Analytical self-consistent field model of arm-grafted starlike polymers in nonlinear elasticity regime

We develop approximate analytical (AA) model to describe the structure of a brush made of starlike polymers (regularly branched dendrons of the first generation) grafted by one arm onto a planar surface. It is demonstrated that introduction of two sub-layers with distinct populations of strongly and weakly stretched dendrons allows for adequate semi-analytical description of these end-grafted macromolecules in nonlinear elasticity regime. We calculate brush thickness, fraction of strongly stretched dendrons and monotonously decreasing polymer density profiles as a function of polymer grafting density and number of branches in starlike macromolecule. The predictions of AA model are compared with the results of numerical self-consistent field model of Sheutjens and Fleer (SF-SCF). Good agreement between the two models is found at high grafting densities and/or at large number of branches of starlike polymers.