Depletion interaction between spheres

We first consider emulsion droplets submitted to attractive interactions of the order of ks T. Reversible flocculation may be simply produced by adding excess surfactant in the continuous phase of emulsions. As already mentioned in Chapter 2, micelles may induce an attractive depletion interaction between the dispersed droplets. For equal spheres of radius a at center-to-center separation r, the depletion... 

Fig. 30. Interaction between spheres of radius a at separation r showing overlap of depletion layers of thickness L.

Fig. 1.8 Sketch of the depletion interaction between two hard spheres...

Theoretical work on depletion interactions and their effects on macroscopic properties such as phase stability commenced along various routes. First, Vrij [40] considered the depletion interaction between hard spheres due to dilute non-ad-sorbing polymers such as penetrable hard spheres (see Sect. 1.2.5 and Sect. 2.1). Vrij [40] referred to the work of Vester [82], Li-In-On et al. [55] and preliminary experiments at the Van t Hoff Laboratory on micro-emulsion droplets mixed with free polymer [40] for experimental evidence of depletion effects. 

Baranov et al. [239] showed that the attractive depletion forces were effective in the shape selective separation of CdSe/ CdS-xoAs from a mixture of rods and CdSe spheres. Mason [281] showed that the depletion interaction between plate-... 

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 force method and the extended Gibbs adsorption equation can also be applied to obtain the depletion interaction between a sphere and a flat plate. For the Gibbs adsorption route we use (again)... 

Because for the ideal chain result higher-order h/Rg terms are not available the /(I) =0 limit can not be accessed. In Fig. 2.33 we present the functions/ for ideal chains (small h), spheres, rods and plates. It is clear that the dependence on the interparticle separation/(/z/.() is similar for greatly different depletants. The results for depletion interaction between big spheres discussed here are based on the Derjaguin approximation valid for R = a, L, D for spheres, rods and disks). 

In Sect. 2.2 we discussed the relationship between phs and ideal polymers in the depletion interaction between flat plates and between spheres. It turns out that the depletion thickness 6 of ideal polymers in the case of a flat plate is given by... 

The depletion interaction between two large spheres induced by oblate spheroids was first investigated in the low density limit by Kech and Walz. " Applying the Derjaguin approximation, they found for the limiting case of infinitely thin circular discs... 

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