Roles of entropic excluded-volume effects in colloidal and biological systems: Analyses using the three-dimensional integral equation theory

In the theory proposed here, the hypernetted-chain integral equations are solved on a three-dimensional cubic grid to calculate the spatial distribution of the potential entropically induced between a very big body of arbitrary geometry and a big sphere immersed in small spheres. Effects due to the geometric feature of the very big body (e.g., step edges, trenches, corners, and changing curvature) can then be investigated by analyzing the potential along a specific trajectory of the big sphere. Several model calculations are performed, and the results obtained are interpreted in terms of the roles of the entropic excluded-volume effects in highly ordered processes occurring within colloidal and biological systems (e.g., the lock and key steric interaction between macromolecules). Discussion is also given to related subjects such as the formation of secondary structures of a protein molecule in aqueous solution, the construction of controlled particle arrays, and the synthesis of a molecular tube using the complex formation by cyclic molecules and linear polymers.