  Electric field produced inside a solute by a uniformly polarized liquid is
strongly affected by dipolar polarization of the liquid at the interface. We
show, by numerical simulations, that the electric "cavity" field inside a
hydrated non-polar solute does not follow the predictions of standard Maxwell's
electrostatics of dielectrics. Instead, the field inside the solute tends, with
increasing solute size, to the limit predicted by the Lorentz virtual cavity.
The standard paradigm fails because of its reliance on the surface charge
density at the dielectric interface determined by the boundary conditions of
the Maxwell dielectric. The interface of a polar liquid instead carries a
preferential in-plane orientation of the surface dipoles thus producing
virtually no surface charge. The resulting boundary conditions for
electrostatic problems differ from the traditional recipes, affecting the
microscopic and macroscopic fields based on them. We show that relatively small
differences in cavity fields propagate into significant differences in the
dielectric constant of an ideal mixture. The slope of the dielectric increment
of the mixture versus the solute concentration depends strongly on which
polarization scenario at the interface is realized. A much steeper slope found
in the case of Lorentz polarization also implies a higher free energy penalty
for polarizing such mixtures.
