99 research outputs found
The influence of droplet size on line tension
Within the effective interfacial Hamiltonian approach we evaluate the excess
line free energy associated with cylinder-shaped droplets sessile on a
stripe-like chemical inhomogeneity of a planar substrate. In the case of
short-range intermolecular forces the droplet morphology and the corresponding
expression for the line tension - which includes the inhomogeneity finite width
effects - are derived and discussed as functions of temperature and increasing
width. The width-dependent contributions to the line tension change their
structure at the stripe wetting temperature T_W1: for T<T_W1 they decay
exponentially while for T>T_W1 the decay is algebraic. In addition, a geometric
construction of the corresponding contact angle is carried out and its
implications are discussed
Formation of capillary bridges in AFM-like geometry
We discuss the phase diagram of fluid confined in AFM-like geometry. It
combines the properties of capillary condensation and complete filling of a
wedge.Comment: 9 pages, 7 figure
The influence of line tension on the formation of liquid bridges
The formation of liquid bridges between a planar and conical substrates is
analyzed macroscopically taking into account the line tension. Depending on the
value of the line tension coefficient \tau and geometric parameters of the
system one observes two different scenarios of liquid bridge formation upon
changing the fluid state along the bulk liquid-vapor coexistence. For \tau >
\tau * (\tau * < 0) there is a first-order transition to a state with
infinitely thick liquid bridge. For \tau < \tau * the scenario consists of two
steps: first there is a first-order transition to a state with liquid bridge of
finite thickness which upon further increase of temperature is followed by
continuous growth of the thickness of the bridge to infinity. In addition to
constructing the relevant phase diagram we examine the dependence of the width
of the bridge on thermodynamic and geometric parameters of the system.Comment: 4 pages, 5 figure
The problem of uniqueness in the reduced description of adsorption on the wedge-shaped substrate
In the reduced one-dimensional description of the adsorption on the
wedge-shaped substrate the mid-point interface height serves as the order
parameter. We point at the ambiguity which appears in the transfer-matrix
approach to this problem. We also propose how to avoid this problem by
introducing the appropriate order parameter.Comment: 7 pages, 4 Postscript figures, uses psfrag.sty; double reference
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Phase Transitions in Multicomponent String Model
We propose a one-dimensional model of a string decorated with adhesion
molecules (stickers) to mimic multicomponent membranes in restricted
geometries. The string is bounded by two parallel walls and it interacts with
one of them by short range attractive forces while the stickers are attracted
by the other wall. The exact solution of the model in the case of infinite wall
separation predicts both continuous and discontinuous transitions between
phases characterised by low and high concentration of stickers on the string.
Our model exhibits also coexistence of these two phases, similarly to models of
multicomponent membranes.Comment: letter, 8 pages, 3 figure
Free energy asymptotics of the quantum Heisenberg spin chain
We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin S≥1/2. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature
Interfacial fluctuations near the critical filling transition
We propose a method to describe the short-distance behavior of an interface
fluctuating in the presence of the wedge-shaped substrate near the critical
filling transition. Two different length scales determined by the average
height of the interface at the wedge center can be identified. On one length
scale the one-dimensional approximation of Parry et al. \cite{Parry} which
allows to find the interfacial critical exponents is extracted from the full
description. On the other scale the short-distance fluctuations are analyzed by
the mean-field theory.Comment: 13 pages, 3 figure
Complete Wetting of Pits and Grooves
For one-component volatile fluids governed by dispersion forces an effective
interface Hamiltonian, derived from a microscopic density functional theory, is
used to study complete wetting of geometrically structured substrates. Also the
long range of substrate potentials is explicitly taken into account. Four types
of geometrical patterns are considered: (i) one-dimensional periodic arrays of
rectangular or parabolic grooves and (ii) two-dimensional lattices of
cylindrical or parabolic pits. We present numerical evidence that at the
centers of the cavity regions the thicknesses of the adsorbed films obey
precisely the same geometrical covariance relation, which has been recently
reported for complete cone and wedge filling. However, this covariance does not
hold for the laterally averaged wetting film thicknesses. For sufficiently deep
cavities with vertical walls and close to liquid-gas phase coexistence in the
bulk, the film thicknesses exhibit an effective planar scaling regime, which as
function of undersaturation is characterized by a power law with the common
critical exponent -1/3 as for a flat substrate, but with the amplitude
depending on the geometrical features.Comment: 12 page
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