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The influence of a homogeneous constant electric field on water properties was assessed.

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.

The thermodynamic and structural properties of the 2D hexagonal soft-sites fluid are examined by integral equation theory benchmarked against extensive Monte Carlo simulations. Hexamers are built of six equal Lennard-Jones segments. Site-site integral equation theory is used to compute site–site correlation functions, excess internal energies and isotherms over a wide range of conditions and compared with results obtained from Monte Carlo simulations. Various approaches for computing the pressure are discussed as well. Satisfactory qualitative agreement between theory and simulations is found with details depending on the applied closure relation.

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...

A goal in computational chemistry is computing hydration free energies of nonpolar and charged solutes accurately, but with much greater computational speeds than in today's explicit-water simulations. Here, we take one step in that direction: a simple model of solvating waters that is analytical and thus essentially instantaneous to compute. Each water molecule is a 2-dimensional dipolar hydrogen-bonding disk that interacts around small circular solutes with different nonpolar and charge interactions. The model gives good qualitative agreement with experiments. As a function of the solute radius, it gives the solvation free energy, enthalpy and entropy as a function of temperature for the inert gas series Ne, Ar, Kr, and Xe. For anions and cations, it captures relatively well the trends versus ion radius. This approach should be readily generalizable to three dimensions.

Alcohols are organic compounds characterized by one or more hydroxyl groups 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, the Mercedes-Benz model of water is used to design simple two-dimensional (2D) models of lower alcohols. The structural and thermodynamic properties of the constructed simple models are studied by conducting Monte Carlo simulations in the isothermal-isobaric ensemble. We show that 2D models display similar trends in structuring and thermodynamics as in experiments. The present work on the smallest amphiphilc organic solutes provides a simple testing ground to study the competition between polar and non-polar effects within the molecule and physical properties.

The aggregation of proteins into fibrillar, amyloid-like aggregates generally results in an improved, positive effect on various techno-functional properties within food products, such as gelation, emulsification, and foam stabilization. These highly stable structures, characterized by their repetitive, β-sheet rich motifs, may develop as the result of the thermal treatment of protein-rich food products. Heavy metal ions can influence amyloid-like aggregation of food proteins. Lead(II) and cadmium(II) represent some of the most abundant and common environmental water and food pollutants. In this work, the influence of heavy metal ions, lead and cadmium on amyloid-like aggregation of ovalbumin at high temperatures (90 °C) and under acidic conditions (pH 2.0) was investigated. Ovalbumin is used as a general model for how heavy metals can affect amyloid-like aggregation of a food protein. Structural changes were monitored via Thioflavin T and 8-Anilino-1-naphthalenesulfonic acid fluorescence, Fourier-Transform infrared spectroscopy, atomic force microscopy, dynamic light scattering, as well as computational analyses. The obtained results indicate that the added heavy metal ions bind to different sites within ovalbumin prior to thermal treatment. Lead binding sites are closer to the hydrophobic regions of an protein, while cadmium ion binding sites are more exposed. This specific binding of metal ions affects the morphologies of amyloid-like aggregates, resulting in lead-induced branching of amyloid-like fibrils, or cadmium-induced tangling of fibrils into dense amyloid clusters. This additive effect of heavy metal ions is most evident in ovalbumin samples which contain a mixture of both heavy metal ions.

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.

The modelling-based design of microfluidic devices leads to highly efficient process intensification, which provides insights into different temporal and spatial scales at which processes in various fields of application could be performed. This requires not only an understanding of the underlying mechanisms of different processes at the micro scale, but also the development of relevant computational tools. The macroscopic models are often unable to produce conclusive evidence for a given mechanism in systems with the complexity characterizing almost all chemical and biochemical processes. By contrast, mesoscale methods possess the unique ability to model relatively large physical systems, and, at the same time, effectively capture the essential features of the micro- and nanoscale structure, architecture, and relevant interactions. We demonstrate the feasibility and usefulness of this novel tool by considering a movement of neutrally buoyant particles in straight microchannels. The two-dimensional lattice Boltzmann method with immersed boundary conditions was used to study the influence of Reynolds number and particle diameter ratio on formation of particle trains. It was shown that an increase in particle diameter ratio leads to a less stable final particle configuration. An increase in Reynolds number was not found to significantly influence the train stability in the tested range.

Liquid water is considered poorly understood. How are water's physical properties encoded in its molecular structure? We introduce a statistical mechanical model (CageWater) of water's hydrogen-bonding (HB) and Lennard-Jones (LJ) interactions. It predicts the energetic and volumetric and anomalous properties accurately. Yet, because the model is analytical, it is essentially instantaneous to compute. This model advances our understanding beyond current molecular simulations and experiments. Water has long been regarded as a "2-density liquid": a dense LJ liquid and a looser HB one. Instead, we find here a different antagonism underlying water structure-property relations: HBs in water-water pairs drive density, while HBs in cooperative cages drive openness. The balance shifts strongly with temperature and pressure. This model interprets the molecular structures underlying the liquid-liquid phase transition in supercooled water. It may have value in geophysics, biomolecular modeling, and engineering of materials for water purification and green chemistry.

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.

We have studied the effect of rotational and translational degrees of freedom on solvation of nonpolar solutes. In this study a simple two-dimensional Mercedes-Benz (MB) water model was used. By separating temperature on rotational and translational part, the effect of different degrees of freedom on solvation was investigated. Increasing rotational temperature reduces tendency of water to form hydrogen bonds, therefore the effect of rotational degrees of freedom on solvation can be used to assess how hydrogen bonds affect solvation and what kind of liquid is more favourable for solvation of different solute. Considering the size there are three different regimes of solvation of nonpolar solutes and the effect of hydrogen bonds. The rotational temperature and thus hydrogen bonds have almost zero effect on solvation and aggregation of small solutes which are equally soluble in liquids that do and liquids that do not form hydrogen bonds. When size of solute is larger than HB length increasing rotational temperature improves solvation and diminishes association of solute molecules, thus large solutes are more soluble in liquids without hydrogen bonds. On the other hand when solute size is similar to HB length, increasing rotational temperature diminishes solvation and improves association of solute molecules, thus solutes of similar size are more soluble in liquid with hydrogen bonds, that means hydrogen bonds have favourable effect on solvation of such solutes. Hydrophobic effect appears only when solute is larger than HB length, on the other hand when solute size is similar to HB length inverse hydrophobic effect appears.

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

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.

In this paper we propose extension of the second-order thermodynamic perturbation theory (TPT2) for the inverse patchy colloids (IPC) with arbitrary number of patches. The theory is used to study thermodynamical properties and liquid-gas phase behavior of the IPC model with one, two and three patches. To validate the accuracy of the TPT2 we compare theoretical predictions against corresponding results obtained by computer simulations. The theory is accurate for the one-patch version of the model at all values of the temperature and density studied and less accurate for two- and three-patch versions at lower temperature and higher density. Theoretical predictions for the critical temperature and density of the two- and three-patch IPC models are relatively accurate, however the overall shape of the theoretical phase diagram appears to be too narrow. No liquid-gas phase coexistence for the one-patch IPC model was found.

In this work, the lattice Boltzmann (LB) method was applied to simulate incompressible steady and unsteady low Reynolds number (Re) flows around a confined cylinder. In the LB method, different collision models (Bhatnagar–Gross–Krook model, two-relaxation-time model, multi-relaxation-time model, and entropic lattice Boltzmann model) and a regularization model were used, and the results were compared. Numerical results pertaining to a two-dimensional flow around a cylinder are reported and compared with numerical and experimental data available in the literature. The results agree with the predictions made from the literature. A correlation for Strouhal number (St) for 55 $$\le$$≤ Re $$\le$$≤ 300 is suggested.

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.

The lattice Boltzmann method (LBM) is a computational method for a wide variety of fluid flow and multi-physics phenomena. These include systems governed by reaction-diffusion and reaction-diffusion-advection equations which are of major interest in many scientific and engineering fields. Typically, reactions are incorporated into LBM by means of a reactive source term identical to the macroscopic reaction kinetics equations which is dependent on the local concentration of the chemical species. Alternatively we can formulate the source term at the level of the particle distribution function, which is the main variable in LBM simulations. This way we can mimic the velocity-dependent reactive collisions of particles. This was done in our work and we implemented it to a bimolecular reaction for several geometries and initial conditions. Comparison was made with the macroscopic reaction source term.

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.

The behavior of water, methanol, and water-methanol mixtures confined in narrow slit graphite pores as a function of pore size was investigated by Monte Carlo, hybrid Monte Carlo, and Molecular Dynamics simulations. Interactions were described using TIP4P/2005 for water, OPLS/2016 for methanol, and cross interactions fitted to excess water/methanol properties over the whole range of concentrations, which provide a rather accurate description of water-methanol mixtures. As expected for hydrophobic pores, whereas pure methanol is adsorbed already from the gas phase, pure water only enters the pore at pressures well beyond bulk saturation for all pore sizes considered. When adsorbed from a mixture, however, water adsorbs at much lower pressures due to the formation of hydrogen bonds with previously adsorbed methanol molecules. For all studied compositions and pore sizes, methanol adsorbs preferentially over water at liquid-vapor equilibrium conditions. In pure components, both water and methanol are microscopically structured in layers, the number of layers increasing with pore size. This is also the case in adsorbed mixtures, in which methanol has a higher affinity for the walls. This becomes more evident as the pore widens. Diffusion of pure water is higher than that of pure methanol for all pore sizes due to the larger size of the methyl group. In mixtures, both components present similar diffusivities at all pore sizes, which is explained in terms of the coupling of molecular movements due to strong hydrogen bonding between methanol and water molecules. This is particularly evident in very narrow pores, in which pure methanol diffusion is completely impeded on the time scale of our simulations, but the presence of a small amount of water molecules facilitates alcohol diffusion following a single-file mechanism. Additionally, our results indicate that pure water diffusivities display a non-monotonous dependence of pore size, due to effects of confinement (proximity to a fluid-solid-fluid transition induced by confinement as reported in previous work) and the dynamic anomalies of water.

Methanol is the simplest alcohol and possible energy carrier because it is easier to store than hydrogen and burns cleaner than fossil fuels. It is a colorless liquid, completely miscible with water and organic solvents and is very hygroscopic. Here, simple two-dimensional models of methanol, based on Mercedes–Benz (MB) model of water, are examined by Monte Carlo simulations. Methanol particles are modeled as dimers formed by an apolar Lennard-Jones disk, mimicking the methyl group, and a sphere with two hydrogen bonding arms for the hydroxyl group. The used models are the one proposed by Hribar-Lee and Dill (Acta Chimica Slovenica, 53:257, 2006.) with the overlapping disks and a new model with tangentially fused dimers. The comparison was done between the models, in connection to the MB water, as well as with experimental results and with new simulations done for 3D models of methanol. Both 2D models show similar trends in structuring and thermodynamics. The difference is the most pronounced at lower temperatures, where the smaller model exhibits spontaneous crystallization, while the larger model shows metastable states. The 2D structural organization represents well the clustering tendency observed in 3D models, as well as in experiments. The models qualitatively agree with the bulk methanol thermodynamic properties like density and isothermal compressibility, however, heat capacity at the constant pressure shows trend more similar to the water behavior. This work on the smallest amphiphilic organic solute provides a simple testing ground to study the competition between polar and non-polar effects within the molecule and physical properties.

One of the most important electrostatic interactions between molecules is most definitely the hydrogen bond. Understanding the basis of this interaction may offer us the insight needed to understand its effect on the macroscopic scale. Hydrogen bonding is for example the reason for anomalous properties in compounds like water and naturally life as we know it. The strength of the bond depends on numerous factors, among them the electronegativity of participating atoms. In this work we calculated the strength of hydrogen bonds between hydrides of the upper-right part of the periodic table (C, N, O, F, P, S, Cl, As, Se, Br) using quantum-chemical methods. The aim was to determine what influences the strength of strong and weak hydrogen bonds in simple hydrides. Various relationships were checked. A relation between the strength of the bond and the electronegativity of the participating atoms was found. We also observed a correlation between the strength of hydrogen bonds and the inter-atomic distances, along with the dependence on the charge transfer on the atom of the donor. We also report characteristic geometries of different dimers.

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.

International audience; The structural properties of model two-dimensional (2D) ionic liquids are examined, with a particular focus on the charge ordering process, with the use of computer simulation and integral equation theories. The influence of the logarithmic form of the Coulomb interaction, versus that of a 3D screened interaction form, is analysed. Charge order is found to hold and to be analogous for both interaction models, despite their very different form. The influence of charge ordering in the low density regime is discussed in relation to well known properties of 2D Coulomb fluids, such as the Kosterlitz-Thouless transition and criticality. The present study suggests the existence of a stable thermodynamic labile cluster phase, implying the existence of a liquid-liquid " transition " above the liquid-gas binodal. The liquid-gas and Kosterlitz-Thouless transitions would then take place inside the predicted cluster phase.

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.

In this paper we applied analytical theories for the two dimensional chain-forming fluid. Wertheims thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids were used to study thermodynamical and structural properties of the chain-forming model. The model has polymerizing points at arbitrary position from center of the particles. Calculated analytical results were tested against corresponding results obtained by Monte Carlo computer simulations to check the accuracy of the theories. The theories are accurate for the different positions of patches of the model at all values of the temperature and density studied. The IET’s pair correlation functions of the model agree well with computer simulations. Both TPT and IET are in good agreement with the Monte Carlo values of the energy, chemical potential and ratios of free, once and twice bonded particles.

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.

Knowledge of water-water potential is important for an accurate description of water. Potential between two molecules depends upon the distance, relative orientation of each molecule and local environment. In simulation, water-water hydrogen bonds are handled by point-charge water potentials and by polarizable models. These models produce good results for bulk water being parameterized for such environment. Water around surfaces and in channels, however is different from bulk water. Using quantum-mechanical methods, hydrogen bond strength was calculated in the vicinity of different monoions. A simple empirical relationship was discovered between the maximum hydrogen bond and the electric field produced by ion.

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.

Understanding the spatial folding of proteins from their amino acid sequences has an enormous potential in contemporary life sciences. The ability to predict secondary and tertiary structures from primary ones through the use of computers will enable a much faster and more efficient discovery of organic substances with therapeutic or otherwise bioactive potential, largely eliminating the need for synthesis and testing of large numbers of organic substances for physiological effects. Our manuscript presents an application of correlation function analysis, usually used to describe properties of liquids, to protein structures in order to elucidate statistically favored distances among amino acids. Pairwise distribution functions were calculated between C-alpha atoms of 20 amino acids in a large ensemble of Protein Data Bank structures. The correlation functions show characteristic distances in amino acid interactions. Different propensities for forming various secondary structure elements among all 210 possible amino acid pairs have been visualized and some have been interpreted. Notably, we found helices to be surprisingly common among certain pairs.

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.

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.