On the pressure equation for chain molecules

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Abstract
The pressure equation is derived for fluids containing chain molecules interacting with site–site potentials. Three models are considered: a flexible chain with harmonic potentials for bond-length and bond-angle variations, a flexible chain in the limit as the force constants for the vibrations become infinite, and a chain where bond angles and lengths are rigidly constrained to their equilibrium values. In the flexible model, the pressure is found to depend on only site–site correlations and contains both inter- and intramolecular contributions. Forces arising from angular potentials, however, do not appear in the equation. In the limit as the force constants for internal vibration become infinite, the intermolecular contribution to the pressure remains a function of pair correlations, but the intramolecular term becomes a function of chain orientation and depends on three-site correlations. The result is consistent with an expression used previously for dimers and trimers, but disagrees with a site–site equation previously used to study longer chains. The equation of state for the rigidly constrained model takes the same functional form as the equation for the infinitely stiff model. However, the two-molecule correlation function appearing in the rigid equation differs from its stiff counterpart as a result of the imposed constraints.