A modified box model including charge regulation for protein adsorption in a spherical polyelectrolyte brush

Recent experiments showed significant adsorption of bovine serum albumin (BSA) in spherical polyelectrolyte brushes (SPB) consisting of polyacrylic acid, even for pH values above the isoelectric point of the protein, when both protein and polyion are negatively charged. To describe these experimental findings theoretically, we have constructed a spherical box model for an annealed brush consisting of a weak polyelectrolyte that includes the adsorption of BSA. At equilibrium the chemical potential of BSA in solution equals that at each location in the brush, while the net force on the polyions (including osmotic, stretching, and excluded volume terms) is zero at each location. Protein adsorption is predicted above the isoelectric point and--in agreement with experimental data--is a strong function of ionic strength and pH. Adsorption of protein in the brush is possible because the pH in the brush is below the isoelectric point and protein reverses its charge from negative to positive when it adsorbs.     

Analysis of electrokinetic transport of a spherical particle in a microchannel

Electrokinetically driven microfluidic devices that are used for biological cell/particle manipulation (e.g., cell sorting, separation) involve electrokinetic transport of these particles in microchannels whose dimension is comparable with particles' size. This paper presents an analytical study on electrokinetic transport of a charged spherical particle in a charged parallel-plate microchannel. Under the thin electric double-layer assumption, solutions in closed-form solutions for the particle velocity and disturbed electrical and fluid velocity fields are obtained for plane-symmetric (along the channel centerline) and asymmetric (off the channel centerline) motions of a sphere in a parallel-plate microchannel. The effects of relative particle size and eccentricity (i.e., off the centerline distance) on a particle's translational and rotational velocities are analyzed.     

Analysis of self-electrophoretic motion of a spherical particle in a nanotube: effect of nonuniform surface charge density

Autonomous motions of a spherical nanoparticle in a nanotube filled with an electrolyte solution were investigated using a continuum theory, which consisted of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. Contrary to the usual electrophoresis, in which an external electric field is imposed to direct the motion of charged particles, the autonomous motion originates from the self-generated electric field due to the ionic concentration polarization of the liquid medium surrounding an asymmetrically charged particle. In addition to the particle motion, the interaction between the electric field generated and the free charges of the polarized solution induces electroosmotic flows. These autonomous motions of the fluid as well as the particle were examined with focus on the effects of the surface-charge distribution of the particle, the size of the nanotube, and the thickness of the electric double layer, which affected the direction and the speed of the particle significantly.     

Electrophoretic motion of a spherical particle with a symmetric nonuniform surface charge distribution in a nanotube

The electrophoretic motion of a spherical nanoparticle, subject to an axial electric field in a nanotube filled with an electrolyte solution, has been investigated using a continuum theory, which consists of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. In particular, the effects of nonuniform surface charge distributions around the nanoparticle on its axial electrophoretic motion are examined with changes in the bulk electrolyte concentration and the surface charge of the tube's wall. A particle with a nonuniform charge distribution is shown to induce a corresponding complex ionic concentration field, which in turn influences the electric field and the fluid motion surrounding the particle and thus its electrophoretic velocity. As a result, contrary to the relatively simple dynamics of a particle with a uniform surface charge, dominated by the irradiating electrostatic force, that with a nonuniform surface charge distribution shows various intriguing behaviors due to the additional interplay of the nonuniform electro-osmotic effects.     

Interaction forces between a deformable air bubble and a spherical particle of tuneable hydrophobicity and surface charge in aqueous solutions

Unsupported nanosized MoS(2) and CoMo-sulfide catalysts were synthesized, and their catalytic performances for the deep hydrodesulfurization (HDS) of treated gas oil were investigated as compared with that of a CoMo/Al(2)O(3) catalyst. The HDS reactions were carried out in a batch autoclave reactor at 340 °C and 3 MPa H(2). The CoMo-sulfide catalyst shows the highest activity and can reduce the sulfur content to less than 10 ppm. The decrease in total sulfur content as a function of reaction time was found to follow pseudo-second order kinetics (empirical form). The change in the concentration of some individual representative sulfur-containing species in gas oil as a function of time was found to follow pseudo-first-order kinetics. However, the change in combined concentration of these species in the gas oil during HDS with the reaction time was found to corroborate pseudo-second-order kinetics. A kinetic model approach was proposed from which an estimation of the intrinsic kinetic data can be achieved. The model fitted the obtained data reasonably well, suggesting its potential for better assessment of the catalytic activity in the HDS of real feedstock. The study reveals that ranking of catalyst activities using model refractory sulfur-containing compounds does not necessarily imply a typical rank in case of investigating the real feedstocks.     

Electrophoresis of a spherical particle normal to an air-water interface

Electrophoresis of a spherical particle normal to an air-water interface is considered theoretically in this study. The presence of the air-water interface is found to reduce the particle mobility in general, especially when the double layer is very thick. This boundary effect diminishes as the double layer gets very thin. The higher the surface potential, the more significant the reduction of mobility due to the polarization effect from the double layer deformation when the particle is in motion. Local extrema are observed in the mobility profiles with varying double layer thickness as a result. Comparison with a solid planar boundary is made. It is found that the particle mobility near an air-water interface is smaller than that near a solid one when the double layer is thick, and vice versa when the double layer is thin, with a critical threshold value of double layer thickness corresponding roughly to the touch of the interface. The reason behind it is clearly explained as the buildup of electric potential at the air-water interface, which reduces the driving force as a result.     

A new parameter to control heat transport in nanofluids: surface charge state of the particle in suspension

Although various conjectures have been proposed to explain the abnormal increase in thermal conductivity of nanofluids, the detailed mechanism has not been fully understood and explained. The main reason is due to the lack of knowledge of the most fundamental factor governing the mechanisms such as Brownian motion, liquid layering, phonon transport, surface chemical effects, and agglomeration. Applying a surface complexation model for the measurement data of hydrodynamic size, zeta potential, and thermal conductivity, we have shown that surface charge states are mainly responsible for the increase in the present condition and may be the factor incorporating all the mechanisms as well.     

Electrokinetic characterization of a microporous non-commercial polysulfone membrane: phenomenological coefficients and transport parameters

Electrical and electrokinetic phenomena (electrical resistance, streaming potential and membrane potential) in a porous polysulfone membrane was studied in the framework of the linear thermodynamics of irreversible processes and the phenomenological coefficients were determined for different concentrations of NaCl and MgCl₂ solutions (10⁻³M<5×10⁻²M). From experimental values, other characteristic membrane parameters such as the concentration of fixed charge in the membrane (=−3×10⁻³M), the ionic transport numbers and permeabilities through the membrane (t(Na⁺)=0.392 and t(Mg⁺²)=0.363; P(Na⁺)=3.5×l0⁻⁸m/sec and P(Mg⁺²)=2.9×10⁻⁸m/sec) were also obtained. Membrane surface-electrolyte solution interface was characterized by zeta potential values. The effect of both salt concentration and pH on zeta potential results was also studied.     

Effect of ionic strength and protein concentration on the transport of proteins through chitosan/polystyrene sulfonate multilayer membrane

The influence of ionic strength and protein concentration on the transport of bovine serum albumin (BSA), ovalbumin and lysozyme through chitosan (CHI)/polystyrenesulfonate (PSS) multilayers on polyether sulfone supports are investigated under ultrafiltration conditions. The percentage transmission and flux of BSA, ovalbumin and lysozyme were found to increase with increase in salt concentration in the protein. The percentage transmission of BSA through 9 bilayer membrane was found to increase from 5.3 to 115.6 when the salt concentration was varied from 0 to 1 M. It was observed that 0.1 M NaCl in BSA solution is capable of permeating all the BSA. When the salt concentration in BSA was further increased, a negative solute rejection (solute enrichment in permeate) was found to take place. With 9 bilayer membrane, the percentage transmission of ovalbumin was found to increase from 23.3 to 125.8 when the salt concentration in protein was increased from 0 to 0.05 M. The effect of protein concentration on protein transport is studied taking BSA as a model protein. BSA was rejected by the multilayer membrane at all the studied concentrations (0.25, 0.5, 1 and 2 mg/ml). With increase in feed concentration, maximum rejection of protein occurred at higher number of CHI/PSS bilayers. BSA solution flux was found to decrease with an increase in BSA concentration. This study indicates that it is possible to fine tune the transport properties of proteins through multilayer membranes by varying the concentration and ionic strength of protein solutions.     

Single molecule charge transport: from a quantum mechanical to a classical description

This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.     

Maximum stability of a single spherical particle attached to an emulsion drop

The stability of a single, solid, spherical particle attached to a liquid drop in an emulsion is discussed. Ignoring effects due to gravity and line tension, we calculate the energies required to either detach the particle from the drop or to engulf the particle within the drop. The stability of the attached particle is here defined as the smaller of these two energies. A simple formula is derived for the value of Young's angle which gives maximum stability for a given radius ratio of particle to detached drop. For maximum stability the particle should be preferentially wetted by the liquid forming the drop.     

Procedures and computer program for deriving the Ferguson plot from electrophoresis in a single pore gradient gel: application to agarose gel and a polystyrene particle.

This study presents a computerized evaluation of pore gradient gel electrophoretograms to arrive at estimates for both the particle-free mobility and retardation coefficient, which is related to particle size. Agarose pore gradient gels ranging from 0.2 to 1.1% agarose were formed. Gel gradients were stabilized during their formation by a density gradient of 0-20% 5-(N-2,3-dihydroxypropylacetamido)- 2,4,6-triiodo-N,N'bis-(2,3-dihydroxypropyl)-isophthalamide (Nycodenz). Densitometry of gelled-in Bromophenol Blue showed that these pore gradients exhibited a linear central segment and were reproducible. Migration distances of polystyrene sulfate microspheres (36.5 nm radius) in agarose pore gradient gel electrophoresis were determined by time-lapse photography at several durations of electrophoresis. These migration distances were evaluated as a function of migration time as previously reported (D. Tietz, Adv. Electrophoresis 1988, 2, 109-169). Although this is not necessarily required, the mathematical approach used in this study assumed linearity of both the pore gradient and the Ferguson plot for reasons of simplicity. The data evaluation on the basis of the extended Ogston model is incorporated in a user-friendly program, GRADFIT, which is designed for personal computers (Macintosh). The results obtained are compared with (1) conventional electrophoresis using several gels of single concentration with and without Nycodenz, and (ii) a different mathematical approach for the analysis of gradient gels (Rodbard et al., Anal. Biochem. 1971, 40, 135-157). Moreover, a simple procedure for evaluating linear pore gradient gels using linear regression analysis is presented. It is concluded that the values of particle-free mobility and retardation coefficient derived from pore gradient gel electrophoresis using the different mathematical methods are statistically indistinguishable from each other. However, these values are different, albeit close, to those obtained from conventional Ferguson plots. One of the possible reasons for this relatively minor discrepancy is that the particle-free mobility changed slightly during electrophoresis, which has a different effect on electrophoresis in homogeneous gels (single time measurement) and pore gradient gels (multiple time measurements). The characterization of particles according to size and charge by pore gradient electrophoresis provides a significant operational simplification and sample economy compared to that requiring the use of several gel concentrations, although at the price of increased requirements of instrumentation.     

The surface potential of a spherical colloid particle: functional theoretical approach

By using the iterative method in functional analysis, the potential of the electrical double layer of a spherical colloid particle, which is represented by the so-called Poisson-Boltzmann (PB) equation, has been solved analytically under general potential conditions. With the help of the diagram method in mathematics, the surface potential of the particle has been defined from the second iterative solution. The influence of the parameters included in the solutions on the surface potential has been studied. The results show that the surface potential of the particle increases as the temperature of the system, the aggregation number, and the concentration of ions increase, but decreases with an increase in the dielectric constant and the valence of the ions. The corresponding space charge density also has been illustrated in this work.     

Flocculation of microgel particles with sodium chloride and sodium polystyrene sulfonate as a function of temperature

The flocculation behavior of poly(N-isopropylacrylamide) (PNIPAM) microgel particles, containing surface sulfate groups, has been studied as a function of sodium chloride [NaCl] concentration, between 0.1 and 800 mM NaCl and over the temperature range 25-60 degrees C. The critical flocculation temperature (CFT) of the particles was determined as a function of NaCl concentration. Three regions of NaCl concentration were established. First, at very low values of [NaCl] (< approximately 25 mM), no CFT value could be determined; this implies that the interparticle electrostatic repulsion is sufficient to prevent any flocculation occurring. This remains the case even at temperatures well in excess of the lower critical solution temperature for PNIPAM in solution, where the particles are essentially deswollen. Second, at intermediate [NaCl] (approximately 25-100 mM), the CFT decreased strongly with increasing [NaCl]. In this region, the electostatic forces are weakened sufficiently for the van der Waals forces to cause flocculation. Third, at higher [NaCl] (> approximately 100 mM), the electrostatic repulsion is screened out, and the CFT decreases linearly with [NaCl]. The reason for this decrease is the fact that aqueous solutions of NaCl become increasingly poorer solvent environments for PNIPAM with increasing [NaCl]. These trends are apparent also in the values determined for the hydrodynamic size of the stable PNIPAM particles as a function of [NaCl] and temperature. It is shown that the flocculation of the PNIPAM particles is consistent with a weak, reversible flocculation model. This is apparent, for example, from the fractal dimensions of the flocs (approximately 2.0), determined from the power law used to fit the time evolution of the hydrodynamic size of the flocs, and also from the estimated depth of the mimimum in the interparticle pair potential, based on the critical size of the primary particles where flocculation just begins to occur. The effect of adding sodium poly(styrene sulfonate) [PSS] to the PNIPAM dispersions, in the absence of NaCl, was also investigated. The minimum amount of PSS required to induce flocculation was found to decrease with increasing temperature.     

Facilitated transport in spherical shells: application of the combined damköhler number technique

In cell membranes, double emulsion drops, or other particles with spherical shell geometry, reversible carriers may be present which serve to facilitate transport of solutes into the particles. The physical phenomena taking place are both diffusion and chemical reaction. When the reaction deviates from chemical equilibrium, the solution of the conservation equations becomes difficult because the equations are non-linear. The combined Damköhler technique, recently devised by Hoofd and Kreuzer, is a simple analytical method to accurately predict facilitated mass transfer in the presence of non-equilibrium chemical reaction. The application of the combined Damköhler technique to spherical shell geometry gives accurate predictions of the facilitated flux over the full range of Damköhler numbers, when compared to results from a numerical analysis technique. The non-equilibrium facilitated flux depends on the sphericity of the spherical shell.     

Effective polarizability of a molecule physisorbed on a spherical metal particle: nonlocal effects

The electromagnetic interactions between a molecule and a spherical metal particle affect the linear response of the molecule. We present a general method to calculate the effective dynamic polarizability of such physisorbed systems by including the nonlocal character of the electron response in the sphere. Our model takes into account several long-range mechanisms connected to the dispersion, induction and local field effects. When the sphere reduces to a single atom, we recover results already known for a pair of atoms.     

Electrokinetic phenomena in porous membranes: Determination of phenomenological coefficients and transport numbers

Electrokinetic phenomena in porous membranes were studied in the framework of the linear thermodynamics of irreversible processes. Phenomenological coefficients of two commercial porous membranes were determined. The variation of these coefficients with the different concentrations of NaCl used was also studied. Onsager's reciprocal relationship between cross-coefficients holds within the limits of experimental error.Membrane potentials were measured at concentrations ranging from 10^?3M to 75 X 10^?3M. The apparent transport number of the cation,

, was calculated from the diffusion potential expression. An electrometric method was used to obtain the true cation transport number,

, and the water transport number,

, for different solution concentrations, ranging from 15 x 10^?3M to 75 x 10^?3M. The true transport number of the cation,

, was also determined, taking into account water transport across the membrane. A good agreement was found between

and

values.