Schematic of the EDLs in a nanochannel (h ∼ 50 nm) with negatively charged surfaces for different ionic concentration regimes. (a) At high ionic concentration, the EDLs (solid curved line) are thin when compared with the height h of the channel. (b) At low ionic concentration, the EDLs of top and bottom walls are thicker than h, and the EDLs overlap strongly (solid curved line) and the nanochannel is filled with a unipolar solution of counterions. Dashed lines represent the charge distribution of each EDL considering that the opposite wall was not present.
Nanochannel ionic conductance G. (a) Equivalent electric circuit model used to describe G. G results from the sum of two components: EDLs conductance and bulk conductance. (b) Schematic behavior of G as a function of the electrolyte concentration. At high C, G is dominated by the bulk conductance (G increases with C and h) whereas at low C, G is dominated by the surface charge and saturates (assuming σ is approximately constant) at a value independent of C and h. The asymptotic limits of G (represented in solid lines) are extended to the regime where λD ∼ h (dashed and dotted line) to illustrate the enhancement of G at low C in a charged nanochannel (dashed line) relatively to a non-charged channel filled with an electrolyte solution keeping its bulk properties (dotted line).
Nanofluidic device. (a) Photograph of the complete nanofluidic device. (b) 3-D schematic of the nanofluidic device showing the configuration of the two microchannels and of the electric contacts. (b) Optical micrograph showing the array of nanochannels bridging the two microchannels used to convey the solutions to the nanochannels. Electrodes positioned at both nanochannels terminations allowed the electrical contact across the nanochannels. (c) SEM micrograph of a nanochannel entrance. (d) SEM micrograph showing a cross-sectional view of a nanochannel.
Nanofluidic device microfabrication. The microfabrication process presented has the following critical issues: the thickness and width of the Al sacrificial layer define the height and the width of the nanochannel, respectively; the RIE of the SiO2 layer defines the length of the channel; PDMS microchannels convey the liquid to the hydrophilic SiO2 nanochannel.
(a) Empty nanochannels array. (b) Direct injection of aqueous solution into the microchannels. Many nanochannels do not get filled by the aqueous solution. (c) EtOH immediately fills all nanochannels by capillarity.
Schematic side view of the microchannels linked by nanochannels, planar electrodes, with their corresponding electrical circuit elements. The equivalent electric circuit models the EDL at the electrodes by a constant phase element with impedance ZCPE; the nanochannels resistance by Rsol; the parasitic capacitance of the substrate by Cstray; and the capacitance associated to the solution by Csol. The AC voltage supply, represented by V, applied to the equivalent circuit, drives an AC current I.
Typical Nyquist plots obtained for the impedance of an array of nanochannels (n = 168; h = 30 nm; w = 10 μm; L = 40 μm) filled with different KCl concentrations, from which Rsol is determined (corresponding to the non-zero intersection point of the impedance curves with the horizontal axis): (a) for 1 M KCl solution, Rsol ≈ 30 kΩ; (b) for 0.1 M KCl solution, Rsol ≈ 300 kΩ; and (c) for 10−5 M KCl, solution Rsol ≈ 12 MkΩ.
Schematic of the interfacial structure of ssDNA immobilized, via electrostatic interactions, on an APDMES monolayer grafted to a glass or silica substrate.
Fluorescent micrographs of nanofluidic device for different steps of ssDNA immobilization protocol. (a) Bottom and top microchannels filled with ssDNA solution and PBS, respectively. SsDNA entered the nanochannels by diffusion. (b) After washing the microchannels with DI water, the ssDNA remained immobilized inside the nanochannels. The ssDNA molecules are labeled with the fluorophore FITC for fluorescence microscopy visualization.
Measured nanochannel conductance before and after surface modification as a function of KCl concentration. Full squares are the bare nanochannel array conductance. Full circles and triangles indicate the device conductance after APMES silanization and subsequent ssDNA immobilization, respectively. Solid line and open hexagons are different conductance models for a non-charged array of nanochannels. The difference between the curves is that the solid line assumes the ionic content of the KCl solutions to have only K+ and Cl− contributions, while the hexagons consider also the H+and HCO3 − ions, resultant from the CO2 dissolution in water. Dashed lines connecting the data points are given as guides to the eye.
Surface charge density σ vs. KCl concentration before and after the chemical surface modifications. Bare SiO2 nanochannels (full squares) are negatively charged due to ionized silanol groups. Full triangles either pointing up or down represent the possible nanochannels surface charge densities after APDMES functionalization. In this case, positive or negative surface charges are possible. ssDNA immobilization results in a negatively charged surface, which is more negatively charged than the original bare SiO2 surface. Dashed lines connecting the data points are given as guides to the eye. Data at 10−7M KCl represent the conductance in DI water. For higher KCl concentrations, the conductance is independent of surface charge since 2λD < h (given by Eq. (4) ).
Conductance of two nanofluidic devices with bare SiO2 nanochannels with different widths (10 μm and 30 μm). Circles represent the conductance data of a device consisting of 25 nanochannels (n = 25), each one with h = 40 nm, w = 30 μm, and L = 40 μm. Squares represent the conductance data of a device consisting of 25 nanochannels (n = 25), each one with h = 40 nm, w = 10 μm, and L = 40μm. The calculated bulk values are shown as solid lines. The upward shift of the conductance associated to the device with 30 μm wide nanochannels with respect to the conductance of the device with 10 μm wide nanochannels is predicted by Eqs. (4) and (6) .
Nanofluidic device (n = 25, h = 40 nm, w = 30 μm, and L = 40 μm) filled with 10−4M bulk KCl solutions of different pH. (a) Nyquist plot of the device for different bulk pH values. (b) Measured silica nanochannel conductance (open diamonds) when the pH inside nanochannels (pHnano) is modified. From the conductance values, the surface charge (open circles) could be calculated. The surface charge density data between pH 3.4 and 4.1 were taken from Table I . The solid line represents a fit to the silica nanochannels charge density data using Eq. (33) . Dashed and dashed-dotted lines connecting the data points are given as guides to the eye.
Calculated values of the surface charge density σ, and of the counterion concentration inside the nanochannels, before and after each chemical surface modification (leftmost column), for different electrolyte concentrations (top row).
Properties of the nanofluidic system for 10−4 M KCl solutions with different pH.
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