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Anchoring poly(ethylene glycol) (PEG) to inorganic nanoparticles (NPs) permits control over NP properties for a variety of technological applications. However, the core-shell structure tremendously complicates the interpretation of the ubiquitous ζ-potential, as furnished by electrophoretic light-scattering, capillary electrophoresis or gel electrophoresis. To advance the ζ-potential-and the more fundamental electrophoretic mobility-as a quantitative diagnostic for PEGylated NPs, we synthesized and characterized Au NPs bearing terminally anchored 5 kDa PEG ligands with univalent carboxymethyl end groups. Using the electrophoretic mobilities, acquired over a wide range of ionic strengths, we developed a theoretical model for the distributions of polymer segments, charge, electrostatic potential, and osmotic pressure that envelop the core: knowledge that will help to improve the performance of soft NPs in fundamental research and technological applications.

Nanoparticle gel electrophoresis has recently emerged as an attractive means of separating and characterizing nanoparticles. Consequently, a theory that accounts for electroosmotic flow in the gel, and coupling of the nanoparticle and hydrogel electrostatics and hydrodynamics, is required, particularly for gels in which the mesh size is comparable to or smaller than the particle radii. Here, we present an electrokinetic model for charged, spherical colloidal particles undergoing electrophoresis in charged (polyelectrolyte) hydrogels: the gel-electrophoresis analogue of Henry's theory for electrophoresis in Newtonian electrolytes. We compare numerically exact solutions of the model with several independent asymptotic approximations, identifying regions in the parameter space where these approximations are accurate or break down. As previously assumed in the literature, Henry's formula, modified by the addition of a constant electroosmotic flow mobility, is accurate only for nanoparticles that are small compared to the hydrogel mesh size. We derived an exact analytical solution of the full model by judiciously modifying the theory of Allison et al. for uncharged gels, drawing on the superposition methodology of Doane et al. to account for hydrogel charge. This furnishes accurate and economical mobility predictions for the entire parameter space. The present model suggests that nanoparticle size separations (with diameters ≲40 nm) are optimal at low ionic strength, with a gel mesh size that is selected according to the particle charging mechanism. For weakly charged particles, optimal size separation is achieved when the Brinkman screening length is matched to the mean particle size., (Copyright © 2012 Elsevier Inc. All rights reserved.)

A theoretical analysis of the dynamic electrophoretic mobility of surfactant-stabilized nano-drops is undertaken. Whereas the theory for rigid spherical nanoparticles is well developed, its application to nano-drops is questionable due to fluid mobility of the interface and of the surfactant molecules adsorbed there. At zero frequency, small drops with surface impurities are well known to behave as rigid spheres due to concentration-gradient-induced Marangoni stresses. However, at the megahertz frequencies of electroacoustic (and other spectral-based) diagnostics, the interfacial concentration gradients are dynamic, coupling electromigration, advection and diffusion fluxes. This study addresses a parameter space that is relevant to anionic-surfactant-stabilized oil–water emulsions, using sodium-dodecylsulfate-stabilized hexadecane as a specific example. The drop size is several hundred nanometres, much larger than the diffuse-layer thickness, thus motivating thin-double-layer approximations. The theory demonstrates that fluid mobility and fluctuating Marangoni stresses can have a profound influence on the magnitude and phase of the dynamic mobility. We show that the drop interface transits from a rigid/immobile one at low frequency to a fluid one at high frequency. The model unifies electrokinetics and equilibrium interfacial thermodynamics. Therefore, with knowledge of how the interfacial tension varies with electrolyte composition (oil, surfactant and added salt concentrations), the particle radius might be adopted as the primary fitting parameter (rather than the customary $\unicode[STIX]{x1D701}$ -potential) from an experimental measure of the dynamic mobility. This theory is general enough that it might be applied to aerosols and bubbly dispersions (at sufficiently high frequencies). [ABSTRACT FROM AUTHOR]

Gel electrophoresis of spherical nanoparticles (NPs) is studied using an electrokinetic model that couples the ion conservation equations to the Poisson and fluid momentum equations, thus including the socalled polarization and relaxation processes. This model is therefore the charged gel electrophoresis analogue of the well-known O'Brien and White solution of the standard electrokinetic model for free-solution electrophoresis. Results are provided for the small NPs (size around 10 nm) to which gel electrophoresis is relevant, because particles must be small enough to permeate the gel: these include the particle drag coefficient (or Brownian diffusivity), which is subject to hydrodynamic screening and electroviscous effects, and the electrophoretic mobility, which is subject to nonlinear electrostatic and charge polarization influences. Also addressed are the influences of charge-regulating gels and the accompanying particle-induced immobile charge-density perturbations. Ion-concentration perturbations attenuate the electrophoretic mobility and enhance the drag coefficient according to the particle charge and the mobility of the most abundant counterion. However, dynamic regulation of the hydrogel charge--termed the secondary immobile charge-density perturbation--has a negligible influence on the particle mobility, and may therefore be neglected for most practical purposes. [ABSTRACT FROM AUTHOR]

Abstract: Nanoparticle transport in porous materials, including nanoparticle gel electrophoresis, hinges on knowledge of the hydrodynamic drag coefficient. Here, we compute the drag force on a soft core–shell sphere translating in a porous medium from a continuum hydrodynamic model in which slow viscous flow in the soft shell and embedding porous medium are modelled using Brinkman''s equations. This model unifies the Brinkman force for bare spheres in porous media and the drag force of Masliyah et al. (1987) for soft core–shell spheres in pure viscous fluids. We compare the drag force with the Brinkman force evaluated using the composite sphere hydrodynamic radius, showing that this convenient approximation is reasonable when the Brinkman screening length of the embedding porous medium is large compared to the core radius; otherwise, the Brinkman force can significantly underestimate the force. [Copyright &y& Elsevier]

Nanoparticle-hydrogel interactions are important in many applications. In drug delivery, for example, these control the release rate and may prevent nanoparticle (NP) migration from a targeted site. In this paper, electroacoustic spectroscopy is used to study the NP-hydrogel interaction, focusing on the influence of polymer adsorption and hydrogel composition. Electroacoustic spectroscopy is a powerful noninvasive tool to complement microrheological characterization. We study the interaction of polyacrylamide (PA) with laponite and silica NPs as model systems with strong and weak attraction, respectively. Stronger adsorption of PA on laponite compared to silica imparts distinctly different rheological properties to PA solutions and decreases the laponite mobility significantly more than silica when embedded in PA hydrogels. However, the mobilities of both NPs exhibit qualitatively similar variations with acrylamide and chemical cross-linker concentrations, as indicated by viscoelastic and electrokinetic characterizations. The electrokinetic charge changes with polymer concentration more than with the chemical cross-linker concentration, whereas elastic coupling increases with the polymer concentration and decreases with the chemical cross-linker concentration. These reflect significant physicochemical changes to the hydrogel microstructure from the NP doping, so optimization of material properties for a specific application must explicitly consider the NP-polymer pairing. [ABSTRACT FROM AUTHOR]

Highlights: [•] 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. [Copyright &y& Elsevier]

For over half a century, alternating electric fields have been used to induce particle transport, furnishing the ζ-potential of analytes with sizes ranging from a few nanometers to several micrometers. Concurrent advances in nanotechnology have provided new materials for catalysis, self-assembly, and biomedical applications, all of which benefit from a thorough understanding of particle surface charge. [ABSTRACT FROM AUTHOR]

Electromigration of nanoparticles (NPs) is relevant to many technological and biological applications. We correlate the experimentally observed electromigration of Au NPs with a closed-form theoretical model that furnishes key NP characteristics, including the previously unknown values of Au NP core ζ-potential, PEG-corona permeability, and particle-hydrogel friction coefficient. More generally, the theory furnishes new understanding of NP electromigration in complex environments, establishing a robust and predictive model to guide the design and characterization of functionalized NPs. [ABSTRACT FROM AUTHOR]