10
Dilute Solution Properties of Poly(1,4-phenylene Terephthalamide) in Sulfuric Acid D. G. BAIRD and J. K. SMITH, Monsanto Textiles Company, Pensacola, Florida 32575 Synopsis The intrinsic viscosity [q] of dilute solutions of poly(l,.l-phenylene terephthalamide) (PPPT) is found to depend strongly on sulfuric acid strength, exhibiting a maximum at about 100% HzS04. This behavior instigated measurements of [*I and light scattering from dilute solutions of unfrac- tionated PPPT in concentrated (=96%)and 100% HzS04. From [q] and weight-averagemolecular weight aw relationships, Mark-Houwink exponents a were determined to be 1.36 in 96.6% and 1.62 in 100.2 f 0.2% HzS04, indicating that the PPPT molecule can undergo considerable expansion in 100% H2.304. For the case of 100% HzS04, a noticeable polyelectrolyte effect is observed in the re- duced viscosityversus concentration curves. This result suggests that the repulsivechargesgenerated along the PPPT backbone may be responsible for the change in configuration of PPPT upon in- creasing the acid strength from 96.6% to 100% HzS04. It is pointed out that there is considerable experimental difficulty in measuring consistent values of uw, and this may be the reason for the variation among published data. INTRODUCTION It has been reported recently that several aromatic polyamides form aniso- tropic solutions (i.e., polymer liquid crystals) when dissolved in dialkylamide and strong acid so1vents.ls2 The ability of these molecules to form anisotropic solutionshas been partially attributed to their rigid rodlike configuration in these solvents. Subsequent measurements of the Mark-Houwink exponent a from intrinsic viscosity 9 and weight-averagemolecular weight Mw data have produced values approaching 2,173which is indicative of a highly extended m~lecule.~ On the other hand, the more recent data of Schaefgen et al.5 and Arpin and Strazielle6indicate that both poly-1,4-benzamide (PBA) and poly(1,Cphenylene terephthalamide) (PPPT) in concentrated H2S04 are only semirigid. Schaefgen et al. reported that a = 1.7 for Mw up to 12,000,but for Uw > 12,000 a = l.Wl.08. Arpin and Strazielle studied similar solutions and reported that a = 1.09 for 1680 I BW I 63,000. Although there is some agreement in the values of a, there are distinct differences in values of Mw. For this reason, further measurements of Mw for dilute solutions of PPPT in 96% H2S04 are justified. Furthermore, there have been very few studies reported on the effect of acid strength on the dilute solution properties of PBA or PPPT. Sokolova et studied the effect of acid strength on [q] for solutions of PPPT ([q] = 3.1 in 96% HzS04) and found that [o] increased with increasing acid strength, passing through a maximum at 9&99% H&04 (see Cox8 for an explanation of acid strengths) and decreasing with acid strengths greater than 100%H2S04. They attributed this increase in [o] to a change in the configuration of the molecule as a result of changes in the properties of the solvent. Likewise, Schaefgen et Journal of Polymer Science: 0 1978 John Wiley & Sons, Inc. Polymer Chemistry Edition, Vol. 16,61-70 (1978) 0360-6376/78/0016-0O1$01 .OO

Dilute solution properties of poly(1,4-phenylene terephthalamide) in sulfuric acid

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Dilute Solution Properties of Poly( 1,4-phenylene Terephthalamide) in Sulfuric Acid

D. G. BAIRD and J. K. SMITH, Monsanto Textiles Company, Pensacola, Florida 32575

Synopsis

The intrinsic viscosity [q] of dilute solutions of poly( l,.l-phenylene terephthalamide) (PPPT) is found to depend strongly on sulfuric acid strength, exhibiting a maximum at about 100% HzS04. This behavior instigated measurements of [*I and light scattering from dilute solutions of unfrac- tionated PPPT in concentrated (=96%) and 100% HzS04. From [q] and weight-average molecular weight aw relationships, Mark-Houwink exponents a were determined to be 1.36 in 96.6% and 1.62 in 100.2 f 0.2% HzS04, indicating that the PPPT molecule can undergo considerable expansion in 100% H2.304. For the case of 100% HzS04, a noticeable polyelectrolyte effect is observed in the re- duced viscosity versus concentration curves. This result suggests that the repulsive charges generated along the PPPT backbone may be responsible for the change in configuration of PPPT upon in- creasing the acid strength from 96.6% to 100% HzS04. It is pointed out that there is considerable experimental difficulty in measuring consistent values of uw, and this may be the reason for the variation among published data.

INTRODUCTION

It has been reported recently that several aromatic polyamides form aniso- tropic solutions (i.e., polymer liquid crystals) when dissolved in dialkylamide and strong acid so1vents.ls2 The ability of these molecules to form anisotropic solutions has been partially attributed to their rigid rodlike configuration in these solvents. Subsequent measurements of the Mark-Houwink exponent a from intrinsic viscosity 9 and weight-average molecular weight Mw data have produced values approaching 2,173 which is indicative of a highly extended m~lecule .~

On the other hand, the more recent data of Schaefgen et al.5 and Arpin and Strazielle6 indicate that both poly-1,4-benzamide (PBA) and poly( 1,Cphenylene terephthalamide) (PPPT) in concentrated H2S04 are only semirigid. Schaefgen et al. reported that a = 1.7 for Mw up to 12,000, but for Uw > 12,000 a = l.Wl.08. Arpin and Strazielle studied similar solutions and reported that a = 1.09 for 1680 I BW I 63,000. Although there is some agreement in the values of a , there are distinct differences in values of Mw. For this reason, further measurements of Mw for dilute solutions of PPPT in 96% H2S04 are justified.

Furthermore, there have been very few studies reported on the effect of acid strength on the dilute solution properties of PBA or PPPT. Sokolova et studied the effect of acid strength on [q] for solutions of PPPT ( [ q ] = 3.1 in 96% HzS04) and found that [o] increased with increasing acid strength, passing through a maximum at 9&99% H&04 (see Cox8 for an explanation of acid strengths) and decreasing with acid strengths greater than 100% H2S04. They attributed this increase in [o] to a change in the configuration of the molecule as a result of changes in the properties of the solvent. Likewise, Schaefgen et

Journal of Polymer Science: 0 1978 John Wiley & Sons, Inc.

Polymer Chemistry Edition, Vol. 16,61-70 (1978) 0360-6376/78/0016-0O1$01 .OO

62 BAIRD AND SMITH

al.5 reported that the inherent viscosity of solutions of PPPT is somew-hat de- pendent on acid strength.

The purpose of this paper is to investigate not only the dilute solution prop- erties of unfractionated PPPT in concentrated H2S04, but to extend our work to include 100% solutions. We have determined Pw values by means of light scattering from dilute solutions of both acids. Furthermore, we compare the reduced viscosity curves obtained from solutions of PPPT in both acids. A certain amount of attention is given to the experimental techniques because of the complications imposed by the presence of polyelectrolytes and the low scattering intensities due to the small values of Bw. Changes in the configuration of PPPT with acid strength are observed and explained through the presence of charged molecules. Finally, our results are compared with those of Schaefgen et al. and Arpin and Strazielle.

EXPERIMENTAL

Polymers

Poly( 1,4-phenylene terephthalamide) was prepared by a polycondensation reaction according to procedures given by Blades2 and Bakg Polymer molecular weight was controlled by the temperature and concentration of the reactants.

Solvents

H2SO4 of various acid strengths (or containing various amounts of SO3) was prepared by mixing concentrated &So4 (46.6% H2S04) with oleum containing 22% free SO3 (see Cox8 for an explanation of acid strengths >loo%). The acid strength of each solution was determined by titrating a quantity of the solution to determine the amount Of SO3 with aqueous NaOH. In the case of excess SO3, the solutions were dissolved in a known amount of H2O and then titrated. So- lutions of 96.6,98.0, and 98.5,100.2 f 0.2,101.0,102.0, and 105.0% HzSO4 were prepared.

Molecular Weight

Weight-average molecular weights Bw of unfractionated polymers dissolved in 96.6% and 100.2 f 0.2% H2S04 were determined using a Bausch and Lomb light-scattering photometer. Measurements were conducted at 25 "C by using green light (A = 5461 A). There was no evidence of fluorescence for wavelengths of this magnitude.

Light-scattering intensities were obtained at four concentration levels (usually concentrations of 0.0005,0.001,0.002, and 0.004 g/ml were used) over a range of angles from 30" to 150'. Values of Pw were determined from the 90" scat- tering intensities by using eq. (1):

where K* is the optical constant, RW is the Rayleigh ratio at 90", c is the polymer concentration, and P-1(900) is the particle scattering factor. Values of P-l(90) were selected from standard tableslo by using values of the intrinsic disymmetry

POLY (1,CPHENYLENE TEREPHTHALAMIDE) 63

TABLE I Values of aw Obtained from Zimm Plots and Intrinsic Viscosities for Solutions of PPPT in

96.6% and 100.2%

hl, d1k R W

96.6% 100.2% 96.6% 100.2% Sample HzS04

1 1.00 1.28 12,000 16,200 2 1.34 1.45 12,800 9620 3 2.68 3.40 23,700 25,270 4 3.74 4.80 26,800 - 5 5.9 9.40 40.100 43.100

[Zd] and assuming a rodlike particle shape. (This procedure is questionable because of having to assume a particle shape in order to obtain values of am and will be discussed in the next section.) In addition, values of aw were determined by the double extrapolation method devised by Zimm.ll The double-extrapo- lation procedure was carried out by means of a computer program. Values of aw obtained from the Zimm plots are given in Table I, while those obtained from the 90' data are presented in Table 11.

The critical step in obtaining consistent light-scattering results was the clar- ification of the solutions. Standard filtration techniques were not practical because of the high viscosity of the solutions. Long filtration times were required which increased the exposure of the hygroscopic H2S04 solutions to the atmo- sphere. For this reason, we employed the technique of ultracentrifugation using a Sorvall Supesspeed centrifuge (Model SS-4). This method facilitated handling and reduced contact time with the moisture in the air. Solutions were centri- fuged for 1 hr at 13,000 rpm.

The refractive index increment (dnldc) was obtained for both acid strengths at 25OC by using a Brice-Phoenix differential refractometer (Model BP-200-V). The refractometer cell was purged with solution three times in order to absorb any H20 from the glass walls. A period of about 30 min was required before the readings stabilized. Values of dnldc for solutions of PPPT in 96.6 and 100.2% H2SO4 were 0.2701 and 0.2699, respectively.

No measurements of the number-average molecular weight an were made. I t seems reasonable to assume that Mm/Mn/=2 for these polymers synthesized

- -

TABLE I1 Values of nw Obtained by Method of Angular Dissymmetry (for 100.2% and 96.6% HzS04)

Sample % [Zd] L h P-'(W) n W zw (corrected) HzS04,

1 100.2 1.602 0.50 96.6 1.250 0.28

2 100.2 1.18 ? 96.6 1.051 0.13

3 100.2 1.854 0.54 96.6 1.414 0.36

4 100.2 1.031 0.10 5 100.2 1.409 0.36

96.6 1.288 0.30

1.746 1.180 1.18 1.036 1.718 1.304 1.718 1.296 1.270

10,400 11,400 15,000 14,800 14,050 17,160 29,700 17,950 31,800

16,660 13,452 17,700 15,320 24,000 22,400 30,350 23,260 35.600

64 BAIRD AND SMITH

4.0

3.5 h m 1. 3 n 3.0 s

2.5

2.07

by a poIycondensation rea~tion.~ Furthermore, values of GW/Mn for PBA were found to be about 1A5

-

-

-

- kzz 2q0000

I I I I I I 1 96 98 100 102 104 106 108

Viscometry

Intrinsic viscosities were measured by extrapolating the reduced viscosities (q&) obtained at five different concentrations to zero concentration. All measurements were conducted at 25OC in Cannon-Fenske viscometers (model 200). Drop times were greater than 100 sec, which justified the neglect of kinetic energy corrections.

For solutions in 100% H2SO4, there was considerable curvature in the qsp/c curves which made it difficult to obtain values of [q] by extrapolating to zero c6ncentration. The extrapolation was carried out by using only those points which gave a fairly straight line. Examples of the qsp/c curves are given in Fig- ures 2-4, and [q] is recorded in Table I.

RESULTS AND DISCUSSION

Effect of Acid Strength on Intrinsic Viscosity

As suggested in the Introduction, there is apparently little information on the part the acid strength plays in determining the configuration of PPPT molecules in dilute H2S04 solutions. In Figure 1, [q] is plotted versus the acid strength for a sample of PPPT of aW = 25,000 [a, estimated from eq. (2)]. We can see that [q] increases at first with increasing acid strength, exhibiting a maximum at about 100% H2SO4 and then decreasing with concentrations greater than 100% H2S04. Since [q] is a measure of the hydrodynamic volume of a molecule, these results suggest that PPPT can undergo configurational changes with variations in acid strength.

These results are similar to those reported by Sokolova et al.7 for a similar

POLY(1,CPHENYLENE TEREPHTHALAMIDE) 65

polymer/solvent system. However, they found that [q] took on its maximum value for acid strengths between 98% to 99% H2S04. We feel that the maximum value of [q] at 100% H2SO4 is probably more reasonable, since the ionic nature of H2SO4 changes more drastically at 100% HzSO~.~ In particular, there is very little dissociation of 100% H2SO4 (the concentration of HSO4- ions is only 0.027”): whereas just 1% of H20 (i.e., 99%) H2S04) produces 1 mole of HS04- per liter of solution.

Sokolova et al.7 attribute the increase in [q] to a change in the configuration of the PPPT molecule as a result of changes in the nature of the solvent. This rather brief explanation seems reasonable, but not specific enough. We suspect that the increase in [77] in 100% H2S04 is the result of repulsive electrostatic forces due to positive charges generated by protonation along the backbone of PPPT. In 96% H2SO4, the concentration of free counterions formed from the dissociation of H2S04 is very high. These counterions shield the positive charges and allow the molecule to coil slightly. As the acid strength increases, the concentration of counterions decreases and the shielding effect decreases. Finally at 100% H2S04 the concentration of counterions is nearly negligible (0.027”) and the repulsive forces expand the molecule.

Further investigations for acid strengths greater than 100% were not carried out because of the difficulty in maintaining the acid strength. We suspect that a shielding mechanism similar to that proposed above is responsible for the de- creasing values of [q], although the nature of the counterions may change.8 We realize that polymer degradation may possibly occur in the presence of free SO3 and could account for some of the decrease in [q].

In the remainder of this paper, we will be concerned on!y with the dilute so- lution properties of PPPT in 96.6% and 100.2% H2S04.

Dilute Solution Viscosity

Reduced viscosity versus concentration (sS,/c vs. c) curves are presented in Figures 2-4 for three samples of PPPT of different molecular weight (MW). In

I I I I 1 I 1

I .2 1.4 C WdlI

08 0.2 0.4 0.6 0.8 1.0

Fig. 2. Comparison of reduced viscosity ( ~ s p / c ) vs. concentration for PPPT (aw = 12,000): (0) in 96.6% HzSO,; (A) in 100.4% Hfi04.

66 BAIRD AND SMITH

0.2 0 4 0.6 0.8 I .o 1.2 I .4 C (Wdl)

Fig. 3. Comparison of qsp/c vs. c for PPPT (aw = 23,700): (0) in 96.6% H2S04; (A) in 100.4% HzS04.

96.6% HzS04, q S p h is essentially linearly dependent on c. There is, however, a slight tendency for qsp/c in Figures 2 and 3 to decrease nonlinearly with de- creasing concentration for concentrations less than 0.2 g/dl. In the case of the highest molecular weight sample, q,,h is linearly dependent on c for 0.01 5 c I 0.4 g/dl. Above c = 0.4 g/dl, qsp/c increases rapidly with increasing concen- tration.

On the other hand, qsp/c curves are highly irregular for solutions of PPPT in 100.2% H2S04. In Figure 4, qsp/c decreases rapidly with concentrations less than 0.1 g/dl. In Figures 2 and 3, qsp/c increases with decreasing concentration.

The behavior exhibited by PPPT in HzS04 is similar to that reported by Schaefgen et a1.12 for nylon 6 in H2S04 and formic acid. In 96% HzS04, qsp/c

, , , , , , ,

0.2 0.4 0.6 0.6 I .o I .2 1.4

c (Vd9 Fig. 4. Comparison of qsp/c vs. c for PPPT (gw = 40,100): (0) in 96.6% H2S04; (A) in 100.2%

HzS04.

POLY (1,4-PHENYLENE TEREPHTHALAMIDE) 67

curves varied linearly with c. They attributed this to the high concentration of counterions which shield the charges along the backbone over a large range of c , allowing the molecules to take on their most natural configuration. In 100% HzS04, qsp/c decreased nonlinearly with c . This was attributed to the increased shielding of charges along the polymer backbone at low c, because of the increased number of counterions relative to the number of protonated amide groups. In anhydrous formic acid, the concentration of counterions is negligible. As c de- creases, there is increasing volume for the molecule to expand. In the case of the data in Figures 2 and 3, the acid strength was 0.2% higher than used for the solution of Figure 4. It is possible that this slight increase in acid strength could reduce the concentration of counterions considerably.

Although the behavior exhibited by PPPT is similar to that of nylon 6, there is one noticeable difference. For nylon 6, the polyelectrolyte effect is readily noticeable in qsp/c curves for c in the range of 1.0-2.0 g/dl. For PPPT, this effect is not observed until c = 0.1-0.2 g/dl. This may be an indication of the difference in the configuration and flexibility of the two molecules. For PPPT, which is highly extended and probably less flexible than nylon 6, the repulsive charges are a larger distance apart. Thus, before a significant change in the configuration of the PPPT molecule can occur, a larger number of counterions relative to the number of charges along the polymer backbone are required.

The significance of the data in Figures 2-4 is that they show that the poly- electrolyte effect is evident over the whole range of molecular weights studied here. Even for the low molecular weight samples there is a distinct effect. This is in contrast to the information reported by Schaefgen et al.5 In the range of molecular weight where a = 1.7, they reported that there was no observable polyelectrolyte effect. However, above aw = 12,000, it was evident and increased with increasing Bw. They indicated that this was in agreement with the semi- flexible nature of PPPT. However, part of the reason for not observing this effect is because in concentrated H2SO4 it is mostly disguised by the counterions.

Light-Scattering Data

Values of aw obtained from Zimm plots are given in Table I. For samples 3-5, there is good agreement between values of Bw obtained from the two solu- tions. This not only gives us confidence in our measurements of aW, but indi- cates that polymer degradation is probably not responsible for the variation of [q] with acid strength. There is, however, a noticeable variation of Bw values for the two samples of lowest molecular weight, but no trend is suggested by the data. We suspect that the variation is associated with experimental errors in obtaining precise scattering intensities for the low molecular weight species and difficulties in extrapolating values of the scattering factor P(0) to zero concen- tration because of the nonlinear dependence of P(0) on c. (This nonlinearity is probably due to the changes in configuration of the molecules with c.)

Values of a, determined by the method of angular dissymmetry [see eq. (111 are given in Table 11. There is only fair agreement between these values and those of Table I. However, this is somewhat expected, since small amounts of gel, aggregates of highly associated molecules, and small amounts of impurities can lead to values of [Zd] which are too high.lo Furthermore, we found it difficult to obtain consistent values of [Z,] because 142 - 1) was not linearly dependent

68 BAIRD AND SMITH

4

5

Fig. 5. [q] vs. z,,, for PPPT (0) in 96.6% (A) in 100.2% HzS04.

on c as is usually the case.lo Again, we think this anomalous behavior is asso- ciated with the presence of polyelectrolytes which change shape with c. The values of [Zd] seem somewhat high, as they give values of LIX (where L is the length of the rodlike molecule and X is the wavelength) which are unrealistic for the given values of Mw. Furthermore, [Zd] does not increase with molecular weight as should be the case. On the other hand, the double extrapolation procedure of Zimm" gives consistent values of Mw, even in the presence of mi- crogels.1° In addition, no assumptions about the shape of the particle need to be made in order to obtain Mw. Thus, for a system such as the one studied here, it seems necessary that the Zimm method be used rather than the method of angular dissymmetry.

Intrinsic Viscosity-Molecular Weight Relationships

In Figure 5, values of log [a] for both 96.6% and 100.2% H2S04, are plotted versus log gw (aw values taken from Table I under 96.6% H2S04). The rela- tionships (2) and (3) between [a] and Rw are obtained from the data:

For 96.6% HzS04:

= 1.95 x 10-6Xl~1.36 (2)

= 2.19 x 10-7R~1.62 (3)

For 100.2% H2S04:

It should be noted that the values of a were found to be statistically different. This increase in values of a indicates that the molecule undergoes further ex- pansion in 100.2% HzS04 and confirms our hypothesis of molecular expansion used to explain the data in Figure 1.

These data are of further significance for the following reasons. Although the molecule is highly extended in 96.6% H2S04, it can undergo further changes

POLY(1,4-PHENYLENE TEREPHTHALAMIDE) 69

4

3 1

4 6 0 lo5 - 3 4 6 6 d 2

M W

Fig. 6. Comparison of [q] vs. Mw data for PPPT in concentrated HzS04: (A) obtained by Schaefgen et al.;5 ( 0 ) Arpin and Strazielle;6 (0) Baird and Smith (this study).

of configuration in 100.2% H2S04. This suggests that PPPT is only semirigid. Furthermore, it seems apparent that the solvent (i.e., the acid strength) makes an important contribution to the configuration of the molecule. Finally, it is reported by Kwolekl that no anisotropic phase formed below acid strengths of 98% H2S04. This fact, coupled with the data of Figure 5, suggests that there may be a minimum value of a below which anisotropy cannot occur.

Comparison with Other Data

In Figure 6, our values of Mw [estimated from eq. (2)] are compared with those of Schaefgen et. al. and Arpin and Strazielle. We see that for the lower values of Mw there is poor agreement, but for Bw > 20,000 there is fair agreement in the data. In general, there is no tendency for a set of data to agree more closely with a particular set of data.

Of more significance is the difference in the values of a. Schaefgen et al. report a value of a = 1.06 which is at first sight in agreement with that of Arpin and Strazielle. However, a least-squares linear regression analysis of their data gives a value of a = 1.28 which is closer to our value of 1.36.

directly, we note there are some important differences in the determination of Bw. Schaefgen et al. determined aw by the method of angular dissymmetry [see eq. (1) of this paper]. However, they apparently made no corrections for particle dissymmetry or optical anisotropy. In the case of the data of Arpin and Stra- zielle, there is some question about what corrections they made in order to obtain Mw. They implied that they corrected their values of Mw for fluorescence, but a check of their corrected values indicated they corrected for depolarization of the transmitted light. Our values of Mw were determined from Zimm plots, a method which requires less correction and assumptions for determining aw.

Although we cannot account for the differences in values of a and

70 BAIRD AND SMITH

CONCLUSIONS

The following conclusions can be drawn from this work. (1) The maximum [v] for PPPT occurs at 100% H2S0.4 and can be attributed

to the expansion of the molecules. This is confirmed by an increase in the Mark-Houwink exponent from 1.36 in 96.6% H&04 to 1.62 in 100.2% HzS04.

(2) A distinct polyelectrolyte effect which is observed in the reduced viscosity curves for solutions of PPPT in 100.2% suggests that the expansion of the molecules can be attributed to repulsive electrostatic forces along the polymer backbone.

(3) The configuration of PPPT is highly dependent on the acid strength and suggests that the molecules may be partially flexible rather than completely rigid.

(4) Because of low scattering intensities and only small changes of aw with large changes in [ q ] , values of aw should be obtained from Zimm plots rather than by the method of angular dissymmetry.

( 5 ) For values of gw > 20,000 there is fair agreement between our values of aw and those of Schaefgen et al. The differences in aw values < 20,000 can probably be attributed to the methods used for determining Mw.

The authors are indebted to E. L. Lawton of the Monsanto Research Triangle, Durham, North Carolina for preparing the polymers used in this work and to R. D. Ulrich, E. Drott, and R. Bonifay for helpful discussions and assistance in working out the details of light scattering from HzS04 so- lutions and to J. A. Burroughs for the dilute-solution viscosity measurements. They are grateful to the Monsanto Company for permission to publish this work.

References

1. S. L. Kwolek, U. S. Pat. 3,671,542 (June 20,1972). 2. H. Blades, U. S. Pat. 3,767,756 (March 29,1972). 3. S. P. Papkov, V. G. Kulchikhin, V. D. Kalmykova, and A. Ya. Malkin, J. Polym. Sci. Polym.

4. P. J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, N.Y., 1953. 5. J. R. Schaefgen, V. S. Foldi, F. M. Loguillo, V. H. Good, L. W. Gulrich, and F. L. Killian, paper

presented at American Chemical Society Meeting, 1976; Polym. Prep. , 17, No. 1,69 (1976). 6. M. Arpin and C. Strazielle, Makromol. Chem., 177,581 (1976); C. R. Acad. Sci. (Paris), C280,

1293 (1975). 7. T. S. Sokolova, S. G. Efimova, A. V. Volkhina, S. P. Papkov, and G. I. Kudryavtsev, Khim.

Volokna, I, 26 (1974). 8. R. A. Cox, J. Amer. Chem. Soc., 96,1059 (1974). 9. T. I. Bair, P. W. Morgan, F. L. Killian, paper presented at American Chemical Society Meeting,

Phys. Ed., 12,1753 (1974).

1976; Polym. Prepr., 17, No. 1,59 (1976). 10. M. B. Huglin, Ed., Light Scattering from Polymer Solutions, Academic Press, New York,

1972. 11. B. H. Zimm, J. Chem. Phys., 16,1099 (1948). 12. J. R. Schaefgen and C. F. Trivisonno, J. Amer. Chem. Soc., 73,4580 (1951).

Received October 7,1976 Revised November 17,1976