Introduction and Background
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 dimension, resulting in nonuniform velocity profiles. In such channels, both streamwise and transverse electromigration fluxes contribute to the separation and dispersion of analyte ions. Prior analytical studies have not addressed this coupling of electromigration fluxes for charged analytes migration in channels with finite double layers.
We have performed analytical, numerical, and experimental investigations of nanochannel electrophoretic transport and separation dynamics of neutral and charged analytes. Our study includes continuum-theory-based analytical and numerical studies of nanofluidic electrophoretic separation dynamics as well as experimental validation of these models. Our results suggest a method we term “Electrokinetic Separation by Ion Valence (EKSIV)” whereby both ion valence and bulk mobility may be determined independently from a comparison of micro- and nano-scale transport measurements.
Theory and Experiments
We study continuum-based transport for analytes in systems with finite, but not overlapping double layers. The models use microchannel-based zeta potential measurements as an independent quantification of the nanoscale model boundary condition for potential. We demonstrate that transverse electromigration is in quasi-equilibrium with transverse diffusion flux (Figure 1). The resulting quasi-steady transverse concentration distribution couples with the non-uniform velocity profile and this coupling determines net electrokinetic transport and dispersion.
|Figure 1. Numerical simulations of convective-diffusion dynamics in nanometer-scale electrokinetic channels for (a) a neutral species, and (b) a species with a +2 valence number in a 50 nm deep channel with negatively charged walls. In (b), opposing fluxes of electromigration and diffusion result in strong traverse concentration gradients, and coupling of this distribution with velocity gradients results in effective mobility values significantly different then bulk mobility.|
We experimentally investigate transport phenomena of both charged and uncharged analytes in custom-fabricated fused silica nanochannels using quantitative epifluorescence imaging and current monitoring techniques (Figure 2). In these experiments, we have varied applied electric field, channel depth, background buffer concentration, and species valence to impose variations on zeta potential, effective mobility, and normalized Debye length.
Figure 2. Scanning electron micrograph (SEM) (a) and atomic force microscopy (AFM) scan (b) of the inlet region of a 102 nm deep fluidic channel. The images show 1 mm diameter posts near the inlet of the nanochannel which serve as an integrated filtering structure. (c) Schematic of nanochannel device with 125 mm by 75 mm detection area centered 7 mm from the injection point. Etched tick marks aid in registration and quantitation.
Experimental results are in very good agreement with contniuum-based numerical transport simulations. These simulations use experimentally determined zeta potential values as a boundary condition for electric and velocity fields. We model species transport of analytes with valences z = 0, -1 and –2 and show that transverse electrophoretic migration and associated transverse concentration gradients play a critical role in the axial transport of a charged solute in electrokinetic nanochannels. The model and data demonstrate that the effective mobility governing electrophoretic transport of charged species in nanochannels depends not only on bulk electrolyte mobility values, but also on zeta potential, ion valence, and background electrolyte concentration. Our results suggest new techniques for increased separation resolution of ionic species. In particular, we present a method we term “Electrokinetic Separation by Ion Valence (EKSIV)” whereby both ion valence and bulk mobility may be determined independently from a comparison of micro- and nano-scale transport measurements.
Figure 3. Comparison of measured effective mobility in a nanochannel (normalized by bulk mobility measured in a microchannel) versus model predictions for both 40 nm and 100 nm channels. Normalized mobility is shown as a function of lD/h. Large symbols are measurement data, and smaller, symbols are corresponding error bars. Error bars reflect 95% confidence on the mean of approximately 20 realizations at each condition.
(Mouseover figure to begin movie)
Figure 4. Movie showing separation of 20 mM carboxyl flourescein and 40 mM bodipy in devices with two channel depths. Top channel is 1 mm wide by 2 mm deep filled with 10 mM sodium tetraborate buffer resulting in a bulk velocity of 25 mm/s. Bottom channel is 1 mm wide by 40 nm deep with 1.5 mM sodium tetraborate buffer resulting in a bulk velocity of 24 mm/s. Note that the distance between analytes is clearly not the same between the microchannel and nanochannel, and this is due to an increased effective electrophoretic mobility of the –1 and –2 charged species. This change in effective mobility is due to a coupling of transverse and streamwise electromigration fluxes.
Our results suggest new techniques for increased separation resolution of ionic species. We have proposed a method we term “Electrokinetic Separation by Ion Valence (EKSIV)” whereby both ion valence and bulk mobility may be determined independently from a comparison of micro- and nano-scale channel electrophoresis measurements. The dependence of effective nanochannel mobility on valence (and its deviation from bulk mobility) is summarized in the figure below for two valence values.
Figure 5.Apparent electrophoretic mobility ratio, /nS, as a function of lD/h with lD and z coupled by the relation . Numerical simulations are presented for 40, 80, 100, and 120 nm channels. Values of mobility for the parameter b are taken from the experimentally determined values of mobility for bodipy (zs = -1) and carboxyl flourescein (zs = -2).
- At low lD/h, EDL is thin and the velocity profile is uniform. At the low Peclet numbers of interest, the species concentration distribution is uniform in the transverse direction. Therefore, the coupling of the streamwise velocity and transverse concentration distribution results in bulk values for both velocity and mobility, so /nS = 1.
- /nS also approaches unity for high lD/h. In this limit, the sample analyte is distributed approximately uniformly over the channel cross-section and the analyte is simply advected at the area-averaged liquid velocity.
- At large b, streamwise electromigration velocities are large relative to electroosmotic velocities, resulting in /nS ratios close to unity.
- The strongest coupling between finite EDL effects and streamwise transport occurs for intermediate values of lD/h and low values of b (high values of EOF-to-electrophoretic mobility ratio). For an intermediate range of lD/h, there is a non-uniform velocity profile covering large portions of the channel cross section. In this regime, transverse electromigration plays a strong role in determining the streamwise velocities sampled by the analyte.
1. Probstein RF, 1994, Physicochemical Hydrodynamics: An Introduction, John Wiley, New York.
2. Bharadwaj R. and Santiago J.G., Electrophoresis, 2002, 23, 2729-2744.
3. Hunter RJ, 1981, Zeta Potential in Colloidal Science: Principles and Applications, Academic Press, London.
4. Pennathur, S. and Santiago, J.G., submitted to Analytical Chemistry, 2005.
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Finnegans Wake by James Jocye