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SUMMARY:The calculation of the stress tensor from molecular simulations of atomistic model polymer systems employing periodic boundary conditions is discussed. Starting from the dynamical equations governing the motion of sites, correct double summation forms of the atomic and the molecular virial equations are derived, which are valid for flexible, infinitely stiff and rigid chain models even in the presence of interactions between different images of the same parent macromolecule. A new expression for the true instantaneous stress (flux of momentum through the faces of the simulation box) is derived and shown to exhibit large fluctuations when applied in molecular dynamics simulations. A new equation for the thermodynamic stress, cast exclusively in terms of intermolecular forces on interaction sites, is also derived. Application to Monte Carlo simulations shows that the molecular virial expression exhibits the smallest fluctuations among all stress expressions discussed, and thus allows computation of the thermodynamic stress with least uncertainty. A scheme is developed for the calculation of surface tension from intermolecular forces only.

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Molecular mechanics minimizations were performed on alkyl-substituted biphenyls to explore the effect of the position and length of side chains on the planarity of the phenyl rings. This approach was extended to poly(p-2,5-di-n-alkylphenylene)s. The structural behavior was investigated by systematically modifying the length of the main chain and the side chains. Studies of substituted biphenyls showed that the methyl substituent at 2, 2‘, 6, and 6‘ positions much affected the torsion angle between the phenyls. The torsion angle decreased and converged to an asymptotic value of ∼70° from trans as the length of side chains was increased in 2,2‘,5,5‘-tetraalkylbiphenyls. The results of a single poly(p-2,5-di-n-alkylphenylene) chain clearly showed that the main chain and side chains cooperate on the molecular level to make a stable conformation. Poly(p-2,5-di-n-alkylphenylene)s with long side chains showed partial ordering of side chains with a plain plate structure, whereas those with short side chains did not show side-chain ordering and had cylindrical, or hairy-rod structure. The onset of side-chain ordering for this single-chain system was found to occur for a sexiphenylene unit with eight carbons in the side chains. The average torsion angles of poly(p-2,5-di-n-alkylphenylene)s decreased from 89° to 61° relative to trans as the length of side chains was increased from methyl to dodecyl.