Critical and near-critical phase behavior and interplay between the thermodynamic Casimir and van der Waals forces in a confined nonpolar fluid medium with competing surface and substrate potentials

Abstract

We study, using general scaling arguments and mean-field type calculations, the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance L from each other, confining some fluctuating fluid medium, say a non-polar one-component fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials ensuring the so-called (+, +) boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization group sense. Under such conditions one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system L crit for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature T , the chemical potential of the fluid µ, or L. The last implies that by choosing specific materials for the slabs, coatings and the fluid for L L crit one can realize repulsive Casimir force with non-universal behavior which, upon increasing L, gradually turns into an attractive one described by an universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for L L crit . We presented arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can be of interest, e.g., for designing nano-devices and for governing behavior of objects, say colloidal particles, at small distances. We have formulated the corresponding criterion for determination of L crit . The universality is regained for L L crit . We have also shown that for systems with L L crit the capillary condensation phase diagram suffers modifications which one does not observe in systems with purely short-ranged interactions.

On the effects from the simultaneous occurrence of the critical Casimir and dispersion forces between conical colloid particle and a thick plate immersed in nonpolar critical fluid

“…Explicitly these variables are defined in the text below Eq. (2.6) in [2]. According to the scaling hypothesis of the CCF one expects that near the bulk critical point…”

“…Because the included expressions have already been presented in details in [2], here only key results, as well some notations, are going to be given which will be needed in the remainder of the article.…”

“…As explained in [2], we consider a lattice-gas model of a fluid confined between two planar plates, separated at a distance L from each other, with grand canonical potential Ω [ρ(r)] given by…”

“…In Eq. (4) H A is the Hamaker term, whose dependence from the temperature and chemical potential is given by the so-called Hamaker constant [14,15] (for details see the Appendix in [2]). As already explained above, upon approaching the bulk critical point of the system the fluctuations of the order parameter of the confined fluid medium exhibit strong correlations which gives rise to new contribution to the TF, the CCF (see below).…”

“…This study was based on the findings in an earlier research [2], related to the emergence and interplay between the CCF and dispersion vdWF within the gap formed by couple of parallel planar plates, confining a nonpolar fluid which is thought to be at the vicinity of its bulk critical point. There it was shown that the supposed interplay leads to sign change of the net interaction, due to variation of any of the aforementioned external parameters, when the film thickness is less than some threshold value L crit .…”