# 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

## TL;DR

This paper investigates how the total force between colloids and surfaces in a fluid can change sign due to the interplay of critical Casimir and van der Waals forces, with potential applications in nanotechnology and colloid stability.

## Contribution

It introduces a theoretical framework demonstrating sign change in Casimir and total forces caused by competing interactions in colloid-fluid systems.

## Key findings

- Sign change of Casimir force with temperature, chemical potential, and distance.
- Conditions for total force sign reversal in colloid-surface systems.
- Potential applications in controlling colloidal stability and nanotechnology.

## Abstract

We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. We study the interplay between these forces, as well as the {\it 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 $\mu$. 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 so-called $(+,+)$ 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 $T$, $\mu$ or $L$, in {\it sign change} of the Casimir force (CF) {\it 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.