Free Energy and the Equation of State of a System of Solid Spheres in Narrow Cylindrical Pores

Abstract

In this work, the free energy and the equation of state of a system of solid spheres in narrow cylindrical pores are determined using the combined method of accelerated convergence of series. This method includes the Euler method and a method based on taking the behavior of the system into account at high densities near the dense packing and on the idea of the effective number of the nearest neighbors. The results are compared with the data of a computer experiment for three different values of pore size and in all cases good agreement between theory and experiment was obtained. These are much better than the results of virial expansion, and when the transverse pore sizes increase, better than the results found on the basis of a series in powers of pressure as well. The method makes it possible to estimate the limits of applicability of the method of convergence acceleration, based on the transition from a series in density to a series in terms of pressure. To do this, the density with close packing and the maximum allowable density found by the method of Euler are compared. If these densities are close, then only the Euler method can be used. In the case of a significant difference, a combined method of accelerated convergence is required.