(364g) Equation of State of the One-Dimensional Lennard-Jones System: Thermodynamics and Fluctuations

The thermodynamic properties of one-dimensional systems are of interest for several reasons. Exact analytical solutions are, in some cases, obtainable for 1D systems even when the 3D analogue has no such solution. Those solutions can aid in identifying physics and optimum numerical approximation methods in the 3D analogue systems. However, 1D systems also exhibit surprising behaviors not observed in higher dimensions, which are also interesting subjects of research, such as the lack of a phase transition (in the absence of infinitely long-ranged interactions). And, perhaps most interestingly, quasi-1D nanomaterials (nanotubes, nanoribbons, nanowires, etc.) are rapidly gaining interest for a variety of technological applications, and 1D models may serve as a useful first-order approximation or reference state for modeling these materials, in a manner similar to the roles played by, for example, the ideal mixture or the hard sphere fluid when studying real fluids. However, the study of 1D systems is complicated by large fluctuations in density and energy, long-range correlations, and long relaxation times.

The Lennard-Jones pair potential is a simple and familiar interaction model, and thus, a good place to begin studying the properties of 1D systems. We have applied John A. Barker’s general equation of state for 1D systems of classical particles to obtain the equation of state of the 1D Lennard-Jones fluid. In addition to presenting the density, internal energy, and entropy of this system, we consider properties dependent on first-order fluctuations, including heat capacity, compressibility, coefficient of thermal expansion, and thermal pressure coefficient. We obtain numerical solutions for these properties within a large subset of the thermodynamic phase space. We then test the resulting density and internal energy expressions using isothermal-isobaric Monte Carlo simulation, obtaining excellent agreement. We will describe the expressions obtained for these properties, our methods of numerical solution and simulation, and the results obtained.