Negative Thermal Expansion of the One-Dimensional Lattice Gas with Next-Nearest-Neighbor Interaction

Abstract

A one-dimensional lattice gas model with the nearest-neighbor and the next-nearest-neighbor interaction is exactly solved. If the nearest-neighbor interaction(£) is repulsive or attractive with the repulsive next-nearest-neighbor interaction (TJ>-c/2), the coefficient of thermal expansion has negative regions. Recently the negative thermal expansion of one-dimensional fluids has been studied by several authors. 1 H> In a preceding paper 1 > a one-dimensional lattice gas model with the hard-core nearest-neighbor and the next-nearest-neighbor interaction was exactly solved. In the case of the repulsive next-nearest-neighbor interaction, the coefficient of thermal expansion has a negative region, and hence there is an intersection of isotherms and a maximum number density as a function of tempera­ ture in the constant pressure process. In the present paper, the one-dimensional lattice gas with the nearest-neighbor interaction and the next-nearest-neighbor interaction is solved exactly. We investi­ gate the properties of the coefficient of thermal expansion. If the interactions are repulsive, there are three regions in which the coefficient of thermal expansion is negative. We consider a lattice gas on a one-dimensional lattice ofM lattice sites. We assume that the interaction energies between nearest- and next-nearest-neighbor particles in the gas are given by c and 7}, respectively. By using the transfer matrix method, 4 J,s> it wa:s shown 1 > that the eigenvalues of the transfer matrix are determined