Analytical evaluation of third and fourth virial coefficients for hard disk fluids in narrow channels and equation of state

Abstract

The third and fourth virial coefficients of hard disks in narrow channels have been evaluated as a series in powers of the channel width deviations from the one dimensional limit. We have obtained analytically the coefficients of the power series to very high order. These virial coefficients are used in truncated virial series to provide approximate analytical equation of state (EOS). The EOS is shown to accurately describe Monte Carlo simulations over a wide range of pressures and densities near the one dimensional limit. Explicit expressions for the free energy, chemical potential, compressibility and EOS as a function of the channel widths are given. These results represent progress toward understanding the long standing problem of the thermodynamic crossover from a one dimensional to quasi one dimensional fluid. They are also useful in a number of applications. We mention the examples of thermodynamic perturbation theory and stochastic dynamic mobility in anomalous single-file diffusion.