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Simple alcohols such as methanol and ethanol, are organic chemicals that can be used to store energy, which can be used as an alternative to fossil fuels. Each alcohol has at least one hydroxyl group attached to a carbon atom of an alkyl group. They can be considered as organic derivatives of water in which one of the hydrogen atoms is replaced by an alkyl group. In this work, we determined the thermodynamic and structural properties of two dimensional water-alcohol mixtures using the Monte Carlo method. We used two-dimensional Mercedes-Benz (MB) model for water and MB based models for lower alcohols. The structural and thermodynamic properties of the mixtures were studied by Monte Carlo simulations in the isothermal-isobaric ensemble. We show that 2D models display similar trends in the density maxima as in real water-alcohol mixtures. With increasing content of alcohols, the temperature of maxima increases and upon further increase starts to decrease and at high concentrations, the density maxima disappears.

Monte Carlo simulations and integral equation theory were used to study the thermodynamics and structure of mixture of particles interacting through the smooth version of Stell–Hemmer interaction a...

In this manuscript, we develop a two-dimensional coarse-grained model to study equilibrium properties of fibril-like structures made of amyloid proteins. The phase space of the model is sampled using Monte Carlo computer simulations. At low densities and high temperatures proteins are mostly present as monomers while at low temperatures and high densities particles self-assemble into fibril-like structures. The phase space of the model is explored and divided into different regions based on the structures present. We also estimate free-energies to dissociate proteins from fibrils based on the residual concentration of dissolved proteins. Consistent with experiments, the concentration of proteins in solution does not affects their equilibrium state. Also, we study the temperature dependence of the equilibrium state to estimate thermodynamic quantities, e.g., heat capacity and entropy, of amyloid fibrils.

In this paper we propose a model for the two dimensional fluid with one site-site associating point. We studied its structural and thermodynamic properties by the Monte Carlo computer simulations, the site-site integral equation theory (RISM), the Wertheim's thermodynamic perturbation theory (TPT) and the Wertheim's integral equation theory (WIET) for associative liquids. The model can have arbitrary position of the associating point from the center of particles. All particles have Lennard-Jones core while interactions between associating points are modeled as Gaussian like potential where the interaction depends only on the distance between sites. The methods were used to study the thermodynamic and structural properties as a function of the position of associating point, temperature and density. The accuracy of the analytic theories were checked by comparing the theoretical results with the corresponding Monte Carlo ones. The theories are quite accurate for cases when the associating point is on the surface and only dimers can be formed. In this case, the theories correctly predict the pair correlation functions of the model, internal energy, ratios of free and bonded particles and chemical potential. This is no longer true when associating point is away from the surface of particles and the higher clusters are formed.

Monte Carlo simulations, molecular dynamics and integral equation theory were used to study the thermodynamics and structure of particles interacting through the core softened interaction. Core-softened disks have two length scales of interaction, a hard core with one diameter and a soft corona with a larger diameter. We checked the possibility that a fluid with a core-softened potential reproduces anomalies of liquid water and attempted to determine the critical points which we did not observe nor with computer simulations nor with integral equations. We showed that some versions of the integral equation theory completely fail to predict structure and thermodynamics of such system, while others predict it quite well depending on the position in phase space.

In this manuscript we use a two-dimensional coarse-grained model to study how amyloid fibrils grow towards an equilibrium state where they coexist with proteins dissolved in a solution. Free-energies to dissociate proteins from fibrils are estimated from the residual concentration of dissolved proteins. Consistent with experiments, the concentration of proteins in solution affects the growth rate of fibrils but not their equilibrium state. Also, studies of the temperature dependence of the equilibrium state can be used to estimate thermodynamic quantities, e.g., heat capacity and entropy., Graphical abstract

Integral equation theories and Monte–Carlo simulations were used to determine the thermodynamic and structural properties of a two-dimensional asymmetric Coulomb system. We check correctness of different closures in integral equations and their ability to reproduce Kosterlitz–Thouless and vapour–liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared with Monte–Carlo data. 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.

In this paper we applied an analytical theory for the two dimensional dimerising fluid. We applied Wertheims thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the dimerising model with arbitrary position of dimerising points from center of the particles. The theory was used to study thermodynamical and structural properties. To check the accuracy of the theories we compared theoretical results with corresponding results obtained by Monte Carlo computer simulations. The theories are accurate for the different positions of patches of the model at all values of the temperature and density studied. IET correctly predicts the pair correlation function of the model. Both TPT and IET are in good agreement with the Monte Carlo values of the energy, pressure, chemical potential, compressibility and ratios of free and bonded particles.

The structures and properties of biomolecules like proteins, nucleic acids, and membranes depend on water. Water is also very important in industry. Overall, water is unusual substance with more than 70 anomalous properties. The understanding of water is advancing significantly due to theoretical and computational modeling. There are different kind of models, models with fine-scale properties and increasing structural detail with increasing computational expense and simple models which focus on global properties of water like thermodynamics, phase diagram and are less computational expensive. Simplified models give a better understanding of water in ways that complement more complex models. Here, we review a simple model, the two dimensional Mercedes-Benz (MB) model of water. We present results by Monte Carlo simulations for anomalies and phase diagram and application of various theoretical methods.

We developed a fast theory for studying how the rotational temperature (and rotational degrees of freedom) affects the properties of a simple model of liquid water. Wertheim's Thermodynamic perturbation theory (TPT) for associative liquids was applied to the Mercedes-Benz (MB) model. 2D MB model is one of the simplest models of water. The MB particles are modelled as Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically as in the MB logo. We previously applied TPT to this model. We found that the physical properties were well reproduced by the theory. Here, we propose an modified version of the thermodynamic perturbation theory in which it is possible to treat rotational degrees of freedom by using different averaging then used before. By holding translational or rotational temperature constant and varying the other one, we investigate their effect on the properties of the simple water model and how well TPT reproduces computer simulation results. The new results are in good agreement with the Monte Carlo values of the pressure and energy. We also investigated how rotational temperature affects thermodynamic properties of the critical point. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.

We developed an analytical theory for studying of rotational degrees of freedom of a simple model of liquid water. Wertheim's integral equation theory (IET) for associative liquids was applied to the Mercedes-Benz (MB) model, which is among the simplest models of water. The MB water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the MB logo. IET is based on the orientationally averaged version of the Ornstein-Zernike equation. In varying of rotational degrees of freedom we use different averaging then used before. By holding one of the temperatures constant and varying the other one, we investigate the effect of faster motion in the corresponding degrees of freedom on the properties of the simple water model and how well IET reproduce computer simulation results. The pair correlation function of the model water at high rotational or translation temperatures is correctly predicted. IET results are in good agreement with the Monte Carlo values of the pressure, energy, heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.

We investigate by Monte Carlo simulations density, diffusion, and structural anomalies of the simple two-dimensional Mercedes-Benz (MB) model of water, which is a very simple toy model for explaining the origin of water properties. MB water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The model is in a way also a variance of silica-like models. Beside the known thermodynamic anomaly for the model we also found diffusion and structural anomalies and map out the cascade of density, structural, pair entropy, and diffusivity anomalies for MB model. The orientational order parameters with three and six-fold symmetry were determined and maximum for each one observed. The anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region.

Monte Carlo simulations and Wertheim's thermodynamic perturbation theory (TPT) are used to predict the phase diagram and percolation curve for the simple two-dimensional Mercedes-Benz (MB) model of water. The MB model of water is quite popular for explaining water properties, but the phase diagram has not been reported till now. In the MB model, water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The liquid part of the phase space is explored using grand canonical Monte Carlo simulations and two versions of Wertheim's TPT for associative fluids, which have been used before to predict the properties of the simple MB model. We find that the theory reproduces well the physical properties of hot water but is less successful at capturing the more structured hydrogen bonding that occurs in cold water. In addition to reporting the phase diagram and percolation curve of the model, it is shown that the improved TPT predicts the phase diagram rather well, while the standard one predicts a phase transition at lower temperatures. For the percolation line, both versions have problems predicting the correct position of the line at high temperatures.

We develop an analytical statistical-mechanical model for hydrophobic solvation in water. In this three-dimensional Mercedes-Benz–like model, two neighboring waters have three possible interaction states: a radial van der Waals interaction, a tetrahedral orientation-dependent hydrogen-bonding interaction, or no interaction. Nonpolar solutes are modeled as van der Waals particles of different radii. The model is sufficiently simple that we can calculate the partition function and thermal and volumetric properties of solvation versus temperature, pressure, and solute radius. Predictions are in good agreement with results of Monte Carlo simulations. And their trends agree with experiments on hydrophobic solute insertion. The theory shows that first-shell waters are more highly structured than bulk waters, because of hydrogen bonding, and that that structure melts out faster with temperature than it does in bulk waters. Because the theory is analytical, it can explore a broad range of solvation properties and anomalies of water, at minimal computational expense.

Non–equilibrium Monte Carlo and molecular dynamics simulations are used to study the effect of translational and rotational degrees of freedom on the structural and thermodynamic properties of the simple Mercedes–Benz water model. We establish a non–equilibrium steady state where rotational and translational temperatures can be tuned. We separately show that Monte Carlo simulations can be used to study non-equilibrium properties if sampling is performed correctly. By holding one of the temperatures constant and varying the other one, we investigate the effect of faster motion in the corresponding degrees of freedom on the properties of the simple water model. In particular, the situation where the rotational temperature exceeded the translational one is mimicking the effects of microwaves on the water model. A decrease of rotational temperature leads to the higher structural order while an increase causes the structure to be more Lennard–Jones fluid like.

Using Monte Carlo computer simulations, hydrophobic effect for a non-polar particle with the diameter of a water molecule was studied in water, confined within a disordered matrix. Freely mobile two-dimensional Mercedes-Benz water was put in a disordered, but fixed, matrix of Lennard-Jones disks. Influence of temperature and matrix properties on the thermodynamic quantities of a non-polar solute solvation was studied. The hydrophobic effect is changed by the presence of the obstacles. Smaller matrix particles change the solute–water structure and thermodynamics drastically, as it was also observed for the properties of pure confined water. The study is bringing new scientific important observations in understanding the role of hydrophobic forces under confinement.

Water confined by the presence of a ‘sea’ of inert obstacles was examined. In the article, freely mobile two-dimensional Mercedes-Benz (MB) water put to a disordered, but fixed, matrix of Lennard-Jones disks was studied by the Monte Carlo computer simulations. For the MB water molecules in the matrix of Lennard-Jones disks, we explored the structures, hydrogen-bond-network formation and thermodynamics as a function of temperature and size and density of matrix particles. We found that the structure of model water is perturbed by the presence of the obstacles. Density of confined water, which was in equilibrium with the bulk water, was smaller than the density of the bulk water and the temperature dependence of the density of absorbed water did not show the density anomaly in the studied temperature range. The behaviour observed as a consequence of confinement is similar to that of increasing temperature, which can for a matrix lead to a process similar to capillary evaporation. At the same occupancy of sp...

Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures.

A statistical model for a simple three-dimensional Mercedes-Benz model of water was used to study phase diagrams. This model on a simple level describes the thermal and volumetric properties of waterlike molecules. A molecule is presented as a soft sphere with four directions in which hydrogen bonds can be formed. Two neighboring waters can interact through a van der Waals interaction or an orientation-dependent hydrogen-bonding interaction. For pure water, we explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility and 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. The model exhibits also two critical points for liquid-gas transition and transition between low-density and high-density fluid. Coexistence curves and a Widom line for the maximum and minimum in thermal expansion coefficient divides the phase space of the model into three parts: in one part we have gas region, in the second a high-density liquid, and the third region contains low-density liquid.

Water is an unusual liquid in its solvation properties. Here, we model the process of transferring a nonpolar solute into water. Our goal was to capture the physical balance between water's hydrogen bonding and van der Waals interactions in a model that is simple enough to be nearly analytical and not heavily computational. We develop a 2-dimensional Mercedes-Benz-like model of water with which we compute the free energy, enthalpy, entropy, and the heat capacity of transfer as a function of temperature, pressure, and solute size. As validation, we find that this model gives the same trends as Monte Carlo simulations of the underlying 2D model and gives qualitative agreement with experiments. The advantages of this model are that it gives simple insights and that computational time is negligible. It may provide a useful starting point for developing more efficient and more realistic 3D models of aqueous solvation.

We study water that is confined within small geometric spaces. We use the Mercedes-Benz (MB) model of water, in NVT and muVT Monte Carlo computer simulations. For MB water molecules between two planes separated by a distance d, we explore the structures, hydrogen bond networks, and thermodynamics as a function of d, temperature T, and water chemical potential mu. We find that squeezing the planes close enough together leads to a vaporization of waters out of the cavity. This vaporization transition has a corresponding peak in the heat capacity of the water. We also find that, in small pores, hydrogen bonding is not isotropic but, rather, it preferentially forms chains along the axis of the cavity. This may be relevant for fast proton transport in pores. Our simulations show oscillations in the forces between the inert plates, due to water structure, even for plate separations of 5-10 water diameters, consistent with experiments by Israelachvili et al. [Nature 1983, 306, 249]. Finally, we find that confinement affects water's heat capacity, consistent with recent experiments of Tombari et al. on Vycor nanopores [J. Chem. Phys. 2005, 122, 104712].

What are the properties of water in the presence of a 'sea' of inert obstacles? This question arises because biological cells are highly crowded media, and it is of interest to know the properties of water inside them. It also arises for understanding water in confined molecular environments and for mixtures of water with non-polar solutes. We study two-dimensional Mercedes-Benz (MB) water that is freely mobile in a disordered, but fixed, matrix of Lennard-Jones disks. We use the associative replica Ornstein-Zernike equations supplemented by the corresponding hypernetted chain approximation, and we tested the theory using Monte Carlo simulations. We find that the structure of model water is perturbed by the presence of the obstacles. When the density of obstacles is small, the obstacles induce an increased ordering and 'hydrogen bonding' of the MB model molecules and increased compressibility, relative to pure fluid, in agreement with previous theoretical and experimental studies. However, interestingly, high obstacle densities reduce MB water structuring, 'hydrogen bonding', and compressibility, because the obstacles interfere so extensively with all the possible ways that the fluid can form good 'hydrogen bonding' networks. 2003 Elsevier B.V. All rights reserved.

We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein–Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properties; for example, it does not predict liquid water’s density maximum with temperature or the negative thermal expansion coefficient.

We recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the Mercedes–Benz (MB) model of pure water. These analytical theories offer the advantage of being computationally less intensive than the Monte Carlo simulations by orders of magnitudes. The long-term goal of this work is to develop analytical theories of water that can handle orientation-dependent interactions and the MB model serves as a simple workbench for this development. Here we apply the IET and TPT to the hydrophobic effect, the transfer of a nonpopular solute into MB water. As before, we find that the theories reproduce the Monte Carlo results quite accurately at higher temperatures, while they predict the qualitative trends in cold water.

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.

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.

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.

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.