Quadrupole terms in the Maxwell equations: Born energy, partial molar volume, and entropy of ions

A new equation of state relating the macroscopic quadrupole moment density Q to the gradient of the field del E in an isotropic fluid is derived: Q = alpha(Q)(del E - U del . E/3), where the quadrupolarizability alpha(Q) is proportional to the squared molecular quadrupole moment. Using this equation of state, a generalized expression for the Born energy of an ion dissolved in quadrupolar solvent is obtained. It turns out that the potential and the energy of a point charge in a quadrupolar medium are finite. From the obtained Born energy, the partial molar volume and the partial molar entropy of a dissolved ion follow. Both are compared to experimental data for a large number of simple ions in aqueous solutions. From the comparison the value of the quadrupolar length L-Q is determined, L-Q = (alpha(Q)/3 epsilon)(1/2) = 1-4 angstrom. Data for ion transfer from aqueous to polar oil solution are analyzed, which allowed for the determination of the quadrupolarizability of nitrobenzene. (C) 2014 AIP Publishing LLC.