9,084 research outputs found
Dynamical density functional theory: phase separation in a cavity and the influence of symmetry
Consider a fluid composed of two species of particles, where the
interparticle pair potentials . On confining an
equal number of particles from each species in a cavity, one finds that the
average one body density profiles of each species are constrained to be exactly
the same due to the symmetry, when both external cavity potentials are the
same. For a binary fluid of Brownian particles interacting via repulsive
Gaussian pair potentials that exhibits phase separation, we study the dynamics
of the fluid one body density profiles on breaking the symmetry of the external
potentials, using the dynamical density functional theory of Marconi and
Tarazona [{\it J. Chem. Phys.}, {\bf 110}, 8032 (1999)]. On breaking the
symmetry we see that the fluid one body density profiles can then show the
phase separation that is present.Comment: 7 pages, 4 figures. Accepted for the proceedings of the Liquid Matter
conference 2005, to be publication in J. Phys.: Condens. Matte
Dynamical density functional theory and its application to spinodal decomposition
We present an alternative derivation of the dynamical density functional
theory for the one body density profile of a classical fluid developed by
Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation
elucidates further some of the physical assumptions inherent in the theory and
shows that it is not restricted to fluids composed of particles interacting
solely via pair potentials; rather it applies to general, multi-body
interactions. The starting point for our derivation is the Smoluchowski
equation and the theory is therefore one for Brownian particles and as such is
applicable to colloidal fluids. In the second part of this paper we use the
dynamical density functional theory to derive a theory for spinodal
decomposition that is applicable at both early and intermediate times. For
early stages of spinodal decomposition our non-linear theory is equivalent to
the (generalised) linear Cahn-Hilliard theory, but for later times it
incorporates coupling between different Fourier components of the density
fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We
describe the results of calculations for a model (Yukawa) fluid which show that
the coupling leads to the growth of a second maximum in the density
fluctuations, at a wavenumber larger than that of the main peak.Comment: 23 pages, 3 figure
Microscopic theory of solvent mediated long range forces: influence of wetting
We show that a general density functional approach for calculating the force
between two big particles immersed in a solvent of smaller ones can describe
systems that exhibit fluid-fluid phase separation: the theory captures effects
of strong adsorption (wetting) and of critical fluctuations in the solvent. We
illustrate the approach for the Gaussian core model, a simple model of a
polymer mixture in solution and find extremely attractive, long ranged solvent
mediated potentials between the big particles for state points lying close to
the binodal, on the side where the solvent is poor in the species which is
favoured by the big particles.Comment: 7 pages, 3 figures, submitted to Europhysics Letter
Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft core fluid
Using density functional theory we calculate the density profiles of a binary
solvent adsorbed around a pair of big solute particles. All species interact
via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase
separation and for thermodynamic states near to coexistence the big particles
can be surrounded by a thick adsorbed `wetting' film of the coexisting solvent
phase. On reducing the separation between the two big particles we find there
can be a `bridging' transition as the wetting films join to form a fluid
bridge. The potential between the two big particles becomes long ranged and
strongly attractive in the bridged configuration. Within our mean-field
treatment the bridging transition results in a discontinuity in the solvent
mediated force. We demonstrate that accounting for the phenomenon of bridging
requires the presence of a non-zero bridge function in the correlations between
the solute particles when our model fluid is described within a full mixture
theory based upon the Ornstein-Zernike equations.Comment: 28 pages, 8 figure
Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study
We present dynamical density functional theory results for the time evolution
of the density distribution of a sedimenting model two-dimensional binary
mixture of colloids. The interplay between the bulk phase behaviour of the
mixture, its interfacial properties at the confining walls, and the
gravitational field gives rise to a rich variety of equilibrium and
non-equilibrium morphologies. In the fluid state, the system exhibits both
liquid-liquid and gas-liquid phase separation. As the system sediments, the
phase separation significantly affects the dynamics and we explore situations
where the final state is a coexistence of up to three different phases. Solving
the dynamical equations in two-dimensions, we find that in certain situations
the final density profiles of the two species have a symmetry that is different
from that of the external potentials, which is perhaps surprising, given the
statistical mechanics origin of the theory. The paper concludes with a
discussion on this
Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids
The Local Molecular Field Theory (LMF) developed by Weeks and co-workers has
proved successful for treating the structure and thermodynamics of a variety of
non-uniform liquids. By reformulating LMF in terms of one-body direct
correlation functions we recast the theory in the framework of classical
Density Functional Theory (DFT). We show that the general LMF equation for the
effective reference potential phi_R follows directly from the standard
mean-field DFT treatment of attractive interatomic forces. Using an accurate
(Fundamental Measures) DFT for the non-uniform hard-sphere reference fluid we
determine phi_R for a hard-core Yukawa liquid adsorbed at a planar hard wall.
In the approach to bulk liquid-gas coexistence we find the effective potentials
exhibit rich structure that can include damped oscillations at large distances
from the wall as well as the repulsive hump near the wall required to generate
the low density 'gas' layer characteristic of complete drying. We argue that it
would be difficult to obtain the same level of detail from other (non DFT
based) implementations of LMF. LMF emphasizes the importance of making an
intelligent division of the interatomic pair potential of the full system into
a reference part and a remainder that can be treated in mean-field
approximation. We investigate different divisions for an exactly solvable one-
dimensional model where the pair potential has a hard-core plus a linear
attractive tail. Results for the structure factor and the equation of state of
the uniform fluid show that including a significant portion of the attraction
in the reference system can be much more accurate than treating the full
attractive tail in mean-field approximation. We discuss further aspects of the
relationship between LMF and DFT.Comment: 35 pages, 10 Fig
Dynamical model for the formation of patterned deposits at receding contact lines
We describe the formation of deposition patterns that are observed in many
different experiments where a three-phase contact line of a volatile
nanoparticle suspension or polymer solution recedes. A dynamical model based on
a long-wave approximation predicts the deposition of irregular and regular line
patterns due to self-organised pinning-depinning cycles corresponding to a
stick-slip motion of the contact line. We analyze how the line pattern
properties depend on the evaporation rate and solute concentration
Soft core fluid in a quenched matrix of soft core particles: A mobile mixture in a model gel
We present a density-functional study of a binary phase-separating mixture of
soft core particles immersed in a random matrix of quenched soft core particles
of larger size. This is a model for a binary polymer mixture immersed in a
crosslinked rigid polymer network. Using the replica `trick' for
quenched-annealed mixtures we derive an explicit density functional theory that
treats the quenched species on the level of its one-body density distribution.
The relation to a set of effective external potentials acting on the annealed
components is discussed. We relate matrix-induced condensation in bulk to the
behaviour of the mixture around a single large particle. The interfacial
properties of the binary mixture at a surface of the quenched matrix display a
rich interplay between capillary condensation inside the bulk matrix and
wetting phenomena at the matrix surface.Comment: 20 pages, 5 figures. Accepted for Phys. Rev.
Mean-field dynamical density functional theory
We examine the out-of-equilibrium dynamical evolution of density profiles of
ultrasoft particles under time-varying external confining potentials in three
spatial dimensions. The theoretical formalism employed is the dynamical density
functional theory (DDFT) of Marini Bettolo Marconi and Tarazona [J. Chem. Phys.
{\bf 110}, 8032 (1999)], supplied by an equilibrium excess free energy
functional that is essentially exact. We complement our theoretical analysis by
carrying out extensive Brownian Dynamics simulations. We find excellent
agreement between theory and simulations for the whole time evolution of
density profiles, demonstrating thereby the validity of the DDFT when an
accurate equilibrium free energy functional is employed.Comment: 8 pagers, 4 figure
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