2,697 research outputs found
Two Parameters for Three Dimensional Wetting Transitions
Critical effects at complete and critical wetting in three dimensions are
studied using a coupled effective Hamiltonian H[s(y),\ell]. The model is
constructed via a novel variational principle which ensures that the choice of
collective coordinate s(y) near the wall is optimal. We highlight the
importance of a new wetting parameter \Omega(T) which has a strong influence on
critical properties and allows the status of long-standing Monte-Carlo
simulation controversies to be re-examined.Comment: 4 pages RevTex, 2 encapsulated postscript figures, to appear in
Europhys. Let
Interfacial Structural Changes and Singularities in Non-Planar Geometries
We consider phase coexistence and criticality in a thin-film Ising magnet
with opposing surface fields and non-planar (corrugated) walls. We show that
the loss of translational invariance has a strong and unexpected non-linear
influence on the interface structure and phase diagram. We identify 4
non-thermodynamic singularities where there is a qualitative change in the
interface shape. In addition, we establish that at the finite-size critical
point, the singularity in the interface shape is characterized by two distint
critical exponents in contrast to the planar case (which is characterised by
one). Similar effects should be observed for prewetting at a corrugated
substrate. Analogy is made with the behaviour of a non-linear forced oscillator
showing chaotic dynamics.Comment: 13 pages, 3 figure
Droplet shapes on structured substrates and conformal invariance
We consider the finite-size scaling of equilibrium droplet shapes for fluid
adsorption (at bulk two-phase co-existence) on heterogeneous substrates and
also in wedge geometries in which only a finite domain of the
substrate is completely wet. For three-dimensional systems with short-ranged
forces we use renormalization group ideas to establish that both the shape of
the droplet height and the height-height correlations can be understood from
the conformal invariance of an appropriate operator. This allows us to predict
the explicit scaling form of the droplet height for a number of different
domain shapes. For systems with long-ranged forces, conformal invariance is not
obeyed but the droplet shape is still shown to exhibit strong scaling
behaviour. We argue that droplet formation in heterogeneous wedge geometries
also shows a number of different scaling regimes depending on the range of the
forces. The conformal invariance of the wedge droplet shape for short-ranged
forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.
An exact solution for two dimensional wetting with a corrugated wall
An exact solution of a two dimensional RSOS model of wetting at a corrugated
(periodic) wall is found using transfer matrix techniques. In contrast to
mean-field analysis of the same problem the wetting transition remains
second-order and occurs at a lower temperature than that of the planar system.
Comparison with numerical studies and other analytical approaches is made.Comment: 11 pages LaTex with 1 eps figure. To appear in J.Phys.
Corrugation-Induced First-Order Wetting: An Effective Hamiltonian Study
We consider an effective Hamiltonian description of critical wetting
transitions in systems with short-range forces at a corrugated (periodic) wall.
We are able to recover the results obtained previously from a `microscopic'
density-functional approach in which the system wets in a discontinuous manner
when the amplitude of the corrugations reaches a critical size A*. Using the
functional renormalization group, we find that A* becomes dependent on the
wetting parameter \omega in such a way as to decrease the extent of the
first-order regime. Nevertheless, we still expect wetting in the Ising model to
proceed in a discontinuous manner for small deviations of the wall from the
plane.Comment: 9 pages RevTex with 2 EPS figures. To appear in Eur. Phys. J.
Coupled Hamiltonians and Three Dimensional Short-Range Wetting Transitions
We address three problems faced by effective interfacial Hamiltonian models
of wetting based on a single collective coordinate \ell representing the
position of the unbinding fluid interface. Problems (P1) and (P2) refer to the
predictions of non-universality at the upper critical dimension d=3 at critical
and complete wetting respectively which are not borne out by Ising model
simulation studies. (P3) relates to mean-field correlation function structure
in the underlying continuum Landau model. We investigate the hypothesis that
these concerns arise due to the coupling of order parameter fluctuations near
the unbinding interface and wall. For quite general choices of collective
coordinates X_i we show that arbitrary two-field models H[X_1,X_2] can recover
the required anomalous structure of mean-field correlation functions (P3). To
go beyond mean-field theory we introduce a set of Hamiltonians based on proper
collective coordinates s near the wall which have both interfacial and
spin-like components. We argue that an optimum model H[s,\ell] in which the
degree of coupling is controlled by an angle-like variable, best describes the
non-universality of the Ising model and investigate its critical behaviour. For
critical wetting the appropriate Ginzburg criterion shows that the true
asymptotic critical regime for the local susceptibility \chi_1 is dramatically
reduced consistent with observations of mean-field behaviour in simulations
(P1). For complete wetting the model yields a precise expression for the
temperature dependence of the renormalized critical amplitude \theta in good
agreement with simulations (P2). We highlight the importance of a new wetting
parameter which describes the physics that emerges due to the coupling effects.Comment: 34 pages, RevTex, 8 eps figures. To appear in Physica
Coupled Fluctuations near Critical Wetting
Recent work on the complete wetting transition has emphasized the role played
by the coupling of fluctuations of the order parameter at the wall and at the
depinning fluid interface. Extending this approach to the wetting transition
itself we predict a novel crossover effect associated with the decoupling of
fluctuations as the temperature is lowered towards the transition temperature
T_W. Using this we are able to reanalyse recent Monte-Carlo simulation studies
and extract a value \omega(T_W)=0.8 at T_W=0.9T_C in very good agreement with
long standing theoretical predictions.Comment: 4 pages, LaTex, 1 postscript figur
Tricritical wedge filling transitions with short-ranged forces
We show that the 3D wedge filling transition in the presence of short-ranged
interactions can be first-order or second order depending on the strength of
the line tension associated with to the wedge bottom. This fact implies the
existence of a tricritical point characterized by a short-distance expansion
which differs from the usual continuous filling transition. Our analysis is
based on an effective one-dimensional model for the 3D wedge filling which
arises from the identification of the breather modes as the only relevant
interfacial fluctuations. From such analysis we find a correspondence between
continuous 3D filling at bulk coexistence and 2D wetting transitions with
random-bond disorder.Comment: 7 pages, 3 figures, 6th Liquid Matter Conference Proceedings (to be
published in J. Phys.: Condens. Matter
Correlation function algebra for inhomogeneous fluids
We consider variational (density functional) models of fluids confined in
parallel-plate geometries (with walls situated in the planes z=0 and z=L
respectively) and focus on the structure of the pair correlation function
G(r_1,r_2). We show that for local variational models there exist two
non-trivial identities relating both the transverse Fourier transform G(z_\mu,
z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2
and z_3. These relations form an algebra which severely restricts the possible
form of the function G_0(z_\mu,z_\nu). For the common situations in which the
equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an
odd or even reflection symmetry in the z=L/2 plane the algebra simplifies
considerably and is used to relate the correlation function to the finite-size
excess free-energy \gamma(L). We rederive non-trivial scaling expressions for
the finite-size contribution to the free-energy at bulk criticality and for
systems where large scale interfacial fluctuations are present. Extensions to
non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte
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