Ion-sensitive phase transitions driven by Debye-H\"uckel non-ideality

Abstract

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.