Overlap Of Double Layers Research Articles

Effect of wall permittivity on electroviscous flow through a contraction.

The electroviscous flow at low Reynolds number through a two-dimensional slit contraction with electric double-layer overlap is investigated numerically for cases where the permittivity of the wall material is significant in comparison with the permittivity of the liquid. The liquid-solid interface is assumed to have uniform surface-charge density. It is demonstrated that a finite wall permittivity has a marked effect on the distribution of ions in and around the contraction, with a significant build-up of counter-ions observed at the back-step. The development length of the flow increases substantially as the wall permittivity becomes significant, meaning that the electric double-layers require a longer distance to develop within the contraction. Consequently, there is a corresponding decrease in the hydrodynamic and electro-potential resistance caused by the contraction. The effect of wall-region width on the flow characteristics is also quantified, demonstrating that the development length increases with increasing wall-region width for widths up to 5 channel widths.

Microfluidic circuit analysis I: Ion current relationships for thin slits and pipes

Existing microfluidic circuit theories consider conservation of volume and conservation of total charge at each channel intersection (node) that exists within a circuit. However, in a strict sense conservation of number (or charge) for each ion species that is present should also be applied. To be able to perform such a conservation the currents due to the movement of each ion species (electrokinetic ion currents) that occur within each channel need to be known. Hence, we here present analytical and numerical methods for calculating these ion currents (and fluid flowrates) in Newtonian binary electrolyte solutions flowing within two-dimensional thin slits and pipes. Analytical results are derived in the limits of low potential, high potential, and thin double layers. We show that irrespective of double layer overlap, the Boltzmann distribution is valid provided that a local geometric mean is used for the reference ion concentration. While the real significance of the work lies in its application to multi-channel microfluidic circuit theory (see the accompanying paper of Biscombe et al. [1]), the present results show that even in single channels, ion current behaviour can be surprisingly complex.

Transport and Sensing in Nanofluidic Devices

Ion transport and sensing in nanofluidic devices are receiving a great deal of attention because of their unique transport properties and potential analytical applications. Some aspects of microscale transport transfer directly to the nanoscale, but nanofluidic systems can be significantly influenced by phenomena such as double-layer overlap, surface charge, ion-current rectification, diffusion, and entropic forces, which are either insignificant or absent in larger microchannels. Micro- and nanofabrication techniques create features with a wide range of well-defined geometries and dimensions in synthetic and solid-state substrates. Moreover, these techniques permit coupling of multiple nano- and microscale elements, which can execute various functions. We discuss basic nanofluidic architectures, material transport properties through single and multiple nanochannels, and characterization of single particles by resistive-pulse sensing.

Calculation of double layer interaction between colloidal aggregates

This paper examines the interaction between the electric double layers of aggregates. Commonly, rather simplified models are used like the approximation of primary particle interaction (APPI), which just considers the interaction of the closest pair of primary particles having a double layer as if they were isolated. However, for nanoparticles the double layer thickness may be in the same order of magnitude as the particle size or even larger, what leads to a considerable double layer overlap inside the aggregates and between two interacting aggregates. Consequently, such approximations will fail. The paper presents a numerical scheme for the double layer interaction of arbitrarily shaped aggregates, which can e.g. help to establish criteria for the applicability of approximate models. The calculation employs a singularity method, which is based on the linearised Poisson–Boltzmann equation. Additionally, a linear model for charge regulation is implemented. The impact of charge regulation and double layer thickness were studied for fractal DLCA aggregates and hexagonal closed-packed aggregates.

Electric Conductivity and Electrophoretic Mobility in Suspensions of Charged Porous Spheres

The electric conduction and electrophoresis of a suspension of charged porous spheres in an electrolyte solution with an arbitrary thickness of the electric double layers are analytically studied. The porous particle can be a solvent-permeable and ion-penetrable polyelectrolyte molecule or charged floc with uniformly distributed frictional segments and fixed charges. The effect of particle interactions is taken into account by employing a unit cell model, and the overlap of the electric double layers of adjacent particles is allowed. The electrokinetic equations, which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell, are linearized by assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved with the dimensionless density of the fixed charges as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of each charged porous sphere and for the effective electric conductivity of the suspension correct to the first and second orders, respectively, of the fixed charge density are obtained in closed forms. The effect of particle interactions on the electrophoresis and electric conduction of the suspension can be significant in typical situations. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The dependence of the electrophoretic mobility and the electric conductivity on the particle volume fraction and other properties of the particle−solution system is found to be quite complicated.

Nonlinear changes in pore size induced by temperature in the design of smart membranes

A new kind of synthetic membranes prepared by crosslinking of two different organic polymers was designed, the membranes has the ability to adjust the pore diameter in a wide range of sizes (from 3 to 100 microns) just by changing the time of thermal treatment in an aqueous media at constant temperature where they are immersed; in this way it is possible to control externally the pore size of the membrane. A nonlinear mathematical model, on the basis of the overlap of the electrical double layers of charged particles, was developed to explain the oscillatory behavior of the pore size when the time of thermal treatment was varied. The model deduced fits correctly to the experimental results and describes the oscillatory behavior of the pore size.

Numerical analysis of Debye screening effect in electrode surface potential mapping by scanning electrochemical potential microscopy

We investigate the effects of the probe apex geometry, overlap of the electric double layers (EDLs) and Debye screening on surface potential mapping with scanning electrochemical potential microscopy (SECPM). The simulation consists of scanning a tip parallel to the electrode surface over a charged hemispherical nano-particle adsorbed on the electrode surface. As expected, a clear dependence of the apparent size of the imaged particle on the probe apex geometry has been noticed. The Debye screening has a significant effect on the probe sensitivity, while the electrolyte concentration affects the observed size of the imaged particles.

Smart polymeric membranes: pH-induced non-linear changes in pore size

A new kind of synthetic membrane was designed with the capacity to adjust the pore diameter in a wide range of sizes (from 0.8 to 22.3 microns) just by changing the pH of the aqueous medium where it is immersed; in this way it is possible to control externally the pore size of the membrane. A non-linear mathematical model, based on the overlap of the electrical double layers of charged particles, was developed to explain the oscillatory behavior of the pore size when the pH was varied. This model fits correctly this oscillatory behavior. Scanning electron microscope images were obtained in low-vacuum conditions to reduce, as much as possible, possible changes in the external conditions after the immersion in water.

Thermodynamic Reversibility Analysis of Electrokinetic Energy Conversion in Nanofluidic Channels

The thermodynamic efficiencies of electrokinetic pumping and electrical power generation are investigated numerically using a two-dimensional axisymmetrical model containing a finite-length nanoscale cylindrical capillary and reservoirs connecting at the capillary ends. The Navier-Stokes, Laplace, Poisson, and Nernst-Planck equations are solved simultaneously to obtain the fluid and electric current flows. The main goal of this study is to justify the reversibility of electrokinetic energy conversion resulting from one-dimensional analysis. Based on our numerical results, it is found that the reversible electrokinetic energy conversion between the pump and electric power generation is valid only when the dimensionless Debye length is greater than 2. Because of the electric double layer (EDL) overlap and current due to the electrostatic potential gradient, significant deviation in maximum efficiencies between the numerical and one-dimensional analysis results are found when the dimensionless Debye length is less than 2.

Estimating vertical and lateral pressures in periodically structured montmorillonite clay particles

Given a montmorillonitic clay soil at high porosity and saturated by monovalent counterions, we investigate the particle level responses of the clay to different external loadings. As analytical solutions are not possible for complex arrangements of particles, we employ computational micromechanical models (based on the solution of the Poisson-Nernst-Planck equations) using the finite element method, to estimate counterion and electrical potential distributions for particles at various angles and distances from one another. We then calculate the disjoining pressures using the Van't Hoff relation and Maxwell stress tensor. As the distance between the clay particles decreases and double-layers overlap, the concentration of counterions in the micropores among clay particles increases. This increase lowers the chemical potential of the pore fluid and creates a chemical potential gradient in the solvent that generates the socalled 'disjoining' or 'osmotic' pressure. Because of this disjoining pressure, particles do not need to contact one another in order to carry an 'effective stress'. This work may lead towards theoretical predictions of the macroscopic load deformation response of montmorillonitic soils based on micromechanical modelling of particles.

Current Blockade in Nanopores in the Presence of Double-Stranded DNA and the Microscopic Mechanisms

We have carried out Brownian Dynamics calculations to investigate the mechanism of current blockade by double-stranded DNA (dsDNA) in a nanopore. We find that the blockade current crosses over from negative to positive as the ionic concentration decreases, similar to experiment. In addition to the volume exclusion and the counterion condensation, we find that the electric double layer overlap is a significant factor in the current blockade. The electric double layer overlap causes the ionic concentration beyond the immediate neighborhood of dsDNA and the wall to be lower in a dsDNA-blocked nanopore than the plateau ionic concentration away from the wall in an open nanopore, thus contributing importantly to the blockade current. On the basis of the calculated ion distribution function in the nanopore, we examined the counterion condensation to the dsDNA. We find the excess counterion condensation to be about 60% of the charge on the dsDNA, which is within the range of percentages obtained from experiments. We performed equilibrium and nonequilibrium (under an applied electric field) Brownian dynamics simulations to calculate the average mobility of the ions in nanopores. The calculated ion mobility is found to be reduced in DNA-blocked nanopores.

Electroosmotic Flow Can Generate Ion Current Rectification in Nano- and Micropores

This paper introduces a strategy for generating ion current rectification through nano- and micropores. This method generates ion current rectification by electroosmotic-driven flow of liquids of varying viscosity (and hence varying conductance) into or out of the narrowest constriction of a pore. The magnitude of current rectification was described by a rectification factor, R(f), which is defined by the ratio of the current measured at a positive voltage divided by the current measured at a negative voltage. This method achieved rectification factors in the range of 5-15 using pores with diameters ranging from 10 nm to 2.2 microm. These R(f) values are similar to the rectification factors reported in other nanopore-based methods that did not employ segmented surface charges. Interestingly, this work showed that in cylindrical nanopores with diameters of 10 nm and a length of at least 275 nm, electroosmotic flow was present and could generate ion current rectification. Unlike previous methods for generating ion current rectification that require nanopores with diameters comparable to the Debye length, this work demonstrated ion current rectification in micropores with diameters 500 times larger than the Debye length. Thus this method extends the concept of fluidic diodes to the micropore range. Several experiments designed to alter or remove electroosmotic flow through the pore demonstrated that electroosmotic flow was required for the mode of ion current rectification reported here. Consequently, the magnitude of current rectification could be used to indicate the presence of electroosmotic flow and the breakdown of electroosmotic flow with decreasing ionic strength and hence increasing electric double layer overlap inside nanopores.

Effect of Conical Nanopore Diameter on Ion Current Rectification

Asymmetric nanoscale conduits, such as conical track-etch pores, rectify ion current due to surface charge effects. To date, most data concerning this phenomenon have been obtained for small nanopores with diameters comparable to the electrical double layer thickness. Here, we systematically evaluate rectification for nanopores in poly(ethylene terephthalate) membranes with tip diameters of 10, 35, 85, and 380 nm. Current-voltage behavior is determined for buffer concentrations from 1 mM to 1 M and pHs 3.4 and 6.7. In general, ion current rectification increases with decreasing tip diameter, with decreasing ionic strength, and at higher pH. Surface charge contributes to increased pore conductivities compared to bulk buffer conductivities, though double layer overlap is not necessary for rectification to occur. Interestingly, the 35 nm pore exhibits a maximum rectification ratio for the 0.01 M buffer at pH 6.7, and the 380 nm pores exhibit nearly diodelike current-voltage curves when initially etched and strong rectification after the ion current has stabilized.

Electrochemical charge of silica surfaces at high ionic strength in narrow channels

We present a theoretical framework to calculate the electrochemical charge on silica surfaces in contact with high-ionic-strength solutions in narrow channels. Analytical results indicate that the contribution of the adsorbed metal cations to the total surface charge is not negligible when the salinity is larger than 1 mM. The electrical triple-layer model is proved much better than other models for high ionic strength. The charge regulation caused by the double-layer overlap in narrow channels will reduce the surface charge density but increase the zeta potential on silica surfaces.

Ionic Conductivity Measurements in a SiO2 Nanochannel with PDMS Interconnects

Silica nanofluidic channels with 50 nm height were fabricated on glass substrates. A PDMS microfluidic network was integrated with the nanochannels for fluidic handling. Ionic conductivity measurements were performed across the nanochannels with several KCL concentrations. Ionic conductivity saturation at ∼700 μS cm-1 was observed at low salt concentrations (<10-4 M) due to of the overlap of the electrical double layers of the top and bottom surfaces of the nanochannel.

A quantitative model to evaluate the ion-enrichment and ion-depletion effect at microchannel–nanochannel junctions

In a nanometer-scale fluidic channel (nanochannel), coions are depleted while counterions are concentrated due to the electric double layer (EDL) overlap. When an electric field is applied across the nanochannel, ions are enriched at one end and depleted at the other end of the nanochannel. This phenomenon is termed the ion-enrichment and ion-epletion (IEID) effect. In this paper, we develop a theoretical model to evaluate this effect. The model takes into accounts not only the biased electrophoretic migrations but also the net charge transportation caused by electroosmotic flow. In addition, we consider the conductance change inside the nanochannel in assessing the electric field strength across it. We employ our recently developed protocol to measure these values. We establish a protocol to measure/quantitate the IEID effect. Finally, we compare the calculated results with the experimentally measured data and show good agreements between them.

Numerical particle-scale study of swelling pressure in clays

The particle level responses to different external loadings of a montmorillonitic clay soil are investigated numerically. The soil is saturated by a solution of monovalent counterions, of varying concentrations. We use finite element micromechanical models (based on the Poisson-Nernst-Planck equations) to estimate counterion and electrical potential distributions around individual clay particles at various distances from one another, since analytical solutions are not possible for these complex arrangements of particles. Disjoining pressures are then estimated using the Van’t Hoff relation and Maxwell stress tensor. As the distance between the clay particles decreases and double-layers overlap, the concentration of counterions in the micropores between clay particles increases. This increase lowers the chemical potential of the pore fluid and creates a chemical potential gradient in the solvent that generates the so-called “disjoining” or “osmotic” pressure. Because of this disjoining pressure, it is clear that particles need not contact one another in order to carry an “effective stress”. This work may lead towards theoretical predictions of the macroscopic load deformation response of montmorillonitic soils based on micro-electro-chemo-mechanical modelling of particles.

Proton-Conductive Nanochannel Membrane for Fuel-Cell Applications

Novel design of proton conductive membrane for direct methanol fuel cells is based on proton conductivity of nanochannels, which is acquired due to the electric double layer overlap. Proton conductivity and methanol permeability of an array of nanochannels were studied. Anodic aluminum oxide with pore diameter of 20 nm was used as nanochannel matrix. Channel surfaces of an AAO template were functionalized with sulfonic groups to increase proton conductivity of nanochannels. This was done in two steps; at first -SH groups were attached to walls of nanochannels using (3-Mercaptopropyl)-trimethyloxysilane and then they were converted to -SO3H groups using hydrogen peroxide. Treatment steps were analyzed by Fourier Transform Infrared spectroscopy and X-ray Photoelectron Spectroscopy. Proton conductivity and methanol permeability were measured. The data show methanol permeability of membrane to be an order of magnitude lower, than that measured of Nafion. Ion conductivity of functionalized AAO membrane was measured by an impedance analyzer at frequencies ranging from 1 Hz to 100 kHz and voltage 50 mV to be 0.15 Scm(-1). Measured ion conductivity of Nafion membrane was 0.05 Scm(-1). Obtained data show better results in comparison with commonly used commercial available proton conductive membrane Nafion, thus making nanochannel membrane very promising for use in fuel cell applications.

Fluidic Diodes in Nano- and Microscale Pores to Detect Drug Aggregation

We present a novel method of producing ion current rectification (ICR) in nano- and micro- scale pores that does not require electrical double layer overlap within a pore. ICR in nanopores has typically been constrained in two ways: i) at least one dimension or component of the channel must be on the order of the Debye screening length and ii) charge asymmetry must be induced within the pore. Asymmetric channel geometries, modified surface charges, and asymmetric bulk ion concentrations are commonly applied to produce the necessary charge asymmetry. In the method presented here, ICR is dependent on electroosmotic flow (EOF) to position two solutions of different conductance within a pore. Substrates containing pores with diameters of 10 nm, 30 nm, and 500 nm were used to separate the two different solutions. We have achieved rectification factors ranging from 2-15, as a function of solution properties, in conical and cylindrical pores with diameters much larger than the Debye screening length. Thus, ICR can be achieved at higher ionic strengths (here up to 300 mM), in pores with large diameters (here up to 3 μm), and in pores without patterned surface charges. We also present a phenomenon unique to the two-solution system that we introduce here. Dissolving a drug in one solution, which contains 75%, DMSO, and then moving the molecules through the pore into a purely aqueous solution leads to detectable aggregation of the drug in the pore. The aggregate typically proceeds to the point of blocking the pore (>85% reduction in current) and subsequently ejects from the pore. We have investigated the aggregation and subsequent clearance of the aggregate from the pore and propose a mechanism for the cyclic process.

Field-effect based attomole titrations in nanoconfinement

This paper describes a novel capacitive method to change the pH in micro- and nanofluidic channels. A device with two metal gate electrodes outside an insulating channel wall is used for this purpose. The device is operated at high ionic strength with thin double layers. We demonstrate that gate potentials applied between the electrodes cause a release or uptake of protons from the silicon nitride surface groups, resulting in a pH shift in the channel and a titration of solution compounds present. Due to the high quality silicon nitride insulating layer, the effect is purely capacitive and electrolysis can be neglected. Fluorescein was employed as a fluorescent pH indicator to quantify the induced pH changes, and a maximum change of 1.6 pH units was calculated. A linear relationship was found between applied potential and fluorescein intensity change, indicating a linear relation between actuated proton amount and applied voltage. Since this pH actuation method avoids redox reactions and can be operated at physiological ionic strength, it can be very useful as a "soft" way to change the pH in very small volumes e.g. in bioassays or cell-based research. The sensitivity of the optical detection method poses the only limit to the detectable amount of substance and the observed volume. In a preliminary measurement we show one possible application, namely titration of 100 attomol of TRIS in a 7 pL detection volume. It is important to stress that this pH actuation principle fundamentally differs from the pH changes occurring in ionic transistors which are due to counterion enrichment and coion exclusion, because it does not rely on double-layer overlap. As a result it can be operated at high ionic strength and in channels of up to at least 1 microm height.