Colloidal particles exhibit the remarkable ability to self-assemble, suggesting that colloids could be used as templates for complex microstructures, precursors for advanced materials, or even as end products themselves. Precise control of colloidal self-assembly, however, relies upon accurate knowledge of the forces between colloids and between colloids and surfaces, such as electrostatics or hydrodynamic mediated interactions. Another important class of forces, known as depletion forces, is induced by asymmetries in the local arrangement of colloids (or non-adsorbing polymers) about other larger colloidal particles. If the colloids behave in a hard-particle-like manner, i.e., no interaction beyond their impenetrable hard cores, the depletion forces arise solely as a result of entropic considerations. As recently suggested (Dinsmore et al., 1996, Nature 383, 239), passive structures etched into the walls of containers can create entropic potential fields of sufficient range and magnitude such that the motion and position of large colloids can be effectively controlled, thereby offering a straightforward method for the production of novel materials.

Depletion forces between colloids and surfaces, typically flat walls, have been calculated with models spanning from, for example, simple excluded volume arguments (Asakura and Oosawa, 1954, J. Chem. Phys. 22, 1255), to density functional theory (Götzelmann et al., 2003, Europhys. Lett. 63, 233) and to scaled particle theory (Corti and Reiss, 1998, Mol. Phys. 95, 269). The simpler models, while qualitatively useful and easily applied to various surfaces, predict only attractive depletion forces and/or fail to accurately describe complex depletion effects. Conversely, the elaborate methods provide more accurate descriptions of depletion forces but are often limited in application due to the impracticalities that arise when numerically solving their equations.

We therefore present a geometrically-based model of the entropic forces that develop between particles and surfaces in hard-sphere colloidal dispersions that is more descriptive than various simple models while still being solvable for a large variety of surface shapes. In our method, where we utilize a highly accurate approximation first put forth within the successfully updated version of scaled particle theory (Heying and Corti, 2004, J. Phys. Chem. B 108, 19756), the local colloidal arrangement that determines the entropic potential is calculated from the change in the volume of overlap between the smaller particle's equivalent cavity and the larger colloid or surface of interest. Our method is more general than that of Asakura and Oosawa (AO), though it does reduce to the AO approximation in a limiting case. With an appropriately chosen known reference state, our approach yields predictions that agree well with molecular simulation results performed at experimentally relevant conditions (unlike AO). For more complex geometries such as corners and wedges, our method predicts topologically interesting entropic potential force fields that yield a new description of colloidal motion near surfaces. We also input our depletion force predictions into Brownian Dynamics simulations and track the motion of individual colloids to study deposition pathways and structural lifetimes near a geometrically structured surface. The success of our model, given its relatively straightforward nature, suggests that our method could potentially be used in conjunction with the above simulations to engineer surfaces in order to achieve desired colloidal behavior.