Electric-field-enhanced transport in polyacrylamide hydrogel nanocomposites

Electroosmotic pumping through uncharged hydrogels can be achieved by embedding the polymer network with charged colloidal inclusions. Matos et al. [M.A. Matos, L.R. White, R.D. Tilton, J. Colloid Interface Sci. 300 (2006) 429-436], recently used the concept to enhance the diffusion-limited flux of uncharged molecules across polyacrylamide hydrogel membranes for the purpose of improving the performance of biosensors. This paper seeks to link their reported macroscale diagnostics to physicochemical characteristics of the composite microstructure. The experiments are characterized by a Debye screening length that is much larger than the radius of the silica nanoinclusions and the Brinkman screening length of the polymer skeleton. Accordingly, closed-form expressions for the incremental pore mobility are derived, and these are evaluated by comparison with numerically exact solutions of the full electrokinetic model. A mathematical model for the bulk electroosmotically enhanced tracer flux is proposed, which is combined with the electrokinetic model to ascertain the electroosmotic pumping velocity from measured flux enhancements. Because the experiments are performed with a known current density, but unknown bulk conductivity and electric field strength, theoretical estimates of the bulk electrical conductivity are adopted. These account for nanoparticle polarization, added counterions, and non-specific adsorption. Theoretical predictions of the flux enhancement, achieved without any fitting parameters, are within a factor of two of the experiments. Alternatively, if the Brinkman screening length of the polymer skeleton is treated as a fitting parameter, then the best-fit values are bounded by the range 0.9-1.6 nm, depending on the inclusion size and volume fraction. Independent pressure-driven flow experiments reported in the literature for polyacrylamide gels without inclusions suggest 0.4 or 0.8 nm. The comparison can be improved by allowing for hindered ion migration, while uncertainties regarding the inclusion surface charge are demonstrated to have a negligible influence on the electroosmotic flow. Finally, and perhaps most importantly, anomalous variations in the flux enhancement with particle size and volume fraction can be rationalized at present only by acknowledging that particle-particle and particle-polymer interactions increase the effective permeability of the hydrogel skeleton. This bears similarities to the increase in polymer free volume that accompanies the addition of silica nanoparticles to certain polymeric membranes.