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Ionic Interactions in Biological and Physical Systems: a Variational Treatment

Chemistry is about chemical reactions. Chemistry is about electrons changing their configurations as atoms and molecules react. Chemistry studies reactions as if they occurred in ideal infinitely dilute solutions. But most reactions occur in nonideal solutions. Then everything (charged) interacts with everything else (charged) through the electric field, which is short and long range extending to boundaries of the system. Mathematics has recently been developed to deal with interacting systems of this sort. The variational theory of complex fluids has spawned the theory of liquid crystals. In my view, ionic solutions should be viewed as complex fluids. In both biology and electrochemistry ionic solutions are mixtures highly concentrated (~10M) where they are most important, near electrodes, nucleic acids, enzymes, and ion channels. Calcium is always involved in biological solutions because its concentration in a particular location is the signal that controls many biological functions. Such interacting systems are not simple fluids, and it is no wonder that analysis of interactions, such as the Hofmeister series, rooted in that tradition, has not succeeded as one would hope. We present a variational treatment of hard spheres in a frictional dielectric. The theory automatically extends to spatially nonuniform boundary conditions and the nonequilibrium systems and flows they produce. The theory is unavoidably self-consistent since differential equations are derived (not assumed) from models of (Helmholtz free) energy and dissipation of the electrolyte. The origin of the Hofmeister series is (in my view) an inverse problem that becomes well posed when enough data from disjoint experimental traditions are interpreted with a self-consistent theory.