Nanoparticle gel electrophoresis: Soft spheres in polyelectrolyte hydrogels under the Debye–Hückel approximation

• Electrokinetic theory furnishes the soft-sphere electrophoretic mobility in polyelectrolyte gels.
• Mobility is sensitive to the gel charge and permeability.
• Mobility is sensitive to the core dielectric constant when gels are charged.
• Matlab routines are available for parametric studies and interpretation of experiments.

A mathematical model for electrophoresis of polyelectrolyte coated nanoparticles (soft spheres) in polyelectrolyte hydrogels is proposed, and evaluated by comparison to literature models for bare-sphere gel electrophoresis and free-solution electrophoresis. The utilities of approximations based on the bare-particle electrophoretic mobility, free-solution mobility, and electroosmotic flow in hydrogels are explored. Noteworthy are the influences of the particle–core dielectric constant and overlap of the polyelectrolyte shell. The present theory, which neglects ion-concentration and charge-density perturbations, indicates that the gel electrophoretic mobilities of metallic-core nanoparticles in polyelectrolyte gels can be qualitatively different than for their non-metallic counterparts. These insights will be beneficial for interpreting nanoparticle gel-electrophoresis data, optimizing electrophoretic separations, and engineering nanoparticles for technological applications.

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