Compression of Linear and Cyclic Polymer Brushes: Interpenetration and Topology-Dependent Normal Stiffness

Polymer brushes anchored at surfaces enable coatings capable of resisting normal loads and stabilizing solid–solid interfaces. In recent years, looped or cyclic topologies have attracted attention due to experimental reports of mechanical and tribological responses distinct from those of linear brushes. Here, we investigate the equilibrium compression response of opposing linear and cyclic polymer brushes using Scheutjens–Fleer self-consistent field (SF-SCF) computations. We systematically analyze how chain topology, grafting density, and polymer length affect the compression response. We show that the relative stiffness depends sensitively on the comparison criterion used between cyclic and linear architectures. When brushes are compared at nearly identical unperturbed segment density profiles (and thus comparable unperturbed heights), linear brushes sustain higher normal loads than cyclic brushes, particularly at low compression. This behavior originates from a broader overlap zone and higher integrated interpenetration for linear brushes and can be rationalized using an effective-medium description of the layered compressed interface. These results identify interpenetration as a key equilibrium structural descriptor governing topology-dependent mechanical response under compression. While frictional forces are not computed, the results provide equilibrium structural and mechanical descriptors of the compressed contact state that may aid interpretation of experimental trends, with the understanding that any connection to friction depends on lubrication regime and nonequilibrium dissipation mechanisms beyond the scope of the present approach.