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used as fitting parameter), and λ is the Debye length, defined as λ = kB T ε , where e i z i2 n 0i n0i is the bulk number density (concentration) of ion species i. Unfortunately, this model usually only works at low concentrations and many more sophisticated models are very complex and use a plethora of fitting parameters to be able to accurately predict ionic activity coefficients, especially at high concentrations, where ion-ion correlations and water-ion interactions become important to consider. In this work, we provide a simple continuum theory of electrostatic correlations in electrolytes based on the linearized 4th-order BSK model that has been proposed for ionic liquids [8] and concentrated electrolytes [6, 97]. Furthermore, we make a simple addition to this model to take in account solvent effects via the Born energy [104]. We then compare this model to a wide range of experimental activity coefficient data [42, 35, 95, 101] from both aqueous and non-aqueous solutions to show the model’s viability. 6.2 Mathematical Model 6.2.1 Born Energy Modification The first modification that we will make is to take in account solvent effects in addition to the electrostatic effects that are taken in account by the Debye-Huckel activity. For solvent effects, we will use the relatively simple formula suggested by Born [11] that has been used by others to modify activity formulas, to calculate the energy change of moving an ion from one dielectric medium to another dielectric medium. Of course, this also requires that we make the dielectric constant a function of the bulk electrolyte concentration. For this dependence, we will use the empirical formula suggested by Zuber et al [125] εw εw εc=1+αx =1+αx (6.2) iii where εw is the dielectric constant of pure water (78.46), αi is an ion-dependent parameter, xi is the mole fraction of ion i, x is the mole fraction of the salt, and 142PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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