Hard-particle fluids, such as rectangles, spherocylinders, ellipses, cubes, and squares are interesting building blocks for assembly as they have the ability to produce diverse structures depending on their aspect ratio, concentration, and subtle differences in their geometry. Depletion interactions that arise in mixtures of particles with only hard-core repulsion are entropically driven and have been observed in colloidal systems consisting of a collection of large particles in a solution of smaller, depletant particles. Depletion interactions have been extensively studied for large spheres in small rods and large spheres in small spheres. In all of these studies, the large particles (spheres) have no rotational entropy and hence no preferred orientation as they approach one another. It is of interest to study the interplay between depletion interactions and the rotational entropy of larger particles with anisotropic shapes.

In this work, we use Monte Carlo simulations to examine the depletion interactions of several two-dimensional systems. We study squares and rods depleted by disks, as well as squares depleted by rods. We determine the effect of depletant size and concentration, as well as the aspect ratio (squares vs. rectangles) of the large particles on the potential of mean force. We find that both disks and rods induce an attraction between the squares as well as between rods in a suspension of disks. The strength of the attraction increases with increasing depletant concentration and depends on depletant size. By subtracting the potential of mean force for two large objects in vacuum from that in the presence of depletant, we are able to separate the effect of rotational entropy from that of depletion. We find under certain conditions that the disks cause the squares to be attractive over some separations and repulsive over others. We also probe the relative orientation that two squares adopt as they approach each other in a sea of depletant. We observe rich behavior, in which this relative orientation varies with inter-particle separation (e.g., for some separations, particles adopt a face-to-face orientation, while for others, the vertex-vertex orientation is preferred) and depends on depletant size and concentration.