A “gel” model for coal

Abstract

Coal is a sedimentary, organic “rock” which is almost never in a state of thermal equilibrium. Because of its importance, the thermal properties of this ill-characterized substance are of great interest. Recent work has shown that coal has many of the characteristics of a gel-type structure. We have made this observation the basis for a model study of the thermal properties of a gel system, using the equation-of-motion method to determine the density of states for the system and, thereby, its heat capacity. This model has one of the essential features of a model of coal, namely, a porous structure. With a hexagonal close-packed lattice as the basis for our gel, we have calculated the frequency spectrum for several particle densities. The disorder in the system has a marked effect on the frequency spectrum, shifting a larger number of modes from high to low frequencies. Also, for a gel with 3% vacancies, and in-plane, out-of-plane bond strengths at the ratio 2∶ 1, there is a further shift to lower frequencies and the two-peaked spectrum expected for such an anisotropic structure develops. The heat capacity is affected only at low temperatures. We conclude that the gel model provides a satisfactory basis for development as a model of coal.