4 research outputs found
Critical adsorption at chemically structured substrates
We consider binary liquid mixtures near their critical consolute points and
exposed to geometrically flat but chemically structured substrates. The
chemical contrast between the various substrate structures amounts to opposite
local preferences for the two species of the binary liquid mixtures. Order
parameters profiles are calculated for a chemical step, for a single chemical
stripe, and for a periodic stripe pattern. The order parameter distributions
exhibit frustration across the chemical steps which heals upon approaching the
bulk. The corresponding spatial variation of the order parameter and its
dependence on temperature are governed by universal scaling functions which we
calculate within mean field theory. These scaling functions also determine the
universal behavior of the excess adsorption relative to suitably chosen
reference systems
Interplay of critical Casimir and dispersion forces
Using general scaling arguments combined with mean-field theory we
investigate the critical () and off-critical ()
behavior of the Casimir forces in fluid films of thickness governed by
dispersion forces and exposed to long-ranged substrate potentials which are
taken to be equal on both sides of the film. We study the resulting effective
force acting on the confining substrates as a function of and of the
chemical potential . We find that the total force is attractive both below
and above . If, however, the direct substrate-substrate contribution is
subtracted, the force is repulsive everywhere except near the bulk critical
point , where critical density fluctuations arise, or except at
low temperatures and , with and the characteristic distance between the molecules of
the fluid, i.e., in the capillary condensation regime. While near the critical
point the maximal amplitude of the attractive force if of order of in
the capillary condensation regime the force is much stronger with maximal
amplitude decaying as . Essential deviations from the standard
finite-size scaling behavior are observed within the finite-size critical
region for films with thicknesses , where
, with and as the
standard bulk critical exponents and with as the dimensionless
parameter that characterizes the relative strength of the long-ranged tail of
the substrate-fluid over the fluid-fluid interaction. We present the modified
finite-size scaling pertinent for such a case and analyze in detail the
finite-size behavior in this region.Comment: 26 pages, 14 figure
Critical dynamics in thin films
Critical dynamics in film geometry is analyzed within the field-theoretical
approach. In particular we consider the case of purely relaxational dynamics
(Model A) and Dirichlet boundary conditions, corresponding to the so-called
ordinary surface universality class on both confining boundaries. The general
scaling properties for the linear response and correlation functions and for
dynamic Casimir forces are discussed. Within the Gaussian approximation we
determine the analytic expressions for the associated universal scaling
functions and study quantitatively in detail their qualitative features as well
as their various limiting behaviors close to the bulk critical point. In
addition we consider the effects of time-dependent fields on the
fluctuation-induced dynamic Casimir force and determine analytically the
corresponding universal scaling functions and their asymptotic behaviors for
two specific instances of instantaneous perturbations. The universal aspects of
nonlinear relaxation from an initially ordered state are also discussed
emphasizing the different crossovers that occur during this evolution. The
model considered is relevant to the critical dynamics of actual uniaxial
ferromagnetic films with symmetry-preserving conditions at the confining
surfaces and for Monte Carlo simulations of spin system with Glauber dynamics
and free boundary conditions.Comment: 64 pages, 21 figure