Electrophoresis of fd-virus particles: experiments and an analysis of the effect of finite rod lengths

Deposition of Human-Serum-Albumin-Functionalized Spheroidal Particles on Abiotic Surfaces: Reference Kinetic Results for Bioparticles

Human serum albumin (HSA) corona formation on polymer microparticles of a spheroidal shape was studied using dynamic light scattering and Laser Doppler Velocimetry (LDV). Physicochemical characteristics of the albumin comprising the zeta potential and the isoelectric point were determined as a function of pH for various ionic strengths. Analogous characteristics of the polymer particles were analyzed. The adsorption of albumin on the particles was in situ monitored by LDV. The stability of the HSA-functionalized particle suspensions under various pHs and their electrokinetic properties were also determined. The deposition kinetics of the particles on mica, silica and gold sensors were investigated by optical microscopy, AFM and quartz microbalance (QCM) under diffusion and flow conditions. The obtained results were interpreted in terms of the random sequential adsorption model that allowed to estimate the range of applicability of QCM for determining the deposition kinetics of viruses and bacteria at abiotic surfaces.

Quantifying Nanoparticle Layer Topography: Theoretical Modeling and Atomic Force Microscopy Investigations

A comprehensive method consisting of theoretical modeling and experimental atomic force microscopy (AFM) measurements was developed for the quantitative analysis of nanoparticle layer topography. Analytical results were derived for particles of various shapes such as cylinders (rods), disks, ellipsoids, hemispheres (caps), etc. It was shown that for all particles, their root-mean-square (rms) parameter exhibited a maximum at the coverage about 0.5, whereas the skewness was a monotonically decreasing function of the coverage. This enabled a facile determination of the particle coverage in the layer, even if the shape and size were not known. The validity of the analytical results was confirmed by computer modeling and experimental data acquired by AFM measurements for polymer nanoparticle deposition on mica and silica. The topographical analysis developed in this work can be exploited for a quantitative characterization of self-assembled layers of nano- and bioparticles, e.g., carbon nanotubes, silica and noble metal particles, DNA fragments, proteins, vesicles, viruses, and bacteria at solid surfaces. The acquired results also enabled a proper calibration, in particular the determination of the measurement precision, of various electron and scanning probe microscopies, such as AFM.

Polyelectrolyte Complexes from Oppositely Charged Filamentous Viruses

Here, we present an explorative study on a new type of polyelectrolyte complex made from chemically modified filamentous fd viruses. The fd virus is a semiflexible rod-shaped bacteriophage with a length of 880 nm and a diameter of 6.6 nm, which has been widely used as a well-defined model system of colloidal rods to investigate phase, flow, and other behavior. Here, chemically modified viruses have been prepared to obtain two types with opposite electrical charges in addition to a steric stabilization layer by poly(ethylene glycol) (PEG) grafting. The complex formation of stoichiometric mixtures of these oppositely charged viruses is studied as a function of virus and salt concentration. Furthermore, static light scattering measurements show a varying, strong increase in scattering intensity in some samples without visual macroscopic complex formation. Finally, the results of the complex formation are rationalized by comparing to model calculations on the pair interaction potential between oppositely charged viruses.

QCM-D Investigations of Anisotropic Particle Deposition Kinetics: Evidences of the Hydrodynamic Slip Mechanisms

Deposition kinetics of positively charged polymer microparticles, characterized by prolate spheroid shape, at silica and gold sensors was investigated using the quartz microbalance (QCM) technique. Reference measurements were also performed for positively charged polymer particles of spherical shape and the same mass as the spheroids. Primarily, the frequency and bandwidth shifts for various overtones were measured as a function of time. It is shown that the ratio of these signals is close to unity for all overtones. These results were converted to the dependence of the frequency shift on the particle coverage, directly determined by atomic force microscopy and theoretically interpreted in terms of the hydrodynamic model. A quantitative agreement with experiments was attained considering particle slip relative to the ambient oscillating flow. In contrast, the theoretical results pertinent to the rigid contact model proved inadequate. The particle deposition kinetics derived from the QCM method was compared with theoretical modeling performed according to the random sequential adsorption approach. This allowed to assess the feasibility of the QCM technique to furnish proper deposition kinetics for anisotropic particles. It is argued that the hydrodynamic slip effect should be considered in the interpretation of QCM kinetic results acquired for bioparticles, especially viruses.

Electrophoresis of soft particles with hydrophobic inner core grafted with pH-regulated and highly charged polyelectrolyte layer

Electrophoresis of core-shell composite soft particles possessing hydrophobic inner core grafted with highly charged polyelectrolyte layer (PEL) has been studied analytically. The PEL bears pH-dependent charge properties due to the presence of zwitterionic functional groups. The dielectric permittivity of the PEL and bulk aqueous medium were taken to be different, which resulted in the ion-partitioning effect. Objective of this study was to provide a simple expression for the mobility of such core-shell soft particles under Donnan limit where the thickness of the PEL well exceeds the electric double layer thickness. Going beyond the widely used Debye-Hückel linearization, the nonlinear Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations was solved to determine the electrophoretic mobility. The derived expression further recovers all the existing results for the electrophoretic mobility under various simplified cases. The graphical presentation of the results illustrated the impact of pertinent parameters on the electrophoretic mobility of such a soft particle.

Effect of core hydrophobicity on the electrophoresis of pH-regulated soft particles

We propose a theoretical study on the electrophoresis of core-shell composite soft particles considering the effect of hydrodynamic slip length of the hydrophobic inner core. The surface of the inner core as well as the soft polymeric shell bear zwitterionic functional groups and the charged conditions depend on the nearby micro-environment. Within a low potential and weak electric field framework, the mathematical equations of the generalized electrokinetic theory for soft surfaces are solved analytically subject to appropriate boundary conditions, and a general electrophoretic mobility expression in an integral form involving the pH-dependent electrostatic potential is derived. With the help of suitable numerical schemes, electrophoretic mobility can easily be obtained. The effect of hydrophobicity of the inner core on the electrophoretic mobility of pH-regulated soft particles is illustrated for a wide range of pertinent parameters.

Thermophoresis of a Colloidal Rod: Contributions of Charge and Grafted Polymers

In this study, we investigated the thermodiffusion behavior of a colloidal model system as a function of the Debye length, λ_DH, which is controlled by the ionic strength. Our system consists of an fd-virus grafted with poly(ethylene glycol) (PEG) with a molecular mass of 5000 g mol^-1. The results are compared with recent measurements on a bare fd-virus and with results of PEG. The diffusion coefficients of both viruses are comparable and increase with the increasing Debye length. The thermal diffusion coefficient, D_T, of the bare virus increases strongly with the Debye length, whereas D_T of the grafted fd-virus shows only a very weak increase. The Debye length dependence of both systems can be described with an expression derived for charged rods using the surface charge density and an offset of D_T as adjustable parameters. It turns out that the ratio of the determined surface charges is inverse to the ratio of the surfaces of the two systems, which means that the total charge remains almost constant. The determined offset of the grafted fd-virus describing the chemical contributions is the sum of D_T of PEG and the offset of the bare fd-virus. At high λ_DH, corresponding to the low ionic strength, the S_T values of both colloidal model systems approach each other. This implies a contribution from the polymer layer, which is strong at short λ_DH and fades out for the longer Debye lengths, when the electric double layer reaches further than the polymer chains and therefore dominates interactions with the surrounding water.

Complex coacervation in charge complementary biopolymers: Electrostatic versus surface patch binding

In this review, a number of systems are described to demonstrate the effect of polyelectrolyte chain stiffness (persistence length) on the coacervation phenomena, after we briefly review the field. We consider two specific types of complexation/coacervation: in the first type, DNA is used as a fixed substrate binding to flexible polyions such as gelatin A, bovine serum albumin and chitosan (large persistence length polyelectrolyte binding to low persistence length biopolymer), and in the second case, different substrates such as gelatin A, bovine serum albumin, and chitosan were made to bind to a polyion gelatin B (low persistence length substrate binding to comparable persistence length polyion). Polyelectrolyte chain flexibility was found to have remarkable effect on the polyelectrolyte-protein complex coacervation. The competitive interplay of electrostatic versus surface patch binding (SPB) leading to associative interaction followed by complex coacervation between these biopolymers is elucidated. We modelled the SPB interaction in terms of linear combination of attractive and repulsive Coulombic forces with respect to the solution ionic strength. The aforesaid interactions were established via a universal phase diagram, considering the persistence length of polyion as the sole independent variable.

Charging and Aggregation Behavior of Cellulose Nanofibers in Aqueous Solution

To understand the charging and aggregation of cellulose nanofibers (CNFs), we performed the following experimental and theoretical studies. The charging behavior of CNFs was characterized by potentiometric acid-base titration measuring the density of deprotonated carboxyl groups at different KCl concentrations. The charging behavior from the titration was quantitatively described by the 1-pK Poisson-Boltzmann (PB) model for a cylinder. The electrophoretic mobility of CNFs was measured as a function of pH by electrophoretic light scattering. The mobility was analyzed with the equation for an infinitely long cylinder considering the relaxation of the electric double layer. Good agreement between experimental mobilities and theoretical calculation was obtained by assuming a reasonable distance from the surface to the slipping plane. The result demonstrated that the negative charge of CNFs originates from the deprotonation of β(1-4)-d-glucuronan on the surface. The aggregation behavior of CNFs was studied by measuring the hydrodynamic diameter of CNFs at different pH and KCl concentrations. Also, we calculated the capture efficiencies of aggregation, using interaction energies of perpendicularly and parallelly oriented cylinders. The interaction energies between cylinders in both orientations were obtained by the Derjaguin, Landau, Verwey, and Overbeek theory, where the electrostatic repulsion was calculated from the surface potential obtained by the 1-pK PB model. From comparison of the theoretical capture efficiency with the measured hydrodynamic diameter, we suggest that CNFs can be aggregated in perpendicular orientation at low pH and low salt concentration, and the fast aggregation regime of CNFs is realized by the reduction of electric repulsion for both perpendicularly and parallelly interacting CNFs. Meanwhile, the application of Smoluchowski's equation to the mobility of CNFs results in the underestimation of the zeta potential.

Microelectrophoresis of Silica Rods Using Confocal Microscopy

The electrophoretic mobility and the zeta potential (ζ) of fluorescently labeled colloidal silica rods, with an aspect ratio of 3.8 and 6.1, were determined with microelectrophoresis measurements using confocal microscopy. In the case where the colloidal particles all move at the same speed parallel to the direction of the electric field, we record a xyz-stack over the whole depth of the capillary. This method is faster and more robust compared to taking xyt-series at different depths inside the capillary to obtain the parabolic flow profile, as was done in previous work from our group. In some cases, rodlike particles do not move all at the same speed in the electric field, but exhibit a velocity that depends on the angle between the long axis of the rod and the electric field. We measured the orientation-dependent velocity of individual silica rods during electrophoresis as a function of κa, where κ^-1 is the double layer thickness and a is the radius of the rod associated with the diameter. Thus, we determined the anisotropic electrophoretic mobility of the silica rods with different sized double layers. The size of the double layer was tuned by suspending silica rods in different solvents at different electrolyte concentrations. We compared these results with theoretical predictions. We show that even at already relatively high κa when the Smoluchowski limiting law is assumed to be valid (κa > 10), an orientation dependent velocity was measured. Furthermore, we observed that at decreasing values of κa the anisotropy in the electrophoretic mobility of the rods increases. However, in low polar solvents with κa < 1, this trend was reversed: the anisotropy in the electrophoretic mobility of the rods decreased. We argue that this decrease is due to end effects, which was already predicted theoretically. When end effects are not taken into account, this will lead to strong underestimation of the experimentally determined zeta potential.

Approximate Analytic Expression for the Electrophoretic Mobility of Moderately Charged Cylindrical Colloidal Particles

An approximate analytic expression for the electrophoretic mobility of an infinitely long cylindrical colloidal particle in a symmetrical electrolyte solution in a transverse electric field is obtained. This mobility expression, which is correct to the order of the third power of the zeta potential ζ of the particle, considerably improves Henry's mobility formula correct to the order of the first power of ζ (Proc. R. Soc. London, Ser. A 1931, 133, 106). Comparison with the numerical calculations by Stigter (J. Phys. Chem. 1978, 82, 1417) shows that the obtained mobility formula is an excellent approximation for low-to-moderate zeta potential values at all values of κa (κ = Debye-Hückel parameter and a = cylinder radius).

Stimuli responsive chiral liquid crystal phases of phenylboronic acid functionalized rodlike viruses and their interaction with biologically important diols

M13 viruses decorated with phenylboronic acid moieties form pH-responsive chiral LC phases that are regulated by binding with biological diols.