Critical adsorption and Casimir torque in wedges and at ridges

Abstract

Geometrical structures of confining surfaces profoundly influence the adsorption of fluids upon approaching a critical point Tc in their bulk phase diagram, i.e., for t = (T −Tc)/Tc → ±0. Guided by general scaling considerations, we calculate, within mean-field theory, the temperature dependence of the order parameter profile in a wedge with opening angle γ < π and close to a ridge (γ > π) for T ≷ Tc and in the presence of surface fields. For a suitably defined reduced excess adsorption Γ±(γ, t → ±0) ∼ Γ±(γ)|t| β−2ν we compute the universal amplitudes Γ±(γ), which diverge as Γ±(γ → 0) ∼ 1/γ for small opening angles, vary linearly close to γ = π for γ < π, and increase exponentially for γ → 2π. There is evidence that, within mean-field theory, the ratio Γ+(γ)/Γ−(γ) is independent of γ. We also discuss the critical Casimir torque acting on the sides of the wedge as a function of the opening angle and temperature.

Critical adsorption and critical Casimir forces for geometrically structured confinements

“…The scaling functions P ± are universal once the nonuniversal amplitudes a and ξ + 0 are fixed as the amplitude of the bulk order parameter and of the true correlation length corresponding to an exponential decay of the pair correlation function. For distances from the substrate which are small compared to ξ ± , or for T → T c , the scaling functions and the order parameter exhibit power law singularities 46,47 :…”

Critical Casimir interaction of ellipsoidal colloids with a planar wall

“…As far as torque due to critical fluctuations is concerned, in Ref. [45] the critical Casimir torque on the confining walls of a wedge has been analyzed. Based on field-theoretic techniques the interaction of non-spherical particles, embedded into a solution of long polymers, with a planar wall has been investigated in the limiting case that the size of the particle is much smaller than the distance from the wall ("protein limit") and which, in turn, is assumed to be much smaller than the correlation length [46,47,48,49].…”

On the statistical mechanics of fluids adsorbed in chemically non-symmetric linear wedges

“…The same quantity can equally be applied to edge geometry, although the concept of confinement is no longer appropriate. The line tension can also be obtained from a line adsorption, À ' , from (3) and an obvious extension of the Gibbs adsorption equation: À@=@ ¼ À ' [23,30]. Here, it is worth noting that Djikaev and Widom [31] have shown that this result does not hold for the line tension of a fluid lens adsorbed at a fluid-fluid interface or of a liquid drop adsorbed at a solid-gas interface; i.e.…”

“…when the geometry varies with . Pala´gyi and Dietrich [30] have stressed that standard adsorption experiments on grooved surfaces could not readily disentangle contributions from the almost inevitable presence of both wedge and edge geometry (but see [21] for special cases). In the derivation of the first-moment sum rule (2), this latter issue is hidden in the choice of far boundary condition, since in the real world one cannot have a single wedge of infinite extent.…”