Model for a mixture of macroions, counterions, and co-ions in a waterlike fluid

We propose an integral equation theory for a mixture of macroions, counterions, and co-ions in a waterlike fluid in which all the components are accounted for explicitly. The macroions can carry positive and negative surface charges simultaneously, mimicking in this way the situation occurring in protein solutions. To solve this complex model numerically, we utilize the associative mean spherical approximation, developed earlier for low-molecular-mass charge-symmetric electrolyte solutions. To illustrate the potential of this approach, we present numerical results for various experimental conditions. Among the measurable properties we choose to calculate the osmotic coefficient, a quantity that reflects the stability of the solution. We show that the osmotic coefficient depends not only on the magnitude of the net charge on the macroion but also on its sign, as well as on the nature of the low-molecular-mass electrolyte present. These specific ion effects are the consequence of differences in hydration between the ions in solution and charged groups on the macroion.