Density functional theory of inhomogeneous liquids. I. The liquid-vapor interface in Lennard-Jones fluids

A simple model is proposed for the direct correlation function (DCF) for simple fluids consisting of a hard-core contribution, a simple parametrized core correction, and a mean-field tail. The model requires as input only the free energy of the homogeneous fluid, obtained, e.g., from thermodynamic perturbation theory. Comparison to the DCF obtained from simulation of a Lennard-Jones fluid shows this to be a surprisingly good approximation for a wide range of densities. The model is used to construct a density functional theory for inhomogeneous fluids which is applied to the problem of calculating the surface tension of the liquid-vapor interface. The numerical values found are in good agreement with simulation

Density Functional Theory of Inhomogeneous Liquids: II. A Fundamental Measure Approach

Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail and a simple linear correction in the core region constructed so as to reproduce the (known) bulk equation of state of the fluid(Lutsko, JCP 127, 054701 (2007)). Here, this model is combined with ideas from Fundamental Measure Theory to construct a density functional theory for the free energy. The theory is shown to accurately describe a range of inhomogeneous conditions including the liquid-vapor interface, the fluid in contact with a hard wall and a fluid confined in a slit pore. The theory gives quantitatively accurate predictions for the surface tension, including its dependence on the potential cutoff. It also obeys two important exact conditions: that relating the direct correlation function to the functional derivative of the free energy with respect to density, and the wall theorem.Comment: to appear in J. Chem. Phy

Mapping a Homopolymer onto a Model Fluid

We describe a linear homopolymer using a Grand Canonical ensemble formalism, a statistical representation that is very convenient for formal manipulations. We investigate the properties of a system where only next neighbor interactions and an external, confining, field are present, and then show how a general pair interaction can be introduced perturbatively, making use of a Mayer expansion. Through a diagrammatic analysis, we shall show how constitutive equations derived for the polymeric system are equivalent to the Ornstein-Zernike and P.Y. equations for a simple fluid, and find the implications of such a mapping for the simple situation of Van der Waals mean field model for the fluid.Comment: 12 pages, 3 figure

On the thermodynamic stability and structural transition of clathrate hydrates

Gas mixtures of methane and ethane form structure II clathrate hydrates despite the fact that each of pure methane and pure ethane gases forms the structure I hydrate. Optimization of the interaction potential parameters for methane and ethane is attempted so as to reproduce the dissociation pressures of each simple hydrate containing either methane or ethane alone. An account for the structural transitions between type I and type II hydrates upon changing the mole fraction of the gas mixture is given on the basis of the van der Waals and Platteeuw theory with these optimized potentials. Cage occupancies of the two kinds of hydrates are also calculated as functions of the mole fraction at the dissociation pressure and at a fixed pressure well above the dissociation pressure

Liquid‐Liquid Equilibrium and Interfacial Properties of the System Water + Hexylacetate + 1‐Hexanol

Experimental and theoretical investigations of the phase diagram and the interfacial tension are presented. The theoretical framework was able to predict the phase behavior and the interfacial tension with a high accuracy, where only binary experimental data enter the model parameter. The theory permits the calculation of the concentration profiles across the interface. The profiles show that 1-hexanol will be enriched, which was expected. In same circumstances a competition between hexylacetate and 1-hexanol was figured out leading to slight minima in the profile of 1-hexanol

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.Comment: 12 pages, 15 figure

Theoretical description of the nucleation of vapor bubbles in a superheated fluid

The nucleation of vapor bubbles within a superheated fluid is studied using density functional theory. The nudged elastic band technique is used to find the minimum energy pathway from the metastable uniform liquid to the stable uniform gas thus emphasizing the analogy between the the nucleation problem and that of chemical reactions. The result is both an accurate determination of the critical nucleus and an unbiased description of the density profile at various points along the path between the free energy extrema. This calculation is compared to two other methods: the use of parametrized profiles and constrained minimization of the free energy. The results indicate that the recent claim, based on the constraint method, that bubble nucleation and growth involves an activated instability is incorrect.Comment: To appear in Europhysics Letter

Transport of heat and mass in a two-phase mixture. From a continuous to a discontinuous description

We present a theory which describes the transport properties of the interfacial region with respect to heat and mass transfer. Postulating the local Gibbs relation for a continuous description inside the interfacial region, we derive the description of the Gibbs surface in terms of excess densities and fluxes along the surface. We introduce overall interfacial resistances and conductances as the coefficients in the force-flux relations for the Gibbs surface. We derive relations between the local resistivities for the continuous description inside the interfacial region and the overall resistances of the surface for transport between the two phases for a mixture. It is shown that interfacial resistances depend among other things on the enthalpy profile across the interface. Since this variation is substantial the coupling between heat and mass flow across the surface are also substantial. In particular, the surface puts up much more resistance to the heat and mass transfer then the homogeneous phases over a distance comparable to the thickness of the surface. This is the case not only for the pure heat conduction and diffusion but also for the cross effects like thermal diffusion. For the excess fluxes along the surface and the corresponding thermodynamic forces we derive expressions for excess conductances as integrals over the local conductivities along the surface. We also show that the curvature of the surface affects only the overall resistances for transport across the surface and not the excess conductivities along the surface.Comment: 25 pages, 2 figure

A branch-point approximant for the equation of state of hard spheres

Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value, and it is as accurate as the rescaled virial expansion and better than the Pad\'e [3/3] equations of state. Consequences regarding the convergence properties of the virial series and the use of similar equations of state for hard-core fluids in $d$ dimensions are also pointed out.Comment: 6 pages, 4 tables, 3 figures; v2: enlarged version, extension to other dimensionalities; v3: typos in references correcte

Time scales in shear banding of wormlike micelles

Transient stress and birefringence measurements are performed on wormlike micellar solutions that "shear band", i.e. undergo flow-induced coexistence of states of different viscosities along a constant stress "plateau". Three well-defined relaxation times are found after a strain rate step between two banded flow states on the stress plateau. Using the Johnson-Segalman model, we relate these time scales to three qualitatively different stages in the evolution of the bands and the interface between them: band destabilization, reconstruction of the interface, and travel of the fully formed interface. The longest timescale is then used to estimate the magnitude of the (unknown) "gradient" terms that must be added to constitutive relations to explain the history independence of the steady flow and the plateau stress selection