Investigation of vapour--liquid nucleation properties for spherical and chain-like fluids by density functional theory

The excess Helmholtz free energy functional for nonpolar chain-like molecules is formulated in terms of a weighted density approximation （WDA） for short-range interactions and a Weaks Chandler Andersen （WCA） approximation and a Barker Henderson （BH） theory for long-range attraction. Within the framework of density functional theory （DFT）, vapour liquid interracial properties including density profile and surface tension, and vapour-liquid nucleation properties including density profile, work of formation and number of particles are investigated for spherical and chain- like molecules. The obtained vapour liquid surface tension and the number of particles in critical nucleus for Lennard- Jones （L J） fluids are consistent with the simulation results. The influences of supersaturation, temperature and chain length on vapour liquid nucleation properties are discussed.[第一段]     

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.     

Hydrophobic force,a Casimir-like effect due to hydrogen-bond fluctuations

Hydrophobic force, interfacial tension, and transverse density profile in a confined water system are addressed from first principles of statistical mechanics in a lattice model for water. Using the molecular mean field theory technique we deduce explicit expressions for each of the above mentioned phenomena and show that hydrophobic force is a manifestation of a Casimir-like effect due to hydrogen-bond fluctuations in confined water. It is largely influenced by the long range correlations of orientational fluctuations. Furthermore, the temperature dependence of hydrophobic force between large non-polar surfaces is suggested to be different from that between small solutes. The mechanisms contributing to characteristic behavior in each case are identified. In the case of large surfaces, the prevalence of discrete fluctuation modes in the confinement direction and their entropic contribution to the overall free energy dominate the temperature dependence. Mode discretization is also implicated in the variation of interfacial tension with separation distance between confining surfaces and characteristic density profile of the confined fluid. All the computations are parameter free and compare favorably with results of molecular dynamics simulations and experiments.     

Relationship Between Total Surface Tension of Monomer and Its Homopolymer

The surface and interfacial properties of polymers are important for their applications. In one of our previous articles, we discussed the relationship between the dispersive surface tension component and the density and molecular weight of solvents and polymers to seek a simple and easy method to estimate the rationality of surface tension results of polymers. We found that for 30 organic solvents and 12 polymers, there was a good relationship between the dispersive surface tension and the experiential parameter 1/ρ² M ^0.2 _w . In this article, the existence of the squared density term is simply deduced from the general molecular interaction energy equation and is proved with four pairs of polymer/monomer; these are polystyrene/styrene, polyisoprene/isoprene, polymethyl methacrylate/methyl methacrylate, and polyvinyl acetate/vinyl acetate.     

Lattice-Boltzmann simulations of dynamic interfacial tension due to soluble amphiphilic surfactant

An amphiphilic Lattice-Boltzmann approach is adopted to model dynamic interfacial tension due to non-ionic surfactant. In the current system, the surfactant adsorption kinetics is diffusion dominated and the interface separates two immiscible fluids. A rotational relaxation time and a diffusive/viscous relaxation time are associated with the surfactant. The model results are compared with experimental data for the dynamic interfacial tension of a pendant oil droplet in water, with oil soluble surfactant. We demonstrate how to adapt and calibrate the model to capture the adsorption timescale of the surfactant and the magnitude of interfacial tension reduction due to surfactant. A scheme to overcome numerical instabilities due to the relatively low surfactant concentration, is devised. We are able to qualitatively match the Frumkin equation of state for the interfacial tension.     

A kind of extended Korteweg——de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio $\varepsilon $, represented by the ratio of amplitude to depth, and the dispersion ratio $\mu $, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin {\it et al} in the study of the surface waves when considering the order up to $O(\mu ^2)$. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin {\it et al} for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.     

Statistical mechanics of fluids at spherical structureless walls

Statistical mechanical theories of spherical fluid interfaces are discussed in the context of fluids in contact with structureless walls. The thermodynamic route to the surface tension leads to a formula involving gradients of the external field, which is especially suited to the study of fluid-wall systems. The surface tension is found to be determined by the curvature dependence of the density in the region of the wall. For hard walls, potential distribution theory is used to obtain the exact relationship between the statistical mechanical surface tension expression and the grand potential. The accuracy of simple scaled particle theory calculations of the surface tension is estimated from predictions for the equation of state of pair potential fluids with hard core plus attractive tail interactions. Problems with the mechanical route to the curvature dependence of the surface tension are discussed. The planar wall and results for lower dimensionality are included in appendices.     

Calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function in the interface zone

A detailed study is presented of the calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function and the density profile. To do so, a modification is made to Lekner and Henderson's statistical mechanics approach by introducing two simple analytical expressions for the radial distribution function of the interface zone. In these expressions the radial distribution functions of the liquid and vapour phases are weighted via step or exponential variations. The well- known exponential model for the density profile in the interface zone is considered. Finally, results are compared with values from experiment, from computer simulation and from relevant theoretical developments. It is shown that the use of the proposed radial distribution function in the interface zone represents a significant improvement in applying Lekner and Henderson's approach.     

Perturbation methods in the kinetics of nanocluster growth

The rigorous perturbation theory of the evolution of a small-sized cluster is developed in the framework of the density functional method. The solution of the general equation for relaxation of the order parameter field is derived in the form of a power series of the metastability parameter (an analog of supersaturation or supercooling) and the curvature. The profile of the cluster density and the cluster growth rate are determined in an analytical form. The surface tension and the Tolman parameter are calculated. The results obtained are applied to a van der Waals three-dimensional gas and a two-dimensional lattice gas. It is shown that the theoretical results are in good agreement with experimental data.     

Interfacial properties of Morse fluids

The interfacial properties as reflected in the interfacial tension values and the density profile of Morse fluids has been studied. The parameter range is chosen to coincide with that describing the behaviour of solid metals. The interfacial tension has been found to follow Guggenheim's and MacLeod's relations. However, the constants, while independent of temperature for each metal, are not the universal values predicted; with the exception of Macleod's exponent p. The density profile illustrates the change in densities across the interface dividing the coexisting vapour and liquid phases. The correlation length is also found to follow the universal relation with temperature, but again the constants, while independent of temperature, are dependent on the type of metal. The value of constant ν is found to be different for all five metals considered and is found to differ from the three-dimensional Ising model value of ν?=?0.630, which is also predicted by applying the Lennard–Jones model.     

Wavelength dependence of liquid-vapor interfacial tension of Ga

The wave-vector dependence of the liquid-vapor interfacial tension of Ga, gamma(q), has been determined from diffuse x-ray scattering measurements. The ratio gamma(q)/gamma(0)=1 for q<0.05 A(-1) decreases to 0.5 near q=0.22 A(-1), and increases strongly for larger q. The observed form for gamma(q)/gamma(0) is consistent with the prediction from the Mecke-Dietrich theory when the known stratified liquid-vapor interfacial density profile of Ga and a pseudopotential based pair interaction with appropriate asymptotic (r--> infinity ) behavior are used. The detailed behavior of gamma(q)/gamma(0) depends on the particular forms of both the interfacial density profile and the asymptotic falloff of the atomic pair interaction.     

Novel surface tension isotherm for surfactants based on local density functional theory

In this Letter we report a new general method for calculating of surface tension isotherms in the presence of surfactants, based on a local density functional. We illustrate this method by deriving the interfacial tension isotherm for nonionic surfactants at an air-water or oil-water interface by using the self-consistent field theory of polymer brushes. We consider a particular case of local density functional to calculate explicitly how the interfacial tension and the surfactant adsorption depend on the surfactant bulk concentration. Experimental data for the surface tension and the surfactant adsorption isotherm for nonionic surfactants were interpreted with the help of the new isotherm. Very good agreement between the adsorption of n-dodecyl pentaoxyethylene glycol ether (C12E5) at an air-water interface, calculated from the surface tension isotherm and small-angle neutron-scattering is obtained.     

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.     

制备均一性靶丸过程中的影响因素

在激光聚变实验中,高球形度、高厚度均一性的靶丸经常通过乳液微封装方法来制备。利用T.Norimatsu的模型研究在靶丸制备过程中,界面间表面张力、油相粘度、壳层尺寸、壳层厚度的影响。结果显示:较大的表面张力,较小的壳层尺寸,会使胶囊具有更好的均一性。当外部变形形式不同的时候,油相的粘度对于壳层均一性会有不同作用。     

Weak and strong coupling theories for polarizable colloids and nanoparticles

A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nanoparticles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far field. All the results are compared with the Monte?Carlo simulations, showing an excellent agreement between the theory and the simulations.     

Field-induced phase separation in one dimension

Phase separation is induced in the one-dimensional Ising chain (or lattice-gas model of a fluid) by means of an external field that changes sign in the middle of the chain. The magnetization profile (or density profile of the analogous fluid) is obtained analytically. It is found to decay exponentially rapidly to the bulk-phase magnetizations (or densities), the exponential decay parameter being the correlation length in the bulk phases in the presence of the field. This is in accord with earlier theoretical ideas. The interfacial tension is also obtained analytically. In an appropriately defined limit of large neighboring-site spin-spin interactions and small external field the interface becomes infinitely broad while the amplitude of the profile and the interfacial tension both vanish, in close imitation of the approach to a critical point in a real fluid. In this asymptotic limit the interfacial tension is related to the amplitude of the profile in the way that is predicted by earlier theories of interfaces near critical points, with critical-point exponents now those appropriate to one dimension. The exact interfacial profile and tension are used to test several approximations, including a corrected form of the barometric law and local (square-gradient) and nonlocal forms of the van der Waals theory.     

Density functional study of the pressure tensor for inhomogeneous Lennard—Jones fluids

Based on classical density functional theory,an expression of the pressure tensor for inhomogeneous fluids is presented.This takes into account greater correlation between particles,especially for systems that are geometrically confined or involve an interface.The density and pressure components of Lennard-Jones fluids confined in hard and softened nano-cavities are calculated.A comparison between the results of this work and IK expression suggests that the agreement depends on temperature.The interfacial tension for hard sphere fluids agrees well with the Monte Carlo result when the bulk density is not too large.The results of the solid-fluid interfacial tension for Lennard-Jones fluids demonstrate that different types of external potentials modulate the interfacial tension in different manners.