Conformational characteristics of poly(ethylene sulfide) (PES), poly(ethylene oxide) (PEO), and their oligomeric model compounds have been investigated by the rotational isomeric state (RIS) analysis of ab initio molecular orbital (MO) calculations, NMR vicinal coupling constants, characteristic ratios, and dipole moment ratios. Conformational energies of PES were determined from 1 H and 13 C NMR vicinal constants of its monomeric model compound, 1,2-bis(methylthio)ethane (BMTE), and ab initio MO calculations for BMTE at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) and MP2/6-311+G-(3df,2p)//HF/6-31G(d) levels. By the NMR analysis, the firs-order interaction energies for the gauche states around the C-C and C-S bonds, designated as E σ and EF respectively, were evaluated as follows: in benzene, Eσ ) 0.41 kcal mol -1 and EF ) -0.74 kcal mol -1 ; in chloroform, Eσ ) 0.31 kcal mol -1 and EF ) -0.41 kcal mol -1 . The C-C and C-S bonds were shown to prefer the trans and gauche conformations, respectively. These tendencies are consistent with the MO calculations: B3LYP, Eσ ) 1.39 kcal mol -1 and EF ) -0.24 kcal mol -1 ; MP2, Eσ ) 0.89 kcal mol -1 and EF ) -0.41 kcal mol -1 . Inasmuch as the MO calculations represent gaseous BMTE, the conformational energies were indicated to have large solvent dependence. Ab initio MO calculations at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) and MP2/6-311+G-(3df,2p)//HF/6-31G(d) levels and by the complete basis set (CBS-Q) method were carried out for 1,2dimethoxyethane (DME), a model compound of PEO. All of the MO calculations showed the presence of the (C-H)‚‚‚O attraction in the g ( gconformations for the C-C/C-O bond pairs. The MP2 calculations gave the first-order interaction energies (Eσ and EF) for the gauche states around the C-C and C-O bonds as 0.32 and 1.22 kcal mol -1 , respectively. The conformational energy Eω representing the (C-H)‚‚‚O interaction was evaluated as -1.12 kcal mol -1 . In the RIS scheme, bond conformations of PEO in 1,4-dioxane and dipole moment ratios of PEO in benzene were simultaneously simulated, and the conformational energies of PEO in nonpolar organic solvents were determined: Eσ ) -0.25, EF ) 1.17, and Eω ) -0.79 kcal mol -1 . Ours and Abe and Mark's data [Eσ ) -0.5, EF ) 0.9, and Eω ) 0.4 kcal mol -1 ,

Conformational characteristics of poly(ethylene imine) (PEI) have been investigated by a rotational isomeric state (RIS) analysis of ab initio molecular orbital (MO) calculations and 1H and 13C NMR experiments for a monomeric model compound, N,N ‘-dimethylethylenediamine (di-MEDA). From the MO and NMR data, it was shown that the C−C and C−N bonds of di-MEDA have high gauche (71−93%) and trans (64−86%) preferences, respectively. Conformational energies of PEI were determined from the MO calculations for di-MEDA at the MP2/6-311++G(3df, 3pd)//HF/6-31G(d) level. The high gauche stability in the C−C bond was indicated to stem from a moderate and a weak intramolecular N−H···N hydrogen bonds; the interaction energies were evaluated as −1.54 and −0.58 kcal mol-1, respectively. The RIS scheme including rotational and inversional isomerizations was developed and applied to PEI to evaluate the chain dimension and diad probabilities. With the conformational energies determined as above, the characteristic ratio and meso-diad probability of PEI at 25 °C were calculated to be 2.9 and 0.63, respectively. In polar and protic solvents, the intramolecular hydrogen bonds are weakened, and consequently the PEI chain extends. Branching effects on the conformation were investigated from MO and NMR analysis for monomeric model compounds of branched PEI, N, N,N ‘-trimethylethylenediamine and N, N,N ‘ ,N ‘-tetramethylethylenediamine; the gauche preference in the C−C bonds, due to the hydrogen bonds, is reduced with increasing number of methyl groups. Ab initio MO calculations were carried out for the double-stranded helix found in anhydrous PEI crystal. The PEI chain was indicated to adopt the isotactic form exclusively. The natural bond orbital analysis showed that intermolecular N−H···N hydrogen bonds are formed between paired chains of the double helix. The enthalpy of association per repeating unit was estimated to be −3.6 kcal mol-1 at the MP2/6-311+G(2d,p)//HF/6-31G(d) level.

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Conformational analysis of poly(ethylene terephthalate) (PET) and poly(ethylene-2,6-naphthalate) (PEN) has been carried out by the refined rotational isomeric state (RIS) scheme coupled with ab initio molecular orbital (MO) calculations for a model compound, ethylene glycol dibenzoate (EGDB). 1H and 13C NMR experiments for unlabeled and 13C-labeled EGDBs yielded bond conformations of the central O−CH2−CH2−O bond sequence. The MO calculations satisfactorily reproduced not only the experimental bond conformations but also the dipole moment and molar Kerr constant observed from EGDB. The aromatic ring and ester group of EGDB render its intramolecular interactions more complicated than those of poly(ethylene oxide) with the same O−CH2−CH2−O bonds; CO···H−C and C−O···H−C close contacts and dipole−dipole interactions are simultaneously formed in EGDB. The characteristic ratio of PET, derived from the refined RIS calculations using the MO energies for EGDB, exactly agree with those determined from small angle neutron scattering experiments for the melt. Thermodynamic quantities on PET and PEN, evaluated from the RIS calculations, have well characterized melting and crystallization behaviors of these polyesters.

Conformational characteristics of poly(propylene sulfide) (PPS, [CH2C*H(CH3)S] x ) have been investigated. Proton and carbon-13 NMR vicinal coupling constants observed from its monomeric model compound, 1,2-bis(methylthio)propane (BMTP, CH3S−CH2−C*H(CH3)−SCH3), were analyzed to yield bond conformations of the S−C, C−C*, and C*−S bonds. Ab initio molecular orbital (MO) calculations at the MP2/6-311+G(3df,2p)//HF/6-31G(d) and B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) levels were carried out for BMTP to evaluate free energies and dipole moments of all the possible conformers. Conformational energies and bond dipole moments of BMTP were estimated therefrom. Conformational energies of BMTP and PPS were also determined by simulations based on the rotational isomeric state scheme for experimental observations of bond conformations of BMTP, characteristic ratio of atactic PPS, and dipole moment ratios of isotactic and atactic PPS. The first-order interaction energies for the S−C (E σ) and the C−C* (E α and E β) bonds were obtained as follows:  E σ = −1.0 to −0.60 kcal mol-1, E α = 0.5−0.6 kcal mol-1, and E β = 1.1−1.2 kcal mol-1. The second-order ω1 and ω2 interactions, representing intramolecular C−H···S interactions, are repulsive:  E ω 1 = 0.6−0.9 kcal mol-1 and E ω 2 = 1.0−1.2 kcal mol-1. The S−C, C−C*, and C*−S bonds were found to prefer the gauche, trans, and trans states, respectively. The conformational characteristics of unperturbed PPS are similar to those of poly(ethylene sulfide) but significantly different from those of its corresponding polyether, poly(propylene oxide) (PPO), although isotactic PPS and PPO are isomorphous. The conformational characteristics of PPS are discussed in terms of solvent effect, crystal structure, and thermal properties.

A theoretical methodology based on quantum chemistry to calculate mechanical properties of polymer crystals has been developed and applied to representative polymers. By density functional theory calculations including a dispersion force correction under three-dimensional periodic boundary conditions, crystal structures of poly(methylene oxide) (PMO), polyethylene (PE), poly(ethylene terephthalate) (PET), poly(trimethylene terephthalate) (PTT), and poly(butylene terephthalate) (PBT) were optimized and their mechanical properties, such as crystalline moduli and linear and volume compressibilities, were calculated. The optimized crystal structures were proved to be fully consistent with those determined by X-ray and neutron diffraction. The crystalline moduli ( E ∥ ) parallel to the chain axis were calculated to be 114 GPa (PMO), 333 GPa (PE), 182 GPa (PET), 7.1 GPa (PTT), and 20.8 GPa (PBT) and compared with those determined from X-ray diffraction, Raman spectroscopy, and neutron inelastic scattering experiments. Herein, the E ∥ values thus determined are interpreted in terms of conformational characteristics of the polymeric chains and the validity of the homogeneous stress hypothesis adopted in the X-ray diffraction method is also discussed.

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 mol À1 , whereas the central unit of triglyme has a slightly negative E value of ca. À0:1 kcal mol À1 . For the C-C bond conformations of triglyme, The attractive gauche effect has been found in X-C-C-X bond sequences, where X stands for electronegative atoms such as F, Cl, and O; 1,2 the central C-C bond has been considered to have the inherent gauche preference. In a previous paper, 3 we have proposed 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 segment 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)Á Á ÁO interaction. The E and E ! values, depending on the polarity of environment, shift in the opposite directions: E ¼ þ0:32 and E ! ¼ À1:12 kcal mol À1 for 1,2-dimethoxyethane (DME) in the gas phase; 3 E ¼ À0:25 and E ! ¼ À0:79 kcal mol

Conformational characteristics of poly(methylene sulfide) (PMS) and its oligomeric model compounds have been investigated. Carbon-13 NMR measurements for a dimeric model compound, bis(methylthio)methane, in the gas phase as well as in solutions were carried out, and the first-order interaction energy E σ representing the gauche stabilization of the C−S bond was determined from observed vicinal C−H coupling constants. For example, the E σ value for the gaseous dimer was evaluated as −1.43 ± 0.01 kcal mol-1, being in good agreement with the ab initio molecular orbital calculation (−1.38 kcal mol-1) at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d) level. The conformational energy E σ showed solvent dependence; polar solvents stabilize the trans conformation, in which dipole moments are parallel to each other and hence the molecule becomes polar. The characteristic ratio, dipole moment ratio, and configurational entropy of unperturbed PMS were estimated by the rotational isomeric state scheme and compared with those of poly(methylene oxide) (PMO). The PMS chain was indicated to be more flexible than PMO. The difference in melting point between PMS (245 °C) and PMO (180 °C) was suggested to come mainly from that in enthalpy (ΔH u) of fusion:  ΔH u(PMS) > ΔH u(PMO). The geometrical parameters, electron densities, and atomic charges of trimers of PMS and PMO, obtained from the MO calculations, showed that the gauche stability in the C−S bond of the PMS homologues comes partly from antiparallel dipole−dipole interaction and nS → hyperconjugation formed in the gauche state, partly from steric S···S repulsion occurring in the trans form. It was also shown that sulfur electrons have such flexibility as to reduce the S···S repulsion and unfavorable (parallel) dipole−dipole interaction.