Thermodynamic curvature for attractive and repulsive intermolecular forces

Abstract

The thermodynamic curvature scalar R for the Lennard-Jones system is evaluated in phase space, including vapor, liquid, and solid state. We paid special attention to the investigation of R along vapor-liquid, liquid-solid, and vapor-solid equilibria. Because R is a measure of interaction strength, we traced out the line R=0 dividing the phase space into regions with effectively attractive (R<0) or repulsive (R>0) interactions. Furthermore, we analyzed the dependence of R on the strength of attraction applying a perturbation ansatz proposed by Weeks-Chandler-Anderson. Our results show clearly a transition from R>0 (for poorly repulsive interaction) to R<0 when loading attraction in the intermolecular potential.

Thermodynamic R-diagrams reveal solid-like fluid states

“…In this region, R peaks at about 0.002 nm 3 along a vertical line with T = 315 K, a value of R consistent with the other solid-like values found here and elsewhere [15].…”

“…The first indication of a repulsive/attractive sign interpretation for R came from the quantum Fermi/Bose gasses, with uniformly positive/negative R values (in the R sign convention used here 1 ) [13,14]. These ideas were recently amplified in the condensed liquid and solid phases by the analysis of Lennard-Jones (LJ) computer simulation data, taken varying the interparticle interactions using the WCA perturbation ansatz [15]. 1 Our sign convention is that of Weinberg [11], where the 2-sphere has R < 0.…”

Geometry of Multiscale Nonequilibrium Thermodynamics

“…If we limit ourselves to the level of the classical equilibrium thermodynamics, then the only way we can get the fundamental thermodynamic relation that corresponds to a given macroscopic system is by making experimental measurements. Indeed, the scalar curvature in the vicinity of critical points is calculated in [41] from the results of experimental observations.…”

“…The authors of [40,41] use the Einstein theory of fluctuations to reach from the classical equilibrium thermodynamics to mesoscopic levels that involve fluctuations. Alternatively, if we would start with the Riemannian geometry on a mesoscopic level (i.e., with the Riemannian geometry of M (N ) ), we could then, via MaxEnt, arrive at the Riemannian geometry on the level of the classical equilibrium thermodynamics and obtain in this way the desired mesoscopic interpretation of singular geometrical features seen on the level of the classical equilibrium thermodynamics.…”

Thermodynamic geometry of supercooled water

“…By applying thermodynamic fluctuation theory [4], R can be formulated as an invariant for any thermodynamic coordinate system. In the recent past, this geometric concept has been systematically developed for atomic and molecular fluid systems using thermodynamic data obtained from experiments and computer simulations [5][6][7][8][9][10], These studies take us a long way toward completing the picture of R in fluid and solid systems. Moreover, these investigations reveal interesting features that may bear important information for the ongoing effort of understanding the thermodynamic curvature scalar R in a broader context of thermodynamic systems, including black hole thermodynamics [3,11],…”