We present a model for the theoretical description of the electric double layer of realistic salt-free colloidal suspensions. This kind of systems consist of aqueous suspensions deionized maximally without any electrolyte added during the preparation, in which the only ions present can be (i) the added counterions that counterbalance the surface charge, (ii) the H(+) and OH(-) ions from water dissociation, and (iii) the ions produced by the atmospheric CO2 contamination. Our theory is elaborated in the framework of the classical Poisson-Boltzmann theory, the spherical cell model approach, and the appropriate local equilibrium reactions, and it also includes an efficient mathematical treatment for dealing with the resulting integro-differential equations. We have applied it to the study of the surface electric potential in a wide range of volume fraction and surface charge density values in a variety of cases. The numerical results show that it is necessary to consider the water dissociation influence for volume fractions lower than approximately 10(-2), whereas the atmospheric contamination, if the suspensions are open to the atmosphere, is important in the region of phi<10(-1). The present work sets the basis for theoretical models concerning the equilibrium phase diagram, electrokinetics, and rheology of such systems.
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