170 research outputs found
Monte Carlo simulation results for critical Casimir forces
The confinement of critical fluctuations in soft media induces critical
Casimir forces acting on the confining surfaces. The temperature and geometry
dependences of such forces are characterized by universal scaling functions. A
novel approach is presented to determine them for films via Monte Carlo
simulations of lattice models. The method is based on an integration scheme of
free energy differences. Our results for the Ising and the XY universality
class compare favourably with corresponding experimental results for wetting
layers of classical binary liquid mixtures and of 4He, respectively.Comment: 14 pages, 5 figure
Influence of Capillary Condensation on the Near-Critical Solvation Force
We argue that in a fluid, or magnet, confined by adsorbing walls which favour
liquid, or (+) phase, the solvation (Casimir) force in the vicinity of the
critical point is strongly influenced by capillary condensation which occurs
below the bulk critical temperature T_c. At T slightly below and above T_c, a
small bulk field h<0, which favours gas, or (-) phase, leads to residual
condensation and a solvation force which is much more attractive (at the same
large wall separation) than that found exactly at the critical point. Our
predictions are supported by results obtained from density-matrix
renormalization-group calculations in a two-dimensional Ising strip subject to
identical surface fields.Comment: 4 Pages, RevTeX, and 3 figures include
Local functional models of critical correlations in thin-films
Recent work on local functional theories of critical inhomogeneous fluids and
Ising-like magnets has shown them to be a potentially exact, or near exact,
description of universal finite-size effects associated with the excess
free-energy and scaling of one-point functions in critical thin films. This
approach is extended to predict the two-point correlation function G in
critical thin-films with symmetric surface fields in arbitrary dimension d. In
d=2 we show there is exact agreement with the predictions of conformal
invariance for the complete spectrum of correlation lengths as well as the
detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we
present new numerical predictions for the universal finite-size correlation
length and scaling functions determining the structure of G across the
thin-film. Highly accurate analytical closed form expressions for these
universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let
Properties of the solvation force of a two-dimensional Ising strip in scaling regimes
We consider d=2 Ising strip with surface fields acting on boundary spins.
Using the properties of the transfer matrix spectrum we identify two
pseudotransition temperatures and show that they satisfy similar scaling
relations as expected for real transition temperatures in strips with d>2. The
solvation force between the boundaries of the strip is analysed as a function
of temperature, surface fields and the width of the strip. For large widths the
solvation force can be described by scaling functions in three different
regimes: in the vicinity of the critical wetting temperature of 2D
semi-infinite system, in the vicinity of the bulk critical temperature, and in
the regime of weak surface fields where the critical wetting temperature tends
towards the bulk critical temperature. The properties of the relevant scaling
functions are discussed
The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation
The relation between the bulk correlation length and the decay length of
thermodynamic Casimir forces is investigated microscopically in two
three-dimensional systems undergoing Bose-Einstein condensation: the perfect
Bose gas and the imperfect mean-field Bose gas. For each of these systems, both
lengths diverge upon approaching the corresponding condensation point from the
one-phase side, and are proportional to each other. We determine the
proportionality factors and discuss their dependence on the boundary
conditions. The values of the corresponding critical exponents for the decay
length and the correlation length are the same, equal to 1/2 for the perfect
gas, and 1 for the imperfect gas
The Casimir effect: from quantum to critical fluctuations
The Casimir effect in quantum electrodynamics (QED) is perhaps the best-known
example of fluctuation-induced long-ranged force acting on objects (conducting
plates) immersed in a fluctuating medium (quantum electromagnetic field in
vacuum). A similar effect emerges in statistical physics, where the force
acting, e.g., on colloidal particles immersed in a binary liquid mixture is
affected by the classical thermal fluctuations occurring in the surrounding
medium. The resulting Casimir-like force acquires universal features upon
approaching a critical point of the medium and becomes long-ranged at
criticality. In turn, this universality allows one to investigate theoretically
the temperature dependence of the force via representative models and to
stringently test the corresponding predictions in experiments. In contrast to
QED, the Casimir force resulting from critical fluctuations can be easily tuned
with respect to strength and sign by surface treatments and temperature
control. We present some recent advances in the theoretical study of the
universal properties of the critical Casimir force arising in thin films. The
corresponding predictions compare very well with the experimental results
obtained for wetting layers of various fluids. We discuss how the Casimir force
between a colloidal particle and a planar wall immersed in a binary liquid
mixture has been measured with femto-Newton accuracy, comparing these
experimental results with the corresponding theoretical predictions.Comment: Talk delivered at the International Workshop "60 Years of Casimir
Effect", Brasilia, 23-27 June 2008 (17 pages, 7 figures
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.
Critical Casimir effect and wetting by helium mixtures
We have measured the contact angle of the interface of phase-separated
He-He mixtures against a sapphire window. We have found that this
angle is finite and does not tend to zero when the temperature approaches
, the temperature of the tri-critical point. On the contrary, it increases
with temperature. This behavior is a remarkable exception to what is generally
observed near critical points, i.e. "critical point wetting''. We propose that
it is a consequence of the "critical Casimir effect'' which leads to an
effective attraction of the He-He interface by the sapphire near
.Comment: submitted july 13 (2002), published march 20 (2003
Casimir forces in binary liquid mixtures
If two ore more bodies are immersed in a critical fluid critical fluctuations
of the order parameter generate long ranged forces between these bodies. Due to
the underlying mechanism these forces are close analogues of the well known
Casimir forces in electromagnetism. For the special case of a binary liquid
mixture near its critical demixing transition confined to a simple parallel
plate geometry it is shown that the corresponding critical Casimir forces can
be of the same order of magnitude as the dispersion (van der Waals) forces
between the plates. In wetting experiments or by direct measurements with an
atomic force microscope the resulting modification of the usual dispersion
forces in the critical regime should therefore be easily detectable. Analytical
estimates for the Casimir amplitudes Delta in d=4-epsilon are compared with
corresponding Monte-Carlo results in d=3 and their quantitative effect on the
thickness of critical wetting layers and on force measurements is discussed.Comment: 34 pages LaTeX with revtex and epsf style, to appear in Phys. Rev.
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