Deconvolution of electroosmotic flow in hysteresis ion transport through single asymmetric nanopipettes

Abstract

Unveiling the contributions of electroosmotic flow (EOF) in the electrokinetic transport through structurally-defined nanoscale pores and channels is challenging but fundamentally significant because of the broad relevance of charge transport in energy conversion, desalination and analyte mixing, micro and nano-fluidics, single entity analysis, capillary electrophoresis etc. This report establishes a universal method to diagnose and deconvolute EOF in the nanoscale transport processes through current-potential measurements and analysis without simulation. By solving Poisson, Nernst-Planck (PNP) with and without Navier-Stokes (NS) equations, the impacts of EOF on the time-dependent ion transport through asymmetric nanopores are unequivocally revealed. A sigmoidal shape in the I-V curves indicate the EOF impacts which further deviate from the well-known non-linear rectified transport features. Two conductance signatures, an absolute change in conductance and a 'normalized' one relative to ion migration, are proposed as EOF impact (factor). The EOF impacts can be directly elucidated from current-potential experimental results from the two analytical parameters without simulation. The EOF impact is found more significant in intermediate ionic strength, and potential and pore size dependent. The less-intuitive ionic strength and size dependence is explained by the combined effects of electrostatic screening and non-homogeneous charge distribution/transport at nanoscale interface. The time-dependent conductivity and optical imaging experiments using single nanopipettes validate the proposed method which is applicable to other channel type nanodevices and membranes. The generalizable approach eliminates the need of simulation/fitting of specific experiments and offers previously inaccessible insights into the nanoscale EOF impacts under various experimental conditions for the improvement of separation, energy conversions, high spatial and temporal control in single entity sensing/manipulation, and other related applications.

Scheme 1. (A) Experimental and simulation setup of transport through a single nanopipette with negative surface charges in solution. The directions are sketched corresponding to high conductivity state. A potential is applied on the working electrode (WE/green, bottom) with respect to the reference electrode (RE/black, top). When the bias is positive, the high conductivity state is established with facilitated transport of cations as the majority charge carrier. The light red arrow indicates the direction of migration; and orange arrow indicates the direction of EOF. (B) Impact of EOF on the conductivity measurements at different limiting dimension of the device, either the radius or the ionic strength effect described by the Debye length (λ). The three red i–V sketches represent diagnostic features of non-linear shape for ICR, sigmodal for EOF presence, and more linear ohmic behaviors.

Fig. 1. Simulated conductivity and differential conductance (G_diff) analysis. (A) Conductivity measurement by PNP (olive) and PNP–NS (magenta) of a 12 nm radius nanopore in 1 mM KCl. Dashed line indicate the position of the cross point (CP); arrows indicate the direction of the applied potential with solid arrows defining forward and dashed arrows backward scans. (B) Differential conductance (G_diff) analysis for forward scan in the PNP and PNP–NS model. k₁ and k₂ are the slopes before and after the deviation of G_diff (V_div) from the PNP and PNP–NS models.

Fig. 2. Simulated conductivity measurements from PNP (olive) and PNP–NS (magenta) with a 12 nm radius nanopore in (A) 1 mM; (B) 10 mM; (C) 100 mM. Differential conductance analysis at HC in (D) 1 mM (E) 10 mM (F) 100 Mm; and at LC (G) 1 mM (H) 10 mM (I) 100 mM.

Fig. 3. Simulated response from PNP–NS (top curves) and PNP (bottom curves) with a 12 nm radius nanopore for (A) EOF-IF and (B) EOF-I at 1 mM (red), 10 mM (magenta) and 100 mM (wine). Note the starting potential V_div varies with ionic strength.

Fig. 4. Simulated conductivity measurements from PNP (olive) and PNP–NS (magenta) with a 60 nm radius nanopore in (A) 1 mM; (B) 5 mM; (C) 10 mM. Differential conductance analysis in (D) 1 mM (E) 5 mM (F) 10 mM.

Fig. 5. Simulated response from PNP–NS (top curves) and PNP (bottom curves) with a 60 nm radius nanopore for (A) EOF-IF and (B) EOF-I at 1 mM (red), 5 mM (blue) and 10 mM (magenta).

Fig. 6. Experimental results from a 60 nm nanopore in 50 mM KCl (A–C) and a 200 nm nanopore in 1 mM KCl solution (D–F). The arrows in (B, E and F) suggest trajectories without EOF.

Fig. 7. Experimental I–V data (A) and corresponding analysis of G_diff (B), EOF IF (C) and EOF-I (D) from a large nanopipette (with ca. 60 nm radius) in different KCl concentrations. The black curves are generated by smoothing the scattered data points (EOF-IF and EOF-I) using a 20 point window. Some curves are multiplied by the listed arbitrary factors to fit in the same scale for direct visual comparison.

Fig. 8. Experimental I–V data (A) and corresponding analysis of G_diff (B), EOF IF (C) and EOF-I (D) from a small nanopipette (with ca. 10 nm radius) in different KCl concentrations. The black curves are generated by smoothing the scattered data points (EOF-IF and EOF-I) using a 20 point window. Some curves are multiplied by the listed arbitrary factors to fit in the same scale for direct visual comparison.

Fig. 9. Fluorescence imaging of EOF in a ca. 60 nm radius nanopipette in 50 mM KCl solution. The interior solution also contains 10 μM rhodamine B. (A) Representative frames (taken at time zero and 4s after +1 V was applied). (B) Comparison of the 0s and 4s intensity profiles along the centerline between the yellow crosses. The distance was demarcated by the dashed lines. The background, contrast and size of all time-lapse images are set consistent for direct comparison of grey scale intensity.