the direction of the positive shear rate for
clockwise rotation of the inner cylinder becomes:
and for counterclockwise rotation:
The incident and secondary beam defining apertures were selected so as to maintain the illuminated volume element within the annular area. Data taken in calibration experiments which registered the light scattered by the solvent ifiustrated that the presence of the rotating cup and sta-tionary outer cylinder in no way appreciably altered the secondary inten-sity scattered from the annular area over the range of experimental settings.
EXPERIMENTAL PROCEDURES AND RESULTS Polymer Characterization
Light-scattering data were observed by use of both blue (Xo = 4358 A) and green (X0 = 5461 A) incident light. Data were observed at incre-mental observational angles from 300 to 1500 and at concentrations
rang-1422 COTTIIELL, MERRILL, AND SMITH
TABLE II
Characterization Data Summary for Polyisobutylene in Decalih
For exampl& L300-F4 designates the fourth fraction taken in the fractionation of
the L-300 samp1e
ing from 1.5 .X 10i to 8.0 X 10
g/cc. Sample temperatures were maintained at 25.0 ± 0.1°C.The data were plotted according to the method of Zimm,'6 from which both the z-average radius of gyration,
and the weight-averge
üiolecular weight Jt?W were determined. High-angle light-scattering data were analyzed according to the method of Loucheux'7 which allowed determinations of both the number-average radius of gyration,(p2)1'1, and
the ratio of the weight-average to the number-average moleculai weight, Intrinsic viscosities were determined from first-Newtonian solution vis-cosities measured on the GDM14 viscometer. Sample concentrations
ranging from 1 5 X 10 to 8 0 X 10
g/cc were investigated at T =25.0 ± 0.05°C.
Table II summarizes the characterization data observed for these
samples.
The Mark-Houwink relationship determined for the system is:
[] = 2.2 X i0-4MO.70 (16)
which agrees well with the relationship reported by Ram.'8
The number-average root-mean-squared radius of gyration is related to the numbet-verage molecular weight by the relationship:
(,,2)h/S = 0.24M°
(17) where the radius of gyration is expressed ii Angstroms. This relationship [eq. (17)] agrees well with the Fox-Flóry treatment of the intrinsic
vis-cosity and the empirical eq. (16).
Values of the universal viscosity constant, ci,, were alculated from the relationship:
{i
]j/()h/2(6)/!
(18)The mean value of the data exhibited by the fractionated samples with the standard deviation is;
ci, = (1.46 ± 0.16) x 10" Sample no. Fractions .&3,, X 10 ['plo dug (p2)/2 A (i,,h/i, A
Ji/M,.
LS-1 L-250 5.9 11.3 2000 860 3.2 LS-2 L-300 11.8 20.0 2600 1300 3.1 LS-3 L-300-F3 16.8 25.0 3000 200 1.1 LS-4 L-300-F5 10.5 18.9 2500 2200 1.3 LS-6 L-250.F4 5.3 10.2 1850 1200 L7 LS-9 L-300-F4 15. 23.9 2800 2800 1.1Light-scattering interference function data which were observed for any one sample for both incident beam wavelengths were found to superimpose to a single curve when plotted versus the parameter [sin2(O/2) J/X2 This
normalization technique agrees with the 1)ebye treatment'° of the
inter-ference function.
The differential refractive index required in light-scattering 'calculations was measured in the Rayleigh Laboratory interferometer manufactured by the Carl Zeiss Company. A value of cm/dc = 0.0374 cc/g was obtained for the incident beam wavelength of Xo = 5461 A at25°C. A value of dn/dc
= 0.043 ± 0.004 cc/g was back-calculated from light-scattering data for
the wavelengthX0 = 4358 A.
Orientation Angie Determination
Values of the light scattered by the polymer solution under zero shear conditions; In,,, as well as the change of the light scattered upon shearing LI were taken as data for incremental values of the angle (see Fig. 2).
The observation angle was arbitrarily fixed to either 0 = 90° or0 = 60°.
Values of ' were calculated from eqs. (14) and (15). Values of the ratio of the excess light scattered under shear conditions .to that scattered from
the zero shear state were calculated from the relationship:
-
+
(19)-
JO-
JO)/J,jwhere the subscript zero refers to the zero shear state, p to the polymer
solution, and the superscript zero refers to the solvent. The value of (J2,/I,) of eq. (19) was determined from shear cell measurements while
the value of [(4,, - I0)/4,,] was determined from the zero shear
char-1.2 1.1 1.0 0 0 0.9 0.8' 0.7 I I
-
CONSTANTS USED IN SAMPLE LS -3\ PETERLIN EQUATION a rl.245
- \
b0.96 \ \ ci.o \-\
(25'734o .i-
SOLUTION TO '.. PETERLIN EQUATION S 9 = gO' C 3.6 x1Og/cc 290 sec g 15.5 0 0 20 40 60 80 100 120 140 160 180Fig. 3. Ratio of excess light scattered from sheared to zero shear states vs. orientation
of S with respect to shear field, 0'; (--), solution of Peterlin7 equatiOn with
1424 COrFRELL, MERRILL, kND SMITH 0 0 1_i to 0.9 0.8
.
-I I SAMPLE LS-9-2 0.0688 9/31 -0 90' 3 14.2 120 140 160 180 20 40 60 41Fig. 4. Example of orientation angle determination.
acterization data. Figure 3 illustrates the results of some preliminary
data which were observed over the entire range ofvalues of c1'.
Generally, the data of the type illustrated by Figure 3 were observed to exhibit a maximum and a minimum separated in values of
' by 9O.
The data appear symmetrical around the maximum and minimum and the extreme positions of the curve were unaltered by the selection of the
ob-servation angle.
The orientation angle was determined from the value of 1' at which the value of [(I,, - 10)/(I,,. - 10)] was observed to become a maximum. Data for any one determination were observed at a constant observation angle, 9, shear rate, , and polymer concentration.
In that this value of cf"
('max) is indicative of the orientation of the minor axis of the macromole-cule with respect to the positive shear rate, the orientation angle is cal-culated from the relationship:
-X max
Figure 4 illustrates typical data from which an orientation angle
deter-mination was made.
Data were observed for three fractionated molecular weight samples (10 < il?,, < 1.7 X 10) at a series of concentrations (3 X 10 g/cc < c < .9 X 10 g/cc) under shear rates to approximately 600 sec'. Figure 5 illustrates the summation of these data with the estimated limit of error of each determination.
The abscissa scales of Figure 5, labeled $' and $c0r, are defined by the relationships:
= (21)
and
$cor = $'(,,/c)/(,9/c)o
(22)where is the solvent viscosity (o = 2.48 ep), (,/c) is the viscosity
num-ber at ',
/ç)o is the first-Newtonian value, and the other symbls take on their normal meanings. As illustrated by Figure 5, these parameterso 5 100 I I lollI 2 90 80 70 60 50 40 30 pI 4.' -0 10 10 15 20 -/-20 Cor 30 40 50 25 60 Fig. 5. Oñentation angle with limit of error versus
normalize both the concentration and molecular weight dependence of the orientatiOn angle to a single curve. This type of normalization procedure was first applied to extinction angle data observed in birefringence
experi-ments.'9 Its use is derived from the normalization parameter j3, dictated
by the Rouse and dumbbell macromolecular models. This quantity $ is related to the parameters used here by the relationship:
$ = lim $' = [}0M0/RT
(23)C
The lines drawn on Figure 5 represent the best fit of the data to the theoretical equation:
x = (w/4) + [tan'(8/m)J/2
(24)where m is an adjustable constant.
Extension Ratio Determinations
The extension ratio was determined from the square root of the ratio of the limiting slopes (c = constant, sin2O/ + 0) of the inverse of the inter-ference function (data plotted according to the Zimm16 method) of the sheared to zero shear state. Data for these determinations were observed at constant values ofcJ'
For a fixed macromolecular sample, concentration, and shear rate, the data acquisition procedure fOr determining a major axis extension ratio is
as follows. The value of 4)' by the definition of the experiment, is set to x. Apparatus geometry settings are calculated from eqs. (14) and (15) for values of 0 of 900, 750, 600, and 450 Using these instrument settings,
52 TONI 8cor/2.5)
SYMBOL SAMPLE CONC (flic),
9l0l 02 91/9 0 LS -3 3.60 33.3 0 LS -3 7.20 41.5 V LS-3 667 46.5 o LS-3 5.90 35.7 LS-4 6.50 27.3 LS -4 5.20 21.0 £ LS-4 8.70 31.0 Q LS-9 6.88 360
1426 COTTRELL, MERRILL, AND SMITH 1.5 10 SAMPLE LS-9 l,=4360A 285 SEC
ER0 SHEAR DATA
£SHEAR DATA=-.
10 2.0 3.0
Sin2 I2 KC , K
5 xl0cc/g
Fig. 6. Zimm plot for shear data corresponding to '1" = x
values of the light scattered by the polymer solution, 1,,,, and the change of the scattered intensity upon shearing, Al,, are recorded as data for each observation angle. The ratio (I, - 1°)/(I,,, - 10) is calculated from eq. (19) and applied as a corrective ratio to the zero shear state characterization data. That is, the Zimm plot can be corrected by the relationship
Kc/R9 = Kc/R9,, ('i':
I i)
(25)where K is the optical constant, c the polymer concentration and R9 is the modified Rayleigh ratio, where the subscript zero refers to the zero shear state. Illustrative data of the correction are shown in Figure 6.
As illustrated in Figure 6 and as generally observed in this study, the extrapolation to zero angle on the Zimm plot appears, withm experimental error, to be independent of the shear rate. This fact ifiustrates the
negli-gible dependence of the second virial coefficient on the shear rate. Figure 6 can then be used in the determination of the extension ratio. NOte that the angular slope of the Zimm plot may be evaluated as:
16,r22
f
14.0
and that an equivalent slope, T0' my be determined from the zero shear data. By definition of the extension ratio then:
= (27)
-
.T - hmj2
* oro(Kc/R0n
- (26)1.3 1.2 1.1 1.0 0.9 £ -V ASSUMED M0800ISPERSED 'BCOA2IOP 09
-a :1.0. 0.013 8 SYMBOL SAMPLE LOJC2 9181.10 (h1:0M1 153 6.88 ]73 AV 15.9 4.58 32 6 o L5-3 540 37.8 S LS 4 650 27.] 0 LU-I 5.20 26.0 0 10 20 30 a
Fig. 7. Major and minor axis extension ratios vs.
$'. ()
theoretical results ofpolydispersity analysis.
In this experimentation, the major axis extension ratio a was determined by the method described above. The minor axis extension ratio b was cilculated from data observed at values of 4' = x ± 450, the major axis
extension ratios, and the use of eq. (6).
Three fractionated molecular weight samples were investigated, ranging from 4 X 10-a g/cc to 7 X 10
g/cc and shear rates to 600 sec. The
summation of these data is plotted in Figure 7 versus the parameter i3'.Also shown on Figure 7 are the results of a polydispersity analysis in which the monodisperse behavior was assumed; a Schultz-Zimm distribu-tion of molecular weights was assumed; and the Z-average extension ratio calculated for a corresponding weight-average value of 3. The averaging technique was dictated by the physics governing the interference function and the experimental values of fi which were used. An outline of this
cal-culation may be found in Appendix A.
As illustrated by this plot, the parameter ' does appear to normalize the concentration ependence of the extension ratios. However, a discrep-ancy does exist in comparing the data illustrated bysamples LS-9 and LS-3
with LS-4. Comparison with the results of the polydispersity analysis shows that this discrepancy can easily be explained in terms of varying
degrees of polydispersity which exists between the samples.
Figure 8 graphically represents the statistical shape of the deformed iiacromolecular coils in that it represents a solution to eq. (13) by use of
experimental values of the extension ratios and orientation angles.
Alternative Method of Data Analysis
Peterlin79has developed theoretical relationships determining the inter-ference function for the deformed dumbbell and Rouse macromolecular models. Peterlin's solution to the dumbbell model can be generalized to
Ri, :133
M/
:2
1.4
1428 COTTRELL, MERRILL, AND SMITH Q (Flow Direction)
Fig. 8.. Statistical shape of deformed macromolecular coil..
account for the light scattered by a macromolecule exhibiting extension ratios a, b, and c as well as an orientation angle x. The relationships written in terms of the present. nomenclature and experimental geometry are:
P0 =
2f
(1 - u) exp X'(u + Lu2)ldu
(28)where
= xa'
X = 16,r2 sin2 (O/2)/X2
L=(a2+b2+c2-3)/3
8' =
[a2 ç2 (ëf'- x) +
l$2 Sjfl2(4" - x)]/(L + 1)
The limiting form of eq. (28) as applied to the zero shear state (a b =
c = 1) yields the familiar Debye expression or:
P0, = 2/X2[e_X - (1 + X)j
(29)The absolute values of the interference function calculated from these
equations are inaccurate as is expected of a somewhat polydispersed polymer
in a good solvent. However, the ratio of values, P6/P0,,, when calculated with the extension ratios and orientation angles observed here may be used
to calculate values of (I, JO)/ JO)which agree closely with
experi-méntà1 data. Figure 3 illustrates this comparison; an outline of the
cal-culation is given in Appendix B.
.1=30 '(-85' -125 b=0.94 5=20 Z82 =1.29 b=095 =115, b0.9B = 10,
The values of the minimum and maximum exhibited by the solution to the Peterlin equation on Figure 3 are primarily determined by the major and minor axis extension ratios respectively while their positions are deteriniiied by the oiiciitation angle. The significance of the agreement illustrated by Figure 3 is that conformation extension ratios and orientation angles may be obtained by curve fitting the Peterlin equation to the actual data. This procedure would eliminate the need of acquiring data at incre-mental decreasing observation angles in the extension ratio determinations
and thus greatly simplifying the experimental procedures.
The actual solutions to eq. (28) were carried out by a numerical integra-tion technique on a computer. Experimental variables were used in eqs. (28) and (29) with the exception of the extension ratio c (perpendicular to
the flow and shear rate directions) which was assumed to be unity.
DISCUSSION
The values of the orientation angle reported here agree well with the values observed for the same polymer solvent system by birefringence measurements and with predicted theoretical values.
Table III lists a series of theoretical and experimental values of m of eq.
TABLE III
Theoretical and Experimental Values of m from Equation (24) Experimental system/model
Dumbbell model
Rouse model: free-draining Rouse model: nonfree-draining PIB-gasoJine
PIB-decalin
PIB-decalin (based on
PIB-decalin (based on j5'cor)
m 1.0 2.5 4.88 0.78 1.89 3.6 ± 0.9 2.5 E0.5
Data extrapolated to zero concentratiàn by Peterlin.3
(24) obtained from the macromolecular models, birefringence data, and the results of this study. Comparison of the experimental data is difficult because of the existence of varying degrees of polydispersity of the inves-tigated material. Polydispersity has the effect of lowering the experi-mental values of m. On allowing for this factor, agreement with the
ex-perimental results from birefringence is considered good.
The values of the. extension ratios reported here are markedly different from those predicted by the macromolecular models which assume freely flexible polymer molecules (no internal viscosity). In making this
com-parison, it is most convenient to report values of the mean coil expansion given by eq.. (11). Figure 9 illustrates the comparison of data reported
here to predictions of the dumbbell and Rouse macromolecular models.
Reference Peterlin7 Zimm'° Zirnm2° Tsvetkov andFrisman22 Brodnyam et al.21 This study This study
1430 COTTRELL, MERRILL, AND SMITH
D U NA B B E LL
MODEL
RESULTS OF THIS STUDY
Fig. 9. Comparison of models of freely flexible macromolecules to experimental results.
ROUSE MODEL(3) FREE-DRAINING ROUSE MOOEL(3) NON-FREE- DRAINING 11.0 z 9.0 z 8.0 4 w 7.0 -J G.0
0
Li z 5.0 4 w 4.0 3.0 L 2.0 1.0 0.1 1.0 10 100Fig. 10. Comparison of the experimental mean coil extension with the theoretical result of Cerf5 far nondraining coils with finite internal viscosities.
Figure 10 illustrates the results of the recent calculations of Cerf5 for non-free-drarnmg coils with finite internal viscosities The parameter sho n on
this figure is the thmensionless effective ngidity factor, n, defined by the relationship:
n = (30) where Na is Avogadro's number, and '1' is the intrinsic rigidity factor of the polymer chain representative of steric hindrance to free rotation. Also
shown in Figure 10 are the results of this study ca1cuited from eq. (11)
with experimental values of a and assuming values of b = C = 1.0.
As already pointed out by Cerf,5 direct comparison of the results and theory is not currently possible due to the lack of intrinsic rigidity factor 'I' characteristic of the PIB macromolecule. However, as an order of mag-nitude estimate, a value of n = 45 can be calculated assuming a value of 'I' = 1.6 X 1Q g/sec as has been determined for the polystyrene rnol-cule.23'24 Reference to Figure 10 illustrates that the theoretial.and experi-mental mean coil expansions, compared in this manner, to be of the same
order of magnitude but of divergent forms. CONCLUSIONS
Light-scattering measurements of macromolecular solutions under flow
will allow a direct determination of the flow determined conformation of the macromolecule Complete light-scattering information will yield three
independent extension ratios of the coil and its onentation m the shear
field.
Experimental data reported here for the polyisobutylenedecahn system indicates the deformation of the macromolecules in a simple shear field to be severely limited.. The major axis extension ratio a can be given by the. relationship:
a= 1.0 + 0.013I3°
0 30 (31)while the orientation angle follows the relationship:
x (7r/4)
+ [tan(fi/3.6)]/2
(32) T he form of orientation angle relationship is in agreement with thepre-dictions of the macro inoleculaf tnodels which assume freely flexible
macro-molecules, while the extension ratios are markedly discrepant with the pre-dictions of these models and more in agreement. with the Cerf model5
which assumes a finite coil internal viscosity.
APPENDIX A
The mean-square radius of gyration obtained from light scattering is a
z-average value defined by the relationship:
= (A-i)
where W is the weight fraction of material having a molecular weight of
M to M + dM and
is the mean-square radius of gyration of thismolecular weight species. This same type of relationship can be written for the projected gyration radii.
1432 COTTRELL, MERRILL, AND SMITH
The extension ratio measured in this experimentation is:
tel")
[/(i)]'/2
(A-2)whereas the monodispefsed extension ratio may be given by the relation-ship:
= f($)
(A-3) Equations (4), (16), and (18) may be combined to yield the relationship:= FM'3
(A-4)where F is a constant.
Equations (A-1)--(A-4) may be combined to descnbe the polydispersed
extension ratio as:
[(')
]2' (A-5)The value of , which is experimentally measured, contains the product of the intrinsic viscosity and the weight-average molecular weight. The ihtiinsic viscosity is dependent upon a viscosity-average molecular weight which is assumed to be essentially equal to the weight-average value be-cause of the high value of the exponent in the Mark-Houwink equation and the relatively low degree of polydispersity in the samples. The experi-mental Value of used to characterize the sample is described by the relationship:
= (K0"?/RT)M'.7 (A-6)
where the equivalent relationship for the monodispersed species would be written as:
= (K'qo'/RT)Mj'7 (A-7)
To describe the polydispersity of the polymer sample, a Schultz-Zimm
distribution was used. This function can be written as: W = (yZ+l/z!)MZeYMi
y = (z + 1)/Mu
(A-8)(z + 1)/z =
where W represents the weight fraction of material of molecular weight of
MtoM + dM.
The monodispersed behavior remains to he described. From Figure 7,
the most motiodisperse samples appeared lo yield a In:LJUr axis dependence
on $ of the form
a2 = 1 + i3°-° = fC8)
0(\-9)
Equations (A-6)-(A-9) may then be substituted into eq. (A.5) to yield an expression for the extension ratio for the polydispersed state, a. The
independent variables of this calculation are
and M/A?.
The actual calculation of values of a were carried out by a numerical integration technique on a computer. The results of this calculation are
shown in Figure 7.
APPENIMX B
At finite concentration and observation angle,
Kc/R0 = (P0-'/J(?) + 2A2c + ...
(B-i)For simplification the following quantities are defined:
lim (Kc/R0) D (B-2)
c.O
o tLIId lim (Kc/Re) = E (B-3) o 0 such thatE - D = 2A2c
(B-4)Equations (B-1)-(B-4) may be combined to give:
P0' = [(Kc/R0) - (E - D) ]/D
(B-5)and from the equivalent relationship for the zero shear state:
P
(Kc/R0,) - (E - D)
(B-6)
Po,0
[(I,,, - I0)/(I - I) ](Kc/R9,0) - (E - D)
or
1 10
I p -
(B7)- 10
[(P00/P0) ] [(Kc/Ro,j] - (E - D) + (E - D)
In that values of Kc/R9,0, E, and D are directly determinable from the Zimm plot of zero shear rate data, eq. (B-7) relates the interference function
ratio to the experimental ratio of the excess scattered light.
This work was supported by the Office of Naval Research under Contract Norir 3963(10) and done in part at the Computation Center at the Massachusetts Institute of
Technology, Cambridge, Massachusetts.
References
J. J. Herm:uis, Physiea, 10, 777 (1943).
W. Kuhn arid II. Kuhn, Hclv. C/urn. Ada, 26, 1394 (1943). A. Peterlin, J. Chem. Phys., 39,224 (1963).
Chr. Reinhold and A. Peterlin, J. C/rem. Phys., 44,4333 (1966). R. Cerf, C.R. Acad. Sci. (Paris), C267, 1112 (1968).
1434 COTTR.ELL, MERRILL, AND SMITH
R. Cerf, J. Chim.Phys., 48,59 (1951).
A. Petèrlin, W. Heller, and M. Nakagaki, J. C/tern. Phys., 28,470 (1958). A. Peterlin, J. Polym.&i., 23, 189 (1957).
A. Peterlin and Chr. Reinhold, J. Chem. Ph ye., 40, 1029 (1964).
10 P Debye, Technical Report CR 637, pnvate communication to Reconstruction
Finance Corporation, Office of Rubber Reserve (1945), in Light Scattering from Dilute Polymer Solution.s, D. McIntyre and F. Gornick, Eds., Gordon and Breach, New York,
1964.
A. F. Stevenson and H. L. Bhatragar, J. Chern. Phys., 29, 1336 (1958). Chr. Reinhold and A. Peterlin, Physica, 31,522 (1965).
F. R. Cottrell, Sc.D. Thesis, Massachusetts Institute of Technology, Cambridge,
Massachusetts, 1968.
P. J. Gilinson, C. R. Douwalter, and E. W Merrill, Trans. Soc. Rheol., 7, 319
(1963).
S. Chandrasekhar, Hydrodynarnic and Hydromagnetic Stability, Clarendon Press, Oxford, England, 1961, Chap. VII.
B. H. Zimm, J.. Chem. Phys., 16, 1093 (1948).
C. Loucheux, G. Weill, and H. Benoit, J. C/tim. Phys., 55, 540 (1958).
A Ram, Sc.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mas-sachusetts, 1961.
A. Peterlin, in Rheology Theory and Applications, Vol. I, F. R. Eirich, Ed., Aca-demic Press, New York, 1956.
B. H. Ziinm, J. Chem. Phys., 24,269 (1956).
J. G. Brodnyam, F. H. Gaskins, and W. Philipoff, Trans. Soc. Rheol., 1, 109
(1957).
V. N. Tsvetkov andE. Fristnan, Acta Physicochim. U. R. S. 5., 20, 61(1945). A. Peterlin, J. Polym. Sci. A-., 5, 179 (1967).
R. Cerl, J. Phys. Radium, 19, 122 (1958).
Received March 10, 1969
Technical Library Building
131
Aberdeen Proving Ground, Maryland 21O0 Defense Documentation Center (2Q) Cameron Station
A1e.ndriá, Virginia 2231! Technical Library
Naval Ship Research and Development Center Annapolis Division
Annapolis, Maryland 2JJ.iO2
Professor Bruce Johnson Engineering Departin&it
Naval Acader
Annapolis, Maryland 21LO2 Library Naval Acadexir Annapolis, Maryland 2].h02 Professor W. P. Graebel Department of Engineering Mechanics
The University of Michigan College of Engineering Ann Arbor, Michigan LI.81014.
Professor W. R. Debler
Department of
Engineering Mechanics University of MechanicsAnn Arbor, Michigan Li.8108 Dr. Francis Ogilvie
Department. of Naval Architecture and Marine Engineering
University of Michigan Ann Arbor, Michigan
b8108
Professor S. D. Sharina ....
Department of. Naval Architecture an&Marine Engine ering
University of Michigan Ann Arbor, Michigan'
DISTRIBUTION LIST FOR IJNOLASSIFI TECHNICAL REPORTS ISSUED UNDER
CONTRACT/lj,r' 393()0)IASK ,-333
Professor LW, Wjflxnarth
Department of Aeroppace Engineering University of'Michigan
Aim Arbor, Michigan b8l08 Professor Finn C. Michélsen Naval Architecture and Marine
Engineering
t1Jj,5 West. Engineering Bldg.
University of'Michigan Ann Arbor, Michigafl L.8lOb AFOSR (REM)
]J400 Wilson Boi.tlévard
Arlington, Virginia 222Db Dr. J..Menkes
Institute for, Defense Analyses bOO A y-Navy Drive
Arlington, Virginia 22201i.
Professor S. Corrsin Mechanics Department
The Johns Hopkins' UniitersIty Baltimore, Maryland / 20910
Professor 0, N. Phillips The Johns Hopkins University
Baltire, Maryland 20910
Professor L. S., G. Kovasznay The Johns Hopkins University Baltimore, Maryland 20910
Librarian
Department of Naval Architecture University of California
Berkeley, California 91i.720
ProfessorP. Lieber
Department of' Mechanical Engineering
Univerity of California
Institute of Engineering Research Berkeley, California 9L72O Professor N. Holt
Division of Aeronautical Sciences University of California
Professor J0 V., Wehausen
Department of Naval Architecture University of CVifornia
Berkeley, California 914720
Professor J0 R. Paufling
Department of Naval Architecture University of California
Berkeley, California 914720
Profe.ssor E0
V. Laitone
__--Department of Mechanical Engineering University of California
Berkeley, California 914720
School of Applied Mathematics Indiana University
Bloomington, Indiana 1471401
Comander
Boston Naval Shipyard
Boston, Massachusetts 02129 Director
Office of Naval Reaearch Branch Office
1495 Summer Street
Boston, Massachusetts 02210 Professor N. S. Uberoi
Department of Aeronautical Engineering
Unisityof Colorado
Boulder, Colorado 80303
Naval Applied Science Laboratory Technical Library
Bldg6 1 Code 222
Flushing and Wasbinton Avenues Brooklyn, New York 11251 Professor
J. J.
FoodyChairman, Engineering Department State University of New York Maritime College
Bronx, New York 101465
Dr Irving C. Statler, Head Applied Mechanics Department
Cornell Aeronautical Laboratory, Inc. P. 0. Box 235
Buffalo, New York 114221
Dr., Alfred Ritter
Assistant Head, Applied Mechanics Dept. Cornell Aeronautical Laboi'atory, Inc. Buffalo, New York 114221
Professor G. Birkhoff Department of Mathematics Harvard University
Cambridge, Massachusetts 02138 Coimianding Officer
NROTC Naval Administrative Unit Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 Professor N. Newman
Department of Naval Architecture and Marine Engineering
Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Professor A. H. Shapiro
Department of Mechanical Engineering Maasachusetts Institute of 1echnology
Cambridge, Massachusetts 02139 Professor C. C. Li
Department of Mathematics
Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Professor E. W. Merrill
Department of Mathematics
Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Professor M. A. Abkowitz
Department of Naval Architecture
and Marine Engineeng
Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Professor G. H. Carrier
Department of Engineering and
Applied PIsics
Harvard University
Cambridge, Massachusetts 02139
Professor E. Mob-Christensen
Room 514-1722
Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Professor A. T. Ippen
Department of Civil Engineering
Massachusetts Institute of Technology Cambridge, Massachusetts 02139
Charleston Naval Shipyard U. S Naval Base
Charleston, South Carolina 291408
A. R. Kuhlthau, Director Research Laboratories for the
rigtneering Sciences
Thorton Hall, University of Virginia Charlottesville, Virginia 22903 Pirector
Office of Naval. Research Branch Office
219 Dearborn Street
Chicago, Illinois 606014
Library
Naval Weapons Center
China Lake, California 93557
Library MS
60-3
NASA Lewis Research Center
21000 Brookpark Road
Cleveland, Ohio LL14135 Professor J. M. Burgers
Institute of Fluid Dynaxnics and. Applied Mathematics
University of' Maryland
College Park, Maryland. 207142 Acquisition Director
NASA Scientific & Technical Information
P. 0., Box 33
College Park, Maryland 207140 Professor Pai
Institute for Fluid Dynamics
and Applied Mathtics
University of Maryland
College Park, Maryland 207140 Technical Library
Naval Weapons Laboratory Dahigren, Virginia 2214148
Computation & Analyses Laboratory Naval Weapons Laboratory
Dahigren, Virginia
22))8
0
LTV Research Center
Dallas, Teas 75222
Dr. R, H. Kraichnan
Dublin, New Hampshire 03141414 Commanding Officer
Arny Research Office Box CM, Duke. Station
Durham, North Carolina 27706 Professor A. Charnes
The Technological Institute Northwestern University Evanston, illinois 60201
Dr. Martini H. Bloom
Polytechnic Institute of Brooklyn Graduate Center, Dept. of Aerospace Engineering and Applied Mechanics Farmingdale, New York
11735
Technical Documents Center Building 315
U. S. .Art Nobility Equipment Research and. Development Center Fort Belvoir, V'irginiá 22060 Professor J. E. Cerinak
College of Engineering Colorado State University Ft. Collins, Colorado 80521 Technical Library
Webb Institute of Naval Architecture Glen Cove, Long Island, New York 115142 Professor. E.. V. Lewis
Webb Institute of Naval Architec1.i.re Glen Cove, Long Island, New York 115142
Library MS
185
NASA, Langley Research Center Langley Station Hampton, Virginia 23365 Dr. B. N, Pridmore Brown Northrop Corporation NORA.IR-Djv. Hawthorne, California 90250
-3-Dr. J. P. Breslin
Stevens Institute of
Davidson Laboratory
Hoboken, New Jersey
Mr. D. Savits1r
Stevens Institute of
Davidson Laboratory
Hoboken, New Jersey
Technolor
07030Technolor
07030(2)
Sd.
Mr. Alfonso Alcedan L, Director
Laboratorlo Nacional De Hydraulics
Mtigu.i Caineno, .Ancon
Casjfla Jotal 682
Lixna, tern
C.omand.er
Long Beach Naval Shipyard
Long Beach, California
90802Professor John Laufer
Department of Aerospace Engineering
University Park
Los Angeles, California
90007Professor J. Ripkin
St. Anthony Fftl 1
Hydraulic Lab.
University of Minnesota
Minneapolis, Minnesota
SSIi.1hProfessor'J. M. Kifleri
St. Anthony Fans Hydraulic Lab.
University of Minnesota
Minneapolis, Minnesota
SShulj.Lorenz (1. Straub Library
St. Anthony Falls Hydraulic Lab.
Mississippi River at 3rd Avenue SE.
Minneapolis, Minnesota
SSLI.ilJ.Dr. E. Silberrnan
St. Anthony Falls Hydraulic Lab.
University of Minnesota
Minneapolis, Minnesota
5S141)4Superintendent
Naval Postgraduate School
Library Code 0212
Monterey, California
939)40Professor A. B. Metzner
University of D.elaware
Newark, New Jersey
19711Technical Library
USN Underwater Weapons &
Research & Engineering Station
Newport, Rhode Island
028)40Technical Library
Underwater Sound Laboratory
'Fort Truxribul].
New London, Connecticut
06321Mr. C. H.. Henry
Stevens Institute of Techno1or
Davidson. Laboratory
Hoboken, New Jersey
07030Professor J. F. Kennedy, Director
Iowa Institute of Hydraulic Research
State Unive'sity of Iowa
Iowa City, Iowa
S22)40Professor L. Landweber
Iowa Institute of Hydraulic Resrch'
State University of Iowa
Iowa City, Iowa
22lj.0Profeseor E. L. Resler
Graduate School of
Aeronautical Engineering
Cornell University
Ithaca, New York
l)48S1Professor John 'Miles.
% i.&.p.p.
University of California, San Diego
La Jolla, California
92038
Director
Scripps Institution of
Oceanograpl-University of California
La Jolla, California
. 92037Dr. B. Sternlicht
Mechanical Technology Incorporated
968 Albany-Shaker. Road
Latham, New York.
12110
Mr. P.. Eisenberg, President
Hydronautics
Pind.efl School Road
Howard County
Laurel, Maryland
20810professor A. Ellis
University of California, San. Diego
Department of Aerospace & Nech. Engrg,
La Jolla, California
92037Institute of Mathematical Sciences New York University
21 Mercer Street
New York, New York 10003 Engineering Societies .T4brary
3115 East 147th Stree.t
New York, New York 10017 Office of Naval Research New York Area Office 207 W. 214th Street..
New York, New York .10011 Commanding Officer
Office of Naval Research Branch Office
Box 39
FPO New York, New York
091O
Professor H. ElrodDepartment of Mechanical Engineering Columbia University
New York,, New York 10027 Society of Naval Architects and
Marine Engineering 711. Trinity Place
New York, New, York 10006 Professor S. A.. .Piascek
'Departtnent of Engineering Mechanics University of Notre Dame
Notre Dame, Indiana 14.6SS6
United States Atomic . Ener Commission Division of' Technical In±'ortnatiOn
Extension -.
P. 0. Box 62
Oak Ridge, Tennessee 37830
Miss 0... H. Leach, Librarian National Research Council Aeronaitica1 Library Montreal. Road
Ottawa 7, Canada Technical Library
Naval Ship Research and Development Center
Panainan City, Florida 321401
Jet Propulsion Laboratory
California Institute Of Techno1or 14800 Oak GrQve Avenue
Pasadena, California 91109 Professor M. S. .:Plésset; Engineering Division
California InstitUte Of Technology Pasadena, California 91109
Professor H. .Liepinann Department of' Aeron.antics
CalifQrnia Institute of Technology Pasadena, California 91109
Technical Library
Naval Undersea Warfare Center.. 3202 E. Foothill Boulevard (2S) . Pasadena, California 91107
Dr. J..W. Hoyt
Naval Undersea Warfare Center 3202 B. Foothill Boulevard Pasadena, California 91107 Professor T. Y. Wu
Department of Engineering
California.. Institute of Technolo-Pasadena, California 91109
Director
Office of 'Nal Reàearch Branch Office
1030 E. Green Street
Pasadena, California 91101
Professor A.-Ata
Department of' )Iechanical Engineering California Institute of Technology Pasadena, California 91109
Naval Ship Engineering Center Philadelphia. Divisiox
Technical Library
Philadelphia, Pennsylvania 19112 Technical Library (Code 2149B) Philadelphia Nava1 Shipyard
Professor R. C. Mac
CazrDepartment of Mathematics
Carnegie Institute of Techno].o
Pittsburgh, Pennsylvania
2l3
Dr. Paul Kaplan
Oceanics, Inc.
Plainview, Long Island., New Yoric
11803
Technical Library
Naval Missile Center
Point Nugu, California
931a4JTechnical Library
Naval Civil Engineering Lab.
Port Hueneme, California
9301i1 CommanderPortsmouth Naval Shipyard
Portsmouth, New Herxpshire
03801
Coimnander
Norfolk Naval Shipyard
Portsmouth, Virginia
23709Professor F. E. Bissbbpp
Division of Engineering
Brown University
Providence, Rhode Island
02912
Dr. L. L. Higgins
TRW Space Techno1or Labs, Inc.
One Space Park
Redondo Beach, California
90278Rstone Sciaitific Information Center
Attn:
Chief, Document Section
Aimr Missile Command
Redstone Arsenal, Alabama
3809
Dr. H.. .N
AbramsonSouthwest Research In3titute
8S00 Cuiebra Road
San Antonio, Texas
78228Editor
&pplied Mechanics Review
Southwest Research Institute
8S00 Culebra Road
Sa.nAtonio, Texas
78206Librarian
Naval Coirmiand Control Coinmwnications
Laboratory Center
San Diego, California
92l2
Library & Information Services
General Dynamics-Convair
P. 0. Box 1128
San; Diego, California
92112 Coimnander (Code 21.,6P)Pearl Harbor Naval Shipyard
BoxbOO
-FF0 San Francisco, California
96610Technical Library (Code H215C-3)
Thñiters Point Division
San Francisco Bay Naval Shipyard
San Francisco, California
91i.].3SOffice of Naval Research
San Francisco Area Office
1076 Mission Street
San Francisco, California
9ilO3
Dr. A. May
Naval Ordnance Laboratory
White Oak
Silver Spring, Maryland
20910Fenton Kennedy Document Library
The Johns Hopkins University
Applied Physics Laboratory
8621 Georgia Avernie
Silver Spring, Maryland
20910Librarian
Naval Ordnance Laboratory
White Oak
Silver Spring, Nary1aid
20910Dr. Bryne Perry
Departhient of Civil Engineering
Stanford University
Stanford, California
91j.30SProfessor Milton Van.
Department of Aeromatica1 Engineering
Stanford University
Stanford , California
9L30SProfessor E. Y. Hen
Department of Civil Engineering
Stanford University
Stanford, California
9130SDr. R. L. Street
Department of Civil Engineering
Stanford University
Stanford, California
9IL3OS-6-Departmsnt of Mechanical Engineering Syracuse University
Syraci.ise, New York 13210 Professor R. Pfeffer
Florida State University
Geophysical Fluid Dynamics Institite Tallahassee, Florida 323Q6
Professor J, Foa
Department of Aeronautical Engineei'ing Rennsselaer Polytechnic Institi4e Troy, New York 12180
Professor R. C. Di Frina Department of Mathe3T$t-cs
Renris elaer Polytechnic Institute Tray, New York 12180
Dr. H.. Sevik
Ordnance Research Laboratory Pennsylvania State University
University Park, Pennsylvania
16801
Professor J. LuxnleyOrdnance Research Laboratory Pennsylvania State University
University Park, Pennsylvania
16801
Dr. J. M. RobertsonDepartment of Theoretical and Applied Mechanics
University of Illinois Urbana, flhinois 61803
Shipyard Technical Library Code 130L7 Building Th6
San Francisco Bay Naval Shipyard Vallejo, California 91592 Code L142
Naval Ship Research and Development Center Washington, D.00 20007 Code 800
Naval Ship Research and Development C enter Washington, D.C. 20007 Code 2027
U. S. Naval Research Laboratory
Washington, D.C. 20390 (6)
Chief of Naval Research Department of the Navy Washington, D.C. 20360 Code. Sl3
Naval Ship Research and Development C enter Washington, D.C. 20007 Science & Technolo Division Library of Congress
Washington, D.C.
2OO
OR]) 913 (Library)Naval Ordnance Systems Command Washington, D.C. 20360
Code 6b20
Naval Ship Engineering Center Concept 1)ign Division
-Washington, D.C. 20360
Cod,e 00
Naval Ship Research and Development Center Washington, D.C. 20007 Code 901
Naval Ship Research and Development Center Washington, D.C. 20007 Code S20
Naval Ship Research and Development Center Washington, D.C. 20007.
Code O31j.1
Naval Ship Systems Command Departamient of the Návy Washington, D.C. 20360 Code 202 (Technical Library) Naval Ship Systems Command Department of the Navy Washington, D.C. 20360
Mi. J. L. Schuler (Code 031412) Naval Ship Systems Command
Department of the Navy Washington, D.C. 20360
Dr. J. H. Huth (Code 031)
Naval Ship Systems Command
Departmnnt of the Navy
Washington, D.C.
20360Code Li61
Chief of Naval Research
Department of the Navy
Washügton, DD.
20360Code 530
Naval Ship Research and
Development C enter
Washington, D.C.
20360Code !i.66
Chief of Naval Research
Department of the Navy
Washington, 1D,C.
20360.
Office of Research and Development
Maritime Administration
Lilj.l G. Street, NW.
Washington, D.C.
20235Code 163
Chief of Naval Research
Department of the Navy
Washington, D.C.
20360National Science Foundatirn
Engineering Division
1800 G, Street, NW.
Washington, D.C.
20550Dr. G. Kuhn
National Bureau of StandardS
Washington, D.C.
20231i.Department of the
Arrry-Coastal Engineering Reaearch Center
5201 Little Falls Road, NW.
Washington, D.C.
20011Code 521
Naval Ship Research and
Developznnt Center
Washington, D.C.
20007Code 18i
Chief of Naval Research
Department of the.Navy
Washington, D.C.
20390
-8--Code i21
Chief of Naval Research
Department of the
.NavyWashington, D.C.
20360C oimnander
Naval Ordnance Systems Command
Code ORD 035Washington, D.C.
20360Librarian Station 5-2
Coast Guard Headquarters
1300 E. Street, NW.
Washington, D.C.
20226Division of Ship Design
ritime Administration
UiJ-G.. Street, NW.
Washington, D.C.
20235 HQ IJSAF (AFRSTD) Room 1D 377The Pentagon
Washington, D.C.
20330 CommanderNaval Ship Systems Command
Code 66t1C
Washington, D.C.
20360 Cod.e.525Naval Ship Research and
Development C enter
Washington, D.C.
20007Dr. A. PowejJ. (Code 01)
Naval Ship Research nnd
Development C enter
Washingtnn, D.C.
20007Director of Research Code ER
National Aeronautics &. Space Admin.
600 Independence Avenue, SW.
Washington, D.C.
2051.6Commander
Naval Ordnance Systems Command
Code 03
Washingtnn, D.C.
20360Code ORD 05IJi.
Naval Ordflance Systems Command
Naval Air Systems. Coimnaid
Department of the Navy
Washington, D.C.
20360 AIR 60!iNaval Air Systems Comsand.
Department of the Navy
Washington, D.C.
20360Dr. JOhn Craven
(PM 1100)Deep
brnergence Systems
Proj ec.t
Department of the Navy.
Waøington, D.C.
20360Code 522
Naval Ship Research and
Development C enter
Washington, D0C.
20007 ComnanderNaval Oceanographic Office
Washington, D.C.
20390Ohjef of Research & Developmsnt
Office of Chief of
StaffDera rtment of the A.rnr
The Pentagon, Washington, D.C..
Code 63Li.2A
Naval Ship Systems Commmañd:
Department of the ;Navy
Washington, DC.
20360 Code tj.68Chief of Naval Research
Department. of the Navy
Wshington, D.C...
20360Director
US. Naval. Research
ay
Code 6170
. .shington, D.C.
20390 Code. 1473 .Chief of Naval Research
Department of the Navy
Washington, D.C.
20360Code 6100
Naval Ship. Exgineering Center
Department of the Navy
Washington, D.C.
2036020310
-9-Nava]. Ship Engineering Center
Pepartinant of the Navy
Waahiigton, D.C.
20360Dr. A.. S. .LIbel], President
Genera]. Technica]. Services, Inc.
bS]. Penn
Street
Teadon,
Pennsylvania 19050Dr. H. Cohen
( Reaearch. Center
P.. 0. Box 218
Security Classificati
DOCUMENT CONTROL DATA - R & D
(SecurIty classification of title, body of abstract and indexing annotation must be entered when the overall report is classified,) I. ORIGINATING ACTIVITY (Corporate author)
Massachusetts Institute. of. Technology
20. REPORT SECURITY CLASSIFICATION
UNCLASSIFIED
2b. GROUP
3. REPORT TITLE
Conformation of Poiyisobuty.lene. in Dilute Solution. Subjected to a Hydrodynamic Shear Field
4. PESCRIPTIVE NOTES (Type of report and.lnclusjve dates)
Technical Report
5. AUTHOR(S) (First name, middle initial, last name)
F.R.. Cottrell, EW..Merrii.1,.and K..A. Smith
6. REPORT DATE
May, 1970
70. TOTAL NO. OF PAGES
. 20
7b. NO. OF REFS
24
80. CONTRACT OR GRANT NO.
Nonr 3963 (10)
b. PROJECT NO.
Task NR 062-333
C.
d.
9a. ORIGINATORS REPORT NUMBER(S)
9b. OTHER REPORT NO(S) (Any other numbers that may be a8slgnedthis report)
10. DISTRIBUTION STATEMENT
ii. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
Office. of. Naval Research
13. ABSTRACT
A new. lightP.scattering. experiment.which. allows a. direct determination of the conformation, of. macromolecules, deformed in flow. is. described. Light-scattering relationships. based. on. the. .interference function. are developed, and results of
an. experimental, study. are...detai lecL . The. deformed. conformation of high molecular
weight. po.lyisobuty.lenewas. determined in a Couette-type. shear fIeld.
Deca.lin was the. solvent. Variables: investigated were .the..shear rate. (C. to 600 sec'.1), the polymer molecuiar.we.ight (1.0 X 1O to 1.6 X l07),.and.the.polymer concentration
(2.0x 10' to 8.0X .io: g/cc). Conformation..varjab.les determined were the
orientation, of. thea mo.lecule.,in. the. shear field. and .it.s maximum and minimum
extension ratios. in.the. plane. defined .by. the.direction. of flow and the. direction of. the shear rate ..The. deformation of the macromo.lecule.
was found to be. markedly discrepant when. compared..to the..dynamic macromo.lecular models which assume
complete coil fiexi.bil.ity,..and more closely in.agreement w.ith the recent.. theories of Cerf., deeloped...for.nonfree1..drajnjng coils. which. exhibit a finite, internal v.iscosity. ADM .1 ._....,_ -. I NOV 65 S/N 0101-807-6811 Security ClassificaUon A- 31408
KEY woRDs LIN)( A ROLE LINK wf ROLE B WT ROLE
