569 research outputs found
Crystallisation of soft matter under confinement at interfaces and in wedges
The surface freezing and surface melting transitions exhibited by a model
two-dimensional soft matter system is studied. The behaviour when confined
within a wedge is also considered. The system consists of particles interacting
via a soft purely repulsive pair potential. Density functional theory (DFT) is
used to calculate density profiles and thermodynamic quantities. The external
potential due to the confining walls is modelled via a hard-wall with an
additional repulsive Yukawa potential. The surface phase behaviour depends on
the range and strength of this repulsion: When the repulsion strength is weak,
the wall promotes freezing at the surface of the wall. The thickness of this
frozen layer grows logarithmically as the bulk liquid-solid phase coexistence
is approached. Our mean-field DFT predicts that this crystalline layer at the
wall must be nucleated (i.e. there is a free energy barrier) and its formation
is necessarily a first-order transition, referred to as `prefreezing', by
analogy with the prewetting transition. However, in contrast to the latter,
prefreezing cannot terminate in a critical point, since the phase transition
involves a change in symmetry. If the wall-fluid interaction is sufficiently
long ranged and the repulsion is strong enough, surface melting can instead
occur. Then the interface between the wall and the bulk crystalline solid
becomes wet by the liquid phase as the chemical potential is decreased towards
the value at liquid-solid coexistence. It is observed that the finite thickness
fluid film at the wall has a broken translational symmetry due to its proximity
to the bulk crystal and so the nucleation of the wetting film can be either
first-order or continuous. Our mean-field theory predicts that for certain wall
potentials there is a premelting critical point analogous to the surface
critical point for the prewetting transition. In a wedge...Comment: 11 pages, 12 figure
Coarsening modes of clusters of aggregating particles
There are two modes by which clusters of aggregating particles can coalesce:
The clusters can merge either (i) by the Ostwald ripening process in which
particles diffuse from one cluster to the other whilst the cluster centres
remain stationary, or (ii) by means of a cluster translation mode, in which the
clusters move towards each other and join. To understand in detail the
interplay between these different modes, we study a model system of hard
particles with an additional attraction between them. The particles diffuse
along narrow channels with smooth or periodically corrugated walls, so that the
system may be treated as one-dimensional. When the attraction between the
particles is strong enough, they aggregate to form clusters. The channel
potential influences whether clusters can move easily or not through the system
and can prevent cluster motion. We use Dynamical Density Functional theory to
study the dynamics of the aggregation process, focusing in particular on the
coalescence of two equal size clusters. As long as the particle hard-core
diameter is non-zero, we find that the coalescence process can be halted by a
sufficiently strong corrugation potential. The period of the potential
determines the size of the final stable clusters. For the case of smooth
channel walls, we demonstrate that there is a cross-over in the dominance of
the two different coarsening modes, that depends on the strength of the
attraction between particles, the cluster sizes and the separation distance
between clusters
Selectivity in binary fluid mixtures: static and dynamical properties
Selectivity of particles in a region of space can be achieved by applying
external potentials to influence the particles in that region. We investigate
static and dynamical properties of size selectivity in binary fluid mixtures of
two particles sizes. We find that by applying an external potential that is
attractive to both kinds of particles, due to crowding effects, this can lead
to one species of particles being expelled from that region, whilst the other
species is attracted into the region where the potential is applied. This
selectivity of one species of particle over the other in a localized region of
space depends on the density and composition of the fluid mixture. Applying an
external potential that repels both kinds of particles leads to selectivity of
the opposite species of particles to the selectivity with attractive
potentials. We use equilibrium and dynamical density functional theory to
describe and understand the static and dynamical properties of this striking
phenomenon. Selectivity by some ion-channels is believed to be due to this
effect.Comment: 11 pages, 9 figure
Dynamical density functional theory analysis of the laning instability in sheared soft matter
Using dynamical density functional theory (DDFT) methods we investigate the
laning instability of a sheared colloidal suspension. The nonequilibrium
ordering at the laning transition is driven by non-affine particle motion
arising from interparticle interactions. Starting from a DDFT which
incorporates the non-affine motion, we perform a linear stability analysis that
enables identification of the regions of parameter space where lanes form. We
illustrate our general approach by applying it to a simple one-component fluid
of soft penetrable particles
Binding potentials for vapour nanobubbles on surfaces using density functional theory
We calculate density profiles of a simple model fluid in contact with a
planar surface using density functional theory (DFT), in particular for the
case where there is a vapour layer intruding between the wall and the bulk
liquid. We apply the method of Hughes et al. [J. Chem. Phys. 142, 074702
(2015)] to calculate the density profiles for varying (specified) amounts of
the vapour adsorbed at the wall. This is equivalent to varying the thickness
of the vapour at the surface. From the resulting sequence of density
profiles we calculate the thermodynamic grand potential as is varied and
thereby determine the binding potential as a function of . The binding
potential obtained via this coarse-graining approach allows us to determine the
disjoining pressure in the film and also to predict the shape of vapour
nano-bubbles on the surface. Our microscopic DFT based approach captures
information from length scales much smaller than some commonly used models in
continuum mechanics.Comment: 15 pages, 15 figure
Solvent fluctuations around solvophobic, solvophilic and patchy nanostructures and the accompanying solvent mediated interactions
Using classical density functional theory (DFT) we calculate the density
profile and local compressibility of a
simple liquid solvent in which a pair of blocks with (microscopic) rectangular
cross-section are immersed. We consider blocks that are solvophobic,
solvophilic and also ones that have both solvophobic and solvophilic patches.
Large values of correspond to regions in space where the
liquid density is fluctuating most strongly. We seek to elucidate how enhanced
density fluctuations correlate with the solvent mediated force between the
blocks, as the distance between the blocks and the chemical potential of the
liquid reservoir vary. For sufficiently solvophobic blocks, at small block
separations and small deviations from bulk gas-liquid coexistence, we observe a
strongly attractive (near constant) force, stemming from capillary evaporation
to form a low density gas-like intrusion between the blocks. The accompanying
exhibits structure which reflects the incipient gas-liquid
interfaces that develop. We argue that our model system provides a means to
understanding the basic physics of solvent mediated interactions between
nanostructures, and between objects such as proteins in water, that possess
hydrophobic and hydrophilic patches.Comment: 19 pages, 21 figure
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
The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
In classical density functional theory (DFT) the part of the Helmholtz free
energy functional arising from attractive inter-particle interactions is often
treated in a mean-field or van der Waals approximation. On the face of it, this
is a somewhat crude treatment as the resulting functional generates the simple
random phase approximation (RPA) for the bulk fluid pair direct correlation
function. We explain why using standard mean-field DFT to describe
inhomogeneous fluid structure and thermodynamics is more accurate than one
might expect based on this observation. By considering the pair correlation
function and structure factor of a one-dimensional model fluid,
for which exact results are available, we show that the mean-field DFT,
employed within the test-particle procedure, yields results much superior to
those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that
one should not judge the quality of a DFT based solely on the approximation it
generates for the bulk pair direct correlation function.Comment: 9 pages, 3 figure
Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the
simplest microscopic description of the thermodynamic transition from a fluid
state to a crystalline state. The resulting phase field crystal model describes
a variety of spatially localized structures, in addition to different spatially
extended periodic structures. The location of these structures in the
temperature versus mean order parameter plane is determined using a combination
of numerical continuation in one dimension and direct numerical simulation in
two and three dimensions. Localized states are found in the region of
thermodynamic coexistence between the homogeneous and structured phases, and
may lie outside of the binodal for these states. The results are related to the
phenomenon of slanted snaking but take the form of standard homoclinic snaking
when the mean order parameter is plotted as a function of the chemical
potential, and are expected to carry over to related models with a conserved
order parameter.Comment: 40 pages, 13 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
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