Depletion interaction between spheres ideal chains

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). 

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. 

Until the end of the 1990s most theoretical approaches were based on describing polymer chains as ideal or as penetrable hard spheres. Especially at the turn of the last century a wealth of different approaches were proposed to describe colloid-polymer mixtures in which interactions between polymer segments were accounted for. Essential was the progress made in Monte Carlo computer simulation studies on depletion effects [172-179] to test such theories. 

The effective pair interactions measured with these techniques are the direct pair interactions between two colloidal particles plus the interactions mediated by the depletants. In practice depletants are poly disperse, for which there are sometimes theoretical results available. For the interaction potential between hard spheres we quote references for the depletion interaction in the presence of polydisperse penetrable hard spheres [74], poly disperse ideal chains [75], poly-disperse hard spheres [76] and polydisperse thin rods [77]. 

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