  When adhesive elastomeric materials slide over hard rough surfaces at low
velocities, there are two primary dissipative mechanisms that control how
friction changes with sliding velocity: viscoelastic dissipation and adhesive
dissipation. To distinguish the contribution of these dissipative mechanisms we
have measured frictional shear stresses for crosslinked polydimethylsiloxane
(PDMS) on three different rough surfaces of similar surface chemistry across
nearly six decades of sliding velocity. The results show that the observed
friction is dominated by adhesive dissipation, rather than viscoelastic
dissipation. Prior models for elastomer friction assume that roughness only
influences adhesive dissipation via the amount of contact area; by contrast, we
find that the roughness-induced oscillations occurring across all length scales
from macroscopic to atomic influence the molecular processes governing the
adhesive dissipation. While it was previously known that roughness-induced
oscillations affected the viscoelastic dissipation; this is the first
demonstration that these oscillations also control the behavior of the adhesive
component of friction. Finally, while theory predicts that rough friction
should be independent of elastic modulus ($E'$), we show that a strong
dependence on modulus, with the frictional shear stress scaling as $E'^{1/2}$.
When analyzed in this way, data from four different moduli and three different
roughnesses collapse onto a universal curve to describe the velocity-dependent
friction of soft materials. Taken together, this investigation sheds new light
on the adhesive component of friction, and how it depends on the roughness and
stiffness of the materials.
