Molecular closure to the PRISM equation derived from nonlinear response theory

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model (PRISM) equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein–Zernike (OZ) equation, and is similar in some aspects to the reference “molecular” MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, T_c, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. For an isotopic blend of polyethylene, the new closure predicts a T_c about 25% higher than the experimental value. A more recent improvement to this theory predicts a T_c that is 20% lower than experiment. More accurate experimental estimates of the polarizability of deuterated polyetheylene would help to narrow the uncertainty in these theoretical predictions. Nonetheless, the derivation and its consequences should help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.