Attraction or repulsion between charged colloids? A connection with Debye-Hückel theory

We discuss the phase behaviour of suspensions of charged colloidal particles, specifically at low salt concentrations. The total free energy Fof a three-component system of charged colloids and positive and negative salt ions can be expressed as F= FDLVO +F0 , where FDLVOis the free energy of a one-component system of colloidal particles interacting via the DLVO pair potential, and F0consists of density-dependent contributions from the salt ions. We argue that F0drives a gas-liquid spinodal at low salt concentrations, in accordance with several experimental observations. The underlying mechanism is equivalent to that of the well-established gas-liquid transition in simple electrolytes. The present theory connects directly the classic linearized Poisson-Boltzmann theories for simple electrolytes (Debye-Hückel) and colloidal suspensions (DLVO).