Origin of / scaling of primary and secondary conductivity relaxation times in mixture of water with protic ionic liquid.

Murali [, 2024, 15, 3376-3382] made ambient and high pressure dielectric measurements of a supercooled aqueous mixture of an acidic ionic liquid to find the presence of the primary () conductivity relaxation together with the secondary () conductivity relaxation originating from the water clusters confined by the cations and anions with relaxation times and respectively. From the isothermal and isobaric conductivity relaxation data found on varying thermodynamic conditions ( and ) at constant are the invariance of (i) the frequency dispersion or the Kohlrausch function exponent (1 - ) of the primary conductivity relaxation, and (ii) the ratio of the primary and secondary conductivity times, /. This co-invariance of , , and (1 - ) at constant was observed before in non-aqueous ionic liquids, but it is found for the first time in aqueous ionic liquids. The new data together with PVT measurements enable Murali to show additionally that both and are functions of / with a single exponent = 0.58. The Coupling model is the only theory predicting the co-invariance of , , and (1 - ) as well as the / scaling of both and . It is applied herein to address and explain the data of the ionic liquid-water mixture.