Range Of Surface Charge Densities Research Articles

Finite ion size effects on electrophoresis of a dielectric surfactant-laden droplet in a non-dilute electrolyte

The ion steric repulsion and ion-solvent interactions, due to the finite size of ions, are analyzed for electrophoresis of a droplet in a non-dilute electrolyte in which the ionic volume fraction is O(0.01). In this study, the viscosity of the suspension medium is considered to be dependent on the local ionic volume fraction. The electrochemical potential of the finite-sized ions is modified to take into account the steric interactions. The impact of the Marangoni stress due to the non-uniform distribution of the non-ionized surfactant is taken into account. Governing equations are solved under a weak applied field consideration. At a lower range of surface charge density, the mobility is found to increase with the droplet viscosity, in which the Marangoni stress is found to enhance the mobility. The counterion saturation created by the ion steric interaction attenuates the screening of the surface charge and hence, enhances the mobility. However, the enhanced viscosity of the medium for the non-dilute electrolyte reduces the mobility and this reduction is higher in a monovalent electrolyte as compared to a multivalent electrolyte. The standard model shows a singularity in mobility when the surface potential is varied. However, the dependence of mobility on surface potential in the modified model is found to exhibit a smooth variation.

Dielectric layer modulated nanofluidic transport: Formation of parent–sister vortices

Our analysis, consistent with the induced-charge electrokinetic, aptly discusses the effect of gate potential on the formation of vortices of disparate scales in a nanofluidic channel. The nanochannel considered here is connected with reservoirs at its ends, while a pair of dielectric gate electrodes is also embedded on the outer layer of the channel wall. In this endeavor, we establish that a suitable modulation of the dielectric polarization and inherent surface charge of the channel wall leads to the development of pair of “parent–sister” vortices in the flow field alongside yields a net flow in the channel, as well a unique fluidic functionality achieved at small scale is reported here for the first time. Moreover, we identify for the first time that the critical value of surface charge density (“critical-sigma,” i.e., σc) for two different typical heights of the nanofluidic channel, leading to the formation of maximum strength and size vortices by ceasing the net throughput. Also, we establish a critical range of surface charge density for a window of an arbitrary dimension of the dielectric gate electrode—a range for which optimum vortices are generated in the pathway, simultaneously producing adequate net flow through the channel. Under the present modeling configuration, we obtain that |σc|∼O(1 mC/m2) for a 1 μm long nanochannel having embedded quartz layer gate electrodes with gate potential |Vg|∼O(1 V). We believe that critical-sigma would be a crucial parameter for the design and fabrication of state-of-the-art nanodevices/nanosystems intended for augmented fluidic functionalities, for example, efficient solute mixing.

Influence of finite ion size and dielectric decrement on the ion current rectification in a single conical nanopore

The ion current rectification (ICR) arising due to the transport of ionized liquids within a geometrically asymmetric nanopore is of great significance for the development of smart nanogadgets with unique working capabilities. Though the theoretical framework for the ICR is well developed, the influence of the finite size of ions on the ICR phenomena had not been addressed before. The ion steric repulsion due to finite ion size and dielectric decrement of the medium creates a counterion saturation. In this study, a modified electrokinetic model is adopted to describe the ICR phenomena of a single conical nanopore by considering the hydrated ions as finite-sized dielectric charged spheres. The Nernst–Planck equations for ion transport are modified to incorporate the short-range ion steric interactions modeled by the Boublik–Mansoori–Carnahan–Starling–Leland equation as well as Born force and dielectrophoretic force acting on the hydrated ions engender by the ion–solvent interactions. The counterion saturation attenuates the shielding effect of the surface charge of the nanopore leading to a larger ζ-potential and hence, a larger volume flux and reduced conduction. We find that the ion steric interactions and the dielectric decrement significantly influence the ICR phenomena as well as the ion selectivity of a conical nanopore, especially for moderate to high range of surface charge density, bulk concentration, and applied bias. We find that ICR varies linearly with temperature; however, the variation is found to be marginal. Our results show that the volume flux and the rectification factor of the conical nanopore can be suitably tuned by adding salt of larger counterion size or multivalent ions.

Impact of finite ion size, Born energy difference and dielectric decrement on the electroosmosis of multivalent ionic mixtures in a nanotube

The electroosmotic flow (EOF) in a nanotube is analyzed by considering the finite ion size and dielectric decrement effects. The ion transport is governed by the modified Nernst-Planck equation, which takes into account the ion steric repulsion, Born energy difference, and dielectrophoretic force. The dielectric permittivity is considered to depend on the ionic concentration and ion size. The governing equations for fluid flow, ion transport, and electric field are solved numerically in their full form. The steric interaction is accounted, based on the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model, which considers the nonuniform ion size for monovalent as well as multivalent salts. We made a quantitative comparison with the standard PNP model for the lower range of charge density and highlighted the impact of ion size and dielectric decrement effects. For a highly charged surface, the impact due to finite ion size is non-negligible when the Debye length is in the order of the nanotube radius. However, the dielectric decrement is found to have a strong impact on a higher range of surface charge density or bulk ionic concentration. The EOF and the ion selectivity of the mixed electrolyte solution of different counterion size are considered in the present study. Present study provides an in-depth analysis of EOF through a cylindrical nanotube beyond the dilute solution and low charge density limits, which has not been addressed before.

Principles of surface potential estimation in mixed electrolyte solutions: Taking into account dielectric saturation

The dielectric properties between in-particle/water interface and bulk solution are significantly different, which are ignored in the theories of surface potential estimation. The analytical expressions of surface potential considering the dielectric saturation were derived in mixed electrolytes based on the nonlinear Poisson-Boltzmann equation. The surface potentials calculated from the approximate analytical and exact numerical solutions agreed with each other for a wide range of surface charge densities and ion concentrations. The effects of dielectric saturation became important for surface charge densities larger than 0.30 C/m \begin{document}$ ^2 $\end{document} . The analytical models of surface potential in different mixed electrolytes were valid based on original Poisson-Boltzmann equation for surface charge densities smaller than 0.30 C/m \begin{document}$ ^2 $\end{document} . The analytical model of surface potential considering the dielectric saturation for low surface charge density can return to the result of classical Poisson-Boltzmann theory. The obtained surface potential in this study can correctly predict the adsorption selectivity between monovalent and bivalent counterions.

Electrophoresis of hydrophilic/hydrophobic rigid colloid with effects of relaxation and ion size

This article deals with a semi-analytical study on the electrophoresis of charged spherical rigid colloid by considering the effects of relaxation and ion size. The particle surface is taken to be either hydrophilic or hydrophobic in nature. In order to consider the ion size effect we have invoked the Carnahan and Starling model (J. Chem. Phys. 1969, 51, 635-636). The mathematical model is based on Stokes equation for fluid flow, modified Boltzmann equation for spatial distribution of ionic species and Poisson equation for electric potential. We adopt a linear perturbation technique under a weak electric field assumption. An iterative numerical technique in employed to solve the coupled set of perturbed equations. We have validated the numerically obtained electrophoretic mobility with the corresponding analytical solution derived under low potential limit. Going beyond the widely employed Debye-Hückel linearization, we have presented the results for a wide range of surface charge density, electrolyte concentration, and slip length to Debye length ratio. We have also identified several interesting features including occurrence of local maxima and minima in the mobility for critical choice of pertinentparameters.

Gel electrophoresis and size selectivity of charged colloidal particles in a charged hydrogel medium

The electrophoresis of a charged colloid particle embedded in a charged hydrogel medium is studied based on the numerical computation of Stokes–Nernst–Planck–Poisson equations. In this study, no prior assumption on surface charge density of the particle, Debye length and imposed external electric field are made. We have compared our computed results for a lower range of surface charge density with the existing analytical solution based on the weakly charged particle and found them in good agreement when the fixed charge density of the hydrogel is low. Nonlinearity effects in gel electrophoresis is pronounced for a thick Debye length and higher values of particle ζ-potential. Even in the absence of a gel medium (free-solution), the numerical procedure used in this work yields mobilities different from the previous theoretical analysis based on the Debye–Hückel approximation when the scaled ζ-potential exceeds 2 and the Debye length is in the order of the particle size. The strong background electroosmotic flow (EOF) for a high fixed charge density of the polyelectrolyte hydrogel with a mesh size comparable to the particle radius drags the particle along the direction of the EOF. In this case, the electrophoretic velocity of the particle varies with its size. The particle electrophoretic velocity and forces are determined for a wide range of intrinsic parameters values.

Cell adhesion and spreading at a charged interface: Insight into the mechanism using surface techniques and mathematical modelling

We study the kinetics of adhesion and spreading of an algal cell and its plasma membrane vesicle at the charged interface. A simple system of an isolated plasma membrane vesicle without internal content has been developed and characterized by atomic force microscopy (AFM). We extend the methodology based on the reaction kinetics model and empirical fitting for the analysis of amperometric signals, and demonstrate its validity and pertinence in a wide range of surface charge densities. Adhesion kinetics of the algal cell is slower than that of its plasma membrane vesicle. Isolated plasma membrane contributes about one quarter to the cell contact area. The model reconstructs and quantifies individual states of the three-step adhesion process of the algal cell and makes it possible to associate them with various features of amperometric signal. At the time of current amplitude, the ruptured state predominates and the cell spread contact area is larger than its initial area as well as the contact area of the plasma membrane vesicle. These results suggest that a major structural disruption of the cell membrane, collapse of cytoskeleton and leakage of intracellular material could appear close to the time of current amplitude. Further, slow kinetics of the organic film spreading at the interface to its maximal extent is considered as the rate determining step, which could be a consequence of the attenuated effect of potential at the modified interface, stronger intermolecular interactions and reorganization of molecules in the film. Our findings offer an insight into the mechanism of algal cell adhesion and spreading at charged interfaces, relevant for electroporation based studies.

Structure of a planar electric double layer containing size-asymmetric ions: density functional approach

We have studied the structure of the electrolytes with asymmetries in charge and size near a charged planar electric double layer by a density functional theory. In the present theory, the hard-sphere contribution has been approximated as the direct pair correlation function with the coupling parameter, whereas the electronic contribution has been approximated as the mean-spherical approximation in the bulk phase. This theoretical approach for the size-symmetric and size-asymmetric electrolytes displays a good agreement with the simulation results over a wide range of surface charge densities and electrolyte concentrations. However, the accuracy between the present theory and the simulation results slightly deteriorates for the highly size-asymmetric electrolytes and the multivalent electrolytes. In these cases, the performance of the present theory is comparable to those of the simplified extension of the Poisson–Boltzmann theory and the modified Poisson–Boltzmann theory. The calculated result indicates that the surface charge distribution function, which was introduced as an indicator for studying the charge reversal, layering effect, and surface charge amplification in a planar electric double layer, describes the electronic properties of a planar electric double layer well.

Classical Density Functional Study on Interfacial Structure and Differential Capacitance of Ionic Liquids near Charged Surfaces

We have implemented a generic coarse-grained model for the aromatic ionic liquid [CnMIM+][Tf2N-]. Various lengths for the alkyl chain on the cation define a homologous series, whose electric properties are expected to vary in a systematic way. Within the framework of a classical density functional theory, the interfacial structures of members of this series are compared over a range of surface charge densities, alkyl chain lengths, and surface geometries. The differential capacitance of the electric double layer, formed by ionic liquids against a charged electrode, is calculated as a function of the surface electric potential. A comparison of planar, cylindrical, and spherical surfaces confirms that the differential capacitance increases and varies less with surface potential as the surface curvature increases. Our results are in qualitative agreement with recent atomistic simulations. (Less)

Electric Double Layer at the Rutile (110) Surface. 4. Effect of Temperature and pH on the Adsorption and Dynamics of Ions

Adsorption of Rb+, Na+, Sr2+, and Cl– on hydroxylated (110) rutile surfaces was studied by molecular dynamics (MD) simulations. Our previous work was extended to the range of surface charge densities from −0.2 to +0.1 C/m2 (from −0.4 to +0.1 C/m2 for Sr2+) and to temperatures of 25, 150, and 250 °C. These conditions can be linked to experimental surface charge and pH values from macroscopic titrations of rutile powders with surfaces dominated by 110 crystal planes. Simulations revealed that Na+ and Sr2+ adsorb closer to the surface, shifting from predominately bidentate to tetradentate inner-sphere binding with increasing temperature, whereas Rb+ binding is predominately tetradentate at all temperatures. These differences are related to hydration energies, which must be partially overcome for inner-sphere binding and which decrease with increasing temperature and are lowest for Rb+. The interaction of Cl– with the rutile surface is generally less than that for cations because of repulsion by surface oxygen atoms. These MD results provide molecular-level context for the trends observed in our corresponding macroscopic surface charge titrations. Titration curves steepen in the order Rb+ < Na+ < Sr2+, reflecting the adsorption interactions related to ion charge, radius, and hydration energy.

Fluorescent Labeling and Characterization of Cellulose Nanocrystals with Varying Charge Contents

Cotton-source cellulose nanocrystals (CNCs) with a range of surface charge densities were fluorescently labeled with 5-(4, 6-dichlorotriazinyl) aminofluorescein (DTAF) in a facile, one-pot reaction under alkaline conditions. Three CNC samples were labeled: (I) anionic CNCs prepared by sulfuric acid hydrolysis with a sulfur content of 0.47 wt %, (II) a partially desulfated, sulfuric acid-hydrolyzed CNC sample, which was less anionic with an intermediate sulfur content of 0.21 wt %, and (III) uncharged CNCs prepared by HCl hydrolysis. The DTAF-labeled CNCs were characterized by dynamic light scattering, atomic force microscopy, fluorescence spectroscopy and microscopy, and polarized light microscopy. Fluorescent CNCs exhibited similar colloidal stability to the starting CNCs, with the exception of the HCl-hydrolyzed sample, which became less agglomerated after the labeling reaction. The degree of labeling depended on the sulfur content of the CNCs, indicating that the presence of sulfate half-ester groups on the CNC surfaces hindered labeling. The labeling reaction produced CNCs that had detectable fluorescence, without compromising the overall surface chemistry or behavior of the materials, an aspect relevant to studies that require a fluorescent cellulose substrate with intact native properties. The DTAF-labeled CNCs were proposed as optical markers for the dispersion quality of CNC-loaded polymer composites. Electrospun polyvinyl alcohol fibers loaded with DTAF-labeled CNCs appeared uniformly fluorescent by fluorescence microscopy, suggesting that the nanoparticles were well dispersed within the polymer matrix.

Computational evidence of two driving mechanisms for overcharging in an electric double layer near the point of zero charge

We have adopted an ensemble Monte Carlo simulation method to systematically verify two physical driving mechanisms responsible for overcharging which refers to the adsorption of an effective charge onto a like-charged planar surface around the point of zero charge within the primitive model of mixed electrolytes with varying salt concentrations. One is electrostatic in character dominated by dielectric images and the other is purely entropic in origin by ionic size asymmetry effects, of which the former has never been reported both theoretically and experimentally and the latter could be interpreted satisfactorily in terms of available theoretical approaches. The electrostatically driven mechanism is found to critically depend on the ionic sizes while the entropically driven mechanism occurs with almost the same efficiency in a relative wide range of surface charge density. Depending on the delicate interplay between charge and steric correlations, the two distinct driving mechanisms may cooperatively give rise to a more pronounced overcharging process.

Density functional theory study of the water adsorption at Bi(111) electrode surface

The adsorption of a water molecule on a basal Bi(111) electrode surface, crystallising in the rhombohedral system, has been studied in the framework of cluster model. The quantum chemical calculations were performed at the Density Functional Theory (DFT) level and the electrical double layer effects were analysed by using an external electric field. In contrast to computational predictions reported previously for other metal surfaces, crystallising in the face-centred cubic or hexagonal close-packed systems, a hollow site for Bi(111) was found to be energetically the most preferable; the water adsorption energy amounts to − 28 kJ mol− 1. In a wide range of surface charge densities the water molecule is bound preferentially through the O atom in orientation perpendicular to the surface plane. The Bi(111) hydrophilic properties are compared with those for other metals. Some adsorption characteristics of a hydrogen atom and a hydroxyl group at Bi(111) are reported as well, which give evidence in favour of the non-dissociative adsorption of water molecules.

Image Charges and Dispersion Forces in Electric Double Layers: The Dependence of Wall−Wall Interactions on Salt Concentration and Surface Charge Density

The interaction pressure between two planar charged walls is calculated for a range of conditions. The diffuse electric double layers between the two wall surfaces are treated with ion-wall dispersion forces and ionic image charge interactions taken into account. Both these interactions are due to dielectric discontinuities at the surfaces. Ion-ion and ion-image charge correlations are explicitly included. The ion-wall dispersion interactions can give rise to appreciable ion specific effects, which are particularly strong when the counterions to the surfaces are highly polarizable. The mechanisms of these effects are investigated, and their influence on the net interaction pressure between the walls is studied for a range of surface charge densities, strengths of the anion-wall dispersion interaction and bulk electrolyte concentrations. When the strength of the anion-wall dipersion interaction is increased, the pressure generally becomes less repulsive (or more attractive) for positive surfaces. The opposite happens in general for negative surfaces but to a much lesser extent. The effects are largest for large surface charge densities and high electrolyte concentrations. The image charge interactions give rise to a considerable depletion attraction between the walls for low surface charge densities.

Surface polarization and effective anchoring energy in liquid crystals.

The influence of the surface polarization (SP) on the effective anchoring energy for both homeotropic and planar alignments of polar liquid crystals at a solid substrate is discussed from the energy point of view. It is shown that in a certain range of surface charge density the destabilizing SP mechanism may lead to destruction of the homeotropic or planar alignment of liquid crystalline molecules, such as 4-n-pentyl-4(')-cyanobiphenyl.

Anomalous Adsorption of Polyelectrolyte Layers

We study the adsorption of polyelectrolytes onto oppositely charged surfaces as the surface charge density is varied while keeping the polyelectrolyte charge density fixed. As observed previously from multilayer adsorption studies, 1,2 nonmonotonic adsorption behavior is obtained in the intermediate surface charge density regime, with anomalously thick supermonolayers transitioning to molecularly thin layers over a small range of surface charge densities. A simple adsorption model is introduced to explain these findings, in which the surface is characterized by discrete and fully compensated adsorption sites.

A modified Poisson–Boltzmann equation: II. Models and solutions

The properties of the charged interface between a dielectric particle and a surrounding aqueous electrolyte solution are calculated numerically over a wide range of surface charge densities for plane, cylindrical and spherical geometries. As a basis for the calculations, we present detailed models for the partial molar volumes, the dielectric permittivity and the activities of the components. These models are combined with a generalized set of local balance thermodynamic and electrostatic differential equations derived in the first part of this series. The influences of volume effects, dielectric saturation, polarization and self-atmosphere potentials on surface potential and electrostatic energy of a charged particle are investigated. Deviations from the ordinary Poisson–Boltzmann theory become very important at surface charge densities above 0.2 C m −2 . Quite generally, self-atmosphere potentials are of minor importance. The most important correction of the ordinary Poisson–Boltzmann equation is due to dielectric saturation in combination with the volume effect. It is found that the electrostatic potential, the electric field and the concentration of the counterion near a charged surface strongly depend on the excluded volume of the counterion. This leads to a distinct counterion sensitivity of the Gibbs energy of the system. Assuming a positively charged surface, competition between the counterion pairs Cl −/Br − and Cl −/SO 4 2− is investigated. For sufficiently high surface charge densities it is found that, in the immediate vicinity of the surface, the smaller Br −-ion displaces the larger Cl −-ion and the Cl −-ion, in turn, displaces the larger SO 4 2−-ion, although the latter is divalent.

Response of phosphatidylcholine in the gel and liquid-crystalline states to membrane surface charges

The influence of membrane surface charge on the conformation of the choline head group of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) was investigated in the gel and liquid-crystalline states by using 2H NMR spectroscopy of specifically choline-deuterated DMPC. The surface charge was made progressively more negative through admixture of various proportions of 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG). All membrane compositions showed nearly identical gel- to liquid-crystalline-phase transitions centered about 24 degrees C. The gel-state 2H NMR spectra from all three choline head-group deutero-labeling positions (alpha, beta, and gamma) decreased in intensity and broadened relative to the liquid-crystalline-state spectra. These effects were not so severe that they masked the overriding influence of surface charge on the choline head-group conformation as reflected in the 2H NMR spectra. Thus, in both the liquid-crystalline and gel states, the presence of negative surface charge caused the quadrupole splitting from DMPC-alpha-d2 to increase while causing that from DMPC-beta-d2 and DMPC-gamma-d9 to decrease. These effects were progressive with increasing density of negative surface charge. Correlation plots of the quadrupole splittings obtained, under otherwise identical conditions, from different deutero-labeling positions were linear over most of the range of surface charge densities, in both the liquid-crystalline and gel states, for all three correlations (alpha-beta, beta-gamma, and alpha-gamma). At extreme surface charge densities, the alpha-beta and alpha-gamma correlations showed biphasic behavior in that, at high surface charge densities, the change in the quadrupole splittings from DMPC-alpha-d2 became less pronounced.(ABSTRACT TRUNCATED AT 250 WORDS)

Salt exclusion from charged and uncharged micropores

The exclusion of electrolytes from charged and uncharged capillaries is studied using (a) the Poisson-Boltzmann equation and (b) Grand Canonical Monte Carlo computer simulations. The thermodynamics and structure are examined as a function of the charge fixed on the inner capillary surfaces. The results for 2:2 electrolytes indicate that the classical Poisson-Boltzmann equation breaks down under these conditions, and in fact its predictions are in serious disagreement with the simulation results for the same system over the whole range of surface charge densities. An additional interesting result of this study concerns the ability of microporous materials to exclude electrolytes. The salt exclusion first increases by increasing the charge density, passes through a maximum, and then decreases with further increase of the surface charge. This behavior (completely missed by the Poisson-Boltzmann approximation) can be explained by the influence of the interionic correlations on the distribution of electrolyte inside the capillary.