Fluctuation–dissipation theorem for supersaturated electrolyte solutions

Highly supersaturated electrolyte solutions are prepared and studied employing an Electrodynamic Levitator Trap (ELT) technique. The containerless suspension of pl-size solution microdroplets achieved by means of this technique eliminates dust, dirt, convection flows and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved and studied. The experimental results obtained for solvent activity versus solute concentration have been processed by applying the least-squares regression. This has allowed processing of the data with large error bars obtained for the very high supersaturations. Theoretical study is based on the development of the Cahn–Hilliard formalism for electrolyte solutions. In the approach suggested the metastable state for electrolyte solutions is described in terms of the local conserved order parameter ω(r,t) associated with fluctuations of the mean solute concentration n0. Parameters of the corresponding Ginzburg–Landau free energy functional which defines the dynamics of metastable state relaxation are determined and expressed through the experimentally measured solvent activity. A correspondence of 96–99% between theory and experiment for the all solutions studied was achieved and reported earlier [Izmailov et al., Phys. Rev. 52E (1995) 3923]. The theoretical approach suggested in this study for thermodynamics of supersaturated electrolyte solutions is further developed in order to describe the transient and stationary limits of the metastable state relaxation. Knowledge of these limits has allowed derivation of the Fluctuation–Dissipation Theorem (FDT) for supersaturated electrolyte solutions by specifying a time-dependent product of macroscopic mobility (inverse viscosity) and microscopic diffusivity. It is understood from general relationships of non-equilibrium thermodynamics that this product has a maximum at saturation point and is equal to zero at spinodal point. Further analysis of the FDT has revealed that the product of macroscopic mobility and microscopic diffusivity for electrolyte solutions has another particularity: a local minimum in the deeply undersaturated region of solute concentrations. Numerical analysis of the FDT has been carried out for the supersaturated, binary, electrolyte symmetric solutions.