Influence of Capillary Condensation on the Near-Critical Solvation Force

Abstract

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 Tc. At T slightly below and above Tc, 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.PACS numbers: 05.70. Jk, 64.60.Fr, 68.15.+e, 68.35.Rh Finite-size contributions to the free energy of a fluid confined between two parallel walls, separated by a distance L, give rise to a force per unit area between the walls or an excess pressure which is termed the solvation force f solv (L) [1]. This force is, essentially, that which is measured in the surface force apparatus [2]. Theory predicts that at the critical point of a fluid the solvation force becomes long ranged as a result of critical fluctuations [3], a phenomenon which is a direct analog of the well-known Casimir effect in electromagnetism [4]. The existence of the long-ranged critical Casimir force should be common to all systems characterized by fluctuating quantities with external constraints [5]. As yet there has been no direct, unambiguous experimental verification of the critical Casimir effect in fluids [5], although recent experiments do provide indirect evidence for its existence [6]. One of the difficulties is that the predicted leading power law decay of the Casimir force at bulk crit, of the same form as the solvation force arising from dispersion forces. Moreover the amplitude in many systems may be much smaller than the corresponding Hamaker constant [5,7]. The Casimir amplitude A 12 is a universal number, however, its value depends on the type of boundary conditions imposed on the two walls [5]. The most relevant for experiments on pure fluids or for binary mixtures are symmetry breaking boundary conditions, i.e., when the confining walls exert surface fields on molecules in the fluid. Here we exploit the mapping between fluids and the Ising model and consider Ising spin systems subject to identical surface fields h 1 = h 2 > 0. For these systems f solv (L) is expected to be attractive for all thermodynamic states. In d = 2, the Casimir amplitude is known exactly A 11 ≡ A ++ = −π/48 [8], whereas in d = 3 the most recent theoretical result is -0.428 [9] and the Monte Carlo estimate is -0.35 [10]. In this Letter we show that other, near-critical, thermodynamic states exhibit a significantly stronger solvation force (for fixed, large L) than that found exactly at the bulk critical point, and we suggest that this has repercussions for experimental studies.For Ising-like systems with h 1 = h 2 > 0 in vanishing bulk field h = 0, f solv as a fu...

Critical Casimir interactions and colloidal self-assembly in near-critical solvents

“…Note that this is the region of the solvent phase diagram where the critical Casimir attraction between two identical colloids is expected to be strongest. 11,27,28 Pertinent to our present study is the experimental work of Kaler et al 21,22 who argued that the system of colloids in a binary solvent mixture should be viewed as a true ternary mixture including full fractionation of the components of the solvent. On the theoretical side, Sluckin 29 had argued already in 1990 that colloidal aggregation should be regarded as phase separation in a ternary system.…”

“…The net attraction between the colloids is strongest at off-critical compositions of the solvent, consistent with results of studies of the critical Casimir attraction between walls. 11,27,28 As we model the colloid-fluid interactions via nearest neighbour interactions, and the surface perimeter of our colloid is discretized, the effective two-body potential between colloids is not smooth. Therefore certain solvent sites right next to the colloid can have more than one colloid site as its neighbour, as is clear from Fig.…”

7 Nonelectrolyte solutions exhibiting structure on the nanoscale

“…across the thin film then the above reduce to the average curvatures H and K defined in eqn. (12) and (13). Thus, in the case of ordered phases and infinitely thin surfaces the standard definitions of the average curvatures of the single mathematical surface are recovered in the absence of fluctuations.…”

Critical Casimir forces forO(n)systems with long-range interaction in the spherical limit

“…For σ = 2, 1.5, 1 and 0.75 the minimum at T = T c is found to be at x 2 ≃ 0.084, 0.145, 0.263 and 0.416, respectively. Such an occurrence of a force minimum for a nonzero bulk field has also been reported for the case of (+, +) boundary conditions [53,54]. Here, in this Section, we provide more details for the universal finite-size scaling function of the Casimir force X Casimir (x 1 , x 2 ) presenting the numerical results for it as a function of both x 1 and x 2 ≥ 0 in FIG.…”