Abstract
Here we study the interplay between the van der Waals (vdWF) and critical Casimir forces (CCF), as well as the total force (TF) between a conical colloid particle and a thick planar slab. We do that using general scaling arguments and mean-field type calculations utilizing the so-called “surface integration approach”, a generalization of the well known Derjaguin approximation. Its usage in the present research, requires knowledge on the forces between two parallel slabs, confining in between some fluctuating fluid medium characterized by its temperature T and chemical potential μ. The surfaces of the colloid particle and the slab are assumed coated by thin layers exerting strong preference to the liquid phase of a simple fluid, or one of the components of a binary mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called (+,+) boundary conditions. On the other hand, the core region of the slab and the particle, influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloid-fluid, slab-fluid, and fluid-fluid coupling parameters the competition between the effects due to the coatings and the core regions of the objects, result, when one changes T or μ, in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab. Such an effect can provide a strategy for solving problems with handling, feeding, trapping and fixing of microparts in nanotechnology.
Highlights
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 quantitative, and 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 critical Casimir forces (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
Using the results for d = σ = 4 from the mean-field type numerical study discussed in the text above, together with the surface integration approach" (SIA) approximation, we will present some results for the behavior of the CCF, vdWF and TF between a conical particle and a plate for several orientations of the colloid with respect to the smooth planar substrate in d = 3
Summary
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 quantitative, and 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. We shall envisage that the fluid is in the vicinity of its bulk critical point, with the critical temperature Tc interpreted either as that at the liquid-vapor critical point of a simple fluid or as that at the critical demixing point of a binary liquid mixture When such conditions are present, as first suggested by Fisher and de Gennes [3], an additional component adds up to the already acting forces if any, resulting from the critical fluctuation of the medium.
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