  The classical Poisson-Boltzmann (PB) theory of electrolytes assumes a dilute
solution of point charges with mean-field electrostatic forces. Even for very
dilute solutions, however, it predicts absurdly large ion concentrations
(exceeding close packing) for surface potentials of only a few tenths of a
volt, which are often exceeded, e.g. in microfluidic pumps and electrochemical
sensors. Since the 1950s, several modifications of the PB equation have been
proposed to account for the finite size of ions in equilibrium, but in this
two-part series, we consider steric effects on diffuse charge dynamics (in the
absence of electro-osmotic flow). In this first part, we review the literature
and analyze two simple models for the charging of a thin double layer, which
must form a condensed layer of close-packed ions near the surface at high
voltage. A surprising prediction is that the differential capacitance typically
varies non-monotonically with the applied voltage, and thus so does the
response time of an electrolytic system. In PB theory, the capacitance blows up
exponentially with voltage, but steric effects actually cause it to decrease
above a threshold voltage where ions become crowded near the surface. Other
nonlinear effects in PB theory are also strongly suppressed by steric effects:
The net salt adsorption by the double layers in response to the applied voltage
is greatly reduced, and so is the tangential "surface conduction" in the
diffuse layer, to the point that it can often be neglected compared to bulk
conduction (small Dukhin number).
