Interplay of critical Casimir and dispersion forces

Abstract

Using general scaling arguments combined with mean-field theory we investigate the critical ($T\simeq T_c$) and off-critical ($T\ne T_c$) behavior of the Casimir forces in fluid films of thickness $L$ 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 $T$ and of the chemical potential $\mu$. We find that the total force is attractive both below and above $T_c$. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point $(T_c,{\mu }_c)$, where critical density fluctuations arise, or except at low temperatures and $(L/a)(\beta \Delta \mu )=O(1)$, with $\Delta \mu =\mu -{\mu }_c<0$ and $a$ 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 $L^{-d}$ in the capillary condensation regime the force is much stronger with maximal amplitude decaying as $L^{-1}$. Essential deviations from the standard finite-size scaling behavior are observed within the finite-size critical region $L/\xi =O(1)$ for films with thicknesses $L\lesssim L_{\mathrm{crit}}$, where $L_{\mathrm{crit}}={\xi }_0^{\pm }(16|s|{)}^{\nu /\beta }$, with $\nu$ and $\beta$ as the standard bulk critical exponents and with $s=O(1)$ 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.

26 pages, 14 figures

References in corpus (4)

• Critical Casimir force in ${}^4$He films: confirmation of finite-size scaling
• Fluctuation-induced forces in periodic slabs: Breakdown of epsilon expansion at the bulk critical point and revised field theory
• Solvation force for long ranged wall-fluid potentials
• Finite-size effects on the behavior of the susceptibility in van der Waals films under $+,+$ boundary conditions

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• Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Finite-size effects in presence of gravity: The behavior of the susceptibility in ${}^{3}He$ and ${}^{4}He$ films near the liquid-vapor critical point
• Fluctuations of the critical Casimir force