  The intriguing relationship between entropy and diffusion is a subject of
much current interest. However, the experimentally observed unusual
non-monotonic dependence of limiting ionic conductivity on inverse ion size is
neither described by the Adam-Gibbs entropy crisis theory nor by the Rosenfeld
entropy scaling. This failure is obvious because throughout the size variation
the bulk entropy of the solvent remains the same, or undergoes infinitesimal
change. We show that it is the entropy experienced by the tagged ion that needs
to be calculated. This entropy can be quantified, at least partly, by the
change in the tetrahedral ordering of water molecules in the hydration layer of
the ions which exhibits a nonmonotonic size dependence.
