Geometry of defects at shape-complementary soft interfaces

Shape complementarity can be used to enhance adhesion selectively between elastomeric surfaces. Complementary arrays of surface structures, such as 1D ridges or fibrils arranged in a 2D lattice, can inter-digitate to achieve adhesion enhancement controlled by shape recognition. It has been shown that relative misorientation is accommodated by defects that are meso-scale screw dislocations. The arrangement of such dislocations plays a critical role in determining the mechanical properties of the interface. Here we study the geometric properties of one-dimensional (ridge/channel) and two-dimensional (arrays of pillars) shape-complementary interfaces in the presence of relative misorientation (twist) and difference in lattice spacing. Relative misorientation without difference in lattice spacing is accommodated by arrays of screw dislocations. Difference in lattice spacing without misorientation is accommodated by arrays of edge dislocations. In general, we observe arrays of dislocations with mixed screw and edge character. The spacing and orientation of these arrays can be predicted accurately using the geometry of Moiré patterns. More broadly, we show that soft materials with shape-complementary patterns can be used to generate meso-scale dislocations of arbitrary edge and screw character at the length scale of tens of microns. Because these are easily observed optically, this system can be used to study dislocations and their interaction with each other.