Charged macromolecules in external fields. I. The sphere

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Abstract
The response of rigid macroions in aqueous solution to an external electric field is considered. The external field, which may be steady or oscillating, induces perturbations in the distribution of coions and counterions, and also in the electrical and solvent velocity fields. The basic equations that describe the various fields are reviewed, and then specialized to the special problem of thin double layers. Boundary conditions are derived which differ from those used in previous work. Previous treatments of the counterion flux into the double layer have either omitted the flux, or taken it to be in phase with the applied field. We find that this flux is large, and has a significant component out of phase. The new boundary conditions make substantial changes in the complex dielectric response. The dominant slow process that controls relaxation is the slow diffusion of neutral salt in the environment of the macromolecule. Large perturbations are induced in the neutral salt concentration by charge distortions in the double layer, and in turn modify the response of the charge. The slow diffusion of the salt gives rise to broad dielectric dispersion. An application is made to the charged sphere, and the results are compared with dielectric response measurements on polystyrene latex spheres, and with the theory of Schwarz.