The stability of binary charged colloidal crystals

Abstract

The stability of a binary disordered substitutional colloidal crystal has been examined against the formation of a colloidal liquid. Phase diagrams are constructed by comparing the free energy of the liquid phase to that of the solid phases. The calculations show that the freezing density has a maximum as a function of the number fraction. The maximum in the freezing density becomes more pronounced when the particle diameter ratio differs more from unity. If the particles have very different diameters, the binary colloidal crystals are unstable against the colloidal fluid. The freezing density rises almost vertically when the number fraction differs from 0 or 1 by less than 6%. The pronounced stability of the liquid phase for particles with more different sizes may explain the formation of colloidal glasses as opposed to the formation of disordered substitutional colloidal crystals with particles of more similar diameters. The Hume–Rothery rule for a binary metallic alloy also applies to a binary charged colloid if the diameter ratio is taken from the diameters of the effective hard spheres which are determined by the interparticle interactions but not those of the bare particles.