Analyte preconcentration in nanofluidic channels with nonuniform zeta potential

It is well known that charged analytes in the presence of nonuniform electric fields concentrate at locations where the relevant driving forces balance, and a wide range of ionic stacking and focusing methods are commonly employed to leverage these physical mechanisms in order to improve signal levels in biosensing applications. In particular, nanofluidic channels with spatially varying conductivity distributions have been shown to provide increased preconcentration of charged analytes due to the existence of a finite electric double layer (EDL), in which electrostatic attraction and repulsion from charged surfaces produce nonuniform transverse ion distributions. In this work, we use numerical simulations to show that one can achieve greater levels of sample accumulation by using field-effect control via wall-embedded electrodes to tailor the surface potential heterogeneity in a nanochannel with overlapped EDLs. In addition to previously demonstrated stacking and focusing mechanisms, we find that the coupling between two-dimensional ion distributions and the axial electric field under overlapped EDL conditions can generate an ion concentration polarization interface in the middle of the channel. Under an applied electric field, this interface can be used to concentrate sample ions between two stationary regions of different surface potential and charge density. Our numerical model uses the Poisson-Nernst-Planck system of equations coupled with the Stokes equation to demonstrate the phenomenon, and we discuss in detail the driving forces behind the predicted sample enhancement. The numerical velocity and salt concentration profiles exhibit good agreement with analytical results from a simplified one-dimensional area-averaged model for several limiting cases, and we show predicted amplification ratios of up to ${10}^5$.

Figure 1

Diagram of the described nanofluidic device with embedded electrodes in the top and bottom channel walls, showing example ion distributions in a channel with modified surface charge and potential (top center), as well as the EDL potential and velocity profiles near an embedded electrode (bottom right).

Figure 2

COMSOL mesh and boundary conditions for the 2D numerical model.

Figure 3

Diagram of the three possible enhancement mechanisms: stacking, focusing, and focusing at a midchannel CP interface. Curves depict sample concentration profiles, while arrows show the direction and relative magnitude of the net sample ion transport velocity in each region before steady state is reached.

Figure 4

(a) EDL potential near the midchannel CP interface along with the transient evolution of a 2D sample concentration profile in the channel, (b) the net electric field along the centerline near the midchannel CP interface, (c) the temporal sample profile along the channel center, and (d) the steady state sample concentration along the centerline for varying zeta potential ratio $\alpha ={\zeta }_2/{\zeta }_1$. The axial EDL potential gradient is visible in (a), and its effect on the sample transport is evident from the reversal of the net electric field in (b) as well as the CP-induced analyte focusing in (c) and (d). The zeta potential ratio and BGE concentration for these simulations of a 20 μm long, 100 nm tall channel were fixed at $\alpha =0.4$ and ${\mathrm{C}}_{\mathrm{KCl}}=0.01\mathrm{mM}$, respectively, unless otherwise specified.

Figure 5

Sample enhancement is shown in (a) for varying zeta potential ratios and EDL thicknesses for a fixed 50 nm channel height and 10 kV/m applied field and in (b) for varying zeta potential, sample charge, and applied field. The zeta potential in region 1 was fixed at −100 mV for these simulations, while the sample valence for (a) was fixed at $z=-2$. The corresponding KCl concentrations in (a) range from 50 mM to 1.5 μM. The inset plot in (b) shows maximum concentration enhancement for $\alpha =0$ as the applied electric field is increased to 40 kV/m.