Adhesion of a tape loop

In this work, we revisit experimentally and theoretically the mechanics of a tape loop. Using primarily elastic materials (polydimethylsiloxane, PDMS, or polycarbonate, PC) and confocal microscopy, we monitor the shape as well as the applied forces during an entire cycle of compression and retraction of a half-loop compressed between parallel glass plates. We observe distinct differences in film shape during the cycle; points of equal applied force or equal plate separation differ in shape upon compression or retraction. To model the adhesion cycle in its entirety, we adapt the 'Sticky Elastica' of [T. J. W. Wagner et al., Soft Matter, 2013, 9, 1025-1030] to the tape loop geometry, which allows a complete analytical description of both the force balance and the film shape. We show that under compression the system is generally not sensitive to interfacial interactions, whereas in the limit of large separation of the confining parallel plates during retraction the system is well described by the peel model. Ultimately, we apply this understanding to the measurement of the energy release rate of a wide range of different cross-linker ratio PDMS elastomer half-loops in contact with glass. Finally, we show how the model illuminates an incredibly simple adhesion measurement technique, which only requires a ruler to perform.