THE JOURNAL OF
PHYSICAL CHEMISTRY Registered in U.S. Patent O$ce
@ CopMht, 1966, by the American Chemical Society
VOLUME 69, NUMBER 9 SEPTEMBER 15,1965
Dynamic Mechanical Properties of Cross-Linked Rubbers. 11. Effects of Cross-Link Spacing and Initial Molecular Weight in Polybutadienel
by Etsuji Maekawa, Ralph G. Mancke, and John D. Ferry Departmat of Chemistry, University of WiSconSin, Madieon, W b c o d n (Received May 13,1SS6)
The complex shear compliances of eight samples of polybutadiene cross linked by dicumyl peroxide and four samples cross linked by sulfur have been measured over a frequency range from 0.2 to 2 c.p.s. a t temperatures from -6 to 45" by a torsion pendulum. On four of the samples, measurements were extended by the Fitegerald transducer from 45 to 600 C.P.S. at temperatures from -71 to 55". The vulcanieates had been prepared from polymers of two different molecular weights (180,000and 510,000) with sharp molecular weight distribution; the physical cross-link density ranged from 0.57 to 2.68 X lod4mole/ cc., and the chemical cross-link density calculated following Kraus ranged from 0.22 to 1.49 X lo-' mole/cc. The mechanical data were all reduced to To = 298°K. by shift factors calculated from the equation log UT = -3.64(T - T0)/(186.5 T - To). In the transition zone of frequencies, the viscoelastic functions of the dicumyl peroxide vulcanizates were closely similar, except for a shift toward lower frequencies with increasing cross linking, corresponding to a small but unexpected increase in the monomeric friction coefficient. Cross linking by sulfur caused a somewhat larger shift toward lower frequencies a t a comparable cross-link density. In the rubbery zone, the sample with least cross linking exhibited a substantial secondary loss mechanism at very low frequencies. The low-frequency losses are evident in all the samples, but their magnitude falls rapidly with increasing cross-link density as previously found for natural rubber. It also falls somewhat with increasing initial molecular weight, indicating a contribution from network strands with loose ends. The possible relation of the low-frequency losses to trapped entanglements is discussed.
+
Introduction In an earlier paper,2 we described dynamic mechanical properties of a series of natural rubber vulcanizates, cross linked by dicumyl peroxide and by sulfur, and *Owed that the magnitude Of the anomalous losses at very low frequencies increased with the average
spacing between cross links. Similar behavior was noted by Nielsena in measurements on butyl and eg1'2i;fn'e8
on mechanical prope*ies of substances of
(2) J. D. Ferry, R. G. Mancke, E. Maekawa, Y. &magi, and R. A. Dickie, J. Phys. chent., 68,3414(19134).
2811
E. MAEKAWA, R. G. MANCKE, AND J. D. FERRY
2812
styrene-butadiene rubbers, in which the temperature was varied at roughly constant frequency. While the origin of these losses remains uncertain, they have been tentatively attributed, at least in part, to coupling entanglements trapped between cross We now report some dynamic mechanical measurements over a wide range of frequencies and temperatures on vulcanizates of polybutadiene, again cross linked by both dicumyl peroxide and sulfur. The results show a similar dependence of the low frequency losses on the cross-link spacing and also a dependence to some degree on the initial molecular weight before cross linking, reflecting the proportion of network strands with loose ends.
Experimental Materials. The cross-linked polybutadienes were generously prepared for us by Drs. G. Kraus and C. W. Childers of the Phillips Petroleum Co. Two linear polybutadienes of sharp molecular weight distribution were employed, with the following weight-average molecular weights and microstructures as reported by Dr. Kraus: M , 180,000, 40% cis, 53% trans, 7% vinyl; M , 510,000, 43% czk, 50% trans, 7% Vinyl. These are identified subsequently by their molecular weights. The dicumyl peroxide (DCP) vulcanizates contained amounts of peroxide ranging from 0.04 to 0.38% depending on the density of cross linking desired. The sulfur vulcanizates contained amounts of sulfur ranging from 0.42 to 1.33% and in addition 3% zinc oxide, 2% stearic acid, 3% Resin 731, 1.2% Santocure, and 1%Flexamine (all expressed as parts per 100 parts rubber). The vulcanization was always performed by heating for 45 min. at 150”. The densities, determined pycnometrically under water, were 0.897 g./cm.3 for the dicumyl peroxide vulcanizates and 0.929 for the sulfur vulcanizates. The density of elastically active network chains, in moles of strands per cubic centimeter, Y, was obtained by Drs. Kraus and Childers from swelling measurements in n-heptane, the necessary value of the thermodynamic parameter p having been obtained by calibrating the swelling against elastic measurements on swollen g e k 6 The density of chemically cross-linked chains, Y*, was calculated by the Mullins-Kraus relation5 Y
= Y*
+ a - (v* + a)b/v*M
(1)
with a = 1.5 X lo-’ and b = 2.73 as determined by Kraus5 for polybutadiene networks. These values are summarized in Table I. The equilibrium shear compliances, Je,were measured by torsional deformation with very small strain as previously described. They represent minimum 216
The Journal of Physical Chemistry
Table I : Characteristics of Cross-Linked Rubbers M before VulC&L&
Agent
DCP
S
Y X 104, Y* X 104, moles/cm.J moles/cm.’
Sample code
X 10-
734 735 10H 736 737 738 10D 740
1.8 1.8 1.8 1.8 1.8 1.8 5.1 5.1
0.57 1.42 1.8 1.85 2.37 2.68 1.8 1.99
0.22 0.51 0.76 0.79 1.21 1.49 0.50 0.66
7.027 6.903 6.965
1oc
1.8 1.8 5.1 5.1
1.2 1.79 1.2 1.85
0.39 0.75 0.19 0.55
6,814 6.812 6.882 6.908
739 10B 741
eation
-Log Je
6,445 6.746 6.88 6.893
values since even after equilibration under stress for 12 hr. the slow relaxation processes may not be complete.’ These values are also given in Table I and are plotted logarithmically against Y in Figure 1. For comparison, the prediction of the kinetic theory of rubberlike elasticity
J,
1/vRT (2) is included M a dashed line. The observed compliances are smaller by about a factor of 0.6. Similar discrepancies have been observed recently by Thirion’ and Nielsen, in agreement with the general experiences that the retractive force in unswollen (“dry”) rubbers includes a contribution in addition to that corresponding to eq. 2. No account has been taken, in Table I, of several corrections to eq. 2 which have been pointed out recently: (a) a factor (rE2)/(ro2), in which ( r E 2 ) is the mean-square end-to-end distance of network strands and (rO2) the corresponding value for free chainsg; (b) a factor of 2 associated with the connectivity of a tetrafunctional networklo; and (e) =
(3) L. E. Nielsen, J . Appl. Polyner Sei., 8 , 511 (1964). (4) G. Kraus and G. A. Moczygemba, J. P o l y m r Sci., A2, 277 (1964). (5) G. Kraus, J . Appl. Polyner Sci., 7 , 1257 (1963). (6) R. A. Stratton and J. D. Ferry, J . Phgs. Chem., 67, 2781 (1963). (7) P. Thirion and R. Chassat, “Proceedings of the Fourth Interne tional Congress on Rheology,” Interscience Publishers, New York, N. Y., Part 3, 1965,p. 525. (8) L. Bateman, Ed., “The Chemistry and Physics of Rubber-like Substances,” John Wiley and Sons,Inc., New York, N. Y., 1963,pp.
170,175. (9) A. V. Tobolsky, D. W, Carlson, and N. Indictor, J. Polynter Sci., 54, 175 (1961).
DYNAMIC MECHANICAL PROPERTIES OF CROSS-LINKED RUBBERS
- 7.0
i I
I
-4.2
t ,
1
-4.0
-3.8
-3.6
109 Y
Figure 1. Equilibrium shear compliance plotted logarithmically against elastically effective network strands per cm.8: open circles, DCP d c a n i z a t e s ; black circles, S; untagged, M = 1.8 X lo5; tagged, M = 5.1 X lo6. Some pairs of duplicate determinations are included. Dashed line is kinetic theory prediction, eq. 2.
allowance for a non-Gaussian distribution of end-to-end distances.l1 However, these corrections should affect all the values in a similar manner. Methods. The Fitzgerald transducer12was used for measurements of the storage (J’) and loss (J“) components of the dynamic shear compliance in the range from 45 to 600 c.P.s., and the Plazek torsion pendulum1* from 0.2 to 2 C.P.S. The logarithmic decrement was determined from the recorder tracings of the torsion pendulum by direct matching to exponential envelope~.’~The maximum temperature range was from -71 to 55”. The disk-shaped samples were 1.75 cm. in diameter; the thickness was about 0.19 cm. for the transducer measurements and 0.64 cm. for the torsion pendulum. Four vulcanizates (734, 736, 738, and 739) were studied with both instruments, and the others with the torsion pendulum alone.
Results For plotting with reduced variables, the storage and loss compliances J’ and J” were reduced in magnitude by the usual factor Tp/Topo, where p and po are the densities at the temperature of measurement T and the reference temperature of To = 298.2”K.; the thermal expansion coefficient can be taken as 7.5 X 10-4 deg.-1. The frequency shift factor UT was calculated from the following equation15 log UT = --3.64(T - To)/(186.5
+ T - To)
(3)
in which the numerical coefficients were obtained by preliminary empirical selection of UT and plotting16 (T - TO)/log UT against T - To. Equation 3 also fits the viscosity data of Gruver and KrausUsls rather well
2813
although it differs somewhat from the equations used by them. (The coefficients correspond to a freevolume thermal expansion coefficient of 6.4 X deg. -I, which is reasonable though somewhat high. 15) When plotted logarithmically against the reduced frequency W U T , data from the transducer and torsion pendulum almost overlapped. The loss tangents tan 6 = J”/J‘ agreed closely but the magnitudes of J“ and J’ derived from the two methods differed slightly, a discrepancy attributable to uncertainty in the sample coefficient for the transducer.6 The following small corrections were therefore applied to the transducer data for log J’ and log J” for consistency: sample 734, -0.05; sample 736, -0.06; sample 738, -0.04; sample 739, -0.07. The data for the three dicumyl peroxide vulcanizates are plotted in Figure 2; the points are omitted for sample 736 to avoid confusion, The individual temperatures and all numerical data will be recorded elsewhere”; tables are available upon request to the authors. At high reduced frequencies, corresponding to the beginning of the transition zone, the shapes of the curves of J’ and J” are almost identical. There is a small shift to lower frequencies with increasing degree of cross linking. At low frequencies, the losses for the more densely cross-linked samples resemble the behavior previously reported2J in persisting at a rather low level instead of vanishing with decreasing frequency as expected from molecular theories.E But for v = 0.57 X the loss compliance actually passes through a large secondary maximum. This suggests that the small persistent losses seen at higher v are residues of a secondary mechanism which is prominent only when v is small. This mechanism is also seen in the curve for log J’ which is rising at low frequencies to approach its limiting equilibrium value of about -6.4. In Figure 3, the loss tangent again shows the large and a secondary loss mechanism for v = 0.57 X small one for v = 1.85 X low4. (A minimum in the loss tangent as a function of temperature at constant frequency is also evident in the measurements of (10) J. A. Duiser and A. J. Staverman, “Proceedings of the International Conference on Non-Crystalline Solids,” North-Holland Publishing Co., Amsterdam, 1965,p. 376. (11) W. Prim, ibid., p. 360. (12) E.R. Fitzgerald, Phys. Rev.,108, 690 (1957). (13) D. J. Plazek, M. N. Vrancken, and J. W. Berge, Trans. SOC.
Rheol., 2, 39 (1958). (14) R.A. Dickie, Ph.D. Theais, University of Wisconsin, 1965. (15) J. D. Ferry, “Viscoelastic Properties of Polymers,” John Wiley and Sons, Inc., New York, N. Y.,1961,p. 212. (16) J. T. Gruver and G. Kraus, J. Polymer Sci., 2 , 797 (1964). (17) R. G.Mancke, Ph.D. Thesis, University of Wisconsin, 1966.
Volume 69,Number 9 September 1966
E. MAEKAWA, R. G. MANCKE, AND J. D. FERRY
2814
-6.5
1
a
a
-8.5
0
I
I
I
I
I
I
I
I
2
3
4
5
6
7
109
war
Figure 2. Storage and loss compliance reduced to 25" and plotted logarithmically against reduced radian frequency for three samples cross linked by dicumyl peroxide, identified by values of Y X 104. Pip directions denote different temperatures: Y = 0.57 X 10-4, -64.2 to 54.7" in 13 steps; Y = 1.85 X (points not shown), -73 to 55.5" in -70.8 to 55.4" in 13 steps. 13 steps; Y = 2.68 X Subscript p denotes multiplication by Tp/Topo.
Nielsena on very lightly cross-linked rubbers.) Low frequency measurements on additional samples show a monotonic decrease in the magnitude of tan 6 with increasing V, as previously observed for vulcanizates of natural rubber. The dashed curve shows that, for approximately equal v, a higher initial molecular weight before vulcanization gives a somewhat lower loss, so the loose ends do make a small contribution to the low frequency losses. I n Figure 4, log J' and log J" are plotted against reduced frequency for the sulfur vulcanizate with v = 1.79 X and the data for the dicumyl peroxide vulcanizate most nearly corresponding to it are repeated from Figure 2. At low frequencies, the storage compliances are almost identical, but the sulfur vulcanizate shows somewhat more loss. A slight secondary maximum in J" is evident in both. At high frequencies, the dispersion of the sulfur vulcanizate is somewhat shifted to the left, corresponding to a larger local friction coefficient. The loss tangent for the sulfur vulcanizate is shown in Figure 5 together with low frequency data for three others, in the low frequency region. Here the magnitude of tan 6 decreases with increasing v and with increasing M just as for the dicumyl peroxide vulcanizates.
Discussion Transition Zone. I n Figure 3, the dispersion in the transition zone shifts to the left on the logarithmic frequency scale by 0.28 as v is increased from 0.57 to 2.68 X The curve for the lowest cross linking is
0
I
2
I
I
1
I
I
1
1
I
0
I
2
3
4
5
6
log wa; a t 25"
Figure 3. Loss tangents of dicumyl peroxide vulcanizates, plotted logarithmically against reduced radian frequency: numbers denote Y x 104; dashed line, M = 5.1 X lo6; all others, M = 1.8 X 106.
The J O U T Mof~ Physieal Chemistry
4
3 I09
5
6
waT
Figure 4. Storage and loss compliance reduced to 25" and plotted logarithmically against reduced radian frequency for sample cross linked by sulfur with Y = 1.79 X low4 (curves S), compared with corresponding dicumyl peroxide vulcanizate with Y = 1.85 X lo-' from Figure 2 (curves DCP). Pip directions for S curves denote different temperatures, from -69.3 to 55.8" in 17 steps.
DYNAMIC MECHANICAL PROPERTIES OF CROSS-LINKED RUBBERS
0
I
2
109
3 w a T a t 25’
4
5
6
Figure 5. Loss tangents of sulfur vulcanizatea, plotted logarithmically against reduced radian frequency: numbers denote Y x lo4; dashed lines, M = 5.1 X 106; solid lines, M = 1.8 X lo6.
very close to that for the uncross-linked polymer.18 Plots of the relaxation spectrum H in this region show a similar spacing. The direction of shift is opposite to that which might be expected from a slight plasticizt+ tion by the reaction products from the dicumyl peroxide; actually, the magnitude of the latter effect can be predicted from free-volume calculation^,^^ after estimating the fractional free volume of the polymer at 25’ from the parameters in eq. 3 to be f25 = 0.119, On this basis, from eq. 8 of ref. 19, with a reasonable value of the parameter p’, the logarithmic shift from plasticization should not exceed about 0.02. On the other hand, if a relation is sought between v* and the change in local friction coefficient lo corresponding to this shift, the slope d log lo/dv* is found to be 0.22 X lo4. This could be interpreted as a decreased free volume accompanying formation of a cross link. However, calculating df/dv* = (d log ro/dv*)/(d log lo/df) and taking d log r0/df = -1/2.303fib2, we obtain df/dv* = -71 cc./mole of cross links, which would be surprisingly high; Mason20has estimated for natural rubber cross linked by dicumyl peroxide a contraction in free volume of 34 A.3/cross link or 20 cc./mole. Curiously, in our previous studies of natural rubber2 any shift in frequency scale with dicumyl peroxide cross linking was too small to be clearly detectable. Thus, the origin of the shifts in Figure 3 is uncertain. Another difference between the logarithmic loss tangent curves for polybutadiene and natural rubber in the transition zone is in their slopes, which approximate 0.65 and 0.4, respectively. This discrepancy makes it difficult to compare their relative positions on the logarithmic frequency scale; polybutadiene lies 0.5
2815
to 1.5 decades to the right. (If the Rouse theory applied in this region, the slope would be zero.) In comparing the transition zone in Figure 5 and the corresponding curve in Figure 3, that for the sulfur vulcanizate lies at lower frequencies by about 0.32 on the logarithmic scale. The direction is anticipated from the chemical changes which accompany sulfur dcanization,29 21 but the magnitude is greater than would be expected for 1.33% of combined sulfur on the basis of experience with natural rubber.6 We shall not attempt to interpret these differences at the present time since the primary interest of this study is in the behavior at low reduced frequencies. Low Frequency Loss Mechanism. Since the nature of the frequency dependence, as well as the magnitude of the loss, changes markedly with the degree of cross linking in Figures 2-5, the effect of v cannot be fully described without an analysis of the frequency dependence. As a rough measure, however, we can compare the magnitude of tan 6 at a constant value of frequency (log w = 1) by plotting log tan 6 against log v in Figure 6. The loss tangent drops rapidly with increasing v, and the dicumyl peroxide and sulfur vulcanizates fall approximately on the same curve. The values for M = 510,000 are somewhat below the curve drawn for M = 180,000. Also included are previous data2 for natural rubber vulcanizates with dicumyl peroxide and sulfur. This I
4
I
1
+
-2.0 -4;4
I
-4.2
,
1
-3.8
-4.0
log
-3.6
Y
Figure 6. Log tan 6 at w = 10 rads/sec. plotted against Y for polybutadiene vulcanizates with M = 180,000 (PB) and natural rubber (NR) vulcanizates from ref. 2 ( M probably about 500,000): open circles, cross linked with dicumyl peroxide; black circles, with sulfur; tagged circles, polybutadiene vulcanizates with M = 510,000.
log
(18) R. H. Valentine, unpublished measurements. (19) J. D. Ferry and R. A. Stratton, KoZZo&Z., 171, 107 (1960). (20) P. Mwon, J. Chem. Phys., 35, 1523 (1961); P o l y ” , 5, 625 (1964). (21) H. D. Heinie, K. Schmieder, G. Schnell, and K. A. Wolf, Kautschuk Gummi, 14, 208 (1961).
Volume 69,Number 9 September 1966
E. MAEKAWA, R. G. MANCEE,AND J. D. FERRY
2816
curve lies to the left; it is necessary to have nearly twice the density of elastically active network chains in polybutadiene as in natural rubber to achieve the same level of loss. (The difference is partly, though to a minor extent, attributable to a difference in the initial molecular weights; that for the natural rubber was not determined but was probably about 500,000. Additional experiments on natural rubbers with known initial molecular weights are in progress.) The low-frequency loss mechanism has been tentatively attributed to coupling entanglements involving the network strands.2g422 The important parameter in this concept is the average number of entanglement loci trapped in a network strand. Since the average entanglement spacing is farther apart by about a factor of 2.5 in natural rubber than in polybutadiene,22 it appears consistent that the loss falls off at lower degrees of cross linking in the former. This comparison may be oversimplified, however, since dicumyl peroxide produces more cross links per added molecule in polybutadiene than in natural rubber,za and this difference may be associated with unknown differences in network topology. I n any case, it is necessary to distinguish between trapped entanglements which contribute to the equilibrium modulus as in the calculations of Mullins and Kraus5 and the relaxing entanglements whose contribution to the modulus vanishes with decreasing frequency in the logarithmic range below 3 in Figure 2. In this figure, for example, the large maximum in J” at low frequencies for v = 0.57 X is associated in the usual manner of a frequency dispersion with a change in J’ from 3.6 X low7at equilibrium to 1.1 X in the plateau region near log w = 3. l f the respective magnitudes of J’ are inversely proportional to the number of effective network strands, then the latter value in the plateau is larger than the 0.57 X effective at equilibrium, and it includes 1.30 X mole of effective strands whose contribution relaxes out in the low frequency range. This quantity, v,,, is given for several other dicumyl peroxide vulcanizates in Table I1 and is compared with the number of rionrelaxing entanglement strands, v - v*. With increasing chemical cross linking, v - v* rises, but v,, fads. One possible explanation of this apparent paradox may be outlined as follows. It, may be pointed out that the contribution of an entanglement strand at equilibrium to the modulus is probably somewhat less than that of a cross-linked strand, so v - v* can be less than the actual number of entanglement strands. In other words, an entanglement affects the entropy of strain less than does a real cross link. However, perhaps in the frequency range The .Tournel of Physical Chemistry
Table 11: Relaxing and Nonrelaxing Effective Network Strands; M = 180,000, Cross Linked with DCP - ”* - b/M Y
Sample oode
734 735 736 738
Y
x
104
0.57 1.42 1.85 2.68
-
x
v
Y*
104
0.34 0.91 1.06 1.19
vrx
x
Y*
- v*
4- vrx
Y
Y*
10‘
1.30 0.99 0.46 0
0.21 0.48 0.70 1.00
4.3 2.5 1.6 0.9
near log w = 3 the entanglement strands make their full contribution, as much as though their ends were chemically tied. Then the ratio (v - v * ) / ( v - v* vrx), also given in Table 11, is a measure of the efficiency of an entanglement at equilibrium. It rises from 0.2 to unity with increasing cross-link density. It is correlated inversely with the average number of entanglements per network strand between two chemical cross links, given in the last column of the Table I1 as (Y - v*)/(v* - b / M ) ; in fact, the product of the last two columns is roughly constant. The concept of variable effectiveness of an entanglement in contributing to the equilibrium modulus is not consistent with the treatment of Mullins and Kraus, in which the parameter a of eq. 1 is considered to be a constant. However, the data analyzed by them refer mostly to networks in which the average number of entanglements per strand is sdciently small that each should have at least 0.7 of its full effectiveness on the basis of the limited information in Table 11. The concept of an effectiveness substantially less than unity applies only in very lightly cross-linked networks. No attempt is made at present to account for the effect of loose ends, which is apparent in comparing different initial molecular weights. This subject will be treated in the next paper of this series. Another possible source of relaxation could be the presence of a sol fraction (molecules unattached at either end), but in the networks studied here the sol fraction should have been negligible. The present discussion fails also to account for the topological entanglements, or interlocking structures, produced by the cross-linking process (as distinguished22 from the entanglements in the Mullins-Kraus treatment, which are supposed to be present already in the uncross-linked polymer). The effects of such struc-
+
(22) J. D. Ferry, “Proceedings of the International Conference on Non-Crystalline Solids,” North-Holland Publishing Co., Amsterdam, 1966, p. 333. (23) B. M. E. Van der Hoff, Ind. Eng. Chem., Prod. Res. Develop., 2, 273 (1963).
LIGHTSCATTERING BY POLY-y-BENZYL-L-GLUTAMATE SOLUTIONS
tures on equilibrium properties have been treated recently by C a ~ e . 2 ~Further experiments on other cross-linked systems are in progress. Acknowledgment. We are grateful to Drs. G. Kraus and C. W. Childers for preparing and characterizing the samples. This work was supported in part by the U. S. Army Research Office (Durham), in part by the National Science Foundation, and in part by the Re-
2817
search Committee of the Graduate School of the University of Wisconsin. We are indebted to Miss Monona Ross01 and Miss Marilyn Etzelmueller for help with calculations and to Dr. P. Thirion of the Institut Franpais du Caoutchouc and Mr. Ray A. Dickie for valuable discussions. (24) L.
c. Case and R. V. Wargin, Makromol. Chem., 77, 172 (1964)
Light Scattering by Poly-~-benzyl-L-glutamateSolutions Subjected to Electric Fields
by B. R. Jennings and €3. G . Jerrard Department of Physics, University of Southampton, Southampton, England
(Received June 8, 1964)
The results of a study of the light scattering by solutions of poly-y-benzyl-L-glutamate in dichloroethane are presented. The ratio of the 2-average length of the equivalent rod to the weight-average degree of polymerization was found t o be 1.36 A. This would seem to agree with previous light scattering results which are consistent with the molecule having the configuration of an a-helix. The application of electric fields changes the scattered intensity if the molecules are polar or electrically anisotropic and, in particular, a x . fields enable a distinction to be made between these two cases. The solutions were subjected to d.c.&elds up to 1.9 kv. cm.-l and an a.c. field of 450 v. cm.-l at frequencies up to 10 kc./ sec. The molecule was found to possess a dipole moment of average value 3920 D. corresponding to 3.44 D. per monomer unit. It has negligible electrical anisotropy. The electric field measurements enabled a value of 3250 see.-' to be found for the rotary diffusion constant D,. The variation of D,with molecular weight, found from the present results and those obtained by Wallach and Benoit, indicates the possibility that the molecule could be rodlike and partially flexible.
Recently, Wallach and Benoitl have made lightscattering studies on three samples of poly- y-benzyl-Lglutamate (PBLG) in dichloroethane when subjected to an electric field. The results of investigations on a sample of different molecular weight are presented here. The theory of such measurements has been summarized by Wallach and Benoit, who introduced two parameters a and R , which characterize the electrical
properties of the molecule and its flexibility respectively a is obtainable from the initial gradients of the Zimm2 plots obtained with and without the field and gives a value of the dipole moment, p, if the anisotropy of electrical polarizability, p, is zero, and of p if p is zero. The (1) M. L. Wallach and H. Benoit, J. Polymer Sci., 57, 41 (1962). (2) B. H. Zimm, J. C h m . Phys., 16, 1099 (1948).
Volume 69, Number 9 September 1966
