Continuum and Dipole-Lattice Models of Solvation

Dipole-lattice and continuum-dielectric models, which are two important “simplified” models of solvation, are analyzed and compared. The conceptual basis of each approach is briefly examined, and the relationship between the two methodologies is explored. The importance of dipole lattices in the development of dielectric theory is stressed. The Clausius−Mossotti equation, which is the result of early attempts at relating the dielectric constant to “microscopic” quantities, also applies to cubic lattices of Langevin dipoles or point polarizabilities. The presence of thermal fluctuations, rather than inter-dipolar or specific short range interactions is found to be the fundamental reason for the deviation of dipolar materials from the Clausius−Mossotti equation. The fact that the continuum dielectric is the infinite dipole density limit of a more general dipole-lattice description is shown by recovering the continuum results with dipole lattices of high number density. The linearity of a continuum model is shown to be a direct consequence of being the infinite density limit of a dipole lattice. Finally, it is shown that the discreteness involved in the numerical solution of the Poisson equation cannot capture the effect of the physical discreteness in dipole lattices.