Electrical double layer interactions for spherical charge regulating colloidal particles

A new way of linearising the Poisson-Boltzmann equation is presented which is capable of producing accurate answers for moderately high surface charge and surface potentials. Unlike the Debye-Hückel approximation, the linearisation is based on the fact that electric potential variation, rather than the magnitude of the potential itself, remains small between two charged plates at close separation. The method can be applied quite generally to any type of surface. The cases of constant surface charge, the constant surfaceppotential and charge regulating systems are considered as examples. The results for constant charge and potentials as high as 5 μC/cm2 and 200 mV are within 7% of the exact answers for plate separations of one Debye length or less. In contrast, the Debye-Hückel approximation produces answers that are at least an order of magnitude too large, for the same problems. The application of the method to the problem of calculating the electrostatic forces between charge regulated spherical particles is also addressed in some detail.