Equations of state for hard-sphere chain fluids and square-well chain fluids

Based on the statistical theory for chemical association, equations of state for hard-sphere chain fluids (HSCFs) and square-well chain fluids (SWCFs) can be derived through the n-particle cavity correlation function (CCF) of the corresponding reference system, where n is the chain length or the number of segments of a chain molecule. The reference system is a fluid composed of only corresponding monomers. In this work, the n-particle CCF is approximated by a product of effective two-particle CCFs which accounts for correlations in nearest-neighbour and next-to-nearest-neighbour segment pairs. The CCFs for SWCFs may be expressed by a product of the corresponding function for HSCFs and a perturbation term originated from the square-well attractive potential. All these effective two-particle CCFs and perturbation terms are density dependent. The dependence is determined mainly by using computer-simulation results. The obtained equations can excellently describe compressibility factors and second Virial coefficients for HSCFs and SWCFs covering a wide range of chain length, better than other existing theories. The equations can be used as a basis for developing practical equations of state for polymer solutions and polymer blends.