Ising Paradigm in Isobaric Ensembles.

We review recent work on Ising-like models with "compressible cells" of fluctuating volume that, as such, are naturally treated in NpT and μpT ensembles. Besides volumetric phenomena, local entropic effects crucially underlie the models. We focus on "compressible cell gases" (CCG), namely, lattice gases with fluctuating cell volumes, and "compressible cell liquids" (CCL) with singly occupied cells and fluctuating cell volumes.

Ising model for the freezing transition.

We introduce a three-state Ising model with entropy-volume coupling suitably incorporating a packing mechanism into a lattice gas with no attractive interactions. On working in a great grand canonical ensemble in which the energy, volume, and number of particles are all allowed to fluctuate simultaneously, the model's mean-field solutions illuminate a strictly first-order transition akin to hard-sphere freezing while describing the thermodynamics of solid and fluid phases. Further implementation of attractive interactions in a natural way allows every aspect of the phase diagram of a simple substance to be reproduced, thereby accomplishing the van der Waals picture of the states of matter from first principles of statistical mechanics.

Liquid-Liquid Criticality in TIP4P/2005 and Three-State Models of Water.

Molecular dynamics simulations leading to the isothermal compressibility, the isobaric thermal expansivity, and the isobaric heat capacity of TIP4P/2005 water are found to be consistent with the coordinates of its second, liquid-liquid critical point reported recently by Debenedetti et al. [ 2020, 369, 289-292]. In accord with the theory of critical phenomena, we encounter that the rise in the magnitude of these response functions as temperature is lowered is especially marked along the critical isochore.

Water's Unusual Thermodynamics in the Realm of Physical Chemistry.

While it is known since the early work by Edsall, Frank and Evans, Kauzmann, and others that the thermodynamics of solvation of nonpolar solutes in water is unusual and has implications for the thermodynamics of protein folding, only recently have its connections with the unusual temperature dependence of the density of solvent water been illuminated. Such density behavior is, in turn, one of the manifestations of a nonstandard thermodynamic pattern contemplating a second, liquid-liquid critical point at conditions of temperature and pressure at which water exists as a deeply supercooled liquid. Recent experimental and computational work unambiguously points toward the existence of such a critical point, thereby providing concrete answers to the questions posed by the 1976 pioneering experiments by Speedy and Angell and the associated "liquid-liquid transition hypothesis" posited in 1992 by Stanley and co-workers.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. II. Large Solvophovic Solutes.

We use molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy as a function of temperature and pressure for hard-sphere solutes with diameters ranging from 4 to 36 Å in TIP4P/2005 and Jagla water-like solvents exhibiting unusual thermodynamics. An important piece of our discussion focuses on the nanometer-sized solutes, for which simulation results are found to be accounted for by the most basic classical thermodynamic treatment contemplating bulk and interfacial contributions to the solvation free energy. Thus, since water's liquid-vapor surface tension is only special inasmuch as it takes unusually large values, solvent's water-like unusual thermodynamics manifests through a term proportional to the pressure in the solvation free energy.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. I. Small Solvophobic Solutes.

We analyze the role of temperature, pressure, and solute's molecular size on the pattern of isochoric and isobaric solvation of small hard-sphere solutes in TIP4P/2005 water and in a water-like "Jagla" solvent exhibiting unusual thermodynamics. To this end, we employ molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy along isobaric and isothermal paths covering solvent's stable liquid and supercritical states as well as supercooled and "stretched" liquid states. Results are found to be consistent with the most primitive scaled-particle theory and the Gaussian model of small-length-scale solvation.

Water's two-critical-point scenario in the Ising paradigm.

We present a spin-1, three-state Ising model for the unusual thermodynamics of fluid water. Thus, besides vacant cells, we consider singly occupied cells with two accessible volumes in such a way that the local structures of low density, energy, and entropy associated with water's low-temperature "icelike" order are characterized. The model has two order parameters that drive two phase transitions akin to the standard gas-liquid transition and water's hypothesized liquid-liquid transition.

Ising-like Models with Energy-Volume Coupling.

We consider a regular assembly of singly occupied cells with two accessible volumes. Coupled to cell volumes are interaction energies between nearest neighbors that lead to a phase transition with a critical point. We find that these compressible cell models can serve as Ising-like prototypes of the one-component liquid-liquid and isostructural solid-solid phase transitions that originate in the short-range features of the intermolecular potential.

Water's Thermal Pressure Drives the Temperature Dependence of Hydrophobic Hydration.

With the aid of literature experimental data and reported results from molecular simulation, two thermodynamic relations are found to provide a theoretical basis for the understanding of a variety of characteristic features associated with the solvation of small nonpolar molecules in water. Thus, the large and positive solvation heat capacity, enthalpy-entropy compensation, the solubility minimum and solvation free energy maximum with respect to temperature, enthalpy convergence, and entropy convergence are rationalized in a unified way. Our key finding is that all of these phenomena are driven by the thermal pressure coefficient of pure water, which, via the isobaric thermal expansivity and the isothermal compressibility, reflects its unusual thermodynamics.

Compressible cell gas models for asymmetric fluid criticality.

We thoroughly describe a class of models recently presented by Fisher and coworkers [Phys. Rev. Lett.

Osmotic Second Virial Coefficients of Aqueous Solutions from Two-Component Equations of State.

Osmotic second virial coefficients in dilute aqueous solutions of small nonpolar solutes are calculated from three different two-component equations of state. The solutes are five noble gases, four diatomics, and six hydrocarbons in the range C-C. The equations of state are modified versions of the van der Waals, Redlich-Kwong, and Peng-Robinson equations, with an added hydrogen-bonding term for the solvent water.

Water anomalous thermodynamics, attraction, repulsion, and hydrophobic hydration.

A model composed of van der Waals-like and hydrogen bonding contributions that simulates the low-temperature anomalous thermodynamics of pure water while exhibiting a second, liquid-liquid critical point [P. H. Poole et al.

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 -∞0.

Energetic, entropic, and volumetric effects in nonaqueous associated solutions.

On the basis of a simple two-state association model (TSAM), a comprehensive study of thermodynamic response functions for nonaqueous associated solutions is presented. The excess isobaric heat capacities C(p)(E)(T) and excess thermal expansivities V(p)(E) ≡ (∂V(E)/∂T)(p) for a number of alcohol-alkane, amine-alkane, alcohol-ether, and alcohol-alcohol mixtures have been experimentally determined at atmospheric pressure within 278.15-338.

Critical behavior of static properties for nitrobenzene-alkane mixtures.

We present experimental data of the isobaric heat capacity per unit volume C(p,x)V(-1) for mixtures containing nitrobenzene and an alkane (C(N)H(2N+2), with N ranging from 6 to 15) upon approaching their liquid-liquid critical points along a path of constant composition. Values for the critical amplitude A(+) have been determined. They have been combined with the previously reported ones for the leading term of the coexistence-curve width to obtain, with the aid of well-known universal relations, the critical amplitudes of the correlation length and of the osmotic susceptibility.

Dielectric constant of fluids and fluid mixtures at criticality.

The behavior of the dielectric constant epsilon of pure fluids and binary mixtures near liquid-gas and liquid-liquid critical points is studied within the concept of complete scaling of asymmetric fluid-fluid criticality. While mixing of the electric field into the scaling fields plays a role, pressure mixing is crucial as the asymptotic behavior of the coexistence-curve diameter in the epsilon-T plane is concerned. Specifically, it is found that the diameters, characterized by a |T-Tc|1-alpha singularity in the previous scaling formulation [J.

Heat capacity anomalies along the critical isotherm in fluid-fluid phase transitions.

The behavior of the isochoric heat capacity of pure fluids and the isobaric heat capacity at constant composition of binary mixtures along isothermal paths of approach to liquid-gas and liquid-liquid critical points is studied. From the complete scaling formulation of fluid-fluid criticality, explicit expressions for the critical amplitudes of the leading /Y-Y(c)/(-alpha/beta) (where Y can be the density or the mole fraction) contributions are found to reveal previously discovered features of the scaling function, whereas the nature of the most important asymmetry-related terms is characterized. Data for pure toluene and for the binary mixture nitromethane-isobutanol are described within experimental uncertainty using the /Y-Y(c)/(-alpha/beta) singularity plus a linear term.

Temperature, concentration, and frequency dependence of the dielectric constant near the critical point of the binary liquid mixture nitrobenzene-tetradecane.

Detailed results are reported for the dielectric constant epsilon as a function of temperature, concentration, and frequency near the upper critical point of the binary liquid mixture nitrobenzene-tetradecane. The data have been analyzed in the context of the recently developed concept of complete scaling. It is shown that the amplitude of the low frequency critical Maxwell-Wagner relaxation (with a relaxation frequency around 10 kHz) along the critical isopleth is consistent with the predictions of a droplet model for the critical fluctuations.

Thermodynamic consistency near the liquid-liquid critical point.

The thermodynamic consistency of the isobaric heat capacity per unit volume at constant composition C(p,x) and the density rho near the liquid-liquid critical point is studied in detail. To this end, C(p,x)(T), rho(T), and the slope of the critical line (dT/dp)(c) for five binary mixtures composed by 1-nitropropane and an alkane were analyzed. Both C(p,x)(T) and rho(T) data were measured along various quasicritical isopleths with a view to evaluate the effect of the uncertainty in the critical composition value on the corresponding critical amplitudes.

Thermodynamic response functions of fluids: a microscopic approach based on NpT Monte Carlo.

On the basis of NpT Monte Carlo simulations, a detailed analysis on the microscopic origins of some specific features of thermodynamic response functions of fluids is performed. Specifically, the residual isobaric heat capacity C(p) (res), the isobaric thermal expansivity alpha(p), and the isothermal compressibility kappa(T) for Lennard-Jones methane and optimized potential for liquid simulations (OPLS) methanol have been determined via standard techniques. For the former, data along the liquid, gas, and supercritical regions are presented, while a wide temperature range at a single supercritical pressure is covered for the latter.

Principle of isomorphism and complete scaling for binary-fluid criticality.

The extension of the principle of critical-point universality to binary fluid mixtures, known as isomorphism of critical phenomena, has been reformulated in terms of complete scaling, a concept that properly matches asymmetric fluid-phase behavior with the symmetric Ising model. The controversial issue of the proper definition of the order parameter in binary fluid mixtures is clarified. We show that asymmetry of liquid-liquid coexistence in terms of mole fractions originates from two different sources: one is associated with a correlation between concentration and entropy fluctuations, whereas the other source is the correlation between concentration and density fluctuations.

Heat capacity of associated systems. Experimental data and application of a two-state model to pure liquids and mixtures.

The predictions from a recently reported (J. Chem. Phys.

Griffiths-Wheeler geometrical picture of critical phenomena: experimental testing for liquid-liquid critical points.

An experimental approach to the verification of specific relations between thermodynamic properties as predicted from the Griffiths-Wheeler theory of critical phenomena in multicomponent systems is developed for the particular case of ordinary liquid-liquid critical points of binary mixtures. Densities rho(T) , isobaric heat capacities per unit volume C(p)(T) , and previously reported values of the slope of the critical line (dT/dp)c for five critical mixtures are used to check the thermodynamic consistency of C(p) and rho near the critical point. An appropriate treatment of rho (T) data is found to provide the key solution to this issue.

Towards an understanding of the heat capacity of liquids. A simple two-state model for molecular association.

A model for the temperature dependence of the isobaric heat capacity of associated pure liquids C(p,m)(o)(T) is proposed. Taking the ideal gas as a reference state, the residual heat capacity is divided into nonspecific C(p) (res,ns) and associational C(p) (res,ass) contributions. Statistical mechanics is used to obtain C(p)(res,ass) by means of a two-state model.