Electric-field-induced displacement of charged spherical colloids in compressible hydrogels

Abstract

This paper concerns the electric-field-induced displacement of a charged spherical colloid embedded in an uncharged compressible hydrogel. Previous theoretical calculations for incompressible polymer skeletons predict sub-nanometre particle displacements within the experimentally accessible parameter space (e.g., particle surface charge density, polymer shear modulus, and electric field strength). Accordingly, the prevailing expectation is that an experimental test of the theory would be extraordinarily difficult. In this work, however, we solved the electrokinetic model for compressible polymer skeletons with arbitrary Poisson's ratio. The most striking result, obtained from numerically exact solutions of the full model and an analytical boundary-layer approximation, is that polymer compressibility admits particle displacements that increase linearly with particle size when the radius is greater than the Debye length. This scaling is qualitatively different than previously obtained for incompressible skeletons, where the ratio of the particle displacement to the electric field approaches a particle-size-independent constant. The displacement is also much more sensitive to the hydrodynamic permeability of the polymer skeleton. Therefore, when compressible hydrogels are deformed at frequencies below their reciprocal draining time, our theory identifies the parameter space where displacements could be registered using optical microscopy. In turn, this will help to establish a quantitative connection between the electric-field-induced particle displacement and physicochemical characteristics of the particle–polymer interface.