Ionic fluids with association in dipoles and quadrupoles

The Debye-Hückel theory for an electrolyte solution is considered beyond dipole formation by including neutral clusters with four particles, through association between two positive and two negative ions. The Helmholtz free energy for the interaction between clusters and the ionic solution is evaluated according to Debye-Hückel theory. A simple association constant for the quadrupole complex is used, considering the electrostatic interaction between the ions in a fixed configuration. Hard-core contributions with Carnahan-Starling and free-volume theories are also included. The complete free energy shows phase separation, with a critical point in the region of numerical simulations.