Transport in polymer-gel composites: Response to a bulk concentration gradient

Influence of concentration polarization on DNA translocation through a nanopore

Concentration polarization can be induced by the unique ion-perm selectivity of small nanopores, leading to a salt concentration gradient across nanopores. This concentration gradient can create diffusio-osmosis and induce an electric field, affecting ionic currents on DNA that translocates through a nanopore. Here this influence is theoretically investigated by solving the continuum Poisson-Nernst-Planck model for different salt concentrations, DNA surface charge densities, and pore properties. By implementing the perturbation method, we can explicitly compute the contribution of concentration polarization to the ionic current. The induced electric field by concentration polarization is opposite to the imposed electric field and decreases the migration current, and the induced diffusio-osmosis can decrease the convection current as well. Our studies suggest that the importance of the concentration polarization can be determined by the parameter λ/G where λ is the double-layer thickness and G is the gap size. When λ/G is larger than a critical value, the influence of concentration polarization becomes more prominent. This conclusion is supported by the studies on the dependence of the ionic current on salt concentration and pore properties, showing that the difference between two models with and without accounting for concentration polarization is larger for low salts and small pores, which correspond to larger λ/G.

Electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium

When an electric field is applied to an electrolyte-saturated polymer gel embedded with charged colloidal particles, the force that must be exerted by the hydrogel on each particle reflects a delicate balance of electrical, hydrodynamic, and elastic stresses. This paper examines the displacement of a single charged spherical inclusion embedded in an uncharged hydrogel. We present numerically exact solutions of coupled electrokinetic transport and elastic-deformation equations, where the gel is treated as an incompressible, elastic Brinkman medium. This model problem demonstrates how the displacement depends on the particle size and charge, the electrolyte ionic strength, and Young's modulus of the polymer skeleton. The numerics are verified, in part, with an analytical (boundary-layer) theory valid when the Debye length is much smaller than the particle radius. Finally, we identify a close connection between the displacement when a colloid is immobilized in a gel and its velocity (electrophoretic mobility) when dispersed in a Newtonian electrolyte.

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.