We explore how the entropic notion of depletion forces between spheres, introduced by Asakura and Oosawa, can be extended to depletion torques that affect the orientations of colloidal particles having complex shapes. In prior experimental work, systems of microscale plate-like particles in the presence of a nanoscale depletion agent have been shown to form polymer-like columnar chains; restoring depletion torques act to align lithographically-structured platelets within a chain orientationally about the chain’s axis. We consider depletion torques corresponding to parallel, face-to-face, near-contact pair interactions for complex-shaped, plate-like, prismatic lithographic particles in colloidal dispersions containing a spherical nanoscale depletion agent. We calculate depletion torques for a wide variety of such particles, including rotationally symmetric, asymmetric, achiral, chiral, and elongated particles. Moreover, we determine depletion torques between two non-parallel proximate square platelets connected by a lossless hinge along a common edge. Our investigations show that depletion torques can be tailored through lithographic or synthetic design of specific geometrical features in the shapes of particles.

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