Entropic forces and directed alignment of hard squares in suspensions of rods and disks

We use Monte Carlo simulations in two dimensions to study the depletion forces between two hard squares in a suspension of hard rods or disks. We determine the effects of size and concentration of rods and disks on the potential of mean force between the squares. Both rods and disks produce a short-range depletion attraction between the two squares. The depletion interaction can be strong enough to outweigh the (rotational) entropic repulsion between the squares at certain sizes and concentrations of the rods and disks. We also probe the relative orientation that two squares adopt as they approach each other and we observe rich behavior, in which the relative orientation depends on the size, concentration, and shape of the depletion agent. Simple models based on the ideas of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] can explain trends in the potentials of mean force obtained from the simulations.