LINEAR-DEPENDENCE ON CHAIN-LENGTH FOR THE THERMODYNAMIC PROPERTIES OFTANGENT HARD-SPHERE CHAINS

Equilibrium molecular dynamics simulation techniques are used to obtai n accurate compressibility factors (less than or equal to 0.1% error) for tangent hard-sphere (THS) chains of lengths 2-8, 16, 32, 64, 96, a nd 192. Our simulation results show that, within simulation statistica l errors, the dependence of compressibility factors on chain length ap proaches linearity very rapidly. At volume fractions of 0.4 or above t he linearity starts at a chain length of 3, while al volume fractions of 0.1 or above the linearity starts at a chain length of 6. The therm odynamic perturbation theory (TPT) and the generalized Flory (GF) theo ry equations of state are extended to become a linear combination of t he compressibility factors of any two reference THS chain fluids. It i s found that extended GF theory is identical to extended TPT when the excluded volumes of chains and reference chains are assumed to be line arly 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 fl uids. As an example, a new equation of state for THS chain fluids is o btained from a linear combination of 4-mer and 8-mer equations of stat e. The new equation of state reproduces remarkably well the simulation data on 192-mers at eta > 0.2 with errors less than 0.1%. At low volu me fractions of 0.1-0.2 the relative errors are only 0.5-3%.