The rolling of a cylinder on a flat plate can be viewed as the propagation of two cracks--one closing at the advancing edge and the other opening at the trailing edge. The difference of adhesion in these two regions, i.e. the adhesion hysteresis, depends on the nonequilibrium interfacial processes in an elastic system. This rolling contact geometry was used to study the effects of dispersion forces and specific interactions on interfacial adhesion hysteresis. In order to accomplish this objective, hemicylindrical elastomers of polydimethylsiloxane (PDMS)-both unmodified and plasma oxidized--were rolled on thin PDMS films bonded to silicon wafers. Plasma oxidation generates a silica-like surface on PDMS elastomer, which interacts with PDMS molecules via hydrogen-bonding forces. The adhesion hysteresis in the latter case is large and depends significantly on the molecular weight of the grafted polymer, whereas the hysteresis is rather negligible for purely dispersive systems. These results are interpreted in terms of the orientation and relaxation of polymer chains, which has its origin in the Lake-Thomas effect.