Electrokinetic transport in nanochannels. 1. Theory

Electrokinetic transport in fluidic channels facilitates control and separation of ionic species. In nanometer-scale electrokinetic systems, the electric double layer thickness is comparable to characteristic channel dimensions, and this results in nonuniform velocity profiles and strong electric fields transverse to the flow. In such channels, streamwise and transverse electromigration fluxes contribute to the separation and dispersion of analyte ions. In this paper, we report on analytical and numerical models for nanochannel electrophoretic transport and separation of neutral and charged analytes. We present continuum-based theoretical studies in nanoscale channels with characteristic depths on the order of the Debye length. Our model yields analytical expressions for electroosmotic flow, species transport velocity, streamwise-transverse concentration field distribution, and ratio of apparent electrophoretic mobility for a nanochannel to (standard) ion mobility. The model demonstrates that the effective mobility governing electrophoretic transport of charged species in nanochannels depends not only on electrolyte mobility values but also on zeta potential, ion valence, and background electrolyte concentration. We also present a method we term electrokinetic separation by ion valence (EKSIV) whereby both ion valence and ion mobility may be determined independently from a comparison of micro- and nanoscale transport measurements. In the second of this two-paper series, we present experimental validation of our models.     

Charged species transport, separation, and dispersion in nanoscale channels: autogenous electric field-flow fractionation

Numerical methods are employed to examine the transport of charged species in pressure-driven and electroosmotic flow along nanoscale channels having an electric double-layer thickness comparable to the channel size. In such channels, the electric field inherent to the double layer produces transverse species distributions that depend on species charge. Flow along the channel thus yields mean axial species speeds that also depend on the species charge, enabling species separation and identification. Here we characterize field-flow separations of this type via the retention and plate height. For pressure-driven flows, we demonstrate that mean species speeds along the channel are uniquely associated with a single species charge, allowing species separation based on charge alone. In contrast, electroosmotic flows generally yield identical speeds for several values of the charge, and these speeds generally depend on both the species charge and electrophoretic mobility. Coefficients of dispersion for charged species in both planar and cylindrical geometries are presented as part of this analysis.     

Particle tracking techniques for electrokinetic microchannel flows

We have applied particle tracking techniques to obtain spatially resolved velocity measurements in electrokinetic flow devices. Both micrometer-resolution particle image velocimetry (micro-PMV) and particle tracking velocimetry (PTV) techniques have been used to quantify and study flow phenomena in electrokinetic systems applicable to microfluidic bioanalytical devices. To make the flow measurements quantitative, we performed a series of seed particle calibration experiments. First, we measure the electroosmotic wall mobility of a borosilicate rectangular capillary (40 by 400 microm) using current monitoring. In addition to this wall mobility characterization, we apply PTV to determine the electrophoretic mobilities of more than 1,000 fluorescent microsphere particles in aqueous buffer solutions. Particles from this calibrated particle/ buffer mixture are then introduced into two electrokinetic flow systems for particle tracking flow experiments. In these experiments, we use micro-PIV, together with an electric field prediction, to obtain electroosmotic flow bulk fluid velocity measurements. The first example flow system is a microchannel intersection where we demonstrate a detailed documentation of the similitude between the electrical fields and the velocity fields in an electrokinetic system with uniform zeta potential, zeta. In the second system, we apply micro-PIV to a microchannel system with nonuniform zeta. The latter experiment provides a simultaneous measurement of two distinct wall mobilities within the microchannel.     

Anomalous ion transport in 2-nm hydrophilic nanochannels

Transmembrane proteins often contain nanoscale channels through which ions and molecules can pass either passively (by diffusion) or actively (by means of forced transport). These proteins play important roles in selective mass transport and electrical signalling in many biological processes. Fluidic nanochannels that are 1-2 nm in diameter act as functional mimics of protein channels, and have been used to explore the transport of ions and molecules in confined liquids. Here we report ion transport in 2-nm-deep nanochannels fabricated by standard semiconductor manufacturing processes. Ion transport in these nanochannels is dominated by surface charge until the ion concentration exceeds 100 mM. At low concentrations, proton mobility increases by a factor of four over the bulk value, possibly due to overlapping of the hydrogen-bonding network of the two hydration layers adjacent to the hydrophilic surfaces. The mobility of K+/Na+ ions also increases as the bulk concentration decreases, although the reasons for this are not completely understood.     

Numerical solution of a multi-ion one-potential model for electroosmotic flow in two-dimensional rectangular microchannels

A new more general numerical model for the simulation of electrokinetic flow in rectangular microchannels is presented. The model is based on the dilute solution model and the Navier-Stokes equations and has been implemented in a finite-element-based C++ code. The model includes the ion distribution in the Helmholtz double layer and considers only one single electrical' potential field variable throughout the domain. On a charged surface(s) the surface charge density, which is proportional to the local electrical field, is imposed. The zeta potential results, then, from this boundary condition and depends on concentrations, temperature, ion valence, molecular diffusion coefficients, and geometric conditions. Validation cases show that the model predicts accurately known analytical results, also for geometries having dimensions comparable to the Debye length. As a final study, the electro-osmotic flow in a controlled cross channel is investigated.     

Free-solution oligonucleotide separation in nanoscale channels

In this paper, we report an experimental study of electrokinetic transport and separation of double-stranded deoxyribonucleic acid (dsDNA) oligonucleotides in custom-fabricated fused-silica nanochannels filled with a gel-free sodium borate aqueous buffer. Mixtures of fluorescently labeled dsDNA molecules in the range of 10-100 base pair (bp), fluorescein, and fluorescein-12-UTP (UTP) were separated in less than 120 s in channels of depth ranging from 40 to 1560 nm. We varied the channel depth and background buffer concentration to achieve a 0.006-0.2 range of Debye length-to-channel-half-depth ratio (lambdaD/h), and a 0.004-1.7 range of the ratio of length of dsDNA molecule to channel half-depth (l/h). We find observed oligonucleotide migration times depend on both l/h and lambdaD/h. Electrophoretic mobility estimates agree well with published (micrometer-scale channel) values for background electrolyte (BGE) concentrations greater than approximately 10 mM. At BGE concentrations of 1 and 5 mM, mobility estimates in our nanochannels are higher than published values. Of the cases studied, the highest separation sensitivities were achieved in 100 nm channels with 1-10 mM ion density buffers. Potential applications of this technology include rapid small-scale sequencing and other fluorescence-based oligonucleotide separation and detection assays.     

The characterizations of rheological,electrokinetical and structural properties of ODTABr/MMT and HDTABr/MMT organoclays

In the present paper, we have investigated as a function of surfactant concentration the rheological (yield value, plastic viscosity) and electrokinetic (mobility, zeta potential) properties of montmorillonite (MMT) dispersions. The influence of surfactants (Octadeccyltrimethylammonium bromide, ODTABr and Hexadecyltrimethylammonium bromide, HDTABr) on dispersions of Na-activated bentonite was evaluated by rheological and electrokinetic measurements, and X-ray diffraction (XRD) studies. The interactions between clay minerals and surfactants in water-based Na-activated MMT dispersions (2 wt.%) were examined in detail using rheologic parameters, such as viscosity, yield point, apparent and plastic viscosity, hysteresis area, and electrokinetic parameters of mobility and zeta potentials, and XRD also analyses helped to determine swelling properties of d-spacings. MMT and organoclay dispersions showed Bingham Plastic flow behavior. The zeta potential measurements displayed that the surfactant molecules hold on the clay particle surfaces and the XRD analyses displayed that they get into the basal layers.     

Electrospray ionization high-resolution ion mobility spectrometry-mass spectrometry

A hybrid atmospheric pressure ion mobility spectrometer is described which exhibits resolving power approaching the diffusion limit for singly and multiply charged ions (over 200 for the most favorable case). Using an electrospray ionization source and a downstream quadrupole mass spectrometer with electron multiplier as detector, this ESI-IMS-MS instrument demonstrates the potential of IMS for rapid analytical separations with a resolving power similar to liquid chromatography. The first measurements of gas-phase mobility spectra of mass-identified multiply charged ions migrating at atmospheric pressure are reported. These spectra confirm that collision cross sections are strongly affected by charge state. Baseline separations of multiply charged states of cytochrome c and ubiquitin demonstrate the improved resolving power of this instrument compared with previous atmospheric pressure ion mobility spectrometers. The effects of electric potential, initial pulse duration, ion-molecule reactions, ion desolvation, Coulombic repulsion, electric field homogeneity, ion collection, and charge on the resolving power of this ion mobility spectrometer are discussed.     

Size-dependent electrophoretic migration and separation of liposomes by capillary zone electrophoresis in electrolyte solutions of various ionic strengths

The size-dependent electrophoretic migration and separation of liposomes was demonstrated and studied in capillary zone electrophoresis (CZE). The liposomes were extruded and nonextruded preparations consisting of phosphatidylcholine/phosphatidylglycerol/cholesterol in various ratios and ranging from 125 to 488 nm in mean diameter. When liposomes of identical surface charge density were subjected to CZE in Tris-HCl (pH 8) buffers of various ionic strengths (0.001-0.027), they migrated in order of their size. Size-dependent electrophoretic migration and separation of liposomes in CZE can be enhanced or brought about by decreasing the ionic strength of the buffer. It was shown that size-dependent migration is primarily a function of kappaR, where kappa(-1) is the thickness of the electric double layer (which can be derived from the ionic strength, I, of the buffer) and R, the liposome radius. Liposome mobility depends on kappaR and surface charge density in a manner consistent with that expected from the Overbeek-Booth electrokinetic theory. Thus, the relaxation effect appears to be the physical mechanism underlying the size-dependent electrophoretic separation of liposomes.     

Pressure pulse injection: a powerful alternative to electrokinetic sample loading in electrophoresis microchips

We present a new and simple capillary electrophoresis microsystem in which the sample is injected hydrodynamically using a pressure pulse. This technique maintains the sample composition, in contrast to a classical electrokinetic injection, in which the magnitude of the electric field in the sample reservoir in combination with variations in electrophoretic mobility can lead to a biased injection. The sample is loaded using a well controlled and variable pressure pulse (0.1-1.0 s) generated by the mechanical actuation of a flexible membrane placed on the chip sample reservoir. A fluorescein/calcein-containing borate-Tris-hydroxymethylaminoethane (TRIS) sample solution is taken as a model system for CE analysis. The separation results using pressure pulse injection clearly demonstrate the advantages of our technique. In addition to the reduced bias due to the absence of an electrode in the sample well, this method allows injection of variable plug volumes by simply changing the pulse length. Moreover, a very high speed, repeatability, and sensitivity of the separation is obtained.     

Effect of direct control of electroosmosis on peptide and protein separations in capillary electrophoresis.

The separations of peptide and protein mixtures in capillary zone electrophoresis (CZE) at various solution conditions were studied with the direct control of electroosmosis. The zeta potential at the aqueous/capillary interface and the resulted electroosmosis in the presence of an electric field were directly controlled by using an additional electric field applied from outside of the capillary. The controlled electroosmotic flow affected the migration time and zone resolution of peptide and protein mixtures. The changes in the magnitude and polarity of the zeta potential caused the various degrees of peptide and protein adsorption onto the capillary through the electrostatic interactions. The separation efficiencies of peptide and protein mixtures were enhanced due to the reduction in peptide and protein adsorption at the capillary wall. The direct manipulations of the separation efficiency and resolution of peptide and protein mixtures in CZE were demonstrated by simply controlling the zeta potential and the electroosmotic flow with the application of an external electric field.     

Fabrication of nanofluidic biochips with nanochannels for applications in DNA analysis

With the development of nanotechnology, great progress has been made in the fabrication of nanochannels. Nanofluidic biochips based on nanochannel structures allow biomolecule transport, bioseparation, and biodetection. The domain applications of nanofluidic biochips with nanochannels are DNA stretching and separation. In this Review, the general fabrication methods for nanochannel structures and their applications in DNA analysis are discussed. These representative fabrication approaches include conventional photolithography, interference lithography, electron-beam lithography, nanoimprint lithography and polymer nanochannels. Other nanofabrication methods used to fabricate unique nanochannels, including sub-10-nm nanochannels, single nanochannels, and vertical nanochannels, are also mentioned. These nanofabrication methods provide an effective way to form nanoscale channel structures for nanofluidics and biosensor devices for DNA separation, detection, and sensing. The broad applications of nanochannels and future perspectives are also discussed.     

Micellar electrokinetic capillary chromatography of acidic solutes: migration behavior and optimization strategies.

Micellar electrokinetic capillary chromatography (MECC) is suitable for the separation of mixtures of uncharged and charged solutes. In this paper, the migration behavior of acidic compounds in MECC is quantitatively described in terms of different models. These equations describe the relationships between the two migration parameters in MECC (retention factor and mobility) and the two important experimental parameters (pH and micelle concentration) that have a great influence on the migration behavior and selectivity. Interestingly, the mobility and retention factor of a given solute could behave differently with the variations in pH. This would raise a question of which parameter actually represents the migration behavior of a solute in MECC: retention factor (a chromatographic parameter) or mobility (an electrophoretic parameter). The consequences of micellar-mediated shifts of ionization constants on selectivity and optimization strategies in MECC are discussed. The mathematical models would allow the prediction of migration behavior of solutes based on a limited number of initial experiments. This would greatly facilitate the method development and optimization of separations of ionizable compounds by MECC and, in addition, important physical and chemical characteristics of solutes such as their apparent ionization constants in micellar media and their partition coefficients into micelles (over a wide range pH values) can be determined. The models were verified, as good agreements were observed between the predicted and the experimentally observed migration behavior. Based on the preliminary results, the pH and micelle concentration are likely to be interactive parameters in many situations. As a result, simultaneous optimization of these two parameters would be the most effective strategy to enhance the MECC separation of acidic solutes.     

Desalination of porous building materials by electrokinetics: an NMR study

This article presents the first non destructive measurements of salt ions transport through fired-clay brick during electrokinetic desalination using nuclear magnetic resonance technique. The effect of the strength of an applied electric field on the migration of salt ions is examined by varying the electrical potential gradients from 0.75–2 V cm^?1 across the specimens. The measurements show that for electrokinetic to exceed ion transport by diffusion a minimum level of applied voltage is necessary. Below this threshold salt transport by diffusion is dominant over electromigration. The effect of advection on the salt transport is studied by introducing a hydraulic gradient across the specimen. The results show that advection is a major transport process in the materials studied. To assess the relative magnitude of the various active transport processes during electrokinetic desalination, a scale analysis on the basis of dimensionless numbers is presented. The value of these numbers determines which transport mechanism will dominate the desalination process in a given sample length and time scale.     

Dielectric Response of a Charged Prolate Spheroid in an Electrolyte Solution

We derived the so-called standard set of electrokinetic equations in prolate spheroidal coordinates for all ionic strengths, zeta potentials, and applied electric field frequencies, with the assumption, however, that the particle’s electrophoretic mobility is small. We subsequently solved these equations using finite differences methods. We show that the dipolar coefficient of a prolate spheroid reduces to that of a sphere in the corresponding limit, but deviates strongly from it when the eccentricity of the spheroid is large, for the same particle volume. We also verified that a previously published analytical theory (Chassagne and Bedeaux, J. Colloid Interface Sci., 326:240, 2008) is in good agreement with the numerical results for a large range of zeta potentials, ionic strengths, and frequencies.     

Selective ion extraction: a separation method for microfluidic devices

A separation concept, selective ion extraction (SIE), is proposed on the basis of the combination of hydrodynamic and electrokinetic flow controls in microfluidic devices. Using a control system with multiple pressure and voltage sources, the hydrodynamic flow and electric field in any section of the microfluidic network can be set to desired values. Mixtures of compounds sent into a T-junction on a chip can be completely separated into different channels on the basis of their electrophoretic mobilities. A simple velocity balance model proved useful for predicting the voltage and pressure settings needed for separation. SIE provides a highly efficient separation with minimal additional dispersion. It is an ideal technique for high-throughput screening systems and demonstrates the power of lab-on-a-chip systems.     

Design and fabrication of nanofluidic devices by surface micromachining

Using surface micromachining technology, we fabricated nanofluidic devices with channels down to 10?nm deep, 200?nm wide and up to 8?cm long. We demonstrated that different materials, such as silicon nitride, polysilicon and silicon dioxide, combined with variations of the fabrication procedure, could be used to make channels both on silicon and glass substrates. Critical channel design parameters were also examined. With the channels as the basis, we integrated equivalent elements which are found on micro total analysis (μTAS) chips for electrokinetic separations. On-chip platinum electrodes enabled electrokinetic liquid actuation. Micro-moulded polydimethylsiloxane (PDMS) structures bonded to the devices served as liquid reservoirs for buffers and sample. Ionic conductance measurements showed Ohmic behaviour at ion concentrations above 10?mM, and surface charge governed ion transport below 5?mM. Low device to device conductance variation (1%) indicated excellent channel uniformity on the wafer level. As proof of concept, we demonstrated electrokinetic injections using an injection cross with volume below 50?attolitres (10(-18)?l).     

Investigation of electrophoretic exclusion method for the concentration and differentiation of proteins

This work presents a technique termed as "electrophoretic exclusion" that is capable of differentiation and concentration of proteins in bulk solution. In this method, a hydrodynamic flow is countered by the electrophoretic velocity to prevent a species from entering into a channel. The separation can be controlled by changing the flow rate or applied electric potential in order to exclude a certain species selectively while allowing others to pass through the capillary. The exclusion of various proteins is investigated using a flow-injection regime of the method. Concentration of myoglobin of up to 1200 times the background concentration in 60 s was demonstrated. Additionally, negatively charged myoglobin was separated from a solution containing negatively charged allophycocyanin. Cationic cytochrome c was also differentiated from a solution with allophycocyanin. The ability to differentially transport species in bulk solution enables parallel and serial separation modes not available with other separations schemes.     

Application of free-solution capillary electrophoresis to the analytical scale separation of proteins and peptides

The application of free solution capillary electrophoresis (FSCE) to the separation of protein and peptide mixtures is presented. Both qualitative and quantitative aspects of FSCE separations are considered. In addition, a brief introduction describing the separation principle behind FSCE separations and a discussion of electrophoretic mobility are included. The applications were chosen in order to highlight the selectivity of FSCE separations and to demonstrate applications of potential practical interest to the bioanalytical chemist. Comparison of FSCE relative to traditional analytical separation alternatives is stressed throughout. The examples are presented in three broad categories: protein separations, peptide separations, and the application of both to the analysis of recombinant protein products. In the first section, FSCE separations of peptide mixtures are presented which demonstrate the suitability of FSCE for the analysis of the purity of peptide samples, the homogeneity of peptide samples prior to sequencing, the identity of peptides by using electrophoretic mobility values, and the reduction of an intrachain disulfide bridge. In the second section, protein separations are presented that show the resolution of glycoproteins having the same primary structure and the separation of immune complexes from free unreacted antibody and antigen. In the final section, highly purified and well-characterized samples of biosynthetic human insulin (BHI), biosynthetic human growth hormone (hGH), and their derivatives were used to evaluate FSCE as a complement and/or alternative to conventional analytical separation techniques for the determination of purity and identity of biosynthetic human proteins. In addition, the quantitative aspects of FSCE analysis such as linearity of response, precision, and limit of detection were examined.     

Liposome behavior in capillary electrophoresis

The behavior of liposomes in capillary electrophoresis is studied for the purpose of developing a potential method for characterizing liposomes prepared for use in industrial and analytical applications. This study characterizes the electrophoretic behavior of liposomes under various conditions to provide information about electrophoretic mobility and liposome-capillary surface interactions. The results of this method are compared with the results obtained using traditional laser light-scattering methods to obtain size information about liposome preparations. Additionally, reactions of liposomes and the surfactant n-octyl-β-d-glucopyranoside are performed off-line in bulk solution experiments and on-line in the capillary. Automated delivery of lysis agents by multiple electrokinetic injections is demonstrated as a general method for inducing on-capillary reactions between liposomes and other reagents. Furthermore, some preliminary evidence on the use of liposomes as a hydrophobic partitioning medium for analytical separations is presented.