Measuring Nanoparticle Polarizability Using Fluorescence Microscopy

Using a novel method developed to quantify the polarizability of photoluminescent nanoparticles in water, we present experimental observations of the extraordinary polarizability exhibited by nanoparticles of commensurate size with the Debye screening length, confirming previously reported theory. Semiconductor quantum dots (QDs) are ideal model nanoparticles to demonstrate this assay, due to their tunable size and bright photoluminescence. This assay is based upon microfluidic chambers with microelectrodes that generate trapping potentials that are weaker than thermal energy. By comparing the local electric field strength and variations in QD concentration, their polarizability was computed and found to agree with estimates based upon the hydrodynamic diameter found using light scattering. Strikingly, the polarizability of the nanoparticles increased 30-fold in low salt conditions compared to high salt conditions due to the increased thickness of the Debye layer relative to the particle radius. In addition to providing evidence that corroborates theoretical work studying direct solutions to the Poisson-Nernst-Planck equations, these observations provide an explanation for the previously observed conductivity dependence of biomolecule polarizability. As the polarizability of nanoparticles is of high importance to the electrically directed assembly of particles, as well as their interactions with other materials in complex environments, we anticipate that these results will be highly relevant to ongoing efforts in materials by design and nanomedicine.

Effect of hydrophobic core on the electrophoresis of a diffuse soft particle

Electrophoresis of a diffuse soft particle with a charged hydrophobic core is considered under the weak field and low charge density assumptions. The hydrophobic surface of the core is coated with a diffuse polyelectrolyte layer (PEL) in which a gradual transition of the polymer segment distribution from the impenetrable core to the surrounding electrolyte medium is considered. A mathematical model is adopted to analyse the impact of the core hydrophobicity on the diffuse soft particle electrophoresis. The mobility based on the present model for the limiting cases such as bare colloids with hydrophobic core and soft particles with no-slip rigid cores are in good agreement with the existing results. The presence of PEL charges produces the impact of the core hydrophobicity on the soft particle mobility different from the corresponding bare colloid with hydrophobic surface in an electrolyte medium. The impact of the core hydrophobicity is subtle when the hydrodynamic screening length of the PEL is low. Reversal in mobility can be achieved by tuning the core hydrophobicity for an oppositely charged core and PEL.

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.

Importance of core electrostatic properties on the electrophoresis of a soft particle

The impact of the volumetric charged density of the dielectric rigid core on the electrophoresis of a soft particle is analyzed numerically. The volume charge density of the inner core of a soft particle can arise for a dendrimer structure or bacteriophage MS2. We consider the electrokinetic model based on the conservation principles, thus no conditions for Debye length or applied electric field is imposed. The fluid flow equations are coupled with the ion transport equations and the equation for the electric field. The occurrence of the induced nonuniform surface charge density on the outer surface of the inner core leads to a situation different from the existing analysis of a soft particle electrophoresis. The impact of this induced surface charge density together with the double-layer polarization and relaxation due to ion convection and electromigration is analyzed. The dielectric permittivity and the charge density of the core have a significant impact on the particle electrophoresis when the Debye length is in the order of the particle size. We find that by varying the ionic concentration of the electrolyte, the particle can exhibit reversal in its electrophoretic velocity. The role of the polymer layer softness parameter is addressed in the present analysis.

On the electrophoretic mobility of succinoglycan modelled as a spherical polyelectrolyte: From Hermans-Fujita theory to charge regulation in multi-component electrolytes

Literature interpretations of the electrophoretic mobility of spherical polyelectrolytes are revisited using the capillary-electrophoresis data of Duval et al. (2006) for the extracellular polysaccharide succinoglycan as an example. Subtle changes in the polyelectrolyte mobility have recently been attributed to new electrokinetic theories that feature multi-component electrolytes, charge regulation, and the so-called polarization and relaxation phenomena. However, these calculations exhibit several unusual trends that have yet to be explained, and so the conclusions drawn from them are controversial. Here, independent computations strengthen conclusions drawn from the original model of Duval et al., i.e., the discrepancies between experiments and all the presently available electrokinetic theories reflect changes in the conformation of succinoglycan arising from changes in the electrolyte pH and ionic strength.

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

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 so-called 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.