  Friction between ring-polymer brushes at melt densities sliding past each
other are studied using extensive course-grained molecular dynamics simulations
and scaling arguments, and the results are compared to the friction between
linear-polymer brushes. We show that for a velocity range spanning over three
decades, the frictional forces measured for ring-polymer brushes are half the
corresponding friction in case of linear brushes. In the linear-force regime,
the weak inter-digitation of two ring brushes compared to linear brushes also
leads to a lower number of binary collisions between the monomers of opposing
brushes. At high velocities, where the thickness of the inter-digitation layer
between two opposing brushes is on the order monomer size regardless of brush
topology, stretched segments of ring polymers take a double-stranded
conformation. As a result, monomers of the double-stranded segments collide
less with the monomers of the opposing ring brush even though a similar number
of monomers occupies the inter-digitation layer for ring and linear-brush
bilayers. The numerical data obtained from our simulations is consistent with
the proposed scaling analysis. Conformation-dependent frictional reduction
observed in ring brushes can have important consequences in non-equilibrium
bulk systems.
