Monte Carlo simulation of vapor-liquid equilibrium and critical asymmetry of square-well dimer fluid

Compressible cell gas models for asymmetric fluid criticality

We thoroughly describe a class of models recently presented by Fisher and coworkers [Phys. Rev. Lett. 116, 040601 (2016)]PRLTAO0031-900710.1103/PhysRevLett.116.040601. The crucial feature of such models, termed compressible cell gases (CCGs), is that the individual cell volumes of a lattice gas are allowed to fluctuate. They are studied via the seldom-used (μ, p, T) ensemble, which leads to their exact mapping onto the Ising model. Remarkably, CCGs obey complete scaling, a formulation for the thermodynamic behavior of fluids near the gas-liquid critical point that accommodates features inherent to the asymmetric nature of this phase transition like the Yang-Yang (YY) and singular coexistence-curve diameter anomalies. The CCG_{0} models generated when volumes vary freely reveal local free volume fluctuations as the origin of these phenomena. Local energy-volume coupling is found to be another relevant microscopic factor. Furthermore, the CCG class is greatly extended by using the decoration transformation, with an interesting example being the Sastry-Debenedetti-Sciortino-Stanley model for hydrogen bonding in low-temperature water. The magnitude of anomalies is characterized by a single parameter, the YY ratio, which for the models so far considered here ranges from -∞ to 1/2.

Development of molecular closures for the reference interaction site model theory with application to square-well and Lennard-Jones homonuclear diatomics

Inspired by significant improvements obtained for the performances of the polymer reference interaction site model (PRISM) theory of the fluid phase when coupled with 'molecular closures' (Schweizer and Yethiraj 1993 J. Chem. Phys. 98 9053), we exploit a matrix generalization of this concept, suitable for the more general RISM framework. We report a preliminary test of the formalism, as applied to prototype square-well homonuclear diatomics. As for the structure, comparison with Monte Carlo shows that molecular closures are slightly more predictive than their 'atomic' counterparts, and thermodynamic properties are equally accurate. We also devise an application of molecular closures to models interacting via continuous, soft-core potentials, by using well established prescriptions in liquid state perturbation theories. In the case of Lennard-Jones dimers, our scheme definitely improves over the atomic one, providing semi-quantitative structural results, and quite good estimates of internal energy, pressure and phase coexistence. Our finding paves the way to a systematic employment of molecular closures within the RISM framework to be applied to more complex systems, such as molecules constituted by several non-equivalent interaction sites.

Soluble Model Fluids with Complete Scaling and Yang-Yang Features

Yang-Yang (YY) and singular diameter critical anomalies arise in exactly soluble compressible cell gas (CCG) models that obey complete scaling with pressure mixing. Thus, on the critical isochore ρ=ρ(c), C(μ)≔-Td(2)μ/dT(2) diverges as |t|^(-α) when t∝T-T(c)→0^(-) while ρ(d)-ρ(c)∼|t|^(2β) where ρ(d)(T)=1/2[ρ(liq)+ρ(gas)]. When the discrete local CCG cell volumes fluctuate freely, the YY ratio R(μ)=C(μ)/C(V) may take any value -∞<R(μ)<1/2 but "anticorrelated" free volumes are needed for R(μ)>0. More general decorated CCGs, including "hydrogen bonding" water models, illuminate energy-volume coupling as relevant to R(μ).

Improved renormalization group theory for critical asymmetry of fluids

We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.

Critical asymmetry in renormalization group theory for fluids

The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.