A new equation of state for athermal chains

Abstract

A new equation of state for fluids containing athermal chain molecules is developed and compared to simulation results and existing theories in three, two, and one dimensions. The new expression, which builds upon the generalized Flory theory, contains no adjustable parameters and relates the compressibility factor of an n-mer fluid to the compressibility factors of monomer and dimer fluids at the same volume fraction. Comparisons with Monte Carlo results for three- and two-dimensional freely jointed chains show very good agreement, and the overall accuracy of the new expression appears comparable to Wertheim’s thermodynamic perturbation theory of polymerization. In one dimension the new expression reduces to the exact result. Application of the equation to chain models with internal constraints and overlapping hard sites is discussed and illustrated through comparisons with Monte Carlo results for rigid trimers. An extension of our approach to arbitrary reference fluids shows that the generalized Flory and new equations are the first two members of a family of increasingly accurate equations of state for chains.