Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces

Abstract

We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. The last arise as an effective force between bodies when immersed in a near-critical medium, say a nonpolar onecomponent fluid or a binary liquid mixture. They are due to the fact that the presence of the bodies modifies the order parameter profile of the medium between them as well as the spectrum of its allowed fluctuations. We study the interplay between these forces, as well as the total force (TF) between a spherical colloid particle and a thick planar slab, and between two spherical colloid particles. We do that using general scaling arguments and mean-field type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance L from each other, confining the fluctuating fluid medium characterized by its temperature T and chemical potential µ. The surfaces of the colloid particles and the slab 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 socalled (+, +) boundary conditions. On the other hand, the core region of the slab and the particles, influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes T , µ or L, in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding, trapping and fixing of microparts in nanotechnology. Data for specific substances in support of the experimental feasibility of the theoretically predicted behavior of the CF and TF have been also presented.

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

“…1(a) in [1]. If the fluid medium is in contact with a particle reservoir with a chemical potential µ, the grand canonical potential Ω ex (L|T, µ) per unite area A of this medium in excess to its bulk value A Lω bulk (T, µ) depends on the film thickness L and, thus, one can define the total effective force F tot (L|T, µ) [in a full accord with Eq.…”

“…Finally, we complete the so assembled system by adopting xenon (Xe) as the critical fluctuating medium in which the interacting objects are immersed. For detail comment and argumentation on the choice of the presented substances the reader can refer to [1].…”

“…Thus, one can perform the aforementioned decompositions and identifications given in Eqs. (1) and (3).…”

“…In a recently published work [1], it was shown that the total force (TF) between a spherical colloidal particle and a thick planar substrate, as well as between two spherical particles immersed in some critical nonpolar medium, exhibits not only quantitative, but also qualitative control by simple change of some external to the system parameters like the temperature T and the chemical potential µ of the fluid or the minimal separation L between the interacting objects. 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.…”

Size effects in finite systems with long-range interactions

“…In the renormalization group (RG) theory of critical phenomena, the characteristic spatial length of the system can be introduced as a new relevant parameter, and so, based on this theory, the finite-size effects can be used to determine both the critical parameters and critical exponents [10][11][12]. The general RG ideas have been applied in the context of confined systems with LR interactions in several works [13][14][15][16][17][18]. With this theory, the knowledge of the scaling function, the critical exponents, and critical parameters allows understanding and predicting the behavior of a finite system but only in the proximity of the critical temperature.…”