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1.4 Electrostatic Correlations in Electrolytes Upon dissolution of an electrolyte in a polar solvent it dissociates into cations and anions. While this dissociation is causes each ion to be able to move freely about the solution, the distribution of cations and anions with the solutions is still not random, as they are affected by attractive and repulsive forces between ions, even at low concentrations, though at low concentrations mean-field approximations tend to still perform well. At higher concentrations, these forces can lead to "ordering" of the solution and hence to strong correlations of the distribution of ions within the solution. Many theories have been explored to describe electrostatic correlations in various contexts [64]. The simplest theory to take into account these electrostatic correlations was proposed by Debye and Hückel [20] using a simple statistical description that allowed for the calculation of probabilities of different local ionic configurations, which, together with the linearized Poisson equation, allowed them calculate the energies. This model allowed them to derive an expression for ionic activity, which is widely know as the Debye-Hückel model for ionic activity: ex (zi e)2 μi =kBTlnγi =−8πε(a+λ) (1.16) where μex is the excess chemical potential, k is the Boltzmann constant, T is iB the temperature, γi is the activity coefficient, zi is the charge number of species i, e is the elementary charge, ε is the solvent permittivity, a is the ion size (though this is often used as fitting parameter), and λ is the Debye length, defined as λ = kBTε , where n0i is the bulk number density (concentration) of ion species i. e i z i2 n 0i Note that the excess chemical potential is negative, which is due to the fact that the electrostatic interaction between an ion and its oppositely charged screening cloud is attractive and thereby lowers the electrostatic energy of the system. Overall, the Debye-Hückel model provides a useful estimate for the ionic activity in relatively dilute solutions; however, it breaks down at higher concentrations, in part because ion- solvent interactions and short-range interactions between ions have been neglected. The discussion of correlations in electrolytes becomes even more interesting when 40PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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