Macromolecules 1986,19, 2567-2572
the formation of locally ordered domains or the presence of an isotropic-anisotropic transition; this conclusion is found to hold over a broad range of values of the attractive interaction between beads. While other results presented here qualitatively confirm the prediction of Flory's theory2 modified to include attractive interactions that semiflexible polymers should undergo a phase transition from a globally disordered to a globally ordered state, there are substantial quantitative disagreements with the MC simulation results. Among other things, the simple mean field theory appreciably underestimates the transition temperature, Tt*, and even more drastically overestimates the change in energy and entropy at T,*. Furthermore, it in no way addresses the microheterogeneity seen in the simulations. All of the above clearly point out that satisfactory theory of the configurational statistics of highly dense systems of semiflexible chains is not yet at hand. Such a theory must reproduce the observed local ordering of the chains in the isotropic phase, as well as features seen in the ordered phase such as the appreciable fraction of gauche states near the transition temperature and the curvature in the gauche probability profiles. The latter features seem to reflect the packing and cooperativity present in the ordered phase. Work is now in progress toward the development of this theory. Since the qualitative features observed here seem to be independent of density insofar as these dense tetrahedral lattice polymers resemble real polymers, this work may perhaps point out some essential aspeds of the semiflexible polymer liquid crystal phase transition. Nevertheless, based on the system lacking attractive interactions, substantial questions concerning the effects of the lattice re-
2567
main and we echo Baumgartner's6 concerns about the validity of conclusionsbased on lattice systems as applied to continuum models of semiflexible polymers at the phase transition.13-15
Acknowledgment. This research was supported in part by a grant from the Polymers Program of the National Science Foundation (No. DMR 83-03797). Acknowledgment is made to Monsanto Co. for an institutional research grant for the purchase of a pVAX-I1 computer on which the simulations reported here were predominantly carried out. We thank a referee for suggestions that improved the presentation of these results. References and Notes (1) Kolinski, A.; Skolnick, J.; Yaris, R. Macromolecules, preceding
paper in this issue. (2) Flory, P. J. Proc. R. Soc. London, Ser. A 1956, 234, 73. (3) Baumgartner, A.; Yoon, D. Y. J. Chem. Phys. 1983, 79, 521. (4) Yoon, D. Y.; Baumgartner, A. Macromolecules 1984,17, 2864. (5) Baumgartner, A. J. Chem. Phys. 1984, 81, 484. (6) Baumgartner, A. J. Chem. Phys. 1986,84, 1905. (7) Metropolis, N.; Rosenbluth, A. N.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. J. Chem. Phys. 1953,21, 1087. (8) Binder, K.; Stauffer, D. In Applications of the Monte Carlo Method in Statistical Physics; Springer-Verlag: Heidelberg, 1984. (9) See, for example: Tompa, H. Polymer Solutions; Butterworths: London, 1956. (10) Curro, J. G. Macromolecules 1978, 12, 463. (11) Kolinski, A.; Skolnick, J.; Yaris, R. J. Chem. Phys. 1986, 84, 1922. (12) Domb, C.; Fisher, M. E. Proc. Cambridge Philos. SOC.1958,54, 48.
(13) Gujrati, P. D.; Goldstein, M. J. Chem. Phys. 1981, 74, 2596. (14) Nagle, J. F.; Gujrati, P. D.; Goldstein, M. J. Phys. Chem. 1984, 88, 4599.
(15) Flory, P. J. Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 4510.
Conformational Energies and Random-Coil Configurations of Aliphatic Polyesters Evaristo Riande,* Julio Guzmln, and Humberto Adabbo Znstituto de Pldsticos y Caucho (CSZC), 28006 Madrid, Spain. Received February 12, 1986 ABSTRACT: Values of the mean-square dipole moment ( p z ) of poly( oxyneopentyleneoxyadipoyl) were determined from measurements of dielectric constants and refractive indices of the polymer in benzene. The value of the dipole moment ratio at 30 "C was found to be 0.653, and its temperature coefficient d In (w2)/dT amounts to 1.7 X K-l. Poly(oxyneopentyleneoxyadipoy1) networks were prepared by cross-linking hydroxyl-terminated chains with an aromatic triisocyanate. Stress-strain isotherms obtained at two temperatures fit reasonably well to the Mooney-Rivlin formulation for values of the elongation ratio A, lying in the range 1.3 < X < 2.5; however, for values of X > 2.5 an anomalous increase in the modulus occurs, which was attributed to maximum extension of the chains. The temperature coefficient of the unperturbed dimensions 104(dIn (r2)o/dT), determined from thermoelastic experiments carried out on the networks, was 0.46 f 0.23. The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions were critically interpreted by using the rotational isomeric state model. Good agreement between theory and experiment was obtained by assuming that the gauche states about C(CHJ2-CH2 bonds, which give rise to first-order CH,. -0interactions, have an energy 0.6 kcal/mol lower than the alternative trans states, and that the rotational states about CH2CH2-COOCH2 bonds have similar energy.
.
Introduction Dielectric properties of aliphatic polyesters with cyclohexane rings incorporated in the main chain were recently investigated.l These studies showed a sharp increase in the polarity of poly(oxymethylene-l,4-cyclohexylenemethyleneoxysebacoyl) (PCDMS) when the substitution in the cyclohexane ring changes from equatorial&equatorial (trans isomer) to equatorial-axial (cis isomer). The temperature coefficient of the unperturbed mean-square 0024-9297/86/2219-2567$01.50/0
end-to-end distance, d In (r2)o/dT,was found to be large and negative for both trans and cis isomers.' The critical interpretation of the dipole moment and the temperature coefficient of both the dipole moment and the unperturbed dimensions led to the conclusion that these quantities are very sensitive to the gauche population about the CH2-0 bonds next to the equatorial substitution. An important issue in the configurational analysis of polyesters is to elucidate the value of the conformational 0 1986 American Chemical Society
2568 Riande et al.
energy associated with gauche states about the CH2CH2-COOCH2 skeletal bonds. The information at hand is highly controversial. Thus infrared and Raman studies carried out on methyl propionate by Dirlikov et seem to suggest that the lowest energy conformation arises when the carbonyl group eclipses the C-H bond. However, other studies performed by Moravie and Corset3 suggest that the C=O/C-C eclipsed form is more stable than the C= C/C-H eclipsed form, the enthalpy difference between them being ca. 1.3 f 0.3 kcal mol-'. An intermediate value of 0.08 kcal mol-' has also been reported for this differen~e.~ Recently, the dipole moments of dialkyl esters of some dicarboxylic acids were critically interpreted by Abe5 using the rotational isomeric state (RIS) model. With the exception of diethyl succinate, the experimental values were reasonably reproduced with a three-state scheme compatible with that suggested by Moravie and C ~ r s e t .In ~ order to acquire more information on the conformational characteristics of esters and polyesters, the dipole moment and the temperature coefficient of both the dipole moment and the unperturbed dimensions of poly(oxyneopentyleneoxyadipoyl) chains were analyzed with the RIS model. Experimental Section Synthesis of the Polymer. Neopentyl glycol (2,2-dimethyl-1,3-propanediol)was crystallized from a mixture of acetone/hexane (mp 131 "C; lit? mp 130 "C). Adipic acid was crystallized from distilled water (mp 155 "C; lit.e mp 153 "C). Toluene (Merck)was purified by conventionalmethods and dried with molecular sieve^.^ Poly(oxyneopentyleneoxyadipoy1) (PNA) was obtained in toluene solution by reaction of equimolecular amounts of neopentyl glycol and adipic acid, using p-toluenesulfonic acid as catalyst. The reaction was carried out for 24 h under reflux in a nitrogen atmosphere, and the water formed in the polycondensation was continuously separated by means of a Dean-Stark distillation trap. In the final steps of the reaction a slight excess of glycol was added and the polycondensation was permitted to proceed for an additional 5 h. The reaction products were precipitated with n-hexane and washed several times with water to eliminate the catalyst. Finally the polymer was dissolved in benzene, precipitated with hexane, and dried for 24 h under vacuo. Then the polyester was fractionated at room temperature, using chloroform/hexane as the solvent/nonsolvent system. A fraction of number-average molecular weight 5500 was used in the dielectric measurements and in the preparation of the networks used in the thermoelastic experiments. The melting temperature of the fraction, determined with a Perkin-Elmer DSC-4 calorimeter at a heating rate of 8 K/min, was found to be 40 "C. Thermoelastic and Dielectric Measurements. Networks were prepared by cross-linking hydroxyl-terminatedPNA chains with equivalent amounts of 2,4-bis@-isocyanatobenzyl)phenyl isocyanate. The cross-linking reaction was carried out at 80 "C for 2 days. The networks were extracted with chloroform for 3 days, and the value of the sol fraction was 0.07. Thermoelaatic experiments were conducted on unswollen strips by using standard technique^.^^^ A value of 7.2 X lo4 K-' was obtained by pycnometry for the cubic expansion coefficient. Dielectric constants of solutions of the polymer in benzene were measured at 10 kHz with a capacitance bridge (General Radio, Type 1620 A) and a three-terminal cell. Differences between the refractive indices of the solutions A and the solvent AI were measured at 640 nm with a Chromatix KHX differential refractometer.
Experimental Results Dielectric Results. Values of the increments of the dielectric constant of the solutions with respect to that of the solvent (At = t - el) were measured at 30,40,50, and 60 "C and plotted as a function of the weight fraction w
Macromolecules, Vol. 19, No. 10, 1986 Table I Dielectric Results for Poly(oxyneopentyleneoxyadipoy1) at Several Temperatures T."C d(t - e,)/dw -dIA2 - fh2)/dW (u2)/nm2 30 40 50 60
2.313
2.246 2.192 2.105
0.046
0.653
0.034 0.023 0.011
0.677 0.688
0.667
of the polymer. From these plots the values of d(t - tl)/dw, shown in the second column of Table I, were obtained. Values of d(R2- fi12)/dwat the temperatures of interest were also obtained from plots Aii2 = ii2 - ii,2 against w. The results obtained are shown in the third column of Table I. The mean-square dipole moment (p 2 ) of the chains was calculated a t the temperatures given above by means of the equation of Guggenheim and Smith"J2
where k is the Boltzmann constant, T is the absolute temperature, M is the molecular weight of the solute, p1 is the density of the solvent, and N A is Avogadro's number. Dipole moments of 1.07 and 1.7 D were assigned to the C-0 and O-H bonds of the terminal glycol residues, re~pectively.'~J~ The dipole moment associated with the C-C skeletal bond and with each ester group of the repeating unit were assumed to be 0.00 and 1.89 D, re~pective1y.l~ The experimental values of the mean-square dipole moment ratio expressed in terms of the dipole moment ratio (p2)/nm2, where nm2is the mean-square dipole moment of the chain in the idealization that all the skeletal bonds are freely jointed, are shown in the fourth column of Table I. The uncertainty of these values was estimated to be ca. 6%. The temperature coefficient of the dipole moment of the chains d In (p2)/dTwas obtained by plotting the natural logarithm of the dipole moment ratio against temperature. The value of this quantity amounted to 1.7 X K-l. Thermoelastic Results. Although the un-cross-linked polyester crystallizes from the bulk, crystallinity vestiges were not detected by calorimetry in the unstrained networks kept at room temperature for several weeks. Moreover, crystallinity was apparently not developed in the strained networks. Actually, the stress of the elongated strips remained noticeably constant for several days, even for values of the elongation ratio X as large as 3.5 and temperature as low as 15 "C. This behavior suggests that the cross-linking points hinder the crystallization of the networks. Stress-strain isotherms were obtained at several temperatures and the results interpreted as usual by the Mooney-Rivlin equation16 [f*] = 2C'
+ 2c2x-1
where 2C, and 2Cz are constants independent of the elongation ratio and [f*] is the reduced stress or modulus defined as"
[f*] = f / ( X - h-2)A in which f* is the equilibrium elastic force and A is the undistorted cross-sectional area of the strips. Values of the reduced force vs. the inverse of the elongation ratio at two temperatures are shown in Figure 1. It can be seen that for 0.4 < X-' < 0.8 the results fit reasonably well to the Mooney-Rivlin formulation. However, for values of X-' < 0.4, an increase in the modulus is observed, which
Conformations of Aliphatic Polyesters 2569
Macromolecules, Vol. 19, No. 10, 1986 0.32 -
0.30 -
Figure 3. A segment of the poly(oxyneopentyleneoxyadipoy1) chains in the all-trans conformation.
N
E
-=.
. I -
Table I1 Thermoelastic Results for Poly(oxyneopentyleneoxyadipoy1)at Several Elongation Ratios x 104(dIn (r2),,ldr) x 104(dIn ( r 2 h l d r ) 1.26 9.2 2.03 6.3 1.51 4.4 2.05 2.0 1.53 6.5 2.25 3.6 1.78 2.9 2.50 4.2 1.84 2.5 4.6 i 2.4"
0.28-
0.2
0.L
0.6
A-l
1.0
0.8
Average value.
Figure 1. Stress-strain isotherms at two temperatures for poly(oxyneopentyleneoxyadipoy1) networks.
Table I11
Geometrical Parameters bond lendhs, A bond angles, dee
-
+ 6.8
tz-
1
1.53
Table IV Parameters Used for Nonbonded Interactions atom or van der atomic eff no. of polarizabiliWaals
1.81
~
2.03
2.25
grow
2.50
I I
I
I
I
I
Figure 2. Thermoelastic results for poly(oxyneopenty1eneoxyadipoyl) networks at different elongation ratios A. Open and filled circles represent values of In ( f * / T )obtained at decreasing and increasing temperatures, respectively. can be attributed either to maximum extension of the chain or to crystallinity. The fact that the increase in the modulus occurs in a gradual form instead of a sharp one suggests that the upturn is caused by maximum extension of the chains. It should be pointed out in this regard that generally a sharp increase occurs in the modulus whenever crystallization takes place in the strained networks.16 An important feature of the isotherms is that the upturn appears at approximately the same value of the elongation ratio even though they were obtained at 10 OC below (isotherm A) and 30 "C above (isotherm B) the melting temperature of the un-cross-linked polymer. This is an additional bonus to the assumption that postulates maximum extension of the chains as a cause of the upturn. Force-temperature results were obtained for different values of the elongation ratio in the temperature range 15-70 "C. The thermoelastic data represented in terms of In ( f * / T ) are shown in Figure 2. The good reversibility of the thermoelastic results also suggests that crystallinity is not developed in the strained networks. The temperature coefficient of the unperturbed mean-square end-toend distance was obtained from the standard
where @ is the expansion coefficient. Values of d In ( r2)o/dTobtained at several elongations corresponding to
CHBor C H p C(carbony1) O(carbony1) 0 C
electrons 7 5 7 7 5
tv. loz4cm3 1.77 1.23 0.84 0.70 0.93
~~
radius. 8, 2 1.8 1.6
1.6 1.8
the Gaussian region of the Mooney-Rivlin plot are given in Table 11. The average value of d In (?),/dT was found to be (0.46 f 0.23) X K-l.
Theoretical Analysis Conformational Energies. A portion of the PNA chain in its planar all-trans conformation is shown in Figure 3. The bond length and bond angles used in the calculations of the conformational energies are shown in Table 111. Values of the conformational energies corresponding to the rotational states about the skeletal bonds of the glycol residue were calculated by using CH3COOCH2C(CH3)2CH200CCH3 as a model compound. Three contributions to these energies were computed. Torsional energies were evaluated by using threefold intrinsic potentials with barriers of 2.8 and 1.1kcal mol-l around C-C and C-O bonds, respectively.21-23Nonbonded interactions between atoms separated for more than two bonds were calculated by using the 6-12 Lennard-Jones potential V ( i j ) = Bl,/rl,12- A,/r,", where the parameters A,, and B, were evaluated in the usual mannerZ3sz4 utilizing the polarizability a , effective number of electrons Ne, and the van der Waals radii shown in Table IV. The electrostatic contribution was obtained by assigning partial charges of qc. = qo, = 0.318 and qCHp= -40 = 0.006 to the ester The potential curve correspondingto bonds of type C-0 is shown in Figure 4. It can be seen that as the rotational angle departs from zero, the potential increases, reaching a maximum at C$ = f60"; then the potential slightly de-
2570 Riande et al.
Macromolecules, Vol. 19, No. IO, 1986 more stable (ca. 1.2 kcal mol-') than the other states. It should be pointed out in this regard that although the analysis of the dipole moments of dialkyl esters5supported this latter conclusion, results have also been reported according to which the three rotational states have practically the same energy.4 Semiempirical potential calculations carried out by Abe5 on dimethyl adipate indicate that gauche states about bonds of type i 7 and i 9 have an energy E , of 0.3 kcal mol-l above that of the corresponding trans states. However, the critical interpretation of the configurational properties of cycloaliphatic polyesters suggests that these bonds can be considered free rotating. Therefore the value of E , was considered to be zero in further calculations. Gauche states about CH2-CH2 bonds which give rise to firsth-order CH2- -CH2 interactions were considered to have an energy E , of 0.5 kcal mol-l above that of the alternative trans states as occurs for similar bonds in polyFinally, gauche rotations of different sign about two consecutive C(CH3),-CH2bonds of the glycol residue, which give rise to second-order interactions between two oxygen atoms, were assumed to have an energy E, of 0.6-0.7 kcal mol-l. Rotations of different sign about any other pair of consecutive bonds were considered to be forbidden with the exception of the i + 1, i + 2, and the i + 5, i + 6 pair of bonds, where the gig' conformations have energies of E , + E8 and Ed!,respectively.
+
+
-
100
200
300
0 Figure 4. Calculated conformational energies as a function of rotational angle 4 over CH2-C(CH& (4CHZa= 0') and 0-CH2 (~cH~-c(cH= ~ ) 0'). ~
creases and a small minimum is obtained at f75' whose energy Ed,is c8. 1.0 kcal mol-' above that of the alternative trans states. For values of 4 > 80°, the potential steeply increases as 4 increases owing to strong interactions between the carbonyl and the methyl groups which in the vicinity of 4 = f120° may give rise to repulsive energies of several hundredths kcal mol-l. The potential curve associated with rotations about bonds of type C(CH3)2-CH2(Figure 4) presents three minima located at 0,f120°. The van der Waals contributions are similar for both trans and gauche conformations owing to the fact that trans conformation places the oxygen atom between a methyl and a methylene group. However, the conformational energy Ed associated with gauche states is somewhat lower, ca. 0.2 kcal mol-l, than that of the alternative trans states because the electrostatic attractions are higher in the former states than in the latter. The critical interpretation of the dipole moment and the temperature coefficient of both the dipole moment and the unperturbed dimensions of poly(3,3-dimethyloxetane) (PDO) provides additional information of relevance for the energy associated with the rotational states about CH2C(CH3)2-CH20bonds. According to these studies the most characteristic feature of these bonds is a decisive preference for gauche conformations over the correspondingt r a n ~ . Specifically, ~?~~ such states are found to be ca. 0.7-0.8 kcal mol-l lower in energy than the alternative trans states. Since conformational analysis using semiempirical energy functions gives for the gauche conformations a value of 0.4 kcal mol-l below that of the corresponding trans states, an steric attraction or gauche effect of 0.3-0.4 kcal mol-l is found.27 In view of these results it is also reasonable to expect a similar gauche effect for the C(CH3)2-CH2bonds of the glycol residue of PNA chains. As was stated above, the spectroscopic studies regarding the location of the most preferred conformation about CH2CH2-COOCH2bonds have been highly controversial. The infrared and Raman studies carried out by Dirlikov et al.2on methyl propionate suggest that the lowest energy arises when the C=O group eclipses the C-H bond; this is in sharp contrast with the studies of Moravie and C o r ~ e t which ,~ suggest that the conformation in which C=O is cis to Ct+6-C1+7bonds of Figure 3 is energetically
Theoretical Results The dipole vector associated with each ester group of the repeat unit has a value of 1.89 D and its direction makes an angle of 1 2 3 O with the CH2-C* bond;15the H-0 and C-0 dipoles associated respectively with the ultimate and penultimate skeletal bonds of the terminal glycol residues lie along the bonds. Standard matrix multiplication methods were used to calculate the dipole moment and the temperature coefficient of both the dipole moment and the mean-square end-to-end The rotational angles of all the skeletal bonds were assumed to be located at 0,*120°, with the exception of the CH2-0 bonds of the glycol residue whose rotational angles were considered to be located at h75O and the CO-0 bonds which are restricted to trans states. An inspection of the structure of the chains suggests that their polarity should be very sensitive to the rotational states about bonds of type i + 2 and i + 3 in Figure 3. Whenever the trans states about CH2-0 bonds are strongly preferred, gauche rotations of the same sign about two consecutive CH2-C(CH3)2bonds of the glycol residue increase the opposition in the orientation of the dipole moment vectors associated with the two ester groups of the repeat unit with respect to the orientation of these dipoles in the tt conformation and consequentlythe dipole moment of the chains should decrease. In order to examine the effect of the relative orientation of the ester groups on the dipole moment ratio, the value of this quantity was calculated as a function of the conformational energy E,, associated with gauche states about C(CH3)2-CH2bonds. In the calculations the following set of conformational energies was used: E, = 0.5, E , = 0.0, E& = 1.0, and E, = 0.6, all in kcal mol-'. The theoretical dependence of the dipole moment ratio on E,, for two values of Eoa,the energy associated with gauche states about bonds of type i + 6 and i + 10, is shown in Figure 5. It can be seen that the dipole moment ratio is quite insensitive to E,=,but it is strongly dependent on Ed. Thus for E,- = 1.2 kcal mol-l, the value of ( p 2 ) / n m decreases 2 from 1.02 for E,, = 0.42 to 0.598 for Ed = -0.84 kcal mol-'. This quantity reduces from 1.05 to 0.580 in the same in-
Conformations of Aliphatic Polyesters 2571
Macromolecules, Vol. 19, No. 10, 1986 I
I
/* I-
Y
-0.5
0.5 E kcalmol-'
I
0
-1
E,
1 I
Figure 5. Calculated dependence of the dipole moment ratio and ita temperature coefficient on E,, for En*= 0.0 (-) and En*= 1.0
kcal/mol (---).
0.51
1.5
b Figure 7. Curves A, B, and C in the figure represent the calculated values of the temperature coefficient of the unperturbed ECD, dimensions as a function of the conformational energies ECm, and E,.
i
1
2 -0.5
Figure 6. Theoretical values of the temperature coefficient of the mean-square end-to-end distance as a function of Ed for Ena = 0.00 kcal mol-' (upper curve) and Eo== 1.0 kcal mol-' (lower
curve).
terval of Ed if E,. = 0. This analysis suggests that good agreement between the theoretical and experimental values of the dipole moment ratio can be obtained by assuming that the value of E , is ca. -0.6 kcal mol-'. In Figure 5 the temperature coefficient of the dipole moment ratio is also presented as a function of Ed for the two values of E, indicated above. It can be seen that the value of d In (pS)/dTshows a noticeable increase as E , decreases but it is only slightly dependent on E,-. Satisfactory agreement between the theoretical and experimental values of the temperature coefficient is also obtained for Ed = -0.6 kcal mol-'. In view of these results, the dependence of the configurational properties of the rest of the conformational energies was studied by using the following main set of conformational energies: Ed, = 1.0, Ed = -0.6, E , = E,, = 0.0, and E , = 0.6, all in kcal mol-'. Shown in pigure 6 are the theoretical results for the temperature coefficient of the mean-square end-to-end distance d In (r2),/dT, calculated as a function of E, for two values of E,. The upper and lower curves in the figure represent the values of a d In (r2),/dT for ECa= 1.2 and
0.00 kcal mol-l, respectively. Although in both cases the temperature coefficient increases as E , decreases, a significant difference can be detected in the two curves. Thus the sign of d In (r2),/dT is negative in the whole interval of the values of E , examined when EUa= 1.2 kcal mol-'; however, the temperature coefficient becomes positive for values of E , lower than -0.4 kcal mol-' if E , = 0.00 kcal mol-l. Therefore to obtain a fair agreement 'between the theoretical and experimental values of d In (?),/dT would require that the value of Eoa lie in the vicinity of zero. The temperature coefficient of the unperturbed dimensions is moderately dependent on Ed,for values of this quantity larger than 1.0 kcal mol-'; for example, lo4 (d In (r2),/dn = 2.8 and 2.1 K-l for Ed, = 1.8 and 1.0 kcal mol-', respectively. In the same way, the dipole moment ratio also shows a moderate dependence on Ed,owing to the fact that as the value of this energy rises, the fraction of ttg'g'tt conformations corresponding to the C*O*OCH2C(CH3)&Hz0 O* C* segment increases. Since in these conformations the opposition between the dipole vectors of the two consecutive ester groups is important, the dipole moment of the chains decreases. Thus, (p 2 )/nm2changes from 0.650 for E,, = 1.0 kcal mol-' to 0.575 for E,,/ = 1.8 kcal mol-l, whereas the change in the value of lo3 (d In (p2)/dT)is from 1.78 to 1.94 K-l. The temperature coefficient of the unperturbed dimensions not only is sensitive to E , and E , as was discussed above but also shows a moderate dependence on Epnand E,. The changes in the values of d In (r2),/dT with the values of EOa,E , , and E , are presented in Figure 7, where it can be seen tkat the sign of the property becomes positive as the values of EOaand E , approach zero. Very good agreement between the theoretical and experimental values of d In (r2),/dT are obtained by assuming that gauche states about bonds of type i + 6 and i + 7 are preferred over the alternative trans states. It should be pointed out that the dipole moment ratio and its temperature coefficient are only slightly sensitive to E,* and E, * $he value of d In (?),/dT is almost independent of E, for values of this quantity larger than 0.6 kcal mol-'; however, for E, < 0.6 kcal mol-', the temperature coefficient strongly increases as the value of E , decreases. As for the dipole moment ratio and its temperature coefficient, the values of these quantities respectively increase and decrease as E, decreases as a consequence of the fact that the fraction of ttg*g*tt conformations corresponding to the C*O* OCH2C(CH,),CH20 O* C* segment decreases.
Macromolecules 1986,19, 2572-2575
2572
Concluding Remarks The critical interpretation of the configuration-dependent properties of poly(oxyneopentyleneoxyadipoy1) suggests the following: 1. The dipole moment ratio of the chains is strongly dependent on the conformational energy Ed associated with gauche states about C(CH3)2-CH2 bonds of the glycol residue. In order to obtain agreement between theory and experiment an extra stabilization energy of about -0.40 kcal mol-' must be postulated for these states. 2. The temperature coefficient of the unperturbed dimensions shows a significant dependence on the conformational energy associated with gauche states about CH,-C* bonds. Good agreement between the theoretical and the experimental results is only obtained by assuming that the value of E, is zero or lower. Therefore, the results reported by Moravie and C ~ r s e twhich ,~ suggest that the C=O/C-C eclipsed form is more stable than the C= O/C-H eclipsed form, are not supported by the present study. Acknowledgment. This work was supported by the CAICYT through Grant No. 513/83. Registry No. PNA (SRU),28039-87-4; (neopentyl glycol). (adipic acid) (copolymer), 103439-11-8; 2,4-bis(p-isocyanatobenzy1)phenyl isocyanate, 4326-63-0.
References and Notes (1) Riande, E.; Guzmin, J.; de la Campa, J.; de Abajo, J. Macromolecules 1985, 18, 1583. (2) Dirlikov, S.; Stokr, J.; Schneider, B. Collect. Czech. Chem. Commun. 1971,36, 3028. (3) Moravie, R. M.; Corset, J. Chem. Phys. Lett. 1974,26, 210; J . Mol. Struct. 1975, 24, 91. (4) Bowles, A. J.; George, W. 0.; Cunliffe-Jones, D. B. Chem. Commun. 1970, 103. George, W. 0.; Hassid, D. V.; Madams,
W. F. J . Chem. SOC.,Perkin Trans. 1972,2, 1029. (5) Abe, A. J. Am. Chem SOC.1984, 106, 14. (6) CRC Handbook of Chemistry and Physics, 52nd ed.; CRC: Cleveland, 1971-1972. (7) Riddick, J. A.; Bunger, W. B. Organic Soluents. Physical Properties and Methods of Purification; 1970; Vol. 11. (8) Mark, J. E.; Flory, P. J. J. Appl. Phys. 1966, 37, 4635. (9) Mark, J. E.; Rahalkar, R. R.; Sullivan, J. L. J. Chem. Phys. 1979, 70, 1794. (10) Riande, E. J . Polym. Sci., Polym. Phys. Ed. 1976, 14, 2231. (11) Guggenheim, E. A. Trans. Faraday SOC.1949,45, 714; 1951, 47, 543. (12) Smith, J. W. Trans. Faraday SOC.1950, 46, 394. (13) Abe, A.; Mark, J. E. J . Am. Chem. SOC.1976, 98, 6468. (14) McClellan, A. L. Tables ofErperimenta1 Dipole Moments; W. H. Freeman: San Francisco, 1974; Vol. I. Zbid., Rahara Enterprises: El Cerrito, CA, 1974; Vol. 11. (15) Saiz, E.; Hummel, J. P.; Flory, P. J.; Plavsic, M. J. Phys. Chem. 1981,85, 3211. (16) Treloar, L. R. G. The Physics of Elasticity; Clarendon: Oxford, 1975. Mark, J. E. Rubber Chem. Technol. 1975,48,495. (17) Mark, J. E. Adu. Polym. Sci. 1982, 44, 1. (18) Flory, P. J.; Ciferri, A.; Hoeve, C. A. J. J. Polym. Sci. 1960,45, 235. (19) Flory, P. J.; Hoeve, C. A. J.; Ciferri, A. J. Polym. Sci. 1959,34, 337. (20) Mark, J. E. Rubber Chem. Technol. 1973,46, 593. (21) Yoon, D. Y.; Suter, U. W.; Sundararajan, P. R.; Flory, P. J. Macromolecules 1975, 8, 784. (22) Flory, P. J. Statistical Mechanics of Chain Molecules; WileyInterscience: New York, 1969. (23) Pitzer, K. Adu. Chem. Phys. 1959, 2, 49. (24) Abe, A,; Jernigan, R. L.; Flory, P. J. J. Am. Chem. SOC.1966, 88, 631. (25) Riande, E.; Guzmin, J.; Tarazona, M. P.; Saiz, E. J. Polym. Sci., Polym. Phys. Ed. 1984, 22, 2165. (26) . . Saiz. E.: Riande., E.:, Guzmin., J.:, de Abaio. " , J. J . Chem. Phvs. 1980, 73, 958. (27) Garrido. L.: Riande. E.: Guzmln. J. J . Polvmn. Sci.. Polvm. Phys. Ed. 1982,20, 3378. (28) Flow, P. J. Macromolecules 1974, 7, 381. (29) The-calculations were performed for a chain of 284 skeletal bonds with two hydroxyl terminal groups.
Conformation of Polybutadiene in the Network State by Small-Angle Neutron Scattering A. M. Fernandez, L. H. Sperling,*+and G. D. Wignallr Polymer Science and Engineering Program, Materials Research Center No. 32, Lehigh University, Bethlehem, Pennsylvania 18015. Received December 9, 1985
ABSTRACT: Deuterated polybutadiene (D6) was blended with protonated polybutadiene (He), cross-linked, and swollen in toluene. All three cases were studied by small-angle neutron scattering (SANS). The deuterated polybutadiene had M , = 37 300, with R, = 90 A. Cross-linking does not appreciably affect the molecular dimensions. The molecular deformation induced by swelling agrees with that predicted by the phantom network model but is much lower than that predicted by the affine deformation model. Introduction The reactive forces in elastomers arise through conformational changes of the chains themselves. To the surprise of the polymer community, several small-angle neutron scattering experiments showed that the radius of gyration of network chains increases much more slowly on stretching or swelling than the predictions of the affine model.l+ The most critical experiments were done by Beltzung et a1.,7,8who found that poly(dimethylsi1oxane) network chains swelled according to the predictions of the 'Department of Chemical Engineering, Lehigh University, Bethlehem, PA 18015. *National Center for Small Angle Scattering Research, Oak Ridge National Laboratory, Oak Ridge, TN 37830.
de Gennes C* theorem? with relatively modest changes in molecular dimensions. This paper will present a set of experiments on the molecular dimensions of polybutadiene (PB) in the linear, cross-linked, and swollen states. The networks were randomly cross-linked with peroxide so as to approximate those used in many studies as well as practical applications.
Theory The theory of small-angle neutron scattering has been described in numerous papers and two recent reviews,lOJ1 and details of the application to scattering from polymer solutions have been given by King et a1.12 In brief, the differential scattering cross section, dZ/dQ, per unit volume of sample in units of cm-' is related to the polymer-
0024-9297/86/2219-2572$01.50/00 1986 American Chemical Society
