Hydrogel charge regulation and electrolyte ion-concentration perturbations in nanoparticle gel electrophoresis

Hill, Reghan J.

doi:10.1098/rspa.2015.0523

Cited by 13 publications

(11 citation statements)

References 41 publications

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“…In this section, we also evaluate an hypothesis of Hill 12 that permits the gel-electrophoretic mobility for any nanoparticle architecture to be predicted from knowledge of its free-solution mobility and its diffusion coefficient in a gel. This approximation can be written…”

Section: Polyelectrolyte Coronasmentioning

confidence: 99%

“…Thus, the equilibrium dissociation constants for the underlying charge-regulation models are generally set to values that eliminate charge regulation; under these conditions, it follows that the total fixed charge ρ f (from the corona and gel) equals the equilibrium contribution from the dissociation of H + , i.e., ρ f = ρ 0 f ,1 . The forces on the core-corona composite are from electrical and hydrodynamic tractions and body forces, obtained by adding those recently derived for soft spheres in Newtonian electrolytes 11 to those for bare spheres in gels 12 and subtracting the common terms, giving…”

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confidence: 99%

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Electrokinetics of nanoparticle gel-electrophoresis

Hill

2016

Soft Matter

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Gel-electrophoresis has been demonstrated in recent decades to successfully sort a great variety of nanoparticles according to their size, charge, surface chemistry, and corona architecture. However, quantitative theoretical interpetations have been limited by the number and complexity of factors that influence particle migration. Theoretical models have been fragmented and incomplete with respect to their counterparts for free-solution electrophoresis. This paper unifies electrokinetic models that address complex nanoparticle corona architectures, corona and gel charge regulation (e.g., by the local pH), multi-component electrolytes, and non-linear electrostatics and relaxation effects. By comprehensively addressing the electrokinetic aspects of the more general gel-electrophoresis problem, in which short-ranged steric interactions are significant, a stage is set to better focus on the physicochemical and steric factors. In this manner, it is envisioned that noparticle gelelectrophoresis may eventually be advanced from a nanoparticle-characterization tool to one that explicitly probes the short-ranged interactions of nanoparticles with soft networks, such as synthetic gels and biological tissues. In this paper, calculations are undertaken that identify a generalized Hückel limit for nanoparticles in low-conductivity gels, and a new Smoluchowski limit for polyelectrolyte-coated particles in high-conductivity gels that is independent of the gel permeability. Also of fundamental interest is a finite, albeit small, electrophoretic mobility for uncharged particles in charged gels. Electrophoretic mobilities and drag coefficients (with electroviscous effects) for nanoparticles bearing non-uniform coronas show that relaxation effects are typically weak for the small nanoparticles (radius ≈ 3-10 nm) to which gel-electrophoresis has customarily been applied, but are profound for the larger nanoparticles (radius 40 nm in low conductivity gels) to which passivated gel-electrophoresis experiments have recently been applied. To demonstrate its practical application, the model is applied to (pH charge regulating) carboxylated polystyrene nanospheres in low-density passivated agarose gels (weak steric effects). This furnishes a new theoretical interpretation of literature data for which a finite diffuse-layer-thickness, pH-charge regulation, high charge, and relaxation effects dominate over the steric influences.

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Section: Polyelectrolyte Coronasmentioning

confidence: 99%

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confidence: 99%

Electrokinetics of nanoparticle gel-electrophoresis

Hill

2016

Soft Matter

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“…The steady-state electrokinetic model is the one adopted by Hill (2015) for nanoparticle gel electrophoresis. It comprises the Poisson equation a total of ion-conservation equations with Nernst–Plank fluxes and solvent momentum (inertia-free) and mass (incompressible) conservation equations where is the charge density fixed to the hydrogel skeleton, and is the net (mobile) charge density of ions in the fluid phase.…”

Section: Theorymentioning

confidence: 99%

“…The steady-state electrokinetic model is the one adopted by Hill (2015) for nanoparticle gel electrophoresis. It comprises the Poisson equation…”

Section: Electrokinetic Modelmentioning

confidence: 99%

Ionic conductivity and hydrodynamic permeability of inhomogeneous (cavity doped) polyelectrolyte hydrogels

Hill

2022

J. Fluid Mech.

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Ion transport in polyelectrolyte membranes (charged hydrogels) is of significant technological (and biological) importance, but little is known of how micro-structural inhomogeneity affects ionic conductivity. Whereas a uniform electric field drives uni-directional electro-migrative and electro-osmotic ion fluxes in perfectly uniform microstructures, this study considers the influence of spherical inclusions/cavities on the hydrodynamic and ion permeability of charged hydrogels. Such cavities have a high permeability, but they can bear a much lower conductivity due to the partitioning of counter-ions between the cavity and bulk hydrogel phases, also inducing micro-scale electro-osmotic flow. To understand these, perturbations from a nonlinear Poisson–Boltzmann equilibrium state are used to compute the velocity disturbances, and electrostatic and ion-concentration polarization. These furnish three independent Onsager coefficients: one of which is the effective hydrodynamic permeability, and all of which contribute to the two principal electrical conductivities (distinguished by electrode configuration). Cavities with diameters in the range $10$ – $1000$ nm are found to be readily polarized, decreasing the effective conductivity of an otherwise uniform polyelectrolyte. In highly permeable hydrogels, however, electro-osmosis may enhance the electrical conductivity when flow is blocked by impenetrable electrodes. Explicit formulas for the hydrodynamic permeability are provided, complementing a simplified (Maxwell–Donnan) analysis of the conductivity, which neglects diffuse double-layer effects and ion-concentration perturbations.

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“…The matrix can be composed of a number of different materials, cellulose acetate, including paper, or gels made of polyacrylamide. An electrokinetic model for gel electrophoresis in charge‐regulated gels was solved numerically with appropriate geometrical symmetry and boundary conditions . Most practical applications of electrophoresis are biological and biochemical research, pharmacology, forensic medicine, clinical investigations, protein chemistry, and veterinary science and food control as well as molecular biology .…”

Section: Introductionmentioning

confidence: 99%

Start‐up Brinkman electrophoresis of a dielectric sphere for Happel and Kuwabara models

Saad

2018

Math Methods in App Sciences

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The starting electrophoresis in a charged porous continuum response of a homogeneous suspension of spherical particles to the sudden application of an external electric field is analyzed semianalytically through the use of a unit cell model. The electric double layer in the porous Brinkman medium surrounding each sphere is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is included. The field equation for the fluid outside the double layers is solved based on the unit cell model under the start-up Brinkman model. Expressions of the time-dependent electrophoretic and settling velocities of the particle in the Laplace transform as functions of the permeability, the relative mass density, the electrokinetic particle radius, and the volume fraction of the particles are performed for two different boundary conditions at the fictitious surface of the cell. Numerical results indicate that the timescale for the development of electrophoresis and sedimentation is small for a high permeability, an assemblage of spheres through a dielectric porous medium with a higher particle volume fraction and a smaller particle to porous fluid density ratio; the electrophoretic mobility is a monotonically increasing function of the electrokinetic radius of the sphere at any instant. The start-up of electrophoretic mobility decreases with an increase in the particle volume fraction at a small value of the particle-to-medium density ratio, but it may increase as the particle volume fraction increases at a large value of this density. The particle interaction effect in a swarm on the time-dependent electrophoresis is much smaller than that on the starting sedimentation of the particles. The detailed comparison of the results of the cell model with different boundary conditions at the virtual surface of the cell is obtained and illustrated graphically.

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Hydrogel charge regulation and electrolyte ion-concentration perturbations in nanoparticle gel electrophoresis

Cited by 13 publications

References 41 publications

Electrokinetics of nanoparticle gel-electrophoresis

Electrokinetics of nanoparticle gel-electrophoresis

Ionic conductivity and hydrodynamic permeability of inhomogeneous (cavity doped) polyelectrolyte hydrogels

Start‐up Brinkman electrophoresis of a dielectric sphere for Happel and Kuwabara models

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