Simple model of membrane proteins including solvent

We report a numerical simulation for the phase diagram of a simple two-dimensional model, similar to the one proposed by Noro and Frenkel [J. Chem. Phys. 114, 2477 (2001)] for membrane proteins, but one that includes the role of the solvent. We first use Gibbs ensemble Monte Carlo simulations to determine the phase behavior of particles interacting via a square-well potential in two dimensions for various values of the interaction range. A phenomenological model for the solute-solvent interactions is then studied to understand how the fluid-fluid coexistence curve is modified by solute-solvent interactions. It is shown that such a model can yield systems with liquid-liquid phase separation curves that have both upper and lower critical points, as well as closed loop phase diagrams, as is the case with the corresponding three-dimensional model.     

Parametric studies of interaction strengths in polymer/CO2 systems: discontinuous molecular dynamics simulations

Discontinuous molecular dynamics simulations are performed on homopolymer/solvent and surfactant/solvent systems. The homopolymer and surfactant molecules are modeled as freely jointed square-well chains. Solvent molecules are modeled as both hard spheres and square-well spheres. We explore how the various interaction parameters affect the types of phase behavior and micellization observed in the homopolymer/solvent and surfactant/solvent systems. Increasing the packing fraction of homopolymers in both hard-sphere solvents and square-well solvents increases the solvent's ability to dissolve homopolymers only when the segment-solvent interaction strength exceeds a critical value. Although only upper critical solution temperature (UCST) behavior is observed for homopolymers in hard-sphere solvents, both UCST and lower critical solution temperature (LCST) behavior are observed for homopolymers in square-well solvents, depending upon the interaction strengths and chain length. This indicates that it is necessary to account for the solvent-solvent attraction to model LCST behavior in supercritical CO2. Our simulation results on surfactants in hard-sphere solvents show that it is necessary to account for the interactions experienced by both the head and tail blocks in order to capture the essential features of surfactant/supercritical CO2 systems.     

Determination of the critical parameters of polymer solutions

The contribution of short-range orientation order to the chemical potentials of components in a polymer-solvent system was determined. The temperature dependence of the degree of orientation of solvent molecules relative to polymer chains in a polyisobutylene-benzene system was obtained. It was shown that the short-range order in the polymer-solvent system fails with temperature to a much lesser extent than in the pure solvent. The expressions for the upper and lower critical solution temperatures with allowance for the contribution of short-range order to the entropy and the free energy of solution, as well as to the chemical potentials of components, were found. It was demonstrated that, in the polymer-solvent system, two upper and two lower critical solution temperatures can exist.     

Bubble nucleation in micellar solution: a density functional study

We explore the free energetics of bubble nucleation in the micellar solution subjected to a negative pressure using a density functional model of a non-ionic surfactant solution. In this two-component model, the solvent is represented by a single hard-core sphere and the surfactant is represented by two tangent hard-core spheres connected by a rigid bond. The attractive interactions between the particles are modeled by the simple 1/R(6) form. Under all conditions of pressure and interparticle interactions we studied, the free energy barrier of bubble nucleation is found to be lower in the binary surfactant solution than that in a pure solvent and to continue to decrease as the mole fraction of the surfactant in the solution increases. We analyze the free energy surface of the model system under the conditions where both the critical bubble nucleus and the stable micelle exist in equilibrium with the same metastable solution. Our study shows that at moderately low pressures, bubbles can nucleate from the stable micelle and that the resulting free energy barrier of bubble nucleation is expected to be lower than that in the absence of this mechanism. However, as the spinodal is approached at lower pressures, the mechanism of micelle-assisted bubble nucleation becomes less effective. The liquid-liquid miscibility of the model system correlates well with the mechanism of bubble nucleation from the stable micelle.     

A simple statistical mechanical theory for the mutual solubility of fluid mixtures of water and organic solvents under high pressure

A simple statistical mechanical theory is presented to explain phase diagrams of fluid mixtures with both a lower critical solution temperature and an upper critical solution temperature under pressure. By postulating a temperature dependence for the interaction free energy parameter of the constituent molecules and a pressure dependence for the excess volume, phase diagrams with both lower critical solution temperature, and upper critical solution temperature and their pressure dependence can be reproduced by quadratic surfaces in temperature-concentration-pressure space. The topological aspects of the observed phase diagrams in this space have been related to our theoretical model, and the thermodynamical meaning of the topologies has been interpreted based on our model. Experimental data for the mutual solubility of water and 2-butanol under pressure and that of water and 3-methylpyridine with added salts have been analyzed quantitatively and theoretical parameters are determined.     

Theoretical prediction of multiple fluid-fluid transitions in monocomponent fluids

The authors use the analytical equation of state obtained by the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97, 1225 (1999)] to study the phase diagram of fluids with discrete spherical potentials formed by a repulsive square-shoulder plus an attractive square-well interaction (SS+SW). This interaction is characterized by the usual energy and size parameters plus three dimensionless parameters: two of them measuring the widths of the SS and the SW and the third the relative height of the SS. The matter of interest is that, for certain values of the interaction parameters, the SS+SW systems exhibit more than one first-order fluid-fluid transition. The evidence that several real substances (such as water, phosphorus, carbon, and silica, among others) exhibit an extra liquid-liquid transition has drawn interest into the study of interactions responsible for this behavior. The simple SS+SW fluid is one of the systems that, in spite of being spherically symmetric, shows multiple fluid-fluid transitions. In this work the authors investigate systematically the effect on the phase diagram of varying the interaction parameters. The use of an analytical free-energy equation gives a clear thermodynamic picture of the emergence of different types of critical points, throwing new light on the phase behavior of these fluids and thus clarifying previous results obtained by other techniques. The interplay of attractive and repulsive forces with several scale lengths produces very rich phase diagrams, including cases with three critical points. The region of the interaction-parameter space where multiple critical points appear is mapped for various families of interactions.     

Phase behavior of short-range square-well model

Various Monte Carlo techniques are used to determine the complete phase diagrams of the square-well model for the attractive ranges lambda = 1.15 and lambda = 1.25. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for lambda = 1.15 are new. We find that the fluid-fluid critical point is metastable for both cases, with the case lambda = 1.25 being just below the threshold value for metastability. We compare our results with prior studies and with experimental results for the gamma(II)-crystallin.     

Phase equilibria and phase separation dynamics in a polymer composite containing a main-chain liquid crystalline polymer

Various topological phase diagrams of blends of main-chain liquid crystalline polymer (MCLCP) and flexible polymer have been established theoretically in the framework of Matsuyama–Kato theory by combining Flory–Huggins (FH) free energy for isotropic mixing, Maier–Saupe (MS) free energy for nematic ordering in the constituent MCLCP, and free energy pertaining to polymer chain-rigidity. As a scouting study, various phase diagrams of binary flexible polymer blends have been solved self-consistently that reveal a combined lower critical solution temperature (LCST) and upper critical solution temperature (UCST), including an hourglass phase diagram. The calculated phase diagrams exhibit liquidus and solidus lines along with a nematic–isotropic (NI) transition of the constituent MCLCP. Depending on the strengths of the FH interaction parameters and the anisotropic (nematic–nematic) interaction parameters, the self-consistent solution reveals an hourglass type phase diagram overlapping with the NI transition of the constituent MCLCP. Subsequently, thermodynamic parameters estimated from the phase diagrams hitherto established have been employed in the numerical computation to elucidate phase separation dynamics and morphology evolution accompanying thermal-quench induced phase separation of the MCLCP/polymer mixture. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3621-3630, 2006     

Theoretical and numerical study of the phase diagram of patchy colloids: ordered and disordered patch arrangements

We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.     

Partial miscibility in multicomponent polymer system

It has been shown, using the significant structure theory of liquids, that a lower critical solution temperature behavior as well as a upper critical solution temperature behavior can be expected for polymer–polymer systems and that a phase diagram of closed-loop-type in a polymer–polymer–solvent system can be possible. In this article the sublimation energy of a mixture was expressed as a quadratic form of segment surface fractions on pure components rather than that of mole fractions, and the effect of the segment surface fractions on critical compositions was explained. The calculated partial miscibilities were in good agreement with the experiment.     

Vapor-liquid equilibrium and critical behavior of the square-well fluid of variable range: a theoretical study

The vapor-liquid phase behavior and the critical behavior of the square-well (SW) fluid are investigated as a function of the interaction range, lambdain [1.25, 3], by means of the self-consistent Ornstein-Zernike approximation (SCOZA) and analytical equations of state based on a perturbation theory [A. L. Benavides and F. del Rio, Mol. Phys. 68, 983 (1989); A. Gil-Villegas, F. del Rio, and A. L. Benavides, Fluid Phase Equilib. 119, 97 (1996)]. For this purpose the SCOZA, which has been restricted up to now to a few model systems, has been generalized to hard-core systems with arbitrary interaction potentials requiring a fully numerical solution of an integro-partial differential equation. Both approaches, in general, describe well the liquid-vapor phase diagram of the square-well fluid when compared with simulation data. SCOZA yields very precise predictions for the coexistence curves in the case of long ranged SW interaction (lambda>1.5), and the perturbation theory is able to predict the binodal curves and the saturated pressures, for all interaction ranges considered if one stays away from the critical region. In all cases, the SCOZA gives very good predictions for the critical temperatures and the critical pressures, while the perturbation theory approach tends to slightly overestimate these quantities. Furthermore, we propose analytical expressions for the critical temperatures and pressures as a function of the square-well range.     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Conformation of a flexible chain in explicit solvent: exact solvation potentials for short Lennard-Jones chains

The average conformation of a flexible chain molecule in solution is coupled to the local solvent structure. In a dense solvent, local chain structure often mirrors the pure solvent structure, whereas, in a dilute solvent, the chain can strongly perturb the solvent structure which, in turn, can lead to either chain expansion or compression. Here we use Monte Carlo (MC) simulation to study such solvent effects for a short Lennard-Lones (LJ) chain in monomeric LJ solvent. For an n-site chain molecule in solution these many-body solvent effects can be formally mapped to an n-body solvation potential. We have previously shown that for hard-sphere and square-well chain-in-solvent systems this n-body potential can be decomposed into a set of two-body potentials. Here, we show that this decomposition is also valid for the LJ system. Starting from high precision MC results for the n = 5 LJ chain-in-solvent system, we use a Boltzmann inversion technique to compute numerically exact sets of two-body solvation potentials which map the many-body chain-in-solvent problem to a few-body single-chain problem. We have carried out this mapping across the full solvent phase diagram including the dilute vapor, dense liquid, and supercritical regions and find that these sets of solvation potentials are able to encode the complete range of solvent effects found in the LJ chain-in-solvent system. We also show that these two-site solvation potentials can be used to obtain accurate multi-site intramolecular distribution functions and we discuss the application of these exact short chain potentials to the study of longer chains in solvent.     

Solvent effects on methyl transfer reactions. 2. The reaction of amines with trimethylsulfonium salts.

The reaction of ammonia and pyridine with trimethylsulfonium ion has been studied in gas phase and solution. Density functional theory at the B3LYP/6-31+G level was used to describe the energy changes along the reaction coordinate in the gas phase, and the self-consistent isodensity polarizable continuum model (SCI-PCM) was used to calculate the effect of cyclohexane and dimethyl sulfoxide as the solvent on the energy changes. The effect of water as the solvent was studied using the Monte Carlo free energy perturbation method. The reaction with both ammonia and pyridine follows a similar rather convoluted path in gas phase, with the formation of several reaction complexes before and after the formation of the transition state. All the species found in gas phase persist in cyclohexane, yielding a reaction path very similar to that in gas phase but with significant differences in the relative energy of the critical points. In DMSO, the energy profile is greatly simplified by the disappearance of several of the species found in gas phase and in cyclohexane. The activation free energy increases with the polarity of the solvent in both reactions. Increasing the polarity of the solvent also increases the exothermicity of the reaction of trimethylsulfonium ion with ammonia and reduces it in the reaction with pyridine. In water, the free energy profile follows the same trend as found for DMSO, and free energy of activation is calculated to be larger by about 2-3 kcal/mol. This is in good agreement with an experimental measurement of the effect of solvent on the rate of reaction.     

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.     

Structure and anomalous solubility for hard spheres in an associating lattice gas model

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.     

Phase behavior of colloids and proteins in aqueous suspensions: Theory and computer simulations

The fluid phase behavior of colloidal suspensions with short-range attractive interactions is studied by means of Monte Carlo computer simulations and two theoretical approximations, namely, the discrete perturbation theory and the so-called self-consistent Ornstein-Zernike approximation. The suspensions are modeled as hard-core attractive Yukawa (HCAY) and Asakura-Oosawa (AO) fluids. A detailed comparison of the liquid-vapor phase diagrams obtained through different routes is presented. We confirm Noro-Frenkel's extended law of scaling according to which the properties of a short-ranged fluid at a given temperature and density are independent of the detailed form of the interaction, but just depend on the value of the second virial coefficient. By mapping the HCAY and AO fluids onto an equivalent square-well fluid of appropriate range at the critical point we show that the critical temperature as a function of the effective range is independent of the interaction potential, i.e., all curves fall in a master curve. Our findings are corroborated with recent experimental data for lysozyme proteins.     

Temperature dependence of the configurational free energy of a branched polymer

We consider a lattice model of branched polymers in dilute solution in which the polymer is modelled as an animal, weakly embeddable in the (simple cubic) lattice. In order to model the effect on the thermodynamic properties of changing the temperature or the quality of the solvent, we include an energy associated with the number of nearneighbour contacts between pairs of vertices of the animals. We show that the configurational free energy of the animal is a continuous function of the temperature and derive rigorous upper and lower bounds on the temperature dependence of the free energy. Finally, we comment on similarities between these results and corresponding ones for a model in which the energy is associated with the cyclomatic index of the animal.     

Phase state of the polysulfone-poly(ethylene glycol)-dimethylacetamide system

Via the method of turbidity points, a fragment of the phase diagram of the polysulfone-poly(ethylene glycol) 400-dimethylacetamide three-component system was constructed. This system is a unique object with both an upper critical solution temperature and a second-order lower critical solution temperature. Viscosity characteristics and activation parameters of the viscous flow of concentrated and dilute polysulfone solutions in dimethylacetamide containing poly(ethylene glycol) were studied. An abnormal increase in the solution viscosity with temperature that precedes the phase transition was found. With the use of IR spectroscopy and the viscometry of dilute solutions, it was shown that it is possible to form additive compounds between the components in a solution.     

Liquid–liquid equilibria of polymer solutions: Flory‐huggins with specific interaction

We have developed a new Flory‐Huggins model by adding a specific interaction parameter derived from a modified double‐lattice model for the Helmholtz energy of mixing for binary liquid mixtures. This model is very simple and could be easily integrated into engineering applications. Using this revised model, we can successfully describe the phase behavior of polymer solutions with an upper critical solution temperature (UCST), a lower critical solution temperature (LCST), both UCST and LCST, and a closed miscibility loop. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 162–167, 2010