  We construct an explicitly solvable Landau mean-field theory for volume phase
transitions of confined or fixed ions driven by relative concentrations of
divalent and monovalent counterions. Such phase transitions have been widely
studied in ionic gels, where the mechanism relies on self-attraction or
elasticity of a network. We find here that non-ideal behavior of ions in
aqueous solution can in theory drive phase transitions without a
self-attracting or elastic network. We represent non-ideality by a
Debye-H\"uckel-like power-law activity, or correlation free energy, and retain
a mechanical self-repulsion to avoid runaway collapse due to the non-ideal
term. Within this model we find a continuous line of gas-liquid-type critical
points, connecting a purely monovalent, divalent-sensitive critical point at
one extreme with a divalent, monovalent-sensitive critical point at the other.
An alternative representation of the Landau functional handles the second case.
We include a formula for electrical potential, which may be a convenient proxy
for critically varying volume. Our relatively simple mean-field formulation may
facilitate explorations of tunable critical sensitivity in areas such as ion
detection technology and biological osmotic control.
