425 research outputs found
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
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
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
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
Dynamics on the Way to Forming Glass: Bubbles in Space-time
We review a theoretical perspective of the dynamics of glass forming liquids
and the glass transition. It is a perspective we have developed with our
collaborators during this decade. It is based upon the structure of trajectory
space. This structure emerges from spatial correlations of dynamics that appear
in disordered systems as they approach non-ergodic or jammed states. It is
characterized in terms of dynamical heterogeneity, facilitation and excitation
lines. These features are associated with a newly discovered class of
non-equilibrium phase transitions. Equilibrium properties have little if
anything to do with it. The broken symmetries of these transitions are obscure
or absent in spatial structures, but they are vivid in space-time (i.e.,
trajectory space). In our view, the glass transition is an example of this
class of transitions. The basic ideas and principles we review were originally
developed through the analysis of idealized and abstract models. Nevertheless,
the central ideas are easily illustrated with reference to molecular dynamics
of more realistic atomistic models, and we use that illustrative approach here.Comment: 21 pages, 8 figures. Submitted to Annu. Rev. Phys. Che
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 dimensions are also pointed out.Comment: 6 pages, 4 tables, 3 figures; v2: enlarged version, extension to
other dimensionalities; v3: typos in references correcte
- …