Dipole Interactions and Electrical Polarity in Nanosystems -- the Clausius-Mossotti and Related Models

Point polarizable molecules at fixed spatial positions have solvable electrostatic properties in classical approximation, the most familiar being the Clausius-Mossotti (CM) formula. This paper generalizes the model and imagines various applications to nanosystems. The behavior is worked out for a sequence of octahedral fragments of simple cubic crystals, and the crossover to the bulk CM law is found. Some relations to fixed moment systems are discussed and exploited. The one-dimensional dipole stack is introduced as an important model system. The energy of interaction of parallel stacks is worked out, and clarifies the diverse behavior found in different crystal structures. It also suggests patterns of self-organization which polar molecules in solution might adopt. A sum rule on the stack interaction is found and tested. Stability of polarized states under thermal fluctuations is discussed, using the one-dimensional domain wall as an example. Possible structures for polar hard ellipsoids are considered. An idea is formulated for enhancing polarity of nanosystems by intentionally adding metallic coatings.