10
Birefringence of Amorphous Polyoxides: Stress- Optical Behavior of Poly(3-Methyltetrahydrofuran) ENRIQUE SAIZ and MARiA P. TARAZONA, Departamento de Quimica Fikica, Universidad de Alcala de Henares, Madrid, Spain, and EVARISTO RIANDE and JULIO GUZMAN, Instituto de PZcisticos y Caucho (CSIC), Madrid - 6, Spain Synopsis The stress-optical behavior of an unswollen elastomeric network of poly(3-methyltetrahy- drofuran) was measured for elongation ratios a in the range 1.182-1.549, at several temper- atures between 20 and 60°C. No evidence of strain-induced crystallization was found; moreover, the dependence of birefringence An on true stress f/A was linear in the interval of a inves- tigated. Values of Aa ranged from 2.4 to 2.8 in units of cm3, in the temperature range studied, with a temperature coefficient 3.1 x K-l. Theoretical calculations carried out with the rotational-isomeric-state model gave values of ha noticeably smaller than the ex- perimental results; however, a small increase in the backbone valence angles 6 improved the theoretical result of ha without worsening that of the dipole ratio. Analysis of the Aa results seems to corroborate the conclusion obtained through the study of dipole moments concerning the preference for nucleophilic attack on the less hindered a carbon in the monomer. Theo- retical and experimental values of the temperature coefficient of Aa were in clear disagree- ment; a qualitative explanation for this discrepancy is discussed. INTRODUCTION The configurationdependent properties of the members of the family of polyoxides, with repeating unit (CHJ,--O-, have been widely investigated to gain deeper insight into the relations between structure and properties in polymers.lg The configurational properties most often used for these studies have been dipole moments, unperturbed dimensions, and their tem- perature coefficients. In spite of the simple structure of the polyoxides, studies on the optical properties of these polymers are To our knowledge, only the Kerr effect in poly(oxyethy1ene glycol) and the related molecule poly(oxyethy1ene dimethyl ether) have been studied. A common feature of the polyoxides is that the differences between the values of the molar Kerr constant ,K for the polymers and for the isotropic solvent (usually carbon tetrachloride) are small, and therefore significant errors may be involved in the experimental determination of this configurational optical magnit~de.~ Investigations have not been carried out on the stress- optical behavior of networks prepared from polyoxides. The reason may be that the preparation of the networks implies serious difficulties owing to the degradation of these chains under conditions of classical crosslinking reactions. Moreover, the polyoxides are crystalline and strain-induced crys- tallization may appear in the networks, even at temperatures well above the melting temperature of the uncrosslinked chains. This could alter sig- nificantly the birefringence of the oriented chains. Journal of Polymer Science: Polymer Physics Edition, Vol. 22,2165-2174 (1984) @ 1984 John Wiley & Sons, Inc. CCC 0098-1273/84/ 122165-10$04.00

Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

Embed Size (px)

Citation preview

Page 1: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

Birefringence of Amorphous Polyoxides: Stress- Optical Behavior of Poly(3-Methyltetrahydrofuran)

ENRIQUE SAIZ and MARiA P. TARAZONA, Departamento de Quimica Fikica, Universidad de Alcala de Henares, Madrid, Spain, and

EVARISTO RIANDE and JULIO GUZMAN, Instituto de PZcisticos y Caucho (CSIC), Madrid - 6, Spain

Synopsis

The stress-optical behavior of an unswollen elastomeric network of poly(3-methyltetrahy- drofuran) was measured for elongation ratios a in the range 1.182-1.549, at several temper- atures between 20 and 60°C. No evidence of strain-induced crystallization was found; moreover, the dependence of birefringence An on true stress f/A was linear in the interval of a inves- tigated. Values of Aa ranged from 2.4 to 2.8 in units of cm3, in the temperature range studied, with a temperature coefficient 3.1 x K-l. Theoretical calculations carried out with the rotational-isomeric-state model gave values of ha noticeably smaller than the ex- perimental results; however, a small increase in the backbone valence angles 6 improved the theoretical result of ha without worsening that of the dipole ratio. Analysis of the Aa results seems to corroborate the conclusion obtained through the study of dipole moments concerning the preference for nucleophilic attack on the less hindered a carbon in the monomer. Theo- retical and experimental values of the temperature coefficient of Aa were in clear disagree- ment; a qualitative explanation for this discrepancy is discussed.

INTRODUCTION The configurationdependent properties of the members of the family of

polyoxides, with repeating unit (CHJ,--O-, have been widely investigated to gain deeper insight into the relations between structure and properties in polymers.lg The configurational properties most often used for these studies have been dipole moments, unperturbed dimensions, and their tem- perature coefficients. In spite of the simple structure of the polyoxides, studies on the optical properties of these polymers are To our knowledge, only the Kerr effect in poly(oxyethy1ene glycol) and the related molecule poly(oxyethy1ene dimethyl ether) have been studied. A common feature of the polyoxides is that the differences between the values of the molar Kerr constant ,K for the polymers and for the isotropic solvent (usually carbon tetrachloride) are small, and therefore significant errors may be involved in the experimental determination of this configurational optical m a g n i t ~ d e . ~ Investigations have not been carried out on the stress- optical behavior of networks prepared from polyoxides. The reason may be that the preparation of the networks implies serious difficulties owing to the degradation of these chains under conditions of classical crosslinking reactions. Moreover, the polyoxides are crystalline and strain-induced crys- tallization may appear in the networks, even at temperatures well above the melting temperature of the uncrosslinked chains. This could alter sig- nificantly the birefringence of the oriented chains.

Journal of Polymer Science: Polymer Physics Edition, Vol. 22, 2165-2174 (1984) @ 1984 John Wiley & Sons, Inc. CCC 0098-1273/84/ 122165-10$04.00

Page 2: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

2166 SAIZ ET AL.

By substituting a methyl group for a hydrogen atom in the repeating unit of the members of the family of the polyoxides, amorphous polymers, which should be useful for birefringence studies, would be obtained. In the case of polytetrahydrofuran (PTHF), for example, poly(3-methyltetrahydrofur- an) (PMTHF) and poly(2-methyltetrahydrofuran) (PBMTHF) can potentially be obtained. The synthesis of these polymers requires the ring-opening polymerization of 3-methyltetrahydrofuran and 2-methyltetrahydrofuran, respectively. Although the methyl group renders the free energy of poly- merization of these heterocycles less negative than that of tetrahydrofuran, increasing the difficulty of their polymerization, recent studies have shown that relatively high-molecular-weight chains of PMTHF can be obtained by cationic polymerization of 3-methyltetrahydrofuran using oxonium salts as initiatom8 However, attempts to homopolymerize 2-methyltetrahydrofuran have so far been unsuc~essful.~J~

Analysis of the I3C-NMR spectrum of PMTHF shows that 70% of the scissions in the cationic polymerization of 3-methyltetrahydrofuran occur preferentially through one of the two C-0 bonds of the monomer ring? Consequently, structural irregularities are present in PMTHF chains. The critical interpretation of the dipole moments of these chains seems to sug- gest that the ring-opening polymerization proceeds preferentially by nu- cleophilic attack of the monomer oxygen atom on the less hindered carbon of the heterocycle in the a position with respect to the oxonium ion." In order to obtain confirmatory evidence for the proposed mechanism, it would be useful to study the birefringence of strained networks prepared from this polymer. Actually, earlier studies carried out on asymmetric chains have shown that the optical properties are generally more sensitive probes of the structural irregularities than other more often used configurational properties.12J3 For this purpose, the optical configurational parameter ha was obtained from birefringence-strain experiments and the results were interpreted in terms of the rotational-isomeric-state model. To investigate the effect of the side group on Aa, the value of this parameter was also calculated for PTHF and the results were compared with those for PMTHF.

EXPERIMENTAL

Synthesis of Poly(3-Methyltetrahydrofuran)

3-Methyltetrahydrofuran (Fluka) was refluxed successively over potas- sium hydroxide and sodium for several hours. It was further distilled in uucuo onto a sodium mirror. The initiator, acetyl hexafluoroantimonate, was prepared at -78°C in uucuo by reaction of acetyl chloride (distilled under nitrogen immediately before use) and silver hexafluorantimonate. The silver chloride obtained was eliminated by filtration. The ring-opening polymerization of 3-methyltetrahydrofuran was carried out at - 8°C in uac- uo. The polymerization reaction was terminated with water; the polymer was extracted with benzene and precipitated with methanol.

Page 3: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

BIREFRINGENCE OF AMORPHOUS POLYOXIDES 2167

Preparation of the Networks

The acetyl-terminated chain ends were hydrolyzed by refluxing with a solution of sodium hydroxide in absolute ethanol. The number-average mo- lecular weight of the chains, determined with a Knauer vapor-pressure osmometer, was 6400. Stoichiometric amounts of the polymer and 2,4-bis(p- isocyanate benzyl) phenyl isocyanate, were dissolved in a small amount of chloroform (ethanol free). The solvent was removed by evaporation and the mixture of polymer and crosslinking agent was molded at 70°C for 12 h. The network was extracted with chloroform. The soluble fraction amounted to 0.10. The density of the material measured by pycnometry was 0.962 g ~ m - ~ at 25°C. The thermal expansion coefficient /3, determined with a Per- kin-Elmer thermal analyzer, was 6.9 x K-l.

Birefringence Measurements

Strain-birefringence experiments were performed over the temperature interval 20430°C by use of equipment and methods described elsewhere.14J5 The optical retardation of the strained samples was measured with a Ba- binetSolei1 compensator (Karl-Lambrecht K1148). The elastic force was measured with a Statham strain gauge. Refractive indices were measured with a Abbe refractometer at several temperatures. The results obtained are fitted by

n, = 1.4694 - 3.08 x 1W4t

with t in degrees centigrade.

Results

Values of the birefringence An were obtained at several elongation ratios a in the range 1.182-1.549. For each value of a, the strip was strained at the highest temperature of the experiment (60°C) and kept at that tem- perature until the elastic force was apparently constant. Then the tem- perature was decreased in steps of 10°C and both the birefringence and the stress were measured at 60, 50, 40, 30, and 20"C, with some measurements out of sequence to test for reversibility. The birefringence does not show a noticeable dependence on temperature. In Figure 1, values of the birefr- ingence An are plotted as a function of the true stress T = f /A ( f is the elastic force and A is the distorted cross-sectional area of the strip). In general, the results are fitted reasonably well by a straight line in the interval of a investigated. Values of the stress-optical coefficient C, obtained at each temperature of interest from the slopes of plots similar to those of figure 1, are shown in Table I. The results indicate that for PMTHF this quantity decreases with increasing temperature.

The optical configurational parameter A a is related to the stress-optical coefficient C by the equation16J7

A a = (45kW/2r)n/(n2 + 112

Page 4: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

2168 SAIZ ET AL.

3 flA (N1rnt-d)

Fig. 1. Strain-optical birefringence as a function of true stress f/A at two different tem- peratures for unswollen PMTHF.

where k is the Boltzmann constant, T is the absolute temperature, and n is the refractive index of the network. The values of A a for different tem- peratures are shown in the third column of Table I. By comparing these values with those reported for other polymers, it can be concluded that unswollen PMTHF networks exhibit an optical configurational parameter smaller than the values for swollen polyethylene,16 polyi~obuthylene,'~ poly- butadiene,15 polydimethylsilmethylene,'8 and poly(diethy1ene glycol tere- ~hthalate1. l~ The natural logarithm of ha is plotted as a function of tem- perature in Figure 2. The temperature coefficient d lnAa/dt, obtained from this plot, amounts to 3.1 x

Birefringence measurements of swollen PMTHF networks could not be obtained owing to the poor mechanical properties of the samples (swollen with carbon tetrachloride or other solvents).

K-l.

THEORETICAL ANALYSIS

Conformational Statistics

Figure 3 represents a segment of the isotatic PMTHF chain shown in its planar all-trans conformation, together with the three methyltetrahydro-

TABLE I Summary of Results of Stress-Optical Measurements

t ("C) C = A n A / f

(10-lo cm2 dyn-l) ha cm3)

20 30 40 50 60

1.25 1.20 1.16 1.13 1.10

2.473 2.563 2.653 2.750 2.835

Page 5: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

BIREFRINGENCE OF AMORPHOUS POLYOXIDES 2169

1 a” u” 1 u’ (+‘a

u,= 0 0 0 , u,= 1 a‘ 0 1 0 0 1 0 u’o

I I

l u l

, u,= 1 uo 0

1 u w 1

Fig. 2. Natural logarithm of ha versus temperature for PMTHF.

1 0 u” 1 1 7 )

1 0 7 ) 1 0 0

u,= 1 1 7 ) w , u e = 1 u ” 0 , U r =

furan molecules from which it is obtained by ring-opening polymerization with scission of bond 6 in the first and second units and of bond p in the third onell. There are eleven different kinds of bonds (denoted a through K ) whose statistical weight matrices can be written as l1

1 u” 0

0 0 0 1 0 0

1 1 u 1 ’ 1 1 ug= 1 0 0 , u,= 1 1 ao , u i =

0 0 1 l o u

1 d o u’

1 u’ d o

1 u’o d o

uj =

1 u” u” 1 u” u”

1 u”o 0 , u, = 1 u” 0

1 0 u” 1 0 u”

All the statistical weights were calculated as single Boltzmann factors of their corresponding energies (i.e., 6 = expl -E,IRTI). The values of the energies (taken from a previous paper”) are summarized in Table 11. Three different rotational angles were considered, namely +1 for rotations about bonds b, d, g, and i (i.e., rotation C-CCC-0); 42 for rotations about a, e, f ; j , and k (i.e., C e O ) ; and +3 for the remaining c and h bonds (i.e., C- CCC-C). It was assumed that trans states are located at 0” and gauche at +1 = +120”, +2 = +ll0”, and c $ ~ = i-112.5”. All the valence angles were considered to be 110” and the bond lengths used were 1.53 and 1.43 A for C-C and C-0 bonds, respective1y.l’

Page 6: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

2170 SAIZ ET AL.

Fig. 3. A segment of the isotactic PMTHF chain shown in its planar all-trans conformation, together with the three methyltetrahydrofuran molecules from which it is obtained by scissions 6, 6, and p.

Anisotropic Part of the Polarizability Tensors

Let di represent the contribution to the anisotropic part of the polariz- ability tensor of the chain B due to skeletal bond i (joining atoms i-1 and i) and the groups attached to skeletal atom i-1. Neglecting the small dis- tortions from tetrahedral geometry in the CH, groups, we can represent B(CH3) = -&(CHI and the Bg tensor corresponding to a given C H , - C group by the tensor of a C H 3 4 group by subtracting the tensor for a C-H bond in excess in the following group of the chain. Thus we can write the Bz contributions for all the groups of the chain as

& ( O X ) = B(C0) - B(CH)

B(CHz-4) = B(CC) + B(CH3) - B(CH) = B(CC) - 2B(CH)

d ( C H 3 C H 4 ) = B(CC) + B(CH3) - B(CH) + T( B(CC) - 2B(CH)) TT

where T is the matrix that transforms the coordinate system of the lateral M H 3 group to the reference frame of skeletal bond CH3C-C.20

For purposes of calculation, the initial and terminal groups of the chain were supposed to be CH,. Thus, the tensors of these groups are

TABLE I1 Conformational Energy”

Statistical weight E , (kcal mol-’1

17 w U U’ 0’’

0.14 2.1 2.1

- 0.25 1.2

Page 7: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

BIREFRINGENCE OF AMORPHOUS POLYOXIDES 2171

Bd =

Initial:

0.2340 -0.0819 0.1426

-0.0819 -0.2362 -0.2040

0.1428 -0.2040 0.0023

B(CH3-4) = B(CC) + B(CH3) - &(CHI = B(CC) - 2B(CH)

Final:

B(O-CH3) = B(C0) + B(CH3) = B(C0) - B(CH)

AU = - 3 (rTa?>/(r2>,, 2

The following assumptions were made in order to simplify the calculation. (i) It has been well established11p24-28 that the stereochemical structure has

a negligible effect on conformational properties such as unperturbed di- mensions and dipole moments of polymers in which the substituted carbons are separated by three or more skeletal bonds. Some preliminary calcula- tions showed this to be true for ha of PMTHF, where the substituted carbons are separated by at least four skeletal bonds. Hence, all the results presented below were computed for pure isotactic chains.

(ii) The value of the fraction Wof S units (i.e., units obtained by 6 scission of MTHF) in the polymers has a noticeable effect on the calculated Au result (see below); however, exploratory calculations showed that the sequence of 6 and p units within the chain modifies the result of Au by only ca. 0.1%. Therefore, the effect of the sequence is neglected in all the calculations and the results presented below were computed for a single chain with random sequences of 6 and /3 units but with welldefined values of W(error < 0.1%).

Page 8: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

2172 SAIZ ET AL.

(iii) The results for Au as a function of the polymerization degree x reach an asymptotic limit at x N 50; typical differences between Au(x = 50) and h u h = 100) are ca. 1%. Thus all the results were obtained for x = 100 (i.e., 500 skeletal bonds).

RESULTS AND DISCUSSION

Theoretical values of Au computed at 30°C are shown as a function of the fraction W of 6 units in Figure 4(A). The values for 1OZ4Au/cm3 of 1.5 and 1.7 calculated for W = 0.3 and 0.7, respectively, are smaller than the ex- perimental result, 2.6. This disagreement is found (usually with much larger differences) in many other p ~ l y r n e r s . ~ ~ ~ ~ . ~ ~ ~ ~ However, the value obtained for W = 0.7 is closer to the experimental result than that for W = 0.3,

. which seems to support the conclusion from analysis of dipole moments" that ca. 70% of scissions in the ring-opening polymerization are 6.

As can be seen in Figure 4, the dependence of Au on W is weak; for instance, ha increases by ca. 12% when W changes from 0.3 to 0.7, while the same variation of W produces an increase of 5% in the unperturbed dimensions and a decrease of 17% in the dipole moment. These variations can be qualitatively explained by the greater preference for t conformations in the 66 sequences compared with the /3/3 sequences, which increases the length of the chain, decreases its dipole moment owing to cancellation between the vectors of the consecutive CHz-O-CHz groups, and increases the 3 tensor for the chain. However, the dependence of ha on W is not strong because the differences in t occurrences between 66 and /3/3 se- quences, though definite, are small. Moreover, this insensitivity of ha to W is due to the roughly tetrahedral geometry of the PMTHF chain and the small anisotropy of the groups that it contains; i.e., the difference between the segments CHz-CHz-CHz and CHz-CH(CH3)-CHz (both assumed tet- rahedral) merely involves replacement of a C-H bond havingz1 lOZ4Aa = 0.21 cm3 by a C-CH, bond withz1 lOZ4Aa = 0.53. Accordingly, the 2 tensor

1 .o 0 0.2 0.4 06 0.8 1.0

Dependence of ha on fraction Wof 6 units calculated-at 30°C (A) all skeletal-bond angles 110". (B) skeletal bond angles 8, = CCC = 11C, Oz = CCO = 112, and O3 = COC = 110".

W Fig. 4.

Page 9: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

BIREFRINGENCE OF AMORPHOUS POLYOXIDES 2173

of the whole chain (and thus the ha parameter) will be little affected by the number of units of each kind that it contains. The value 1Wha = 1.5 cm3 calculated for poly(tetramethy1ene oxide) in which there are no CH,- CH(CH3)-CH2 segments agrees with this reasoning.

The variation of ha with the parameters used in the calculation is sum- marized in Table 111. This table does not include variation of the optical anisotropy of the bonds since the values of these parameters are well es- tablished. The most important of all the energies is E,,, which represents the first-order C - -. 0 interaction. A value of E,. = 1.3 kcal/mol would be required to bring the theoretical and the experimental value of ha into agreement, but this value is impossible, not only because it would not re- produce the dipole moment (the value of the dipole ratio calculated using E,. = 1.3 is D = 0.7, while the experimental value" is 0.526) but also because it is well known that this interaction must be attractive (i.e., E,. < 0).

It is interesting to note the strong dependence of A a on the valence angle 8 of the chain. The steep increase of ha with increasing 8 is due to the departure from- tetrahedral geom_etry of the chain. Hence,_ taking for in- stance, 8, = CCC= 114, O2 = CCO= = 112", and O3 = COC = llo", we calculated a value of A a = 2.0 cm3 for W = 0.7 [Fig. 4(B)], while the result of the dipole ratio D = 0.53 is still in excellent agreement with the experimental one." Therefore, a small increase in the valence angles im- proves the theoretical result for ha without worsening that for the dipole ratio.

The calculated value of the temperature coefficient 103d lnha/dT = -0.3 K-l is in clear disagreement with the experimental result 3.1 K-l. The same kind of discrepancy is obtained for the temperature coefficient of the unperturbed dimensions, whereas the theoretical temperature dependence of the dipole ratio is in excellent agreement with experiment.l' We find no quantitative explanation for this behavior. However, as a qualitative hy- pothesis, we could imagine that these discrepancies may be due to a vari- ation of the backbone angle with T. As a matter of fact, if we assume the 8 increases with temperature there will be a positive contribution of (d8/ dT)(d lnAa/d8) to the temperature coefficient which could eventually over- come the negative contribution of the energy. Unfortunately, the calculation

TABLE I11 Variation of Aa with the Parameters" Used in Calculationsb

103d InAa/dE 103d lnAa/dE, 103d lnAa/dE, 103d lnAa/dE,. 103d InAddE LTlt

103d lnAa/dO 103d lnAa/d+, 103d lnAa/d+, 103d InAa/d+3 103d lnAu/dT

~~

184.7 37.0

1.8 309.2 61.9 62.0

-6.3 - 1.3 - 3.0 -0.3

a Energies in kcal mol-I; angles in deg; Tin K. Computed for W = 0.7.

Page 10: Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

2174 SAIZ ET AL.

of dO/dT is neither simple nor accurate. However, some rough estimates, with the results shown in Table 111, indicate that a variation dO/dT = 0.025 deg. K-' would give values for the temperature coefficients of Aa, unperturbed dimension, and dipole moment of 1.3, 0.4, and 1.2 K-1, re- spectively, in fair agreement with experimental values (3.1, 0.6, and 1.6," respectively).

References 1. J. E. Mark, Acc. Chem. Res., 7, 218 (1974). 2. J. E. Mark, Chamcterization of Materials in Research, Cemmics and Polymers, J. J. Burke

3. A Abe and J. E. Mark, J. Am. Chem. Soc., 98, 6468 (1976). 4. M. J. Aroney, R. J. W. Le Fevre, and J. M. J. Parkins, J. Chem. Soc., 2890 (1960). 5. T. Ishikawa and K. Nagai, Polym. J., 2, 263 (1971). 6. K. Kelly, G. D. Patterson, and A. E. Tonelli, Macromolecules, 10, 859 (1977). 7. G. Khanarian and A. E. Tonelli, Macromolecules, 15,145 (1982). 8. L. Garrido, J. Guzman, and E. Riande, Macromolecules, 14, 1132 (1981). 9. G. Pruckmayer and T. K. Wu, Macromolecules, 6,33 (1973).

10. J. Kops and H. Spanggaard, Macromolecules, 16, 1144 (1983). 11. E. Riande, J. Guzman, and L. Garrido, Macromolecules, 17,1234 (1984). 12. A. E. Tonelli, Macromolecules, 10, 753 (1977). 13. E. Saiz, U. W. Suter, and P. J. Flory, J. Chem. Soc. Famday !Duns. 2, 73, 1538 (1977). 14. M. A. Llorente and J. E. Mark, J. Polym. Sci. Polym. Phys. Ed., 19, 1107 (1981). 15. J. E. Mark and M. A. Llorente, Polym. J., 13, 543 (1981). 16. M. H. Liberman, Y. Abe, and P. J. Flory, Macromolecules, 5, 550 (1972). 17. M. H. Liberman, L. C. De Bolt, and P. J. Flory, J. Polym. Sci. Polym. Phys. Ed., 12, 187

18. M. A. Llorente, J. E. Mark, and E. Saiz, J. Polym. Sci. Polym. Phys. Ed., 21, 1173 (1983). 19. E. Riande, J. Guzman, M. P. Tarazona, and E. Saiz, J. Polym. Sci. Polym. Phys. Ed., 22,

20. R. T. Ingwall and P. J. Flory, Biopolymers, 11, 1527 (1972). 21. G. D. Patterson and P. J. Flory, J. Chem. Soc. Faruday Trans. 2,68,1098 (1972); 68,1111

22. P. J. Flory, Statistical Mechanics of Chain Molecules, Interscience, New York, 1969. 23. P. J. Flory, Macromolecules, 7 , 381 (1974). 24. A. Abe, T. Hirano, and T. Tsuruta, Macromolecules, 12, 1092 (1979). 25. G. Allen, C. Bouth, and C. Price, Polymer, 8, 397 (1967). 26. J. E. Mark, J. Polym. Sci. Polym. Symp., 91, 54 (1979). 27. E. Riande, S . Boileau, P. Hennery, and J. E. Mark, J. Chem. Phys., 71, 4206 (1979);

28. A. Abe, Macmmolecules, 13, 541 (1980). 29. R. S . Stein, F. H. Holmes, and A. V. Tobolsky, J. Polym. Sci., 14, 443 (1954). 30. E. Saiz, and E. Riande, and J. E. Mark, Macromolecules, 17, 899 (1984).

and V. Weiss, Eds., Syracuse University, Syracuse, NY, 1975, Chap. 12.

(1974).

917 (1984).

(1972).

Macromolecules, 12, 702 (1979).

Received January 18, 1984 Accepted June 4, 1984