Theory of Y- and Comb-Shaped Polymer Brushes: The Parabolic Potential Framework

The parabolic approximation for self-consistent molecular potential is widely used for theoretical analysis of conformational and thermodynamic properties of polymer brushes formed by linear or branched macromolecules. The architecture-dependent parameter of the potential (topological coefficient) can be calculated for arbitrary branched polymer architecture from the condition of elastic stress balance in all the branching points. However, the calculation routine for the topological coefficient does not allow unambiguously identifying the range of applicability and the accuracy of the parabolic approximation. Here the limits of applicability of parabolic approximation are explored by means of numerical self-consistent field method for brushes formed by Y-shaped and comb-like polymers. It is demonstrated that violation of the potential parabolic shape can be evidenced by appearance of multimodal distribution of the end monomer unit in the longest elastic path of the macromolecule. The asymmetry of branching of Y-shaped polymers does not disturb the parabolic shape of the potential as long as the degree of polymerization of the root segment remains sufficiently large. The same applies to comb-shape polymers with sufficiently long main chain and large number of branching points. For short comb-like polymers multiple modes in the distribution of the end monomer unit of the main chain are observed and related to deviation from the parabolic shape of the potential