Electro-osmosis at inhomogeneous charged surfaces: hydrodynamic versus electric friction

Electrokinetic methods are efficient in probing the electrostatic surface properties of charged systems. However, anomalies observed in experiments indicate that the classical electrokinetic theory should be reconsidered. Using Green's function methods and hydrodynamic simulations, we investigate electro-osmosis driven by electric-field-induced ion motion near a charged planar substrate with smooth or rough boundary. First, a reformulation of electro-osmotic theory for planar charged surfaces employing Green's functions shows that the Helmholtz-Smoluchowski (HS) relation between electrostatic potential and solvent velocity is exact for smooth surfaces, even in the presence of ion correlations. Deviations from HS theory are caused by combined hydrodynamic and electric surface friction, as our hydrodynamic simulations of ions at smooth and corrugated charged surfaces in lateral electric fields demonstrate. Within the simulations, hydrodynamic interactions are treated in the continuum limit and the presence of a no-slip boundary condition at the surface is taken into account. While electrofriction is relevant in highly charged system and/or for multivalent ions, hydrodynamic friction is dominant in systems with moderate surface charge density and/or low ionic valency. We also derive the effective electrokinetic surface charge from the electro-osmotic solvent profiles, which is substantially reduced when compared with the bare value and shows qualitative agreement with the experimental tendency.     

Surface charge density and electrokinetic potential of highly charged minerals: experiments and Monte Carlo simulations on calcium silicate hydrate

In this paper, we are concerned with the charging and electrokinetic behavior of colloidal particles exhibiting a high surface charge in the alkaline pH range. For such particles, a theoretical approach has been developed in the framework of the primitive model. The charging and electrokinetic behavior of the particles are determined by the use of a Monte Carlo simulation in a grand canonical ensemble and compared with those obtained through the mean field theory. One of the most common colloidal particles has been chosen to test our theoretical approach. That is calcium silicate hydrate (C-S-H) which is the main component of hydrated cement and is known for being responsible for cement cohesion partly due to its unusually high surface charge density. Various experimental techniques have been used to determine its surface charge and electrokinetic potential. The experimental and simulated results are in excellent agreement over a wide range of electrostatic coupling, from a weakly charged surface in contact with a reservoir containing monovalent ions to a highly charged one in contact with a reservoir with divalent ions. The electrophoretic measurements show a charge reversal of the C-S-H particles at high pH and/or high calcium concentration in excellent agreement with simulation predictions. Finally, both simulation and experimental results clearly demonstrate that the mean field theory fails not only quantitatively but also qualitatively to describe a C-S-H dispersion under realistic conditions.     

Coupled electrostatic, hydrodynamic, and mechanical properties of bacterial interfaces in aqueous media

The interactions of bacteria with their environment are governed by a complex interplay between biological and physicochemical phenomena. The main challenge is the joint determination of the intertwined interfacial characteristics of bacteria such as mechanical and hydrodynamic softness, interfacial heterogeneity, and electrostatic properties. In this study, we have combined electrokinetics and force spectroscopy to unravel this intricate coupling for two types of Shewanella bacterial strains that vary according to the nature of their outer, permeable, charged gel-like layers. The theoretical interpretation of the bacterial electrokinetic response allows for the estimation of the hydrodynamic permeability, degree of interfacial heterogeneity, and volume charge density for the soft layer that constitutes the outer permeable part of the bacteria. Additionally, the electrostatic interaction forces between an AFM probe and the bacteria were calculated on the basis of their interfacial properties obtained from advanced soft particle electrokinetic analysis. For both bacterial strains, excellent agreement between experimental and theoretical force curves is obtained, which highlights the necessity to account for the interfacial heterogeneity of the bioparticle to interpret AFM and electrokinetic data consistently. From the force profiles, we also derived the relevant mechanical parameters in relation to the turgor pressure within the cell and the nature of the bacterial outer surface layer. These results corroborate the heterogeneous representation of the bacterial interface and show that the decrease in the turgor pressure of the cell with increasing ionic strength is more pronounced for bacteria with a thin surface gel-like layer.     

Molecular dynamics simulations of multilayer polyelectrolyte films: effect of electrostatic and short-range interactions

The effect of the strength of electrostatic and short-range interactions on the multilayer assembly of oppositely charged polyelectrolytes at a charged substrate was studied by molecular dynamics simulations. The multilayer buildup was achieved through sequential adsorption of charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The strong electrostatic attraction between oppositely charged polyelectrolytes at each deposition step is a driving force behind the multilayer growth. Our simulations have shown that a charge reversal after each deposition step is critical for steady multilayer growth and that there is a linear increase in polymer surface coverage after the first few deposition steps. Furthermore, there is substantial intermixing between chains adsorbed during different deposition steps. We show that the polymer surface coverage and multilayer structure are each strongly influenced by the strength of electrostatic and short-range interactions.     

Molecular dynamics simulations of polyelectrolyte multilayering on a charged particle

Molecular dynamics simulations of polyelectrolyte multilayering on a charged spherical particle revealed that the sequential adsorption of oppositely charged flexible polyelectrolytes proceeds with surface charge reversal and highlighted electrostatic interactions as the major driving force of layer deposition. Far from being completely immobilized, multilayers feature a constant surge of chain intermixing during the deposition process, consistent with experimental observations of extensive interlayer mixing in these films. The formation of multilayers as well as the extent of layer intermixing depends on the degree of polymerization of the polyelectrolyte chains and the fraction of charge on its backbone. The presence of ionic pairs between oppositely charged macromolecules forming layers seems to play an important role in stabilizing the multilayer film.     

Monte Carlo simulations of antibody adsorption and orientation on charged surfaces

Monte Carlo simulations were performed to study the adsorption and orientation of antibodies on charged surfaces based on both colloidal and all-atom models. The colloidal model antibody consists of 12 connected beads representing the 12 domains of an antibody molecule. The structure of the all-atom antibody model was taken from the protein databank. The effects of the surface charge sign and density, the solution pH and ionic strength on the adsorption and orientation of different colloidal model antibodies with different dipole moments were examined. Simulation results show that both the 12-bead and the all-atom models of the antibody, for which the dipole moment points from the Fc to (Fab)2 fragments, tend to have the desired "end-on" orientation on positively charged surfaces and undesired "head-on" orientation on negatively charged surfaces at high surface charge density and low solution ionic strength where electrostatic interactions dominate. At low surface charge density and high solution ionic strength where van der Waals interactions dominate, 12-bead model antibodies tend to have "lying-flat" orientation on surfaces. The orientation of adsorbed antibodies results from the compromise between electrostatic and van der Waals interactions. The dipole moment of an antibody is an important factor for antibody orientation on charged surfaces when electrostatic interactions dominate. This charge-driven protein orientation hypothesis was verified by our simulations results in this work. It was further confirmed by surface plasmon resonance biosensor and time-of-flight secondary ion mass spectrometry experiments reported elsewhere.     

Polyion-induced liposomal vesicle aggregation: a radiowave dielectric relaxation study

The radiowave dielectric properties of aqueous heterogeneous systems during the complexation of charged polyions and oppositely charged liposomal particles have been measured in a wide frequency range, between 100 Hz and 2 GHz. The formation of a polyion-liposome complex driven by the correlated polyion adsorption at the particle surface implies two concomitant effects referred to as reentrant condensation and charge inversion. Both of them are governed by electrostatic interactions and there is now strong evidence, based on experiments and simulations, that counterion release is the driving force of the aggregation process. From this point of view, dielectric technique may offer a suitable tool in the investigation of the structural properties of these aggregates. In spite of the fact that interaction of polyions with oppositely charged surfaces was extensively experimentally investigated, there are no papers concerning the dielectric properties during the polyion-induced aggregation. To get an insight into this important topic, the authors present here an extensive set of radiowave dielectric measurements of liposomal vesicle aqueous suspensions where the liposome aggregation was induced by an oppositely charged polyion. The aggregation was followed from the beginning, when most of the isolated liposomes predominate, up to the formation of polyion-coated liposomes of inverted charge, crossing the isoelectric condition, where large, almost neutral, aggregates appear. The authors describe the observed dielectric dispersions as due to counterion polarization in the adjacency of the liposome and liposome aggregate surface, primarily governed by the zeta potential, according to the standard electrokinetic model.     

Mechanism of electrostatic gating at conical glass nanopore electrodes

The mechanism of molecule-based electrostatic gating of redox fluxes at conical glass nanopore (GNP) electrodes has been investigated using finite-element simulations. The results demonstrate that the fluxes of cationic redox molecules through the nanopore orifice can be reduced to negligibly small values when the surface charge of the nanopore is switched from a negative to a positive value. Electrostatic charge reversal can be affected by ionization of surface-bound moieties in response to environmental stimuli (e.g., photoionization or acid protonation), but only if the negative charge of the glass is included in the analysis. Numerical simulations of the responses of GNP electrodes are based on a simultaneous solution of the Poisson and Nernst-Planck equations and are in excellent agreement with our previously reported experimental results for electrostatic gating of the fluxes of Ru(NH 3) 6 (3+) and Fe(bpy) 3 (2+) at GNP electrodes with orifice radii between 15 and 100 nm. The gating mechanism is discussed in terms of three components: (1) migration of ionic redox species in the depletion layer adjacent to the electrode surface; (2) migrational transport along the charged pore walls; (3) electrostatic rejection of charged molecules at the pore orifice. The numerical results indicate that all three components are operative, but that ion migration along the pore walls is dominant.     

Electrokinetic flow and electric conduction of salt-free solutions in a capillary

The electrokinetic flow and accompanied electric conduction of a salt-free solution in the axial direction of a charged circular capillary are analyzed. No assumptions are made about the surface charge density (or surface potential) and electrokinetic radius of the capillary, which are interrelated. The Poisson–Boltzmann equation and modified Navier–Stokes equation are solved for the electrostatic potential distribution and fluid velocity profile, respectively. Closed-form formulas for the electroosmotic mobility and electric conductivity in the capillary are derived in terms of the surface charge density. The relative surface potential, electroosmotic mobility, and electric conductivity are monotonic increasing functions of the surface charge density and electrokinetic radius. However, the rises of the relative surface potential and electroosmotic mobility with an increase in the surface charge density are suppressed substantially when it is high due to the effect of counterion condensation. The analytical prediction that the electroosmotic mobility grows with increases in the surface charge density and electrokinetic radius agrees with the experimental results for salt-free solutions in circular microchannels in the literature.     

带同种电荷胶体颗粒间的相互吸引

带同种电荷颗粒间存在静电吸引是当前胶体科学领域的一大研究热点, 也是颇有争议的一个课题。经典的DLVO 理论认为, 电解质溶液中一对孤立、带同种电荷的球型胶粒将表现出纯粹的库仑排斥。以往的实验事实也证实了DLVO 理论的正确性。然而, 近十几年来的实验研究表明, 在一定条件下, 同性颗粒间的有效相互作用势能可能表现出静电吸引。对此, 至今还没有一个令人信服的理论描述, 甚至连其产生根源也未有定论。带同种电荷颗粒的静电吸引将是一个很值得探讨的问题。     

Simulation of phase equilibria in lamellar surfactant systems

The coexistence of two lamellar liquid crystalline phases has been investigated by means of Monte Carlo simulations. The surfaces of the negatively charged bilayers formed by the surfactant molecules are modeled as planar infinite walls with a uniform surface charge density. Water is treated as a dielectric continuum, and only electrostatic interactions are considered. The counterions are mono- and divalent point ions, and their ratio is allowed to vary. Monovalent counterions lead to a repulsive osmotic pressure at all separations, while an attractive region exists when the counterions are divalent. In the latter case, one would expect a phase separation to take place, although it is not observed experimentally due to the limited stability of the lamellar phase at high water content. In a system with mixed counterions, however, the osmotic pressure exhibits a van der Waals loop under such conditions that two phases can coexist. A phase diagram is constructed, and the agreement with experimental data is excellent.     

Diffusiophoresis in a suspension of spherical particles with arbitrary double-layer thickness

The diffusiophoresis in a homogeneous suspension of identical dielectric spheres with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a constant imposed concentration gradient is analytically studied. The effects of particle interactions (or particle volume fraction) are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the diffusiophoretic velocity of the dielectric sphere in closed form correct to the second order of its surface charge density or zeta potential are obtained from a balance between its electrostatic and hydrodynamic forces. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made.     

Isoelectric point of fluorite by direct force measurements using atomic force microscopy

Interaction forces between a fluorite (CaF2) surface and colloidal silica were measured by atomic force microscopy (AFM) in 1 x 10(-3) M NaNO3 at different pH values. Forces between the silica colloid and fluorite flat were measured at a range of pH values above the isoelectric point (IEP) of silica so that the forces were mainly controlled by the fluorite surface charge. In this way, the IEP of the fluorite surface was deduced from AFM force curves at pH approximately 9.2. Experimental force versus separation distance curves were in good agreement with theoretical predictions based on long-range electrostatic interactions, allowing the potential of the fluorite surface to be estimated from the experimental force curves. AFM-deduced surface potentials were generally lower than the published zeta potentials obtained from electrokinetic methods for powdered samples. Differences in methodology, orientation of the fluorite, surface carbonation, and equilibration time all could have contributed to this difference.     

Modeling spontaneous formation of precursor nanoparticles in clear-solution zeolite synthesis

We present a lattice model describing the formation of silica nanoparticles in the early stages of the clear-solution templated synthesis of silicalite-1 zeolite. Silica condensation/hydrolysis is modeled by a nearest-neighbor attraction, while the electrostatics are represented by an orientation-dependent, short-range interaction. Using this simplified model, we show excellent qualitative agreement with published experimental observations. The nanoparticles are identified as a metastable state, stabilized by electrostatic interactions between the negatively charged silica surface and a layer of organic cations. Nanoparticle size is controlled mainly by the solution pH, through nanoparticle surface charge. The size and concentration of the charge-balancing cation are found to have a negligible effect on nanoparticle size. Increasing the temperature allows for further particle growth by Ostwald ripening. We suggest that this mechanism may play a role in the growth of zeolite crystals.     

Atomistic molecular dynamics simulations on the interaction of TEMPO-oxidized cellulose nanofibrils in water

Atomistic molecular dynamics simulations were carried out to obtain information on the rheological, aggregation and disintegration properties of carboxylated (TEMPO-oxidized) cellulose nanofibrils with different functionalization levels. The magnitude of the inter-fibril interaction was quantified for parallel nanofibrils using the umbrella sampling method. The obtained potential of mean force was found highly sensitive to the charge configuration for intermediate functionalization levels. This feature was further studied with an electrostatic model for similar charge configurations and system periodicity as in the case of the molecular dynamics simulations. The electrostatic contribution of the charged surfaces varied from repulsive to attractive depending on the distribution of the carboxylate groups and nearby counter-ions, as well as the distance between the fibrils. The simulated deviations from average behavior for single fibrils in both models suggest heterogeneity in their aggregation and disintegration behavior. This was seen in disintegration experiments, where the differences in disintegration energy and in the structural variation qualitatively agreed with the model predictions. As to aggregation behavior, the studied case with parallel fibrils reflects the upper boundary of the repulsive interaction.     

On the behavior of electrokinetic streaming potential during protein filtration with fully and partially retentive nanopores

An experimental investigation of the electrokinetic streaming potentials of both fully and partially retentive nanopores as compared with the filtration progress of dilute globular protein solution under different surface charge conditions was performed using hollow fibers. The streaming potential is generated by the electrokinetic flow effect within the electric double layer of the charged surface. Depending on the solution pH, both the protein and the pore wall can be either repulsive or attractive due to the long-range electrostatic interaction. The repulsive electrostatic interaction allows the protein particles to stay in a suspended state above the outer surface of hollow fibers instead of being deposited. The apparent streaming potential value at partially retentive pores is larger than that at fully retentive pores for the oppositely charged case; however, the opposite behavior is shown for the same-charged case. The axial-position-dependent streaming potential was also observed in order to explore the development of a concentration polarization layer during the cross-flow filtration. The time evolution of the streaming potential during the filtration of protein particles is related to the filtrate flux, from which it can be found to provide useful real-time information on particle deposition onto the outer surfaces of hollow fibers.     

Interpretation of conservative forces from Stokesian dynamic simulations of interfacial and confined colloids

This paper presents Stokesian dynamics simulations of experiments involving one or two charged colloids near either a single charged wall or confined between parallel charged walls. Equilibrium particle-particle and particle-wall interactions are interpreted from dynamic particle trajectories in simulations involving (1) a single particle levitated above a wall, (2) two particles below a wall, and (3) two particles confined between two parallel walls. By specifying only repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek (DLVO) potentials and including multibody hydrodynamics, we successfully recover expected potentials in some cases, while anomalous attraction is observed in other cases. Attraction inferred in the latter simulations displays quantitative agreement with literature measurements when particle dynamics are interpreted using reported analyses. Because anomalous attraction is reproduced in simulations using only electrostatic repulsive DLVO potentials, our results reveal the one-dimensional analyses to be invalid for configurations that are inherently multidimensional via multibody hydrodynamics. Parameters related to experimental sampling of particle dynamics are also found to be critical for obtaining accurate potentials. We explain the anomalous attraction in each experiment using effective potentials, which can be employed in an a priori fashion to assist the confident design of future experiments involving interfacial and confined colloids. Ultimately, our findings reveal the importance of dimensionality and multibody hydrodynamics for understanding nonequilibrium dynamics of colloids near surfaces.     

Interactions between charged surfaces immersed in a polyelectrolyte solution

With grand canonical simulations invoking a configurationally weighted scheme, we have calculated interactions between charged surfaces immersed in a polyelectrolyte solution. In contrast to previous simulations of such systems, we have imposed full equilibrium conditions (i.e., we have included diffusive equilibrium with a bulk solution). This has a profound impact on the resulting interactions: even at modest surface charge densities, oppositely charged chains will, at sufficiently large separations, adsorb strongly enough to overcompensate for the nominal surface charge. This phenomenon, known as charge inversion, generates a double-layer repulsion and a free-energy barrier. Simpler canonical approaches, where the chains are assumed to neutralize the surfaces perfectly, will not capture this stabilizing barrier. The barrier height increases with the length of the polyions. Interestingly enough, the separation at which the repulsion becomes attractive is independent of chain length. The short chains here are unable to reach across from one surface to the other. We therefore conclude that the transition to an attractive regime is not provided by the formation of such "intersurface" bridges. With long chains and at large separations, charge inversion displays decaying oscillatory behavior (i.e., the apparent surface charge switches sign once again). This is due to polyion packing effects. We have also investigated responses to salt addition and changes in polyelectrolyte concentration. Our results are in qualitative and semiquantitative agreement with experimental findings, although it should be noted that our chains are comparatively short, and the experimental surface charge density is poorly established.     

Effect of charge inhomogeneity and mobility on colloid aggregation

The aggregation of inhomogeneously charged colloids with the same average charge is analyzed using Monte Carlo simulations. We find aggregation of colloids for sizes in the range 10-200 nm, which is similar to the range in which aggregation is observed in several experiments. The attraction arises from the strongly correlated electrostatic interactions associated with the increase in the counterion density in the region between the particles; this effect is enhanced by the discreteness and mobility of the surface charges. Larger colloids attract more strongly when their surface charges are discrete. We study the aggregation as functions of the surface charge density, counterion valence, and volume fraction.     

The role of electrostatic interactions in protease surface diffusion and the consequence for interfacial biocatalysis

This study examines the influence of electrostatic interactions on enzyme surface diffusion and the contribution of diffusion to interfacial biocatalysis. Surface diffusion, adsorption, and reaction were investigated on an immobilized bovine serum albumin (BSA) multilayer substrate over a range of solution ionic strength values. Interfacial charge of the enzyme and substrate surface was maintained by performing the measurements at a fixed pH; therefore, electrostatic interactions were manipulated by changing the ionic strength. The interfacial processes were investigated using a combination of techniques: fluorescence recovery after photobleaching, surface plasmon resonance, and surface plasmon fluorescence spectroscopy. We used an enzyme charge ladder with a net charge ranging from -2 to +4 with respect to the parent to systematically probe the contribution of electrostatics in interfacial enzyme biocatalysis on a charged substrate. The correlation between reaction rate and adsorption was determined for each charge variant within the ladder, each of which displayed a maximum rate at an intermediate surface concentration. Both the maximum reaction rate and adsorption value at which this maximum rate occurs increased in magnitude for the more positive variants. In addition, the specific enzyme activity increased as the level of adsorption decreased, and for the lowest adsorption values, the specific enzyme activity was enhanced compared to the trend at higher surface concentrations. At a fixed level of adsorption, the specific enzyme activity increased with positive enzyme charge; however, this effect offers diminishing returns as the enzyme becomes more highly charged. We examined the effect of electrostatic interactions on surface diffusion. As the binding affinity was reduced by increasing the solution ionic strength, thus weakening electrostatic interaction, the rate of surface diffusion increased considerably. The enhancement in specific activity achieved at the lowest adsorption values is explained by the substantial rise in surface diffusion at high ionic strength due to decreased interactions with the surface. Overall, knowledge of the electrostatic interactions can be used to control surface parameters such as surface concentration and surface diffusion, which intimately correlate with surface biocatalysis. We propose that the maximum reaction rate results from a balance between adsorption and surface diffusion. The above finding suggests enzyme engineering and process design strategies for improving interfacial biocatalysis in industrial, pharmaceutical, and food applications.