Statistical Mechanics of Density- and Temperature-Dependent Potentials: Application to Condensed Phases within GenDPDE

Abstract

Coarse-grain Lagrangian methods, such as Dissipative Particle Dynamics ( Hoogerbrugge et al., EPL, 1992), are suitable for describing mesoscopic fluid systems that include thermal fluctuations. However, the realistic simulation of liquids using these methods represents a longstanding problem. In this work, we develop a local thermodynamic (LTh) model for the description of condensed phases within the framework of the Generalized Dissipative Particle Dynamics with Energy Conservation (GenDPDE) method (Bonet Avalos et al., PCCP 2019). Such a model is appropriate for the analysis of liquids, due to the explicit account of the thermal expansion coefficient and isothermal compressibility at the mesoscale. We demonstrate the accuracy of the LTh model by examining the thermodynamic properties of argon at both liquid and supercritical conditions, through equilibrium simulations performed around two key reference states (125.7 K, 85.31 MPa, 1419.7 kg/m3 for liquid Ar, and 418.8 K, 85.31 MPa, 695.99 kg/m3 for supercritical Ar). Remarkably, we show that the model is also valid over a range of thermodynamic conditions near the reference states, allowing a correct description of the physics of systems with spatial variations in density and temperature. We further derive analytical expressions for the macroscopic pressure and energy equations of state based on the model parameters, discussing their validity and limitations. We demonstrate that, even at the mean-field level, accurately capturing local particle arrangements is essential for predicting macroscopic thermodynamic properties from mesoscopic data. We also assess the applicability of the HNC approximation in predicting the radial distribution function of the GenDPDE system, exploring its strengths and limitations. With the LTh model, GenDPDE offers a dependable and versatile tool for analysing condensed phases through coarse-grain techniques.

Figures (5)

• Figure 1: Argon radial distribution functions for $R_\text{cut}^* = 1.3365$ (top), $R_\text{cut}^* = 1.6839$ (middle), $R_\text{cut}^* = 2.1564$ (bottom) from GenDPDE simulations.
• Figure 2: Argon radial distribution functions for $R_\text{cut}^* = 2.1564$ from GenDPDE tests considering an input particle pressure $\pi_{00}^*=0.1239$ (continuous line) and $\pi_{00}^*=0.1161$ (dashed line).
• Figure 3: Argon radial distribution functions for $R_\text{cut}^* = 1.3365$ (top), $R_\text{cut}^* = 1.6839$ (middle), $R_\text{cut}^* = 2.1564$ (bottom). The HNC predictions (dashed lines) Eq. \ref{['HNC']} are compared against GenDPDE results (solid lines).
• Figure 4: System pressure $P^*$ as a function of the temperature $T^*$ (top) and number density $n^*$ (bottom), as obtained from GenDPDE simulations of liquid argon considering $R_\text{cut}^* = 2.1564$ and $\pi_{00}^*=0.1239$. The central point in both diagrams refers to the simulation at the reference state point ( cf. Table \ref{['tab-thermo2']}). The numerical results are compared with data available from NIST NIST2024.
• Figure 5: System pressure $P^*$ as a function of the number density $n^*$, as obtained from GenDPDE simulations of supercritical argon considering $R_\text{cut}^* = 2.1564$. The central point in the diagram refers to the reference state point. The numerical results are compared with data available from NIST NIST2024.