Thermodynamic properties of Lennard-Jones fluids residing in two to five spatial dimensions

The thermodynamic properties and the microscopic structure of Lennard-Jones fluids residing in two to five spatial dimensions are discussed. Complementing literature data for one to three dimensions, molecular dynamics simulations are conducted in four and five dimensions. Thermodynamic properties are sampled over wide temperature and density ranges and used to develop accurate Helmholtz energy equations of state that are also adequate near the critical point. The influence of the number of dimensions n on the critical point, vapor-liquid equilibrium, bulk properties, microscopic structure, and second virial coefficient is analyzed. The results show that with an increasing number of dimensions, there is a remarkable loss of structure and a strong expansion of the state region with a gas-like behavior. This is a consequence of the rise of the critical density (for n ≥ 3) that is accompanied by an almost exponential increase of the critical temperature. In addition, a clear reduction of criticality is observed with a rising number of dimensions. Moreover, the second virial coefficient is shifted to higher temperature values as the number of dimensions increases. Based on the power-law scaling behavior of the critical exponent β, a simple estimate of an upper critical dimension nc of Lennard-Jones fluids is given for the first time, roughly confirming the prediction of the Ising model, being nc = 4.