  The three most commonly-used boundary conditions for charged colloidal
systems are constant charge (insulator), constant potential (conducting
electrode) and charge regulation (ionizable groups at the surface). It is
usually believed that the charge regulation is a generalized boundary condition
that reduces in some specific limits to either constant charge or constant
potential boundary conditions. By computing the disjoining pressure between two
symmetric planes for these three boundary conditions, both numerically (for all
inter-plate separations) and analytically (for small inter-plate separations),
we show that this is not, in general, the case. In fact, the limit of charge
regulation is a separate boundary condition, yielding a disjoining pressure
with a different characteristic separation-scaling. Our findings are supported
by several examples demonstrating that the disjoining pressure at small
separations for the charge regulation boundary-condition depends on the details
of the dissociation/association process.
