Quadrupole terms in the Maxwell equations: Debye-Huckel theory in quadrupolarizable solvent and self-salting-out of electrolytes

If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Huckel theory. The quadrupolar version of the Debye-Huckel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Huckel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient gamma +/- known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally gamma +/-. Comparison with experimental data for gamma +/- for various electrolytes allows for the estimation of the quadrupolar length of water: L-Q approximate to 2 angstrom, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy. (C) 2014 AIP Publishing LLC.