Variations of the Depletion Zones around Inclusions Explain the Complexity of Brush-Induced Depletion Interactions

Depletion forces are relevant in a variety of contexts such as the phase behavior of colloid-polymer or colloid-depletant mixtures and clustering of inclusions in mobile brushes. They arise from the tendency to minimize the volume of the depletion zone formed around colloidal particles or inclusions. In comparison to depletion interactions widely studied for colloidal particles or polymers in a suspension of spherical depletants, depletion interactions between nonspherical inclusions in mobile polymer brushes display complex behaviors. When the brush is shorter than the inclusion height, the inclusions in brushes experience apparent attraction; yet, such attraction is reduced or even becomes repulsive when the brush is overgrown beyond the inclusion height. Here we use the self-consistent field theory (SCFT) to calculate the depletion zones around two cylindrical inclusions and offer a clear explanation of how these complex behaviors arise. In tall brushes, the changes of the depletion zone volume with varying intercylinder separation are opposite in sign at the upper and lower parts of cylinders. Consequently, in tall brushes, cylinders even shorter than the size of a correlation blob experience repulsion, but long cylinders attract each other. Our study reveals that brush-induced depletion interactions are decided by the complex interplay among the sizes of brushes, inclusions, and correlation blobs.