The Attractive Gauche Effect of Ethylene Oxides

Polymer Journal, Vol. 38, No. 9, pp. 983–988 (2006) #2006 The Society of Polymer Science, Japan The Attractive Gauche Effect of Ethylene Oxides

y Yuji SASANUMA and Kentaro SUGITA

Department of Applied Chemistry and Biotechnology, Faculty of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

(Received May 1, 2006; Accepted July 4, 2006; Published August 18, 2006)

ABSTRACT: Conformational energies of monomeric (1,2-dimethoxyethane, DME) and trimeric (triglyme) model compounds of poly(ethylene oxide) have been evaluated by accurate ab initio molecular orbital (MO) calculations at

the MP2/6-311++G(3df, 3pd)//HF/6-31G(d) level. The first-order interaction energies (E’s) for gauche states around the C–C bonds of DME and the terminal repeating unit of triglyme are ca. þ0:1 kcal molÀ1, whereas the central À1 unit of triglyme has a slightly negative E value of ca. À0:1 kcal mol . For the C–C bond conformations of triglyme, the MO calculations exactly agree with NMR observations using a nonpolar solvent of cyclohexane-d12. The attractive gauche effect of the ethylene oxides has been shown to exist independently of intramolecular (C–H)ÁÁÁO hydrogen bonds. [doi:10.1295/polymj.PJ2006018] KEY WORDS Poly(ethylene oxide) / Conformation / Ab Initio Molecular Orbital Calculation / NMR / Attractive Gauche Effect / Weak Hydrogen Bond /

The attractive gauche eﬀect has been found in X– opposite directions: E ¼þ0:32 and E! ¼À1:12 C–C–X bond sequences, where X stands for electro- kcal molÀ1 for 1,2-dimethoxyethane (DME) in the 1,2 3 À1 negative atoms such as F, Cl, and O; the central gas phase; E ¼À0:25 and E! ¼À0:79 kcal mol C–C bond has been considered to have the inherent for poly(ethylene oxide) (PEO) in weakly polar sol- 3 3 gauche preference. In a previous paper, we have pro- vents such as 1,4-dioxane and benzene; E ¼À0:5 posed a concept of the competitive balance between intramolecular and intermolecular attractions of ethylene oxides. The isolated (i.e., gaseous) ethylene-oxide chains form the intramolecular hydrogen bonds, which cause an apparent gauche stability of the C–C bond. In polar solvents, however, the O–C–C–O seg- ment tends to prefer the tgt conformation because of attractive interactions with solvents (for the bond sequence, see Figure 1). These phenomena may be observed as variations in two conformational energies: E and E! (for the interactions, see Figure 2). The former energy corresponds to the energy diﬀerence between trans and gauche states, and the latter represents the (C–H)ÁÁÁO interaction. The E and E! values, de- pending on the polarity of environment, shift in the

Figure 2. Intramolecular interactions deﬁned for the ethylene oxides: (a) and (b) : the ﬁrst-order interactions around the C–C and C–O bonds, respectively; (c) !: the second-order interaction occurring in gÆgÇ conformations for the C–O/C–C bond pair; Figure 1. (a) Monomeric (1,2-dimethoxyethane: DME) and (d) : the third-order interaction formed in gÆgÆgÆ conformations (b) trimeric (triglyme) model compounds of poly(ethylene oxide) of the O–C–C–O bond sequence. The ! and interactions repre- (PEO). As indicated, the skeletal bonds are numbered. sent intramolecular hydrogen bonds. The model here is DME. yTo whom correspondence should be addressed (Tel: +81-43-290-3394, Fax: +81-43-290-3394, E-mail: [email protected]).

983 Y. SASANUMA and K. SUGITA

À1 17 and E! ¼þ0:4 kcal mol for PEO in the Â solutions, 0.9135. With the optimized geometry, the self- 4–6 e.g., 0.45 M K2SO4 at 34.5 C. In a good solvent, consistent field (SCF) energy was computed at the water, PEO shows a very small E value of À1:2 MP2/6-311++G(3df, 3pd) level. All the SCF calcu- kcal molÀ1.7 The interdependence of the two confor- lations were performed under the tight convergence. mational energies has so far been pointed out.8–10 The Gibbs free energy was calculated from the SCF The natural bond orbital (NBO) analysis11 on DME and thermal-correction energies, being given here as indicated that the attractive gauche effect comes main- the difference from that of the all-trans conformer Ã ly from C–H bond ! C–O antibond (C{H ! C{O) and denoted as ÁGk (k: conformer number). delocalizations,3 suggesting that the tgt state is more stable than ttt. Here, the designation tgt indicates that NMR Measurements of Triglyme bonds 2, 3, and 4 take t, g, and t states, respectively Commercially available triglyme was used without (see Figure 1a). To our knowledge, however, all ab further purification. Cyclohexane-d12, chloroform-d, initio molecular orbital (MO) calculations performed methanol-d4, dimethyl sulfoxide-d6, and deuterium so far for DME have suggested that the ttt conforma- oxide were used as the solvents, and the solute con- tion is more stable than tgt. In the crystalline state, centration was ca. 5 vol %. The proton NMR spectra PEO is allowed to adopt either tgt or ttt state in the were measured at 500 MHz on a JEOL JNM-LA500 O–C–C–O bonds. The former and latter conforma- spectrometer equipped with a variable temperature tions form a distorted (7/2) helix12,13 and a planar controller in the Chemical Analysis Center of Chiba zigzag structure,14 respectively. It is expected that University. During the measurement the probe tem- PEO prefers the tgt state to ttt, because the ttt confor- perature was maintained within Æ0:1 C fluctuations. mation is formed only in stretched samples.14,15 The The =2 pulse width, data acquisition time, and recy- four (7/2) helical chains form a P21=a monoclinic cle delay were 5.6 ms, 13.1 s, and 3.7 s, respectively. cell,13 in which we can not find any clue to the specific Before the Fourier transform, zero filling was per- interactions such as OÁÁÁH close contacts to stabilize formed so that the digital resolution would be close the tgt conformation. to 0.01 Hz. In the previous study,3 we calculated conformer free energies of monomer (DME) and trimer (tri- RESULTS AND DISCUSSION glyme) of PEO at the B3LYP/6-311+G(3df, 2p)// B3LYP/6-31G(d) level. The gauche energy of the cen- MO Calculations tral C–C bond seems to depend on the chain length: Statistical weight matrices Ui (i: bond number) of DME, 0.76 kcal molÀ1; triglyme, 0.15 kcal molÀ1.It DME and triglyme are given by is known that more expensive MO calculations based 2 3 1 2 2 on the MP2 theory yield more reliable energy data 6 7 than the B3LYP computations. Therefore, accurate U2 ¼ 4 00 05 ð1Þ MO calculations at the MP2/6-311++G(3df, 3pd)// 00 0 HF/6-31G(d) level have been carried out here for tri- 2 3 glyme as well as DME. In addition, we have analyzed 1 3 3 00 0 0 0 0 1H NMR spectra observed from triglyme to evaluate 6 7 U ¼ 4 00 01 ! 00 05 the bond conformations and compare the MO calcula- 3 3 3 3 00 000 0 1 ! tions. If gaseous triglyme has E values significantly 3 3 3 smaller than hydrocarbon chains such as n-alkanes ð2Þ and polyethylene, the attractive gauche effect would be proved to exist independently of the (C–H)ÁÁÁO U4 ¼ U7 ¼ U10 ¼ hydrogen bonds as predicted by the NBO analysis. 2 3 1 i i 00 000 0 6 7 6 00 01 ! 00 07 COMPUTATIONS AND EXPERIMENTS 6 i i i 7 6 7 6 00 00 0 0 1i!i i 7 6 7 Ab Initio MO Calculations 6 1 00 000 07 6 i i 7 Ab initio MO calculations were carried out for 6 7 16 6 00 01i i i!i 00 07 ð3Þ DME and triglyme with the Gaussian03 program in- 6 7 6 7 stalled on an HPC Silent-SCC T2 computer. For each 6 00 00 0 0 1 0 i 7 6 7 conformer, the geometrical parameters were fully op- 6 1 i i 00 000 07 timized at the HF/6-31G(d) level, and the thermal 6 7 4 00 01 000 05 correction to the Gibbs free energy (at 25 C and i 1 atm) was calculated with a calibration factor of 00 00 0 0 1i!i i i

984 Polym. J., Vol. 38, No. 9, 2006 The Attractive Gauche Eﬀect of Ethylene Oxides

Table II. SCF (ÁSCF) and free (ÁG ) energies U ¼ U ¼ k 52 8 3 of conformers of triglymea 1 00000 0 i i statistical ÁSCFc ÁG c 6 7 k gauche bond(s) k 6 00 01 !0 00 07 weightb (kcal molÀ1) (kcal molÀ1) 6 i i i 7 6 0 7 1 none (all-trans) 1 0.00 0.00 6 00 000 0 1i!i i 7 6 7 22 2 1.45 1.25 6 1 i i 00000 07 6 7 33 3 0.03 0.06 6 0 7 6 00 01i i! 00 07 ð4Þ 44 4 1.27 1.09 6 i 7 6 7 55 5 1.23 1.05 6 00 000 0 1 0 i 7 6 7 66 6 À0:13 À0:08 1 00000 0 Æ Ç 6 i i 7 72(g)3(g ) 23!3 0.28 0.15 6 7 Æ Ç 4 00 01i 000 05 83(g)4(g ) 34!4 0.19 À0:03 Æ Ç 0 95(g)6(g ) 56!6 0.04 À0:18 00 000 0 1i!i i Æ Æ Æ 10 2 (g )3(g )4(g ) 234 4 1.42 1.95 Æ Æ Æ 2 and 11 5 (g )6(g )7(g ) 56 7 1.12 1.64 aRelative to the all-trans conformation. At 25 C and 1 atm. U6 ¼ U9 ¼ 2 3 bFor the statistical weights, see eqs 1–5 and Figure 2. cAt the 1 i i 00000 0 MP2/6-311++G(3df, 3pd)//HF/6-31G(d) level. 6 7 6 00 01 ! 00 07 6 i i i 7 6 7 2 6 00 000 0 1i!i i 7 of 23 4. Thus, the ÁGk value may correspond to 6 7 6 7 2E2 þ E3 þ E 4 . The statistical weight is related to 6 1 i i 00000 07 6 7 the corresponding conformational energy through the 6 00 01i i!i 00 07 ð5Þ 6 7 Boltzmann factor; for example, ¼ expðÀE=RTÞ, 6 7 6 00 000 0 1 0 i 7 where R is the gas constant, and T is the absolute tem- 6 7 6 1 i i 00000 07 perature. The E values were determined by minimiz- 6 7 4 5 ing the following function: 00 01i 000 0 ! X X 2 00 000 0 1i!i i 1 SðEÞ¼ LðÞE À ÁG K k Here, the conformational energies, Ei ,(i ¼ i, i, !i, k and ), have been deﬁned for each bond to examine i Â M expðÀÁG =RTÞð6Þ their position dependence. The intramolecular interac- k k tions are illustrated in Figure 2. Tables I and II show The function LðÞ gives the number of conforma- the SCF and Gibbs free energies of the individual con- tional energy E included in the conformation, K is formers of DME and triglyme, respectively. In the the total number of conformers, and Mk is the number 5,18 rotational isomeric state (RIS) scheme, the ÁGk of equivalent conformers. The squared diﬀerence be- values of DME are represented as a function of Ei ’s. tween ÁGk and the sum of E’s was multiplied by þ þ þ For example, the g g g conformation has a weight the Boltzmann factor expðÀÁGk=RTÞ so as to weight low-energy conformations. The temperature was set to 298.15 K. The E values were determined as shown in Table I. SCF (ÁSCF) and free (ÁG ) energies k Table III. The positive E value of DME indicates a 3 of conformers of DME that the ttt state is slightly more stable than tgt. For tri- statistical ÁSCFc ÁG c k conformation M k k weightb (kcal molÀ1) (kcal molÀ1) Table III. Conformational energies of DME and triglymea 1 ttt 1 1 0.00 0.00 Æ 2 ttg 4 2 1.49 1.31 DME triglyme Æ 3tgt23 0.20 0.19 E2 1.30 1.25 Æ Æ 4tgg 4 23 1.61 1.28 E4 1.09 Æ Ç 5tgg 4 23!3 0.38 0.26 E5 1.05 Æ Æ 2 6gtg 2 2 3.05 2.74 E3 0.08 0.06 Æ Ç 2 7gtg 2 2 3.00 2.61 E6 À0:08 Æ Æ Æ 2 8gg g 2 23 4 1.73 2.27 E!3 À1:02 À1:15 Æ Æ Ç 2 9gg g 4 23!3 1.97 1.88 E!4 À1:18 Æ Ç Æ 2 2 10 g g g 2 23!3 2.32 1.77 E!6 À1:14 E À0:42 À0:44 aRelative to the all-trans conformation. At 25 C and 1 atm. 4 E À0:37 bFor the statistical weights, see eqs 1–5 and Figure 2. cAt the 7 MP2/6-311++G(3df, 3pd)//HF/6-31G(d) level. aIn kcal molÀ1.

Polym. J., Vol. 38, No. 9, 2006 985 Y. SASANUMA and K. SUGITA

CH3 -

(a) (b) (c)

a 5 Hz 4 Hz 4 Hz b

1 Figure 3. Observed (above) and calculated (below) H NMR spectra of triglyme dissolved in cyclohexane-d12 at 25 C: (a) methylene group a (satellite peaks); (b) methylene groups a and b; (c) methylene group c. For the designation of protons, see Figure 1. glyme, the MO calculations were so time-consuming lations using the gNMR program19 yielded vicinal 3 3 3 3 0 as to be performed only for specific conformers. From coupling constants, JHH (¼ JAB ¼ JA0B0 ) and JHH 3 0 3 0 the ÁGk values, the Ei values were derived for the (¼ JAB ¼ JA B), as listed in Table IV. The observed individual bonds as listed in Table III. coupling constants can be expressed as The results can be summarized as follows. (1) A 3J0 þ3 J00 À1 3 3 T G narrow range (À1:02 to À1:18 kcal mol )ofE ’s JHH ¼ JG pt þ pg ð7Þ ! 2 were obtained for the two model compounds, the and strength of the intramolecular hydrogen bond may 3J0 ¼ 3J p þ 3J0 p ð8Þ scarcely depend on the chain length and position. HH T t G g 3 3 (2) The E3 and E6 values are slightly positive and where JT’s and JG’s are defined in Figure 4, and negative, respectively; the terminal monomeric unit pt and pg are trans and gauche fractions of the C–C has an E value larger than the inner one. This sug- bond, respectively; therefore, pt þ pg ¼ 1. Here, we 3 3 gests the possibility that PEO can adopt the gauche have adopted J values optimized for DME: JT ¼ 3 0 3 3 0 3 00 7 conformation in the C–C bond without the aid of the JT ¼ 11:4 Hz and JG ¼ JG ¼ JG ¼ 2:3 Hz. The intramolecular hydrogen bonds; therefore, as a single sum of pt and pg values derived from eqs 7 and 8 chain, PEO somewhat prefers the helical structure to was only slightly different from unity, thus being div- the all-trans planar zigzag form. The all-trans PEO ided by the sum. In Table IV, the pt and pg values of chains, whose zigzag planes are parallel to each other, bonds 3 and 6 are compared with those evaluated from 14 are packed in a P1 triclinic lattice. Densities of the the MO calculations. In general, the trans fraction monoclinic (helix) and triclinic (zigzag) lattices are decreases with increasing permittivity of the environ- 1.228 and 1.197 g cmÀ3, respectively; therefore, the ment. This tendency agrees with that found previously helical chains are more densely packed than the planar for DME.7 zigzag ones. The small magnitude of E6 suggests that As outlined in the Introduction, Ei ’s and E!i ’s tend PEO may change the C–C conformation between gau- to vary cooperatively with the medium. Increases in che and trans even in the crystal. E!i ’s with increaseing permittivity of the medium

are compensated by decreases in Ei ’s. Consequently, 1H NMR of Triglyme the bond conformations do not show large variations, 1 Figure 3 shows an example of H NMR spectra and hence the three kinds of energy parameters, Ei ’s, observed from methylene protons of triglyme. Simu- E!i ’s, and Ei ’s, can not be determined only from pt

986 Polym. J., Vol. 38, No. 9, 2006 The Attractive Gauche Eﬀect of Ethylene Oxides

Table IV. Vicinal 1H–1H coupling constants and bond conformations of triglyme at 25 C bond 3 bond 6 3 3 0 3 3 0 solvent permittivity JHH JHH pt pg JHH JHH pt pg MO calca (gas) 1.0 0.21 0.79 0.17 0.83

NMR exptl

cyclohexane-d12 2.0 6.01 4.30 0.21 0.79 6.10 4.03 0.18 0.82 chloroform-d 4.8 6.25 3.30 0.11 0.89 6.30 3.43 0.12 0.88

methanol-d4 32.7 6.27 3.31 0.11 0.89 6.21 3.27 0.11 0.89 dimethyl sulfoxide-d6 46.7 6.30 3.48 0.13 0.87 6.24 3.44 0.13 0.87 deuterium oxide 78.5 6.42 2.66 0.05 0.95 6.36 2.62 0.05 0.95 aEvaluated from the conformational energies shown in Table III.

Figure 4. Conformations around the C–C bond of the ethylene oxides with deﬁnitions of vicinal coupling constants. values of bonds 3 and 6; therefore, we have assumed

E!i and Ei values as follows to derive E3 and E6 of Figure 5. Trans fraction (pt) of bond 6 of triglyme as a func- triglyme. tion of E6 . The horizontal lines represent the pt values deter- The boiling point of triglyme is so high (216 C) mined from the NMR experiments using the solvents indicated. that NMR measurement for gaseous triglyme could Curves A, B, and C were obtained from the following energy not be conducted. In the previous study on DME,20 parameters: curve A, conformational energies of triglyme in 3 3 0 Table III, except for E ; curve B, E ’s = 1.17 and E! ’s = the JHH and JHH versus temperature plots for the 6 i i À0:79 kcal molÀ1; curve C, E ’s = 0.9 and E ’s = 0.4 gas phase and the cyclohexane solution overlap with i !i kcal molÀ1. For curves B and C, E ¼ E was assumed. each other, and no discontinuity was found between 3 6 the two kinds of data. In fact, as seen from Table IV, À1 the pt and pg values for the cyclohexane solution at Ei ’s = 0.9 and E!i ’s = 0.4 kcal mol (the Â solu- 25 C agree with those of the MO calculations for gas- tion of PEO, i.e., 0.45 M K2SO4 at 34.5 C). The hor- eous triglyme at 25 C. In Figure 5, the pt values, cal- izontal lines for chloroform, dimethyl sulfoxide, and culated from Ei ’s (Table III) of triglyme except for methanol intersect with curves B and C around E6 ¼ À1 E6 , are plotted as a function of E6 (curve A). The À0:5 and À0:8 to À0:9 kcal mol , respectively. curve intersects with the horizontal line for the cyclo- Therefore, the E6 values of triglyme in these solvents À1 hexane solution around E6 ¼À0:1 kcal mol . This probably stay within the range. From the intersection value probably corresponds to E6 of not only the cy- between curve C and the horizontal line of water, we clohexane solution but also the gas phase. From bond can estimate the E6 value of triglyme in water as conformations of PEO dissolved in 1,4-dioxane and À1:6 kcal molÀ1. dipole moment ratios for the benzene solution, we From the pt versus E3 plots (not shown), we simi- À1 3 determined E ¼ 1:17 and E! ¼À0:79 kcal mol . larly estimated the E3 values of bond 3 of triglyme These energy parameters are considered to represent in the solvents: cyclohexane, þ0:1 kcal molÀ1; chloro- the ethylene oxides in weakly polar solvents. From form, methanol, and dimethyl sulfoxide, À0:5 to À1 À1 À1 Ei ’s = 1.17, E!i ’s = À0:79 kcal mol , and E3 ¼ À0:9 kcal mol ; water, À1:4 kcal mol . Both MO

E6 , the pt values were calculated and plotted against calculations and NMR experiments indicate that E6

E6 (curve B). Similarly, curve C was obtained from of triglyme is negative even in the gas phase. How-

Polym. J., Vol. 38, No. 9, 2006 987 Y. SASANUMA and K. SUGITA

12. H. Tadokoro, Y. Chatani, T. Yoshihara, S. Tahara, and S. ever, the essential fact here is that E6 is significantly À1 smaller than E (þ0:5 kcal mol ) of hydrocarbon Murahashi, Makromol. Chem., 73, 109 (1964). chains5,21 because this indicates the inherent gauche 13. Y. Takahashi and H. Tadokoro, Macromolecules, 6, 672 stability of the C–C bond adjacent to the ether linkage, (1973). i.e., the attractive gauche effect independent of the 14. Y. Takahashi, I. Sumita, and H. Tadokoro, J. Polym. Sci., Polym. Phys. Ed. 11 (C–H)ÁÁÁO attraction. , , 2113 (1973). 15. K. Tashiro and H. Tadokoro, Rep. Prog. Polym. Phys. Jpn., Finally, the small differences in E ’s between DME 21, 417 (1978). and triglyme (Table III) fairly justify conformational 16. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, analyses of polymers using monomeric model com- M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., pounds, unless very strict discussion is required. T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Acknowledgment. This work was partly supported Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, by the Asahi Glass Foundation and a Grant-in-Aid for M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Scientific Research (B) (18350112) from the Japan Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, Society for the Promotion of Science. J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. REFERENCES Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, 1. E. Juaristi, ‘‘Introduction to Stereochemistry and Conforma- A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. tional Analysis,’’ Wiley & Sons, New York, 1991, chap. 18. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, 2. E. Juaristi and G. Cuevas, ‘‘The Anomeric Effect,’’ CRC Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Press, Boca Raton, FL, 1995, chap. 4. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, 3. Y. Sasanuma, H. Ohta, I. Touma, H. Matoba, Y. Hayashi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. and A. Kaito, Macromolecules, 35, 3748 (2002). Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, 4. J. E. Mark and P. J. Flory, J. Am. Chem. Soc., 87, 1415 B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and (1965). J. A. Pople, Gaussian 03, Revision C.02, Gaussian, Inc., 5. P. J. Flory, ‘‘Statistical Mechanics of Chain Molecules,’’ Wallingford CT, 2004. Wiley & Sons, New York, 1969. 17. J. A. Pople, A. P. Scott, M. W. Wong, and L. Radom, Isr. J. 6. A. Abe and J. E. Mark, J. Am. Chem. Soc., 98, 6468 (1976). Chem., 33, 345 (1993). 7. K. Tasaki and A. Abe, Polym. J., 17, 641 (1985). 18. W. L. Mattice and U. W. Suter, ‘‘Conformational Theory of 8. D. T. Baldwin, W. L. Mattice, and R. D. Gandour, J. Large Molecules: The Rotational Isomeric State Model in Comput. Chem., 5, 241 (1984). Macromolecular Systems,’’ Wiley & Sons, New York, 1994. 9. A. Abe, H. Furuya, M. K. Mitra, and T. Hiejima, Comput. 19. P. H. M. Budzelaar, ‘‘gNMR, version 5.0,’’ IvorySoft & Theor. Polym. Sci., 8, 253 (1998). Adept Scientific plc, Letchworth, U.K., 2004. 10. G. D. Smith, D. Bedrov, and O. Borodin, J. Am. Chem. Soc., 20. K. Inomata and A. Abe, J. Phys. Chem., 96, 7934 (1992). 122, 9548 (2000). 21. A. Abe, R. L. Jernigan, and P. J. Flory, J. Am. Chem. Soc., 11. A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 88, 631 (1966). 899 (1988).

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