  We formulate a general mean-field theory of a flat electric double layer in
ionic liquids and electrolyte solutions with ions possessing static
polarizability and a permanent dipole moment on a charged electrode. We
establish a new analytical expression for electric double layer differential
capacitance determining it as an absolute value of the ratio of the local ionic
charge density to the local electric field on an electrode surface. We
demonstrate that this expression generalizes the analytical expressions
previously reported by Kornyshev and Maggs and Podgornik. Using the obtained
analytical expression, we explore new features of the differential capacitance
behavior with an increase in the static polarizability and permanent dipole
moment of cations. We relate these features to the behavior of ionic
concentrations on the electrode. In particular, we elucidate the role of the
competition between the dielectrophoretic attraction and Coulomb repulsion
forces acting on polarizable or polar cations in the electric double layer in
the behavior of the differential capacitance. The developed theoretical model
and obtained theoretical findings could be relevant for different
electrochemical applications, e.g. batteries, supercapacitors, catalysis,
electrodeposition, etc.
