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The thermodynamic and structural properties of the planar soft-sites dumbbell fluid are examined by Monte Carlo simulations and integral equation theory. The dimers are built of two Lennard-Jones segments. Site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions for a range of elongations and densities and the results are compared with Monte Carlo simulations. The critical parameters for selected types of dimers were also estimated. We analyze the influence of the bond length on critical point as well as tested correctness of site-site integral equation theory with different closures. The integral equations can be used to predict the phase diagram of dimers whose molecular parameters are known.

A simple model is constructed to study the phase diagram and thermodynamic properties of methanol, which is described as a dimer of an apolar sphere mimicking the methyl group and a sphere with core-softened potential as the hydroxyl group. Performing classical Monte Carlo simulations, we obtained the phase diagram, showing a second critical point between two different liquid phases. Evaluating systems with a different number of particles, we extrapolate to infinite size in accordance with Ising universality class to obtain bulk values for critical temperature, pressure, and density. Strong evidence that the structure of the liquid changes upon transition from high- to low-density phase was provided. From the experimentally determined hydrogen bond strength and length in methanol and water, we propose where the second critical point of methanol should be.

A simple and computationally inexpensive core-softened model, originally proposed by Franzese [G. Franzese, J. Mol. Liq. 136, 267 (2007)], was adopted to show that it exhibits properties of waterlike fluid and hydrophobic effect. The potential used between particles is spherically symmetric with two characteristic lengths. Thermodynamics of nonpolar solvation were modeled as an insertion of a modified Lennard-Jones particle. It was investigated how the anomalous predictions of the model as well as the nonpolar solvation compare with the experimental data for water anomalies and the temperature dependence of noble gases hydration. It was shown that the model qualitatively follows the same trends as water. The model is able to reproduce waterlike anomalous properties (density maximum, heat capacity minimum, isothermal compressibility, etc.) and hydrophobic effect (minimum solubility for nonpolar solutes near ambient conditions, increased solubility of larger noble gases, etc.). It is argued that the model yields similar results as more complex and computationally expensive models.

We develop an analytical theory for a simple model of liquid water. We apply Wertheim’s thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the MB model, which is among the simplest models of water. Water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz (MB) logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation function of the model water at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that...

The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy.

Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.

The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

The phase diagram of the two-dimensional particles interacting through a smooth version of Stell-Hemmer interaction was studied using Monte Carlo computer simulations. By evaluating the pressure-volume isotherms, we observed liquid-liquid, liquid-gas phase transitions and three stable crystal phases. The model shows the liquid-liquid critical point in stable liquid phase and is confirmed by observing properties of other thermodynamic functions such as heat capacity and isothermal compressibility, for example. The liquid-gas and the liquid-liquid critical points were estimated within the thermodynamic limit.

Integral equation approaches, based on the Ornstein-Zernike equation, provide a fast way to calculate phase diagrams and thermodynamic properties of systems as opposed to time-consuming and computationally expensive computer simulations. However, when employing integral equations it is necessary to introduce simplifications. The Ornstein-Zernike equation merely relates two unknown functions h(r) and c(r), and another relation (closer) between these two functions is needed. The later function cannot be obtained in a closed form and it is always in some approximations. Various approximations exist with each of its own advantages and disadvantages. In this work we extensively tested hyper-netted chain, Percus-Yevick, Kovalenko-Hirata, and Rogers-Young closure on an interaction model with core-softened potential. Convergence domain was established for each method. We calculated pair distribution functions, pressure, and excess energy. Results were compared with Monte Carlo simulation results and literature data from molecular dynamics simulations.

We developed a statistical model which describes the thermal and volumetric properties of water-like molecules. A molecule is presented as a three-dimensional sphere with four hydrogen-bonding arms. Each water molecule interacts with its neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of a model developed before for a two-dimensional Mercedes-Benz model of water. We explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility as a function of temperature and pressure. We found that the volumetric and thermal properties follow the same trends with temperature as in real water and are in good general agreement with Monte Carlo simulations, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds upon increasing the temperature.

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes–Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.

The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the “right answer,” we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim’s Ornstein–Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation.

The viscosity of aqueous solutions of cesium fullerenehexamalonate T h -C 66(COOCs) 12, a rigid spherical nanometer-sized polyvalent salt, was measured by the Ubbelohde-type viscometer. The measurements were performed without added salt at 25 degrees C in the concentration range between 7 and 320 g/dm (3). THe concentration dependence of the obtained reduced viscosity was compared with the theoretical prediction, taking into account contributions stemming from the intrinsic viscosity, hydrodynamic perturbations of the hypothetically bare fullerenehexamalonate macroion, the primary electroviscous effect, and the secondary electroviscous effect. Using the geometric radius of the bare macroion from the previous measurements of the estimated effective charge of the macroion and from the small-angle X-ray scattering data of the estimated thickness of the compact shell of counterions electrostatically bound to the macroion, a good agreement between theory and the experiment was obtained in the range of the lowest and of the highest concentrations. Electrostatic interactions are identified as the main cause of the increased reduced viscosity at the lowest measured concentrations. At the highest concentrations, electrostatic interactions are effectively screened, and the influence of binary hydrodynamic interactions and perturbations of the hypothetical bare macroion prevails over electrostatic contributions to the increased viscosity. The electrophoretic mobility of the fullerenehexamalonate ion in aqueous salt-free medium was computed with the same value for the radius of the fullerenehexamalonate macroion as that used in the calculation of viscosity. The numerical solution of Ohshima's equation agreed well with the experimental values.

We recently developed an angle-dependent Wertheim integral equation theory (IET) of the Mercedes-Benz (MB) model of pure water [Silverstein et al., J. Am. Chem. Soc. 120, 3166 (1998)]. Our approach treats explicitly the coupled orientational constraints within water molecules. The analytical theory offers the advantage of being less computationally expensive than Monte Carlo simulations by two orders of magnitude. Here we apply the angle-dependent IET to studying the hydrophobic effect, the transfer of a nonpolar solute into MB water. We find that the theory reproduces the Monte Carlo results qualitatively for cold water and quantitatively for hot water.

The phase behavior and the fluid structure of coarse-grain models for alcohols are studied by means of reference interaction site model (RISM) theory and Monte Carlo simulations. Specifically, we model ethanol and 1-propanol as linear rigid chains constituted by three (trimers) and four (tetramers) partially fused spheres, respectively. Thermodynamic properties of these models are examined in the RISM context, by employing closed formulæ for the calculation of free energy and pressure. Gas-liquid coexistence curves for trimers and tetramers are reported and compared with already existing data for a dimer model of methanol. Critical temperatures slightly increase with the number of CH2 groups in the chain, while critical pressures and densities decrease. Such a behavior qualitatively reproduces the trend observed in experiments on methanol, ethanol, and 1-propanol and suggests that our coarse-grain models, despite their simplicity, can reproduce the essential features of the phase behavior of such alcohols. The fluid structure of these models is investigated by computing radial distribution function gij(r) and static structure factor Sij(k); the latter shows the presence of a low-k peak at intermediate-high packing fractions and low temperatures, suggesting the presence of aggregates for both trimers and tetramers.

Properties of superconducting and superfluid thin films, modeled as a two-dimensional classic Coulomb fluid, are connected to the molecular structure of the system. Monte Carlo simulations to explore structural properties and ordering in the classical two-dimensional Coulomb fluid were performed. The density dependence of translational order parameters at various temperatures and cluster distribution below and above the Kosterlitz-Thouless line were studied, and the percolation temperature threshold was determined. Results show that one could detect the insulator-conductor transition by observing the translational order parameters, average cluster number, or mean cluster size besides dielectric constant and dipole moment of the system.

Monte Carlo simulations and integral equation theory were used to predict the thermodynamics and structure of a two-dimensional Coulomb fluid. We checked the possibility that integral equations reproduce Kosterlitz-Thouless and vapor-liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared to Monte Carlo data and the correctness of selected closure relations was assessed. Among selected closures hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz-Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected.

Using Monte Carlo computer simulations, we show that a simple isotropic water-like model with two characteristic lengths can reproduce the hydrophobic effect and the solvation properties of small and large non-polar solutes. Influence of temperature, pressure, and solute size on the thermodynamic properties of apolar solute solvation in a water model was systematically studied, showing two different solvation regimes. Small particles can fit into the cavities around the solvent particles, inducing additional order in the system and lowering the overall entropy. Large particles force the solvent to disrupt their network, increasing the entropy of the system. At low temperatures, the ordering effect of small solutes is very pronounced. Above the cross-over temperature, which strongly depends on the solute size, the entropy change becomes strictly positive. Pressure dependence was also investigated, showing a “cross-over pressure” where the entropy and enthalpy of solvation are the lowest. These results suggest two fundamentally different solvation mechanisms, as observed experimentally in water and computationally in various water-like models.

An interaction model with core-softened potential in three dimensions was studied by Monte Carlo computer simulations and integral equation theory. We investigated the possibility that a fluid with a core-softened potential can reproduce anomalies found experimentally in liquid water, such as the density anomaly, the minimum in the isothermal compressibility as a function of temperature, and others. Critical points of the fluid were also determined. We provided additional arguments that the old notion, postulating that only angular-dependent interactions result in density anomaly, is incorrect. We showed that potential with two characteristic distances is sufficient for the system to exhibit water-like behavior and anomalies, including the famous density maximum. We also found that this model can properly describe the hydrophobic effect.

In-depth knowledge of water-water potential is important for devising and evaluating simple water models if they are to accurately describe water properties and reflect various solvation phenomena. Water-water potential depends upon inter-molecular distance, relative orientation of water molecules, and also local environment. When placed at a favorable distance in a favorable orientation, water molecules exhibit a particularly strong attractive interaction called hydrogen bond. Although hydrogen bond is very important for its effects on the elements of life, industrial applications, and bulk water properties, there is no scientific consensus on its true nature and origin. Using quantum-mechanical methods, hydrogen bond strength was calculated in different local environments. A simple empirical linear relationship was discovered between maximum hydrogen bond strength and the number of water molecules in the local environment. The local environment effect was shown to be considerable even on the second coordination shell. Additionally, a negative linear correlation was found between maximum hydrogen bond strength and the distance, at which it was observed. These results provide novel insights into the nature of hydrogen bonding.

We develop a statistical mechanical model for the thermal and volumetric properties of waterlike fluids. Each water molecule is a two-dimensional disk with three hydrogen-bonding arms. Each water interacts with neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of the Truskett and Dill (TD) treatment of the "Mercedes-Benz" (MB) model. The present model gives better predictions than TD for hydrogen-bond populations in liquid water by distinguishing strong cooperative hydrogen bonds from weaker ones. We explore properties versus temperature T and pressure p. We find that the volumetric and thermal properties follow the same trends with T as real water and are in good general agreement with Monte Carlo simulations of MB water, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds for increasing temperature. The model reproduces that pressure squeezes out water's heat capacity and leads to a negative thermal expansion coefficient at low temperatures. In terms of water structuring, the variance in hydrogen-bonding angles increases with both T and p, while the variance in water density increases with T but decreases with p. Hydrogen bonding is an energy storage mechanism that leads to water's large heat capacity (for its size) and to the fragility in its cagelike structures, which are easily melted by temperature and pressure to a more van der Waals-like liquid state.

We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.