Linear dependence on chain length for the thermodynamic properties of tangent hard-sphere chains

Abstract

Equilibrium molecular dynamics simulation techniques are used to obtain accurate compressibility factors (⩽0·1% error) for tangent hard-sphere (THS) chains of lengths 2–8, 16, 32, 64, 96, and 192. Our simulation results show that, within simulation statistical errors, the dependence of compressibility factors on chain length approaches linearity very rapidly. At volume fractions of 0·4 or above the linearity starts at a chain length of 3, while at volume fractions of 0·1 or above the linearity starts at a chain length of 6. The thermodynamic perturbation theory (TPT) and the generalized Flory (GF) theory equations of state are extended to become a linear combination of the compressibility factors of any two reference THS chain fluids. It is found that extended GF theory is identical to extended TPT when the excluded volumes of chains and reference chains are assumed to be linearly dependent on the chain length. Our simulation data implies that a near exact THS chain equation of state can be obtained from a linear combination of the equations of state for two reference short-chain fluids. As an example, a new equation of state for THS chain fluids is obtained from a linear combination of 4-mer and 8-mer equations of state. The new equation of state reproduces remarkably well the simulation data on 192-mers at η > 0·2 with errors less than 0·1%. At low volume fractions of 0·1–0·2 the relative errors are only 0·5–3%.