Depletion Interaction Between Two Flat Plates

In this chapter we consider the depletion interaction between two flat plates and between two spherical colloidal particles for different depletants (polymers, small colloidal spheres, rods and plates). First of all we focus on the depletion interaction due to a somewhat hypothetical model depletant, the penetrable hard sphere (phs), to mimic a (ideal) polymer molecule. This model, implicitly introduced by Asakura and Oosawa [1] and considered in detail by Vrij [2], is characterized by the fact that the spheres freely overlap each other but act as hard spheres with diameter a when interacting with a wall or a colloidal particle. The thermodynamic properties of a system of hard spheres plus added penetrable hard spheres have been considered by Widom and Rowlinson [3] and provided much of the inspiration for the theory of phase behavior developed in Chap. 3. 

The depletion potential is a potential of mean force and, as stressed by Onsager [4, 5], the system is considered at a given chemical potential of the solvent (and other solution) components the relevant pressure is the osmotic pressure. 

1 Interaction Potential Between Two Flat Plates Using the Force Method 

The force per unit area, K h), between two parallel plates separated by a distance h, is the difference between the osmotic pressure P,- inside the plates and the outside pressure Po 

Lekkerkerker and R. Tuinier, Colloids and the Depletion Interaction, Lecture Notes in Physics, 833, DOI 10.1007/978-94-007-1223-2 2, 

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Depletion Interaction Due to Ideal Polymers 2.2.1 Depletion Interaction Between Two Flat Plates... 

The polymer density profile of ideal chains next to a hard sphere for arbitrary size ratio q was first ealeulated by Taniguchi et al. [125] and later independently by Eisenriegler et al. [126]. Eisenriegler also considered the pair interaction between two colloids for Rg< R [127] and for Rg R [128], as well as the interaction between a sphere and a flat wall due to ideal chains [129]. Depletion of excluded volume polymer chains at a wall and near a sphere was considered by Hanke et al. [130]. One of their results is that the ratio /Rg at a flat plate, which is 1.13 for ideal chains [118, 119], is slightly smaller (1.07) for excluded-volume chains. 

An early theoretical depletion interaction study with polyelectrolytes as depleting agents was made by Bohmer et al. [78] who used the self-consistent field method of Scheutjens and Heer. For high salt concentrations, the polymer concentration dependence of the depletion layer thickness matches with that of an uncharged polymer in solution. Below a salt concentration of 1 mol/L the depletion layer thickness starts to decrease with increasing polyelectrolyte concentration at lower polymer concentration. At low salt concentrations a significant repulsive barrier in the potential between two uncharged parallel flat plates was found. 

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