Depletion forces acting on nanoparticles in confined polymer systems: Potential theory

Abstract

By making use of the developed potential theory, we investigate the polymer-mediated depletion interactions between nanoparticles and hard planar surfaces in the following settings: (i) interaction between two nanoparticles; (ii) interactions between nanoparticle and hard planar surface; (iii) interaction between two nanoparticles in the presence of hard planar surface; and (iv) interaction between nanoparticle and walls of the plane-parallel slab. For each of the listed systems, we have calculated the polymer end density, excess grand potential, and the potential of the depletion forces. On the basis of the obtained results, we have analyzed the effect of the geometric constraints imposed by hard walls on the polymer density structure and the depletion interaction between nanoparticles.

Many-body effects for critical Casimir forces

“…These latter effects can lead, e.g., to a strengthening or weakening of the total force acting on a particle surrounded by more than a single other one, a change of sign of that force, or the appearance of stable or unstable configurations. Many-body effects appear in rather diverse systems such as nuclear matter [1], superconductivity [2], colloidal suspensions [3,4], quantumelectrodynamic Casimir forces [5][6][7][8][9][10], polymers [11,12], nematic colloids [13], and noble gases with van der Waals forces acting among them [14][15][16][17]. Each of these systems is characterized by a wide range of time and length scales.…”

Wall–particle interactions and depletion forces in narrow slits

“…The opposite limit would correspond to the "protein limit" in which the particle radius is much smaller than the polymer coils (this case is by far more complex [32,33]). We will focus on the former case only.…”

“…This generalization can be strongly influenced by the colloid-wall distance, mostly when there exists an oscillatory polymer density profile in the absence of colloids. Chervanyov [32] gives several expressions for the wall-particle and particle-particle effective interactions. The qualitative conclusion would be that confinement can have significant influence on the interparticle potential when the size of the particles and the wall-particle distance are comparable to the polymer correlation length [32,35].…”

“…To tackle down this question it is frequent to consider an infinitely diluted colloidal dumbbell, the confining geometry, and the polymer coils as the only species possessing degrees of freedom. The calculation (by theory [32] or simulation [34]) yields polymer density maps which in turn can be integrated to obtain effective forces that arise between colloidal particles and between the confining objects. Then, the colloidcolloid distance can be changed following a given path and forces integrated to produce the reversible work needed to walk this path [32].…”

“…The calculation (by theory [32] or simulation [34]) yields polymer density maps which in turn can be integrated to obtain effective forces that arise between colloidal particles and between the confining objects. Then, the colloidcolloid distance can be changed following a given path and forces integrated to produce the reversible work needed to walk this path [32]. This work is directly linked to the potential of mean force (alternative routes to calculate it may be found in Refs.…”