Depletion Interaction Due to Ideal Polymers

Depletion Interaction Due to Ideal Polymers 2.2.1 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 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. 

In order to model experimental systems with short-range attractions, different models have been used. Spherically symmetric interaction potentials, such as the simple square well (SW) [22], or the Asakura Oosawa (AO) depletion potential [23], model the colloid-polymer mixture considering that the polymers are ideal [24]. However, due to the short range of these simple potentials, crystallization and fluid-fluid phase separations occur in the same region where gelation is expected, what makes more difficult the interpretation of the data. Therefore, strategies to avoid this equilibrium phase separation have been devised. 

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