Theory of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids

We present results of calculations of the equilibrium surface tension and density profiles for the liquid-vapour interface of a binary mixture of Lennard-Jones 12-6 fluids. The calculations are based on a density-functional theory for the Helmholtz free energy of the inhomogeneous mixture. This is a ‘microscopic’ generalization of the van der Waals-Cahn-Hilliard theory for the interface of a binary mixture.

Our calculations cover the full range of liquid-vapour coexistence and the whole range of concentration. We find a correlation between the excess surface tension of the mixture and the surface segregation (adsorption) of the species with the lower surface tension. The ways in which segregation and excess surface tension depend on the Lennard-Jones parameters of the pure components are briefly discussed. Our results for the excess surface tension of mixtures of Ar and N₂ and Ar and CH₄ are compared with experiment; the agreement is reasonable.     

Statistical thermodynamics of isolated rigid rod-like molecules near a surface

The configurational behaviour and thermodynamic properties of a dilute gas of rigid rod-like molecules in the vicinity of a macroscopic planar adsorption surface are investigated using statistical mechanics. The interaction energy between the surface and a rod-like molecule is determined as a function of both its molecular centre of mass separation R and its orientation relative to the surface. In calculating this interaction energy, each rod segment and molecule comprising the surface is assumed to interact through a Lennard-Jones pair potential. The average molecular order parameter is then determined as a function of R. We find that an isolated rod-like molecule tends to align nearly parallel to the surface for small separations. However, as R increases the order parameter first passes through a maximum then decays to zero as R ^-5 for large R. The configurational behaviour of an isolated rod-like molecule located between two parallel adsorption surfaces is also considered briefly. The surface spreading pressure, excess surface energy and entropy are also obtained for a dilute gas of rod-like molecules near a surface. We find that the extent of surface binding increases nearly exponentially with molecular length at constant temperature and surface density, and that the excess surface energy and entropy are essentially proportional to the molecular length.     

Anion polarizability functions in alkali halide crystals

Anion polarizabilities in alkali halide crystals are analysed as a function of interionic separation R. The anion polarizability is treated as a function of the anion and cation radii, with its partial derivatives approximated by those with respect to R for fixed cation and anion, respectively. With pressure derivatives of the ionic radii deduced from the crystal compressibility, assuming transferability among crystals, the polarizability derivatives with respect to ionic radius yield pressure derivatives of the polarizability that agree with experiment to within a factor of two. These results offer a useful means of predicting the pressure dependence of dielectric data.     

Stability of fluid flow past a membrane

The stability of the flow of a fluid past a solid membrane of infinitesimal thickness is investigated using a linear stability analysis. The system consists of two fluids of thicknesses R and H R and bounded by rigid walls moving with velocities and , and separated by a membrane of infinitesimal thickness which is flat in the unperturbed state. The fluids are described by the Navier-Stokes equations, while the constitutive equation for the membrane incorporates the surface tension, and the effect of curvature elasticity is also examined for a membrane with no surface tension. The stability of the system depends on the dimensionless strain rates and in the two fluids, which are defined as and for a membrane with surface tension , and and for a membrane with zero surface tension and curvature elasticity K. In the absence of fluid inertia, the perturbations are always stable. In the limit , the decay rate of the perturbations is O(k ³ ) smaller than the frequency of the fluctuations. The effect of fluid inertia in this limit is incorporated using a small wave number asymptotic analysis, and it is found that there is a correction of smaller than the leading order frequency due to inertial effects. This correction causes long wave fluctuations to be unstable for certain values of the ratio of strain rates and ratio of thicknesses H. The stability of the system at finite Reynolds number was calculated using numerical techniques for the case where the strain rate in one of the fluids is zero. The stability depends on the Reynolds number for the fluid with the non-zero strain rate, and the parameter , where is the surface tension of the membrane. It is found that the Reynolds number for the transition from stable to unstable modes, , first increases with , undergoes a turning point and a further increase in the results in a decrease in . This indicates that there are unstable perturbations only in a finite domain in the plane, and perturbations are always stable outside this domain. Received: 29 May 1997 / Revised: 9 October 1997 / Accepted: 26 November 1997     

A molecular dynamics study of effective parameters on nano-droplet surface tension

The main purpose of this paper is to numerically study the effect of droplet radius, temperature, and surface wettability on droplet surface tension. Moreover, the validity of Young-Laplace equation (Y-L) for nano-droplet is examined. Simulations of droplet surrounded by its vapor and droplet on solid surface are carried out and the results are compared to each other in order to comprehend the role of surface wettability on droplet surface tension. The pair potential for the liquid-liquid and liquid-solid interaction is considered using Lennard-Jones model. Different numbers of atoms and surface wettabilities are employed to generate droplet of different radiuses. In addition, contact angle of droplet on solid surface is computed. Pressure tensor and density profile is locally calculated. Furthermore, liquid pressure is evaluated far from the interface using the virial theorem and gas pressure is obtained using an equation of state. In order to calculate the surface tension, two different approaches are employed; Young-Laplace equation and direct molecular dynamics (MD) simulation. The surface tension increases with increase in droplet radius and it is seen that the surface wettability does not directly influence the surface tension.     

Adsorption and interfacial phenomena of a Lennard-Jones fluid adsorbed in slit pores: DFT and GCMC simulations

ABSTRACT

Confinement of fluids in porous media leads to the presence of solid–fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in particular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are compared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid–fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability.     

Theory of surface tension and its application to simple fluids

We consider a liquid-vapor interface in thermal equilibrium. The tangential component of the pressure tensor is supposed to depend explicitly upon the position and the density profile. Under this hypothesis the mechanical definition of surface tension becomes a finite summation ofN+1 terms related directly to the local compressibility. When the inhomogeneous compressibility equation is considered, the theory provides a microscopic expression of the surface tension coefficient. A calculation for argon near the critical point is done; the agreement with experiment is satisfactory.     

Effects of finite thickness on interfacial widths in confined thin films of coexisting phases

The capillary broadening of a 2-phase interface is investigated both experimentally and theoretically. When a binary mixture in a thin film with thickness D segregates into two coexisting phases the interface between the two phases may form parallel to the substrate due to preferential surface attraction of one of the components. We show that the interfacial profile (of intrinsic width w₀) is broadened due to capillary waves, which lead to fluctuations, of correlation length of the local interface positions in the directions parallel to the confining walls. We postulate that acts as an upper cutoff for the spectrum of capillary waves on the interface, so that the effective mean square interfacial width w varies as . In the limit of large D this yields or respectively for the case of short- or long-range forces between walls and the interface. We used the Nuclear Reaction Analysis depth profiling technique, to investigate this broadening effect directly in two binary polymer mixtures. Our results reveal that the interfacial width indeed increases with film thickness D, though the observed interfacial width is lower than the predicted w. This is probably due to surface tension effects imposed by the confining surfaces which are not taken into account in our model. Received: 19 February 1998 / Received in final form: 2 September 1998 / Accepted: 8 September 1998     

Observation of vacancy defect migration in the cation sublattice of complex oxides by 18O tracer experiments

We report on 18O tracer diffusion experiments and model calculations for the study of cation vacancy migration in oxide crystals. The model takes advantage of the electrostatic coupling forces between anion and cation defects that allow the evolution of the cation vacancy profile to be observed by anion tracer experiments. Applied to SrTiO3, the ambipolar diffusion of strontium vacancies with H(A)=3.5 eV was found to be the dominant reequilibration mechanism of the cation sublattice. This result is in contrast to earlier studies proposing the formation of SrO intergrowth phases.     

Universality in crossover function for convection in fluids with a free surface

We show that in the onset of convection in a thin fluid layer with a free surface, the passage from surface tension driven to buoyancy driven convection with changing thickness of the fluid layer follows a universal curve and can be calculated very accurately using a variational method. We have shown that the balance between surface tension traction to buoyancy force determines the crossover length scale of the fluid which is independent of viscosity or thermal diffusivity. We suggest a scenario near critical point of fluids in which this crossover can be observed.     

Thermodynamic and transport properties of simple fluids using lattice sums: bulk phases and liquid-vapour interface

Molecular dynamics simulations in the canonical ensemble have been performed to obtain the thermodynamic and transport properties of the Lennard-Jones fluid. The dispersion interactions were calculated using lattice sums. This method makes it possible to simulate the full potential avoiding the inclusion of the long range corrections (LRC) during or at the end of simulations. In the calculation of dynamic properties in bulk phases and thermodynamic quantities of inhomogeneous systems where the interface is physically present, in general the LRC cannot easily be included. By using the lattice sums method, the results are independent of the truncation of the potential. In the liquid-vapour interface simulations it is not necessary to make any pre-judgments about the form of the LRC formula to calculate coexisting properties such as the surface tension. The lattice sums method has been applied to evaluate how well the full interaction can be calculated in the liquid phase and in the liquid-vapour interface. In the liquid phase the pressure, configurational energy, diffusion coefficient and shear viscosity were obtained. The results of the thermodynamic properties are compared with those obtained using the spherically truncated and shifted (STS) potential with the LRC added at the end of simulations, and excellent agreement is found. The transport properties are calculated on different system sizes for a state near the triple point. The diffusion coefficient using the lattice sums method increases with the number of molecules, and the results are higher than those of the STS model truncated at 2.5σ (STS2.5). The shear viscosity does not show any system size dependence for systems with more than 256 molecules, and the lattice sums results are essentially the same as those for the STS2.5. In the liquid-vapour equilibria the coexisting densities and vapour pressures for the full potential agree well with those obtained using the Gibbs ensemble and the NPT + test particle methods. The surface tension using lattice sums and truncation of forces at 2.5σ agrees well with STS results using large system sizes and cutoff distances.     

Equation of state of the transitive layer in a one-component system and some of its applications

We obtain the equation of state relating the interphase tension at the planar interface of a crystal—the melt proper with the surface tension of free surfaces in one-component system. Numerical calculations for metals are performed at the temperature of the triple point. Using the obtained equation, we solve a number of problems, including determination of the work of adhesion, the limiting wetting angle of a crystal by the melt proper, the diffluence coefficient due to Harkins, and construction of a Neumann triangle.     

Spinodal decomposition in a Lennard-Jones fluid

A microscopic theory for the early stages of spinodal decomposition in a one-component fluid is presented. We show that in the unstable region of the phase diagram the amplitude of density fluctuations with wave vectors less than some critical value q_c , where q_c is the position of the pole in the static density response function of the uniform fluid, increases exponentially with time. The corresponding amplification factor is related to the Ornstein-Zernike direct correlation function of the uniform fluid. We have calculated the amplification factor for a Lennard-Jones fluid at several densities and temperatures. We find that these amplification factors are qualitatively different from those obtained from the analogue of Cahn's linearized theory of spinodal decomposition. Our calculated value of q_c at reduced density 0·35 and temperature 0·8 is in fairly good agreement with the result of a recent molecular dynamics simulation of a Lennard-Jones fluid quenched to this state.     

Surface Tension of Multi-phase Flow with Multiple Junctions Governed by the Variational Principle

We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie et al. (J Comput Phys 113:134–147, 1994) as a variational problem related to an infinite dimensional Lie group, the volume-preserving diffeomorphism. The variational principle to the action integral with the surface energy reproduces their Euler equation of the two-phase field with the surface tension. Since the surface energy of multiple interfaces even with singularities is not difficult to be evaluated in general and the variational formulation works for every action integral, the new formulation enables us to extend their expression to that of a multi-phase (N-phase, N\geqslant2N\geqslant2) flow and to obtain a novel Euler equation with the surface tension of the multi-phase field. The obtained Euler equation governs the equation for motion of the multi-phase field with different surface tension coefficients without any difficulties for the singularities at multiple junctions. In other words, we unify the theory of multi-phase fields which express low dimensional interface geometry and the theory of the incompressible fluid dynamics on the infinite dimensional geometry as a variational problem. We apply the equation to the contact angle problems at triple junctions. We computed the fluid dynamics for a two-phase field with a wall numerically and show the numerical computational results that for given surface tension coefficients, the contact angles are generated by the surface tension as results of balances of the kinematic energy and the surface energy.     

Phase behavior of a suspension of hard spherocylinders plus ideal polymer chains

We study isotropic-isotropic and isotropic-nematic phase transitions of fluid mixtures containing hard spherocylinders (HSC) and added non-adsorbing ideal polymer chains using scaled particle theory (SPT). First, we investigate isotropic-nematic (I -N phase coexistence using SPT in the absence of polymer. We compare the results obtained using a Gaussian form of the orientational distribution function (ODF) to minimize the free energy versus minimizing numerically. We find that formal numerical minimization gives results that are much closer to computer simulation results. In order to describe mixtures of HSC plus ideal chains we studied the depletion of ideal chains around a HSC. We analyze the density profiles of ideal chains near a hard cylinder and find the depletion thickness δ is a function of the ratio of the polymer's radius of gyration R_g and the cylinder radius R_c. Our results are compared with a common approximation in which the depletion thickness is taken equal to the radius of gyration of the polymer chain. We incorporate the correct depletion thickness into SPT and find that for R _g/R _c < 1.56 using ideal chains gives phase transitions at smaller polymer concentrations, whereas for R _g/R _c > 1.56 , which is a common experimental situation, the phase transitions are found at larger polymer concentrations with respect to δ = R _g . The differences are significant, especially for R _g ≫ R _c , so we can conclude it is essential to take into account the properties of ideal polymer chains and the resulting depletion near a cylinder. Finally, we present phase diagrams for rod-polymer mixtures which could be realized under experimental conditions.     

Vapour-to-Liquid Nucleation in Associating Lennard-Jones Fluids with Multiple Association Sites

The excess Helmholtz free energy functional for associating Lennard-Jones （L J） fluid is formulated in terms of a weighted density approximation for short-ranged interactions and a Weeks-Chandler-Andersen approximation for long-range attraction. Within the framework of density functional theory, phase equilibria, vapour-liquid surface tension and vapour-liquid nucleation properties including the density profile, work of formation, excess number of particles and critical supersaturation are investigated for associating LJ fluids with different numbers of association sites （M =1,2, 3, 4） per particle. The influences of association energy and association sites on phase equilibria, surface tension and vapour-liquid nucleation properties are discussed.     

Scattering from interface islands: enhanced lifetimes through non-linear effect of cation defects

We present quantitative calculations of scattering lifetimes associated with isovalent anion and cation defects in GaSb/InAs detector heterostructures, and identify the dependence upon the proximity of the defects to the heterointerfaces. The carrier lifetimes arising through scattering from interface islands of anion defects are shown to depend non-linearly upon the presence of additional cation defects. These weakly scattering cation defects are shown to control the larger scattering from the anion islands, enabling lifetimes to be enhanced by more than an order of magnitude through the inclusion of additional lattice imperfections.     

Stability of negative ions near the surface of a solid

Stationary states of molecular negative ions (anions) near the surface of a solid are investigated. The lone electron is assumed to interact with a diatomic molecule and the surface of the solid. The energies of electron levels are determined by solving the 2D Schrödinger equation. It is shown that its stable solutions exist at distances from the surface greater than some critical distance, otherwise the electron is detached from the anion. In the case of attraction between the electron and the solid, the interaction potential between the anion and the solid appears to have the Lennard-Jones form and the ion is separated from the surface by some equilibrium distance.     

Prewetting boundary tensions from Monte Carlo simulation

We examine the boundary tension of a model system along the prewetting saturation line. Boundary tensions are evaluated through a combination of finite-size scaling and grand canonical Monte Carlo simulation. The model system consists of Lennard-Jones particles interacting with a single structureless surface. After scaling our dimensionless results with a characteristic force, we obtain a value of 2 x 10(-11) N for the boundary tension at the system's wetting temperature. This estimate is consistent with theoretical and recent experimental values.