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Specialized Monte Carlo simulations and the moment free energy (MFE) method are employed to study liquid-gas phase equilibria in size-disperse fluids. The investigation is made subject to the constraint of fixed polydispersity, i.e. the form of the `parent' density distribution $\rho^0(\sigma)$ of the particle diameters $\sigma$, is prescribed. This is the experimentally realistic scenario for e.g. colloidal dispersions. The simulations are used to obtain the cloud and shadow curve properties of a Lennard-Jones fluid having diameters distributed according to a Schulz form with a large (40%) degree of polydispersity. Good qualitative accord is found with the results from a MFE method study of a corresponding van der Waals model that incorporates size-dispersity both in the hard core reference and the attractive parts of the free energy. The results show that polydispersity engenders considerable broadening of the coexistence region between the cloud curves. The principal effect of fractionation in this region is a common overall scaling of the particle sizes and typical inter-particle distances, and we discuss why this effect is rather specific to systems with Schulz diameter distributions. Next, by studying a family of such systems with distributions of various widths, we estimate the dependence of the critical point parameters on $\delta$. In contrast to a previous theoretical prediction, size-dispersity is found to raise the critical temperature above its monodisperse value. Unusually for a polydisperse system, the critical point is found to lie at or very close to the extremum of the coexistence region in all cases. We outline an argument showing that such behaviour will occur whenever size polydispersity affects only the range, rather than the strength of the inter-particle interactions., Comment: 14 pages, 12 figures

A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluation—Gibbs’ method (employing the capillarity approximation), the van der Waals–Cahn and Hilliard and a newly developed modified Gibbs’ approach—is given in application to phase formation in multicomponent systems. As an example, processes of boiling in binary liquid–gas solutions, in particular, in nitrogen–helium mixtures are investigated. In addition to the work of critical cluster formation, the bulk properties of the critical bubbles, their characteristic sizes and the values of the surface tension are determined in dependence on the initial supersaturation in the system or, equivalently, on the size of the critical clusters. It is shown that latter two mentioned methods (the van der Waals–Cahn and Hilliard and the modified Gibbs’ approach) lead, in the determination of the work of critical cluster formation, to qualitatively and widely even quantitatively equivalent results. As one of the more general consequences from the present analysis, it has been proven that the modified Gibbs’ approach represents a highly effective tool for the determination of the work of formation of clusters or bubbles of critical sizes not only for one-component and quasibinary systems, discussed earlier, but for phase formation in multicomponent systems of, in general, arbitrary numbers of components as well. It is shown that the modified Gibbs’ approach is preferable as compared with Gibbs’ original treatment not only due to its advantages with respect to an appropriate determination of the properties of clusters of critical sizes, but also from general theoretical considerations. In the limit of large sizes of the critical clusters, both approaches—Gibbs’ original treatment and the modified or generalized Gibbs’ approach—lead to equivalent results.

The nucleation at a planar surface with attraction is investigated by molecular dynamics and compared with the corresponding homogeneous nucleation [J. Chem. Phys. 115, 8913 (2001)]. The attraction caused an increased vapor density near the surface which favors nucleation even for a weak attraction. The contact angle (Young’s angle) for the critical nucleus cannot be obtained from Young’s equation by using the equilibrium values for the tensions, due to the overlap of the solid–liquid interface with the liquid gas interface near the line of contact. After onset of nucleation the droplets grow algebraically with an increase of particles with a time exponent ≈1.25, and different from the Lifshitz–Slyozov growth. For strong attractions the system undergoes a first-order prewetting transition to a thin two-dimensional-like layer of a thickness of only a few particle diameters. This happens at densities less than the density of saturated bulk vapor. The dynamics of prewetting behaves qualitatively as the homogeneous and heterogeneous nucleation and with the onset of prewetting by crossing an activation free energy barrier.

Isotropic Raman line shapes provide information about molecular interactions, structure, and dynamics. Such line shapes have been measured experimentally along the liquid–gas coexistence lines for both nitrogen and oxygen. We extend previous theoretical studies of nitrogen Raman line shapes by including in a systematic way the dependence of the bond lengths and dispersion and repulsive force parameters on vibrational coordinates. In so doing we include the effects of vibration-rotation and resonant vibrational intermolecular interactions. The dispersion and repulsive force parameter dependences are crucial for obtaining a quantitative description (and even the correct sign) of the line shift. Using a recently developed intermolecular potential, we perform similar calculations for oxygen. For both oxygen and nitrogen agreement with experimental Raman line shifts and line widths along the liquid–gas coexistence lines is reasonably good. One interesting feature of our results is that the dependence of the dispersion and repulsive force parameters on the vibrational coordinates is developed in such a way as to be directly useful in calculations of vibrational lifetimes.

We study a model for an argon-like fluid parameterised in terms of a hard-core repulsion and a two-Yukawa potential. The liquid-gas phase behaviour of the model is obtained from the thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) of Hoye and Stell, the solution of which lends itself particularly well to a pair potential of this form. The predictions for the critical point and the coexistence curve are compared to new high resolution simulation data and to other liquid-state theories, including the hierarchical reference theory (HRT) of Parola and Reatto. Both SCOZA and HRT deliver results that are considerably more accurate than standard integral-equation approaches. Among the versions of SCOZA considered, the one yielding the best agreement with simulation successfully predicts the critical point parameters to within 1%., Comment: 10 pages 6 figures

The effects of temperature and pressure nonuniformities at evaporation on the properties of liquid–gas interface are studied by molecular dynamics (MD) simulation and thermodynamic perturbation method on the basis of the van der Waals theory of capillarity. The structure and properties of the interfacial layer of equilibrium and nonequilibrium Lennard-Jones (12-6) systems are investigated. The surface tension, the two-particle distribution functions, the density fluctuation correlation lengths, and the evaporation coefficients are calculated using MD simulation. It is shown that the presence of the temperature gradient at the interface due to evaporation leads to reduction of the surface tension. The results of MD simulations are in agreement with the results of thermodynamic approach.

A Temperature–and–Density–Scaling Monte Carlo (TDSMC) study of the square-well fluid was carried out. The relative excess free energy was obtained directly from the simulations with a standard deviation less then 0.5%. Energy, pressure, compressibility and heat capacity were calculated from the excess free energy data. For the system of 256 particles a reduced density interval of 0.1-0.68 and a reduced temperature interval of 1.053-1.29 was covered. In the simulations a “zoom focus” on the temperature–density grid was used: a “panoramic view” of the whole temperature–density region, on a relatively coarse grid, was combined with a “close-up” of the critical–point region, using a finer (T,ρ) grid. The coexistence curve was obtained with use of the double–tangent construction on the free energy, and the critical temperature and critical density were estimated. The critical parameters found by the TDSMC method are compared with those of other Monte-Carlo techniques.

In two-phase flows, the interface intervening between the two fluid phases intersects the solid wall at the contact line. A classical problem in continuum fluid mechanics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a nonintegrable stress singularity. Recently, various diffuse-interface models have been proposed to explain the contact line motion using mechanisms missing from the sharp-interface treatments in fluid mechanics. In one-component two-phase (liquid-gas) systems, the contact line can move through the mass transport across the interface while in two-component (binary) fluids, the contact line can move through diffusive transport across the interface. While these mechanisms alone suffice to remove the stress singularity, the role of fluid slip at solid surface needs to be taken into account as well. In this paper, we apply the diffuse-interface modeling to the study of contact line motion in one-component liquid-gas systems, with the fluid slip fully taken into account. The dynamic van der Waals theory has been presented for one-component fluids, capable of describing the two-phase hydrodynamics involving the liquid-gas transition [A. Onuki, Phys. Rev. E 75, 036304 (2007)]. This theory assumes the local equilibrium condition at the solid surface for density and also the no-slip boundary condition for velocity. We use its hydrodynamic equations to describe the continuum hydrodynamics in the bulk region and derive the more general boundary conditions by introducing additional dissipative processes at the fluid-solid interface. The positive definiteness of entropy production rate is the guiding principle of our derivation. Numerical simulations based on a finite-difference algorithm have been carried out to investigate the dynamic effects of the newly derived boundary conditions, showing that the contact line can move through both phase transition and slip, with their relative contributions determined by a competition between the two coexisting mechanisms in terms of entropy production. At temperatures very close to the critical temperature, the phase transition is the dominant mechanism, for the liquid-gas interface is wide and the density ratio is close to 1. At low temperatures, the slip effect shows up as the slip length is gradually increased. The observed competition can be interpreted by the Onsager principle of minimum entropy production.

The effective diameters of molecules σcp of some molecular liquids, i.e., liquids halogens, carbon tetrachloride and benzene, have been estimated by a critical packing fraction of ηcp = 0.130 44 predicted for a van der Waals fluid. It turns out that the estimated values of σcp are in good agreement with the effective diameters σsf estimated independently to explain the structure factor of the liquids. It seems that both the liquid structure and the critical point are determined by a common factor, i. e., a common effective diameter of molecules, and that the simple relation of ηcp≂0.13 holds fairly well even in the molecular liquids.

We propose a new unified field‐theoretic path integral treatment of liquid–gas transition occurring in simple neutral fluids and neutral monodisperse polymer solutions. Obtained theoretical results indicate that both systems belong to the same Ising‐type universality class which is strongly supported by the most recent experimental results on the liquid–gas transitions.

The statistical rate theory approach is used to derive the expression for the rate of gas absorption by a liquid. This process involves two sequential rates−the rate of transport from the gas to the surface and the rate of transport from the surface to the bulk liquid. According to the statistical rate theory, the rate limiting step is the rate of transport from the surface. After deriving the rate expression for the rate limiting step, it is incorporated in an integral equation approach for predicting the rate of evolution of a bubble evolving isothermally in a liquid–gas solution. This approach accounts for the movement of the bubble boundary in the diffusion problem. Statistical rate theory leads to a complete expression for the rate of gas absorption; thus by comparing the predicted rate of bubble evolution with a set of measurements, one can investigate the validity of the statistical rate theory. This comparison is carried out and the predictions are found to be in close agreement with the experiments throughout the experimental period.

With the neglect of the translational motion of the bubble, approximate solutions may be found for the rate of solution by diffusion of a gas bubble in an undersaturated liquid-gas solution; approximate solutions are also presented for the rate of growth of a bubble in an oversaturated liquid-gas solution. The effect of surface tension on the diffusion process is also considered.

As a preparation for the study of nucleation and growth of a film, the equation of state is derived for a system of atoms on a two‐dimensional lattice using the cluster‐variation method. Two cases are calculated. In the first portion of the paper the pair approximation is used for the case in which fixed impurities are scattered on the lattice. The isotherm is of the van der Waals type. In the second portion of the paper, a triangle is used as the basic cluster to show how the improved approximation works. It is significant that a flat portion in the pressure—density isotherm results in connection with the phase separation.

Rotational and translational energy levels established from induced IR absorption spectra of dilute solutions of hydrogen and deuterium in liquid argon

The recent paper by Polo and Wilson eliminates the apparent discrepancy between the equations given for the relationship between intensities of a compound in the gas phase and the intensities in the liquid phase. However, the experimental tests of this equation have not been conclusive. This paper applies their equation to the pressure‐induced absorption of methane, and to the temperature dependence of the integrated intensities of liquid cyclohexanone and liquid benzene. The treatment of Polo and Wilson is extended to give an equation which is valid for solutions. In all cases, qualitative agreement is obtained between experiment and calculation and it would seem that the effect of index of refraction on the intensity accounts for a significant part of the changes observed. The agreement for benzene and for the pressure‐induced absorption of methane is excellent.

It is shown that the nonlocal free‐energy density functional of the penetrable sphere model yields, in a mean‐field approximation, a density profile of finite thickness in which the pair correlation function decays slowly in the transverse directions. This result shows that simultaneous occurrence of a finite interfacial thickness and a slow decay of the transverse correlations is not linked to a local free‐energy density functional of the van der Waals type.