Electrophoretic Mobility of a Dilute, Highly Charged “Soft” Spherical Particle in a Charged Hydrogel

Transient Gel Electrophoresis of a Spherical Colloidal Particle

The general theory is developed for the time-dependent transient electrophoresis of a weakly charged spherical colloidal particle with an electrical double layer of arbitrary thickness in an uncharged or charged polymer gel medium. The Laplace transform of the transient electrophoretic mobility of the particle with respect to time is derived by considering the long-range hydrodynamic interaction between the particle and the polymer gel medium on the basis of the Brinkman-Debye-Bueche model. According to the obtained Laplace transform of the particle's transient electrophoretic mobility, the transient gel electrophoretic mobility approaches the steady gel electrophoretic mobility as time approaches infinity. The present theory of the transient gel electrophoresis also covers the transient free-solution electrophoresis as its limiting case. It is shown that the relaxation time for the transient gel electrophoretic mobility to reach its steady value is shorter than that of the transient free-solution electrophoretic mobility and becomes shorter as the Brinkman screening length decreases. Some limiting or approximate expressions are derived for the Laplace transform of the transient gel electrophoretic mobility.

Gel Electrophoresis of a Hydrophobic Liquid Droplet with an Equipotential Slip Surface

A theoretical study has been carried out on the electrophoresis of charged dielectric liquid droplets with an equipotential and hydrodynamically slipping surface moving in a quenched polymeric charged hydrogel medium. The liquid inside the droplet is electrically neutral. The Brinkman-Debye-Bueche model is employed to study the gel electrophoresis of such a hydrophobic and equipotential liquid droplet considering the long-range hydrodynamic interaction between a migrating droplet and the gel skeleton. Within the weak field and Debye-Hückel electrostatic framework, we derive an original closed-form expression for electrophoretic mobility, which further recovers the existing mobility expressions derived under several limiting conditions. The derived expressions for electrophoretic mobility explicitly involve exponential integrals, which are not so convenient for practical applications. Thus, the exact forms of the electrophoretic mobility under various electrohydrodynamic conditions are further approximated to make them free from exponential integrals. The approximate forms are found to be in excellent agreement with the exact results with maximum relative errors of about 1.5%.

A simplified model for gel electrophoresis of a hydrophobic rigid colloid

Electrophoresis of a charged dielectric hydrophobic colloid embedded in a charged hydrogel medium is addressed. A slip velocity condition at the particle surface is considered. The characteristic of the gel electrophoresis is different compared with the free-solution electrophoresis due to the presence of immobile charges of the gel medium, which induces a strong background electroosmotic flow and modifies the Debye layer of the colloid. The gel electrophoresis of the dielectric hydrophobic charged colloid is made based on first-order perturbation analysis. A closed form solution involving simple exponential integrals for the mobility is derived, which reduces to several existing mobility expressions under limiting conditions such as for the gel electrophoresis of hydrophilic particles and a hydrophobic colloid in free-solution electrophoresis. We find that the mobility reversal is achieved by varying the Debye length or gel permeability. For the present first-order perturbation analysis, unlike free-solution electrophoresis, the particle dielectric permittivity is found to influence the mobility. One of the intriguing features of the present study is the derivation of the simplified mobility expression, which can be easily computed for a given set of parameter values.

Enhanced proliferation and angiogenic phenotype of endothelial cells via negatively-charged alginate and chondroitin sulfate microsphere hydrogels

Sodium alginate-based hydrogel was the one of the most used polymers for cell delivery. However, the adsorption of extracellular matrix and proteins was inhibited due to the formation of a hydrated surface layer of these hydrogels. In this study, a novel cell delivery system, negatively-charged alginate and chondroitin sulfate microsphere hydrogel (nCACSMH), was fabricated with excellent permeability and biocompatibility in the action of a high voltage direct-current electric field. Negative charge was introduced to the surface of nCACSMH to obtain the expanded network and enhanced permeability. Additionally, the increasing content of chondroitin sulfate in nCACSMH could give rise to the charge density and its asymmetric structure, thus the uneven, plicate and expanded surface of nCACSMH which was favorable to cell proliferation was developed. Moreover, chondroitin sulfate was released with the degradation of nCACSMH, which played a crucial role in maintaining the normal physiological functions of cells. Thus the proliferation of human umbilical vein endothelial cells (HUVECs) was further accelerated and the angiogenesis related genes expression in endothelial cells was continuously and dramatically up-regulated. After 4 d, the proliferation and viability of HUVECs were significantly improved, the cells were distributed evenly in nCACSMH. The novel nCACSMH has the potential to be used as cell delivery, three-dimensional (3D) cell cultures for cell therapy, 3D bioprinting, high-throughput screening for drugs, and disease model for regeneration and constructing of tissue engineering.

Gel electrophoresis of a soft particle

A review is given on the theory of the gel electrophoresis of a spherical soft particle, i.e., the electrophoresis of a spherical hard particle covered with an ion-penetrable surface layer of polyelectrolytes moving in a polymer gel medium, which may either be charged or uncharged. A detailed study is made on the fundamental electrokinetic equations describing the soft-particle gel electrophoresis due to the long-range hydrodynamic particle-gel interaction on the basis of the Brinkman-Debye-Bueche model. A general expression and several approximate analytic expressions are given for the electrophoretic mobility of a soft particle in a polymer gel medium.

Influence of ionic constituents and electrical conductivity on the propagation of charged nanoscale objects in passivated gel electrophoresis

When determining the electric field E acting on charged objects in gel electrophoresis, the electrical conductivity of the buffer solution is often overlooked; E is typically calculated by dividing the applied voltage by a separation distance between electrodes. However, as a consequence of electrolytic reactions, which occur at the electrodes, gradients in the ionic content of the buffer solution and its conductivity can potentially develop over time, thereby impacting E and affecting propagation velocities of charged objects, v, directly. Here, we explore how the types and concentrations of ionic constituents of the buffer solution, which largely control its conductivity, when used in passivated gel electrophoresis (P-gelEP), can influence E, thereby altering v of charged nanospheres propagating through large-pore gels. We measure the conductivity of the buffer solution in the center of the gel region near propagating bands of nanospheres, and we show that predictions of E based on conductivity closely correlate with v. We also explore P-gelEP involving two different types of passivation agents: nonionic polyethylene glycol (PEG) and anionic sodium dodecyl sulfate (SDS). Our observations indicate that using a conductivity model to determine E from the local current density and the conductivity where spheres are propagating can lead to a better estimate than the standard approach of a voltage divided by a separation. Moreover, this conductivity model also provides a starting point for interpreting the complex behavior created by amphiphilic ionic passivation agents, such as SDS, on propagating nanospheres used in some P-gelEP experiments.

Electrokinetics of nanoparticle gel-electrophoresis

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 gel-electrophoresis 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.