Electrostatic effects on the equilibrium partitioning of spherical colloids in random fibrous media

A theory has been developed to predict the effects of electrostatic interactions on the equilibrium partition coefficient (Phi) of spherical macromolecules in gels, the gels being modeled as random arrays of fibers, The partitioning theory derived by Ogston (Trans. Faraday Sec. 54, 1754-1757 (1958)) for neutral macromolecules and fibers was extended by using a Boltzmann factor, containing an electrostatic free energy, to modify the probability of fitting a sphere in a space between fibers, This approach, which is limited to dilute solutions of macromolecules, is approximate in that the only electrostatic interactions considered are those between the sphere and the nearest fiber, The electrostatic free energy was calculated from finite-element solutions to the linearized Poisson-Boltzmann equation for a sphere interacting with a long cylinder, both with specified surface charge densities, Free energies calculated for many combinations of sphere radius, fiber radius, separation distance, Debye length, and the surface charge densities of the sphere and fiber are presented as a correlation involving the various dimensionless parameters, When the sphere and fiber have like charges, Phi decreases with increases in the sphere size, the volume fraction of fibers, the Debye length, and either surface charge density; results are presented to illustrate each of these effects, Predictions from the theory are in good agreement with recent measurements of Phi for proteins in moderately charged gels. (C) 1996 Academic Press, Inc.