634 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
Microscopic theory for interface fluctuations in binary liquid mixtures
Thermally excited capillary waves at fluid interfaces in binary liquid
mixtures exhibit simultaneously both density and composition fluctuations.
Based on a density functional theory for inhomogeneous binary liquid mixtures
we derive an effective wavelength dependent Hamiltonian for fluid interfaces in
these systems beyond the standard capillary-wave model. Explicit expressions
are obtained for the surface tension, the bending rigidities, and the coupling
constants of compositional capillary waves in terms of the profiles of the two
number densities characterizing the mixture. These results lead to predictions
for grazing-incidence x-ray scattering experiments at such interfaces.Comment: 23 pages, 11 figure
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
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
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
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
Theory of Structural Glasses and Supercooled Liquids
We review the Random First Order Transition Theory of the glass transition,
emphasizing the experimental tests of the theory. Many distinct phenomena are
quantitatively predicted or explained by the theory, both above and below the
glass transition temperature . These include: the viscosity catastrophe
and heat capacity jump at , and their connection; the non-exponentiality
of relaxations and their correlation with the fragility; dynamic heterogeneity
in supercooled liquids owing to the mosaic structure; deviations from the
Vogel-Fulcher law, connected with strings or fractral cooperative
rearrangements; deviations from the Stokes-Einstein relation close to ;
aging, and its correlation with fragility; the excess density of states at
cryogenic temperatures due to two level tunneling systems and the Boson Peak.Comment: submitted to Ann. 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
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
From density to interface fluctuations: the origin of wavelength dependence in surface tensions
The height-height correlation function for a fluctuating interface between
two coexisting bulk phases is derived by means of general equilibrium
properties of the corresponding density-density correlation function. A
wavelength-dependent surface tension can be defined and
expressed in terms of the direct correlation function
, the equilibrium density profile
and an operator which relates density to surface
configurations. Neither the concept of an effective interface Hamiltonian nor
the difference in pressure is needed to determine the general structure of the
height-height correlations or , respectively. This result
generalizes the Mecke/Dietrich surface tension \gmd (Phys. Rev. E {\bf 59},
p. 6766 (1999)) and modifies recently published criticism concerning \gmd (P.
Tarazona, R. Checa and, E.Chac\'{o}n: Phys. Rev. Lett. {\bf 99}, p. 196101
(2007)).Comment: 8 pages, 1 figur
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