Electrokinetics of nanoparticle gel-electrophoresis

Abstract

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.

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

“…For negatively charged SSPS nanospheres, the sign of μ e is negative in all cases. These values are close to theoretical calculations of μ e , as reported by Hill [27] who cites the work of Allison, et al [38] and Palanisami and Miller [39]. Using our measured E c (Fig.…”

“…It would also be interesting in future studies to determine the size‐separation characteristics, such as Darcy permeability , of passivated gels over a wider range of gel concentrations. Such investigations could potentially enhance the understanding already developed by prior publications concerning the role of solvent stresses and Brinkman screening lengths in agarose gel electrophoresis . By performing experiments using other amphiphilic passivation agents, we anticipate that a better understanding of passivation mechanisms in P‐gelEP experiments can be achieved.…”

“…While we emphasize that the values of E c that we report here are in a well‐accepted range, we must note that they are much higher than values of E s in CGS units that were previously reported by Zhu and Mason in P‐gelEP experiments , which when converted to MKS yield several V/m, far below what others have measured and reported. As has been correctly pointed out by Hill and confirmed via personal correspondence, the CGS values of E reported previously in works by Zhu and Mason must be converted to MKS and then divided by a factor of ≈0.018, as suggested by Hill, to obtain properly corrected values of E which can then be used to calculate corresponding electrophoretic mobilities that are in reasonable accord with electrokinetic theory.…”

“…Rigorous electrokinetic models have been developed to account for the complex behavior of objects propagating during gelEP; more recent models incorporate viscous stresses, which can depend on Debye length, as well as varying charges and surface potentials which can depend upon bulk conductivities [27]. Such advanced electrokinetic treatments, which go beyond the classic Smoluchowski (Henry) model, predict v given an assumed value of E. By contrast, the conductivity model that we emphasize herein is constitutive and seeks only to provide a more accurate value of E in some experimental gelEP situations.…”

Gel electrophoretic analysis of differently shaped interacting and non-interacting bioconjugated nanoparticles

“…Gel electrophoresis is a ubiquitous tool for biomolecular analysis and, more recently, for nanoparticle characterization and there are future opportunities for integration into lab-on-a-chip devices and higher-throughput 2D gel analysis. 30 Furthermore, improving both the modeling of nanoparticle transport 44 along with exploring different combinations of NP shapes and sizes will further increase the utility of this platform for the analysis of even more complex mixtures of interacting NP-protein bioconjugates featuring different particle shapes and protein functionalizations. …”