Microscopic equations of state of polyethylene: Hard-chain contribution to the pressure

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Abstract
The athermal contribution to the pressure of polyethylene is investigated via integral equations and mean field generalized Flory-type theories. The molecules are modeled as fused-hard-sphere chains with fixed bond lengths and bond angles; torsional rotations are treated via the rotational isomeric state approximation with literature values for the trans–gauche energies. The hard sphere diameter is obtained by matching structure factor predictions of the polymer reference interaction site model (PRISM) theory for hard chains to data from wide-angle scattering experiments. In all, five hard chain equations of state are investigated: three via different thermodynamic routes in the PRISM theory, and two via different extensions (to fused-sphere chains) of the generalized Flory-dimer (GFD) theory. The integral equation approaches consist of a free energy ‘‘charging’’ route, the compressibility route, and the ‘‘wall’’ route (where the pressure is obtained from the density profile of the fluid at a hard wall). The two GFD approaches correspond to different choices for the reference monomer and dimer fluids required in the theory. Each of the five equations of state results in significantly different predictions for the pressure. The predictions of the various equations relative to each other are nearly independent of chain length, and this allows us to draw conclusions for polymeric fluids (where simulation results are not available) by testing the performance of the equations for diatomics (where simulation results are available). We thus speculate that the charging route overestimates the pressure, the compressibility route underestimates the pressure, and the GFD and wall equations of state are the most accurate.