  We investigate a class of "shape allophiles" that fit together like puzzle
pieces as a method to access and stabilize desired structures by controlling
directional entropic forces. Squares are cut into rectangular halves, which are
shaped in an allophilic manner with the goal of re-assembling the squares while
self-assembling the square lattice. We examine the assembly characteristics of
this system via the potential of mean force and torque, and the fraction of
particles that entropically bind. We generalize our findings and apply them to
self-assemble triangles into a square lattice via allophilic shaping. Through
these studies we show how shape allophiles can be useful in assembling and
stabilizing desired phases with appropriate allophilic design.
