ISSN:0026-8976    

DOI:10.1080/00268979300102571

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Van der Waals theory of a planar liquid-vapour interface, extended with a squared Laplacian term in the expression for the free energy, is used to study curved interfaces. Expressions, closely related to previously derived expressions by Fisher, M. P. A., and Wortis, M., 1984,Phys. Rev.B,29, 6252, and Gompper, G., and Zschocke, S., 1992,Phys. Rev.A,46, 4836 are given for the Tolman length (or, equivalently, spontaneous curvature) and rigidity constants of bending and Gaussian curvature. It is shown that these expressions follow also from a statistical mechanical (or virial) approach in which a local, mean field approximation is made for the pair density. The density profile of the curved surface is calculated to first order in the curvature which allows the derivation of explicit expressions for the various coefficients.

ISSN:0026-8976    

DOI:10.1080/00268979300102581

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The distribution of ions about a planar surface of fixed charge density can be solved within the hypernetted chain (HNC)/mean spherical approximation (MSA) by a simplest yet very accurate method based on the calculus of variations. Here we present an application of that work, the calculation of the potential of mean force and the net pressure for two charged planar surfaces immersed in a salt solution. The expression for the potential of mean force is derived from the Ornstein-Zernike relation for a homogenous fluid by taking the planar geometry limit and employing the conventional HNC approximation. This method requires as input only the distribution of ions about an isolated planar double layer. Though this simple method of pressure calculation is more approximate than some other schemes utilizing the HNC approximation, under many circumstances the agreement among the different theories is excellent. We present results for 1:1 and 1:2 salts as well as mixtures of monovalent and divalent counterions for planar double layers with fixed surface charge densities. Under identical conditions of charge density and bulk coion concentration, the interaction between the surfaces is repulsive at all distances for the case of a monovalent counterion, while regions of attraction are observed for the case of an electrolyte with divalent counterions. It is found that salt solutions with a mixture of monovalent and divalent counterions show properties intermediate to the pure monovalent and divalent cases but the present of only a small amount of divalent ion is sufficient to cause large changes in the interaction between the surfaces. Systems containing a moderate fraction of divalent ions show behaviour nearly identical to the pure divalent counterion case.

ISSN:0026-8976    

DOI:10.1080/00268979300102591

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We propose an analytical mean-field density functional with which to study the coexistence of two surface phases at a prewetting transition. We accurately locate, numerically, the locus of prewetting transitions in the plane of the model's two parameters. To determine the structure and tension of the boundary between the two surface phases we approximate the spatial variations of the system's densities by means of analytic functions with adjustable parameters the values of which are taken to be those that minimize the free energy. The prewetting line implied by this approximation is compared with the exact one. The boundary tension is calculated along the approximate prewetting line. The results are plotted along with those for the line tension calculated in earlier work in states of three-phase equilibrium, for which the point of bulk wetting is approached from the opposite direction. Both tensions increase as the point of the bulk wetting transition is approached but out precision is not great enough to tell if those tensions are finite or infinite at that point.

ISSN:0026-8976    

DOI:10.1080/00268979300102601

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We study some examples of lamellar-lamellar phase equilibria in a previously introduced lattice model of surfactant solutions. The model is treated in a local mean-field approximation. The emphasis is on the properties of the interfaces between coexisting phases. We present an example in which lamellar phases of periods two and four lattice spacings are of equal free energy and both locally stable as bulk phases but metastable with respect to a phase of period three. The interface between the former two is then unstable and nucleates the formation of the latter, which spreads through the entire mass. We conjecture that the period-three phase, had it coexisted as a bulk phase with those of periods two and four, would have wet the period-two/period-four interface, and that this may be a general mechanism for the destruction of metastability. An example is also given of a phase of period three and its antiphase, each being stable as a bulk phase and with a stable interface between them. This case illustrates an ambiguity in the definition of interfacial tension between ordered phases. In general we establish stability both of bulk phases and of interfaces by showing that all the eigenvalues of the matrix of second derivatives of the free energy with respect to the densities are positive.

ISSN:0026-8976    

DOI:10.1080/00268979300102611

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Recent work has highlighted the existence of a unified theory for the asymptotic decay of the density profile ρ(r) of an inhomogeneous fluid and of the bulk radial distribution functiong(r). For a given short-ranged interatomic potential ρ(r) decays into bulk in the same fashion asg(r), i.e. with the same exponential decay length (α0/-1) and, for sufficiently high bulk density (ρb) and/or temperature (T), oscillatory wavelength (2π/α1). The quantities α0and α1are determined by a linear stability analysis of the bulk fluid; they depend on only the bulk direct correlation function. In this paper we reintroduce the concept of the Fisher-Widom (FW) line. This line was originally introduced, in say the (ρb,Tplane, as that which separates pure exponential from exponentially damped oscillatory decay ofg(r). We explore the relevance of the FW line for the form of the density profile at a liquid-vapour interface. Using a weighted density approximation (WDA) density functional theory we locate the FW line for the square-well model of an atomic fluid. We find that this line crosses the liquid branch of the liquid-vapour coexistence curve atT/Tc≈ 0·9, whereTcis the critical temperature. Accordingly, forT≲0·9Tcvery general statistical mechanical theory predicts damped oscillatory decay of the liquid-vapour density profile into the bulk liquid. Since the amplitude of the oscillations is not determined by the linear analysis we have calculated explicit nonlinear numerical solutions of our WDA theory, using a high quality finite element method. Our results show that in a mean-field treatment the amplitude of the oscillatory profile in the saturated liquid tail is about 2% of ρbat temperatures approaching the triple point and decreases rapidly asTincreases towards the FW line. The predictions of the asymptotic profile decay theory are confirmed by our explicit results and the unified nature of the phenomena is illustrated by comparing results for the liquid-vapour profile with profiles calculated for attractive wall-liquid interfaces at the same bulk liquid state point. The effects of capillary-wave fluctuations on the oscillatory nature of liquid-vapour profiles, above the FW line, are discussed, and we argue that while incorporating such fluctuations should lead to a significant reduction in the amplitude of oscillations, ind= 3, at least, there should be no change to the period and decay length for the profile in the liquid tail. The implications of our results for other interfacial properties, for computer simulations of the liquid-vapour interface, for studies of wetting transitions and for the nature of the solvation force that arises when a fluid is confined between two planar walls are considered.

ISSN:0026-8976    

DOI:10.1080/00268979300102621

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The equation of state of the first two members of a homologous series of model alkane-like molecules which incorporate the identities of the backbone and substituent atoms as hard-sphere sites is examined. These polyatomic molecules are formed from tangentially bonded hard spheres with diameters σ1and σ2, where spheres of type 1 make up the backbone of the chain, and spheres of type 2 represent the substituent atoms. The spheres are bonded together in a tetrahedral geometry so that all of the bond angles are ω = 109°; for the second and higher homologues dihedral angles χ about the 1–1 bonds also have to be specified. In order to test the predictions of a recent bonded hard-sphere (BHS) theory, isothermal-isobaric Monte Carlo (MC-NPT) simulations are undertaken for methane- and ethane-like molecules with different diameter ratios σ2/σ1over a range of densities in the fluid state. In the case of the ethane-like molecules trans (χ = 30°) and freely rotating geometries are examined. The simulation data are found to be in excellent agreement with the BHS theory although the theory becomes less accurate at high densities for the systems with large substituent spheres. The assumption inherent in the BHS approach that different conformations and structural isomers of a hard-sphere polyatomic molecule have the same thermodynamical properties is found to be a good approximation for low to moderate fluid densities. The BHS theory is one of the simplest, most accurate and versatile presently available for the properties of polyatomic molecules formed from hard-sphere sites, and could find a use in perturbation and group contribution theories of more realistic models of polyatomic molecules.

ISSN:0026-8976    

DOI:10.1080/00268979300102631

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The experimental results forGEof CH3F + N2O + Xe, at 182·33 K, have been represented by a Redlich-Kister equation. It is shown that the ternary contributionGE123to the excess molar Gibbs energy of the mixtures cannot be neglected. The system studied, and the precision of the results are believed to provide a good model on which statistical theories for liquid mixtures of the type dipolar + quadrupolar + non-polar can be tested.

ISSN:0026-8976    

DOI:10.1080/00268979300102641

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The second virial coefficients of 1,1-difluoroethane, 1,1,1-trifluoroethane, 1,1,1,2-tetrafluoroethane and 1-chloro-1,1-difluoroethane have been calculated on the basis of two-centre-Lennard-Jones + superimposed dipole model potentials and compared with experimental results. These can be explained taking into account the reduced dipole moments and the angle between dipole moment and molecular axis.

ISSN:0026-8976    

DOI:10.1080/00268979300102651

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The variation in Landau free energy while melting platinum was investigated at a number of temperatures using computer simulation with a model potential. The technique used was to apply a biasing potential in a Monte Carlo simulation with umbrella sampling. From the Landau free energy curves one can determine the difference in free energies between the solid and liquid phases easily and accurately, the thermodynamic melting point (Tm), and the limit of metastability of the crystalline phase. The latter occurs at approximately 1·2Tm. It was difficult to freeze the material, but, using a suitable order parameter, this was achieved. Unlike earlier results on a soft sphere system, there was no evidence for nucleation of a metastable body-centred-cubic phase. One possible reason is the existence of local icosahedral order in the liquid phase of the metal. The surface free energy of the solid-liquid surface was estimated from the free energy barrier to melting. Model rhodium behaved in a very similar way.

ISSN:0026-8976    

DOI:10.1080/00268979300102661

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor