Debye–Hückel–Bjerrum theory for charged colloids

We formulate an extension of the Debye–Hückel–Bjerrum theory [M.E. Fisher, Y. Levin, Phys. Rev. Lett. 71 (1993) 3826] to the fluid state of a highly asymmetric charged colloid. Allowing for the formation of clusters consisting of one polyion and n condensed counterions, the total Helmholtz free energy of the colloidal suspension is constructed. The thermodynamic properties, such as the cluster-density distribution and the pressure, are obtained by the minimization of the free energy under the constraints of a fixed number of polyions and counterions. In agreement with the current experimental and Monte Carlo results, no evidence of any phase transition is encountered