Tribological universality in compressed polymer brushes

Compressed polymer brushes exhibit mutual interpenetration that is linked to the tribological properties of brush-coated surfaces. Interpenetration is quantified by the overlap function, defined as the product of the density profiles of two opposing brushes. Using numerical self-consistent field calculations, we show that the shape of the overlap function is remarkably invariant across a broad class of symmetric and asymmetric brush pairs. The brush parameters that varied include chain length, grafting density, chain stiffness, and degree of branching. In the non-draining approximation and at low shearing rates, the overlap integral defines the sliding friction force. We find that normalizing the friction force vs external pressure curves by their values at a fixed reference pressure collapses the data onto a universal master curve for all brush pairs sharing the same equation of state, regardless of all the other parameters, which should simplify the design of lubricating coatings.