Star Brushes Under Deformation: Structure and Thermodynamics

A planar polymer brush of arm-grafted polymer stars subjected to external deformation is studied theoretically We propose a simple mean-field model of the star brush that takes into account segregation of the brush-forming stars in two populations: (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended towards brush periphery. The polymer density profile in the brush is assumed to have a two-step shape. Stars in the extended population are assumed to be equally stretched, the position of extended stars' branching points sets the boundary between two parts of the brush. We show that the theory quantitatively accurately describes earlier numerical results obtained with Scheutjens-Fleer numerical self-consistent field (SF-SCF) approach for free (non-deformed) star brush. We study compression of a star brush by an impenetrable plane by using two complementary models, the SF-SCF approach and the developed mean-field theory, and demonstrate a very good quantitative agreement between the two models. It is shown than depending on the grafting density of the stars, compression could affect the two-population brush structure in opposite ways. In sparsely grafted brushes the fraction of stars in the stretched population increases while in densely grafted brushes it decreases with deformation.