Electrical double layer around a spherical colloid particle: The excluded volume effect

The influence of the excluded volume effect on both the spatial distribution of ionic species and the electrostatic potential distribution in the neighborhood of a suspended spherical particle is examined on the basis of a modified Poisson–Boltzmann equation, which takes into account the finite ion size by means of a Langmuir-type correction. We find that κa (κ and a being the reciprocal Debye length and the particle radius, respectively) ceases to be a valid parameter for the characterization of the electrical double layer, and that it is necessary to use both parameters κ and a to characterize adequately the system. We also find that the excluded volume effect considerably increases the surface potential (for a given value of the surface charge density) as compared to the case when ideal ion behavior is assumed. This suggests the use of the particle charge rather than the surface potential in order to characterize the system. Because of this, an approximate equation for the surface charge density of spherical colloid particles, valid for a wide range of system parameter values, is also reported.

Graphical abstractThe excluded volume effect (cmaxcmax) considerably increases the surface potential ySyS (for a given value of the surface charge density, I) as compared to the case when ideal ion behavior is assumed (PB equation). This suggests the use of the particle charge rather than the surface potential in order to characterize the system.Figure optionsDownload full-size imageDownload as PowerPoint slide