Association of ion pairs in clusters of dielectric solvents

The association of ion pairs in clusters is studied in an extended Bjerrum model using both a Coulombic potential and a potential of mean force calculated from molecular dynamics simulations. Association is found to increase rapidly as the cluster size decreases until a critical size is reached, below which the ions are in the paired state. For NaCl in water this is estimated at 12 water molecules for contact ion pairs. It is also found that the short-range details of the potential are important and that replacing them with a Coulombic assumption leads to a large overestimate of the critical size.