Apparent fracture/adhesion energy of interfaces with periodic cohesive interactions

The apparent fracture/adhesion energy of an interface with periodic cohesive interactions is of general interest to understanding adhesion via periodic adhesion patches (e.g. between micro- and nanostructured surfaces). There are two important length scales for this class of problems: one corresponds to the period of cohesive interaction and the other is the size of the cohesive zone near the tip of a crack along the interface. By theoretical considerations and numerical simulations, we show that the apparent fracture/adhesion energy depends on the ratio between the period of cohesive interaction and the cohesive zone size: it is equal to the average cohesive energy of the interface if the former is much smaller than the latter but becomes the peak value of the local cohesive energy when the opposite is true. This prediction has been confirmed by numerical simulations on the peeling of a thin-film/strip adhering on a substrate via periodic discrete adhesion patches. Our analysis also provides explanations for a recent molecular dynamics simulation which showed that the apparent adhesion energy of a single-stranded DNA (ssDNA) adhering on a graphite sheet is equal to the peak, rather than the average, value of the van der Waals interaction energy between the ssDNA and the substrate.