  We find that the Debye-H\"uckel nonideality of dilute aqueous electrolytes is
sufficient to drive volume phase transitions and criticality, even in the
absence of a self-attracting or elastic network. Our result follows from a
Landau mean-field theory for a system of confined ions in an external solution
of mixed-valence counterions, where the ratio of squared monovalent to divalent
ion concentration provides a temperature-like variable for the phase
transition. Our analysis was motivated by long-studied volume phase transitions
via ion exchange in ionic gels, but our findings agree with existing theory for
volume-temperature phase transitions in charged hard-sphere models and other
systems by Fisher and Levin, and McGahay and Tomozawa. Our mean-field model
predicts 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 this second limit. It follows
that critical sensitivity to ion valence is tunable to any desired valence
ratio. The critical or discontinuous dependent variable can be the confinement
volume; alternatively the internal electrical potential may be more convenient
in applications. Our simplified conditions for ionic phase transitions to
occur, together with our relatively simple theory to describe them, may
facilitate exploration of tunable critical sensitivity in areas such as ion
detection technology, biological switches and osmotic control.
