On the universal behavior of some thermodynamic properties along the whole liquid-vapor coexistence curve

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.     

Water in nanopores. I. Coexistence curves from Gibbs ensemble Monte Carlo simulations

Coexistence curves of water in cylindrical and slitlike nanopores of different size and water-substrate interaction strength were simulated in the Gibbs ensemble. The two-phase coexistence regions cover a wide range of pore filling level and temperature, including ambient temperature. Five different kinds of two-phase coexistence are observed. A single liquid-vapor coexistence is observed in hydrophobic and moderately hydrophilic pores. Surface transitions split from the main liquid-vapor coexistence region, when the water-substrate interaction becomes comparable or stronger than the water-water pair interaction. In this case prewetting, one and two layering transitions were observed. The critical temperature of the first layering transition decreases with strengthening water-substrate interaction towards the critical temperature expected for two-dimensional systems and is not sensitive to the variation of pore size and shape. Liquid-vapor phase transition in a pore with a wall which is already covered with two water layers is most typical for hydrophilic pores. The critical temperature of this transition is very sensitive to the pore size, in contrast to the liquid-vapor critical temperature in hydrophobic pores. The observed rich phase behavior of water in pores evidences that the knowledge of coexistence curves is of crucial importance for the analysis of experimental results and a prerequiste of meaningful simulations.     

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.     

Liquid-liquid phase transitions in supercooled water studied by computer simulations of various water models

Liquid-liquid and liquid-vapor coexistence regions of various water models were determined by Monte Carlo (MC) simulations of isotherms of density fluctuation-restricted systems and by Gibbs ensemble MC simulations. All studied water models show multiple liquid-liquid phase transitions in the supercooled region: we observe two transitions of the TIP4P, TIP5P, and SPCE models and three transitions of the ST2 model. The location of these phase transitions with respect to the liquid-vapor coexistence curve and the glass temperature is highly sensitive to the water model and its implementation. We suggest that the apparent thermodynamic singularity of real liquid water in the supercooled region at about 228 K is caused by an approach to the spinodal of the first (lowest density) liquid-liquid phase transition. The well-known density maximum of liquid water at 277 K is related to the second liquid-liquid phase transition, which is located at positive pressures with a critical point close to the maximum. A possible order parameter and the universality class of liquid-liquid phase transitions in one-component fluids are discussed.     

Surface tension of water and acid gases from Monte Carlo simulations

We report direct Monte Carlo (MC) simulations on the liquid-vapor interfaces of pure water, carbon dioxide, and hydrogen sulfide. In the case of water, the recent TIP4P/2005 potential model used with the MC method is shown to reproduce the experimental surface tension and to accurately describe the coexistence curves. The agreement with experiments is also excellent for CO(2) and H(2)S with standard nonpolarizable models. The surface tensions are calculated by using the mechanical and the thermodynamic definitions via profiles along the direction normal to the surface. We also discuss the different contributions to the surface tension due to the repulsion-dispersion and electrostatic interactions. The different profiles of these contributions are proposed in the case of water.     

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.     

Development of a new polarizable potential model of hydrogen fluoride and comparison with other effective models in liquid and supercritical states

Development of a new polarizable potential of hydrogen fluoride through the reparametrization of the JV-P model is presented: The length of the H-F bond has been shortened and the other parameters of the model have been readjusted accordingly. The structural, thermodynamic, and liquid-vapor equilibrium properties of the new model are compared with those of other effective potential models of HF as well as with experimental data in a broad range of thermodynamic states, from near-freezing to supercritical conditions. It is found that although the reparametrization does not change the structural properties of the HF model noticeably at the level of the pair correlations, it improves the reproduction of the thermodynamic properties of hydrogen fluoride over the entire range of existence of a thermodynamically stable liquid phase and also that of the vapor-liquid coexistence curve. However, the new model, which still overestimates the close-contact separation of the HF molecules, underestimates the density of the coexisting liquid phase and overestimates the saturation pressure, probably due to the too steep repulsion of the potential function.     

Cloud-Point Curves and Coexistence Curves of Several Polydisperse Polystyrenes in Cyclohexane

Cloud-point curves, critical points, and coexistence curves with feed concentrations close to the critical concentration were measured in three systems involving cyclohexane + different polydisperse polystyrenes. The shape of the coexistence curves is analyzed by using a scaling expression. In two systems the critical exponent β possesses values somewhat larger than in actual binary systems (where β ≈ 1/3), whereas in the third system a somewhat smaller value is found. By using a three-parameter Gibbs free energy relation, cloud-point curves and coexistence curves are calculated from the critical point data and from the slope of the cloud-point curve at this point. To account for polydispersity, the method of continuous thermodynamics is applied. The cloud-point curves are well described, but the prediction of the coexistence curves is bad due to the mean-field character of the Gibbs free energy relation resulting in β = 1/2. Hence, the often used practice of fitting the parameters of a mean-field Gibbs free energy relation to the critical point and to some cloud points and then to calculate the coexistence data is to be considered with great care.     

Simulation and theory of a model for tetrahedral colloidal particles

We study the thermodynamic and structural properties of a five-site tetrahedral molecular model by means of different Monte Carlo simulation techniques, and the reference interaction site model (RISM) theory of molecular fluids. Simulations and theory signal the onset, at sufficiently low temperatures, of two different tetrahedral molecular arrangements, with a more open topology progressively giving place to a fully bonded one, as the temperature decreases. The RISM theory reproduces the splitting of the static structure factor at low temperatures, a feature intimately related to the onset of the tetrahedral ordering. Less accurate predictions are obtained for the liquid-vapor coexistence and the short-range correlations.     

Phase diagram of complex fluids using an efficient integral equation method

We present an adaptive technique for the determination of the phase diagram of fluids within the integral equation theory. It enables an efficient and accurate systematic mapping of the thermodynamic space in order to construct the binodal and spinodal lines. Results are obtained with the thermodynamically consistent integral equation proposed by Sarkisov [J. Chem. Phys. 114, 9496 (2001)] within the tangent linear technique that yields an exact differentiation of correlation functions. The generality of the numerical approach is assessed by determining both the liquid-vapor coexistence and the critical parameters of the generalized Lennard-Jones (n,6) potentials with varying repulsive part, including the hard-sphere limit.     

The liquid–liquid coexistence curves of {x dimethyl adipate + (1 − x) n-octane} and {x dimethyl adipate + (1 − x) n-nonane} in the critical region

The liquid–liquid coexistence curves of (dimethyl adipate + n-octane) and (dimethyl adipate + n-nonane) have been determined within about 10 K from the critical temperatures, from which the critical amplitudes and the critical exponents are deduced. The critical exponents corresponding to the coexistence curve β are consistent with the 3D-Ising values. The experimental results have been analyzed to determine Wegner-correction terms and to discuss the asymmetric behaviour of the diameters of the coexistence curves by the complete scaling theory. Molar mass-dependences of the critical amplitude and the critical volume fraction have been shown to be consistent with the theoretical prediction.     

On approximate mathematical modeling of the vapor–liquid coexistence curves by the Van der Waals equation of state and non-classical value of the critical exponent

Van der Waals equation of state as well as power laws and critical exponent theories are prototypes to study the cubic shape, asymmetries and “flatness” of the vapor–liquid equilibrium curves near the critical point. In this work we study two similar methods to determine the phase curves in analytical form, which differ from each other by simplicity of mathematical calculation. We analyze temperature dependence of the coexistence curves asymptotically close to the vapor–liquid critical point. We explain the novelty of our method with respect to the standard thermodynamic limit discussed in the literature. Therefore we show that the shape of the coexistence curves can strongly influence the accepted value of the critical exponent. The results of theoretical studies have been compared with the ones obtained by experimental methods.     

Liquid-vapor interface of square-well fluids of variable interaction range

Properties of the liquid-vapor interface of square-well fluids with ranges of interaction lambda=1.5, 2.0, and 3.0 are obtained by Monte Carlo simulations and from square-gradient theories that combine the Carnahan-Starling equation of state for hard spheres with the second and third virial coefficients. The predicted surface tensions show good agreement with the simulation results for lambda=2 and for lambda=3 in a temperature range reasonably close to the critical point, 0.8相似文献   

On Assessment of the Thermodynamic Consistency of Data on Liquid-Vapor Equilibrium

A new method for assessment of the thermodynamic consistency of binary isothermal data on the liquid-vapor equilibrium by calculating the Redlich-Kiester integral with account of how the pressure of phase coexistence depends on the vapor composition is suggested. The Maple 8 software is used to compare the values of the integral, other characteristics calculated for systems with varied nature of departures from the Raoult law.     

Vapor-liquid coexistence of patchy models: relevance to protein phase behavior

The vapor-liquid coexistence boundaries of fluids composed of particles interacting with highly directional patchy interactions, in addition to an isotropic square well potential, are evaluated using grand canonical Monte Carlo simulations combined with the histogram reweighting and finite size scaling methods. We are motivated to study this more complicated model for two reasons. First, it is established that the reduced widths of the metastable vapor-liquid coexistence curve predicted by a model with only isotropic interparticle interactions are much too narrow when compared to the experimental phase behavior of protein solutions. Second, interprotein interactions are well known to be "patchy." Our results show that at a constant total areal density of patches, the critical temperature and the critical density increase monotonically with an increasing number of uniformly spaced patches. The vapor-liquid coexistence curves plotted in reduced coordinates (i.e., the temperature and the density scaled by their respective critical values) are found to be effectively independent of the number of patches, but are much broader than those found for the isotropic models. Our findings for the reduced width of the coexistence curve are almost in quantitative agreement with the available experimental data for protein solutions, stressing the importance of patchiness in this context.     

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.     

Liquid-vapor and liquid-liquid phase equilibria of the Brodholt-Sampoli-Vallauri polarizable water model

Liquid-vapor and liquid-liquid phase equilibria of the polarizable Brodholt-Sampoli-Vallauri water model have been investigated by Gibbs ensemble Monte Carlo computer simulations. The coexisting liquid and vapor densities and energy of vaporization of the model is found to be in a reasonable agreement with experimental data in the entire temperature range of liquid-vapor coexistence. The critical temperature and density of the model are found to be 615 K and 0.278 gcm(3), respectively, close to the experimental values of 647.1 K and 0.322 gcm(3). In the supercooled state two distinct liquid-liquid coexistence regions are observed. The existence of liquid-liquid phase separation of a polarizable water model is demonstrated for the first time.     

Interfacial and coexistence properties of soft spheres with a short-range attractive Yukawa fluid: molecular dynamics simulations

Molecular dynamics simulations have been carried out to obtain the interfacial and coexistence properties of soft-sphere attractive Yukawa (SAY) fluids with short attraction range, κ = 10, 9, 8, 7, 6, and 5. All our simulation results are new. These data are also compared with the recently reported results in the literature of hard-core attractive Yukawa (HAY) fluids. We show that the interfacial and coexistence properties of both potentials are different. For the surveyed systems, here we show that all coexistence curves collapse into a master curve when we rescale with their respective critical points and the surface tension curves form a single master curve when we plot γ* vs. T/T(c).     

Equation of state for expanded fluid mercury: variational theory with many-body interaction

A variational associating fluid theory is proposed to describe equations of state for expanded fluid mercury. The theory is based on the soft-sphere variational theory, incorporating an ab initio diatomic potential and an attractive many-body potential; the latter is evaluated with quantum chemical methods and expressed as a function of the local atomic coordination number and the nearest-neighbor distance. The resultant equation of state can reproduce the observed gas-liquid coexistence curve with good accuracy, without introducing phenomenological effective pair potentials. Various thermodynamic quantities such as pressure, isocloric thermal pressure coefficient, adiabatic sound velocity, and specific heat are calculated over a wide density-temperature range and compared with available experimental data.     

The measurements of coexistence curves and turbidity for {xC6H5CN + (1 − x)CH3(CH2)14CH3} in the critical region

The coexistence curves and turbidity data for a critical solution of (benzonitrile + hexadecane) have been reported. The critical amplitudes and exponents relating to the difference in density variables of two coexisting phases, the correlation length, and the osmotic compressibility have been calculated. The experimental results of the coexistence curves have also been analyzed to examine the Wegner correction terms and the behaviour of the diameter of the coexistence curves. A combination of the Wegner equation and the expression for the diameter has been used to describe successfully the coexistence curves.