Concentration-Gradient-Dependent Ion Current Rectification in

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Concentration-Gradient-Dependent Ion Current Rectification in Charged Conical Nanopores Liuxuan Cao,‡ Wei Guo,*,† Yugang Wang,‡ and Lei Jiang*,†,§ †

Beijing National Laboratory for Molecular Sciences (BNLMS) and Key Laboratory of Organic Solids, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, PR China ‡ State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, PR China § School of Chemistry and Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China S Supporting Information *

ABSTRACT: Ion current rectification (ICR) in negatively charged conical nanopores is shown to be controlled by the electrolyte concentration gradient depending on the direction of ion diffusion. The degree of ICR is enhanced with the increasing forward concentration difference. An unusual rectification inversion is observed when the concentration gradient is reversely applied. A numerical simulation based on the coupled Poisson and Nernst−Planck (PNP) equations is proposed to solve the ion distribution and ionic flux in the charged and structurally asymmetric nanofluidic channel with diffusive ion flow. Simulation results qualitatively describe the diffusion-induced ICR behavior in conical nanopores suggested by the experimental data. The concentration-gradient-dependent ICR enhancement and inversion is attributed to the cooperation and competition between geometry-induced asymmetric ion transport and the diffusive ion flow. The present study improves our understanding of the ICR in asymmetric nanofluidic channels associated with the ion concentration difference and provides insight into the rectifying biological ion channels.

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hetetojunction23−25 or smooth surface charge gradient26 can significantly enhance the degree of rectification to several hundreds. We have proposed that the extent of ICR can be also regulated by tuning the wettability of the surface-grafted polymer brushes.27 In living systems, the transmembrane ion concentration gradient is fundamental to the membrane potential. It regulates the function of the ion channels and ion pumps on the cell membrane that rectifies the ionic species inward and outward in the cell.28 Recently, Cheng and Guo reported that a difference in ionic concentration induces rectified ion transport in homogeneous silica nanochannels.29 Siwy et al. discovered an asymmetrical diffusive ion flux through the charged conical nanopores.30 However, to date, systematic studies on the ICR in a structurally asymmetric nanofluidic system with concentration-gradient-driven ion flow are still missing in the open literature. In this context, we present here the concentration-gradientdependent ion current rectification in negatively charged conical nanopores. We found that, in such surface charged

ynthetic nanopores and nanochannels that mimic the functions of voltage-gated biological ion channels show outstanding performance in controlling mass and charge transport on the nanoscale.1−3 One important feature inherent in such bioinspired nanofluidic systems is the ion current rectification (ICR), which is observed to be a nonlinear diodelike current−voltage response when switching the potential polarity.4 The strong asymmetric ion conduction indicates a preferential direction for ion flow in the synthetic nanofluidic channel that was initially discovered in biological systems. During the past decade, it has been generally proven, both experimentally and theoretically, that the prerequisites of ICR are the presence of a surface charge on the channel wall and the characteristic length scale of the channel being on the order of the Debye screening length.5−8 Until now, the ICR phenomenon has been identified in several nanofluidic systems with asymmetric characteristics,9−11 such as cone-shaped nanopores12,13 or nanopipettes14,15 and cylindrical nanochannels with an asymmetrical surface charge distribution.16,17 In addition, the ICR in charged nanopores is also found to be dependent on the pressure-driven electrolyte flow18 and the potential scan rate.19 By engineering the surface chemistry on the channel wall, the direction and extent of ionic rectification can be finely tuned.20 For example, reversing the surface charge polarity of a conical nanopore results in the reversal of the ICR direction.21,22 A distinct surface charge © 2011 American Chemical Society

Special Issue: BioinspiredAssemblies and Interfaces Received: September 30, 2011 Revised: December 7, 2011 Published: December 9, 2011 2194

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the nanopore wall, yielding a negative surface charge in the ionic solution. The nanopore used in this work was about 40− 50 nm on the tip side, 1.2 μm on the base side, and ∼12 μm in length. The ionic current was measured with a Keithley 6487 picoammeter/voltage source (Keithley Instruments). Platinum electrodes were used to apply a periodic potential, ranging from −1 to +1 V in 100 mV steps, and to measure the resulting transmembrane ionic current. The reference potential was settled on the tip side of the nanopore. During the measurement, one bath with a low electrolyte concentration (CL) is fixed at 1 mM and the bath on the other side of the membrane is filled with a high-concentration electrolyte (CH, from 1 to 1000 mM). There are offset currents (at zero voltage) associated with the concentration gradient and the nanopore ion selectivity (Supporting Information).31,32 Compared to the current measured at high electrical potential (e.g., at ±1 V), the offset current is small. As shown in Figure 2a, with a 10-fold concentration gradient forward (from tip to base) or reverse (from base to tip), the diffusive ion flow remarkably promotes the ionic current in the same direction while retaining the ionic current in the opposite direction unchanged. In this way, the degree of ICR can be either increased or decreased depending on the direction of ion diffusion (Figure S2 in the Supporting Information). The forward bias conductance (IF), reverse bias conductance (IR), and rectification factor (IF/IR) measured in KCl electrolyte are summarized in Figure 2b,c. In the absence of an ion concentration gradient (1 mM|1 mM), the single conical nanopore displays an evidently asymmetrical conductance with a rectification factor of 0.29 (IR is about 3.5 times higher than IF), similar to the case of classical ICR.9 Qualitatively different ICR phenomena are observed when the forward or reverse concentration gradient is applied. As shown in Figure 2b, the forward concentration gradient enhances the degree of ICR by remarkably increasing the negative current while maintaining the positive current at the same level. With the increase in the forward concentration gradient of up to 300-fold, the rectification factor increases monotonously from 0.29 to 0.023. When the electrolyte concentration on the tip side further increases to 1000 mM, a slight decrease in the rectification factor to 0.052 is observed. As shown in Figure 2c, when a reverse concentration gradient is applied, the positive current increases more rapidly than does the negative current, reducing the degree of ICR from 0.31 to 0.90 (with 30-

and structurally asymmetric nanofluidic systems, the direction and extent of ICR can be controlled by the ion concentration gradient, as illustrated in Figure 1. The forward concentration

Figure 1. Schematic illustration of the concentration-gradientdependent ion current rectification in negatively charged conical nanopores. (a) Under a reversely applied concentration gradient (from base to tip), an unusual rectification inversion is observed. (b) With a symmetrical ion concentration on the two sides of the membrane, the asymmetrical geometry induces a preferential direction for ion transport from the tip to the base, showing classical ICR behavior. (c) Under a forwardly applied concentration gradient (from tip to base), the degree of ICR can be enhanced. The geometry-induced preferential direction (thin arrow) and the diffusive ion flow driven by the concentration gradient (thick arrow) are marked in each panel.

gradient (from tip to base) enhances the ICR. When the concentration gradient is reversely applied, an unusual rectification inversion is observed. These concentrationgradient-dependent ICR properties are similarly found in three representative monovalent inorganic electrolytes: potassium chloride (KCl), lithium chloride (LiCl), and potassium fluoride (KF). A quantitative description is proposed to elucidate the underlying mechanism by numerically solving the coupled Poisson and Nernst−Planck (PNP) equations. In our experiment, single conical nanopores embedded in polyimide films (Kapton 50HN, DuPont) were prepared by an ion-track-etching technique.12 Asymmetrical chemical etching of the single-ion irradiated polymer foils led to the formation of a cone-shaped nanopore in the membrane. We refer here to the wide opening of the conical nanopore as the base side and the narrow opening as the tip side. The chemical etching of polymeric material generates carboxyl groups (−COOH) on

Figure 2. Concentration-gradient-dependent ICR enhancement and inversion in negatively charged conical nanopores. (a) Current−voltage curves measured in KCl electrolyte with or without a different concentration gradient. The experimental configurations are Cbase|Ctip= 1 mM|10 mM (red), 1 mM|1 mM (black), and 10 mM|1 mM (blue). The forward bias conductance (IF, red circle), reverse bias conductance (IR, blue circle), and rectification factor (IF/IR, gray column) were measured under (b) forward and (c) reverse concentration gradients in KCl solution. (b) The degree of ICR is enhanced by the forward concentration gradient. A rectification inversion is observed under the reverse concentration gradient (c). The conical nanopore used in this experiment is about 40−50 nm on the tip side, 1.2 μm on the base side, and ∼12 μm in length. 2195

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Figure 3. Rectification inversion in (a) lithium chloride and (b) potassium fluoride solutions. Similar rectification inversion is observed in both LiCl and KF solutions. The symbols used here are identical to those in Figure 2b,c. A surprisingly high inverse rectification factor of up to 140 is found in KF solution, which cannot be fully understood at the present stage. The rectification factors measured under a reverse concentration gradient are summarized in panel c for KCl (squares), LiCl (circles), and KF (triangles).

Figure 4. Total ion concentration profile along the pore axis (z axis) at different electrical potentials and under forward and reverse KCl concentration gradients. (a) Under a 1000-fold reverse concentration gradient, at +1 V, the diffusive flow facilitates the counterion migration into the nanopore, resulting in a high conducting state, whereas at −1 V, the diffusive flow prohibits the counterions from flowing into the nanopore, leading to a low conducting state, so that a rectification inversion is observed. (b) Without a concentration gradient, the ion depletion at +1 V and ion accumulation at −1 V due to geometrical asymmetry are apparent, resulting in classical ICR. (c) Under a 1000-fold forward concentration gradient, the diffusive ion flow dominates the ion distribution in the nanopore. The ion concentration profile in the nanopore at −1 V is always higher than that at +1 V and is responsible for the ICR.

ent ICR in charged conical nanopores. The interior ion concentration distribution and the ionic flux in response to the applied electrical potential are obtained by numerically solving the coupled Poisson and Nernst−Planck (PNP) equations (Supporting Information). A more accurate model to describe the ICR in nanofluidic channels should include both electrophoresis and electroosmosis.35 However, on the basis of our numerical calculations, we find that the calculated ionic current is several percent larger when taking electroosmosis into consideration. This result is in agreement with the previous work by Daiguji et al.36 When we take ion diffusion into consideration, osmosis becomes a more minor effect. That is because the electroosmotic flow becomes important only when the diameter of the nanopore is about the same size as the Debye length. In the presence of a concentration gradient, only a very short region near the low-concentration side can be shielded within the electrical double layer. We have also noted that Mayer et al. recently demonstrated the ICR generated by the electroosmotic flow through nanopores.37 However, their system is quite different from ours. In particular, the viscosity of their electrolyte (KCl in 75% DMSO and 25% H2O) is much higher than that of the commonly used aqueous solution, which is the critical point in generating ICR in their system. With pure water as the solvent, the electroosmotic flow plays a minor role. Therefore, it is reasonable to neglect electroosmosis here as a good approximation. Figure 4 shows the total ion concentration profile in KCl electrolyte along the pore axis (z axis) under forward and

fold concentration gradient). An unusual rectification inversion is observed with further increases in the electrolyte concentration on the base side. The rectification factor increases inversely from 1.14 to 2.16 (from a 100- to 1000fold concentration gradient). This previously unobserved rectification inversion cannot be found if the forward concentration gradient is applied. The concentration-gradient-dependent ICR in charged conical nanopores is also investigated in two other representative types of monovalent inorganic electrolytes: LiCl and KF. Similar ICR modulation and rectification inversion are observed with all of these 1:1 inorganic salts, as shown in Figure 3. One thing that should be noted is that in the rectification inversion in KF solution it is remarkably evident that the inverse rectification factor approaches 140 under a 1000-fold concentration gradient (Figure S3 in the Supporting Information). The origin of this effect is not fully understood. However, this phenomenon is reproducibly observed in all of the experimental measurements with KF solution. We speculate that a nonelectrostatic interaction brought about by the fluoride ions, such as the hydrophobic interactions, may play a role here.33,34 Another reason may arise from the pH of the KF electrolyte. As listed in Table S1, the pH value of the KF solution is about 1−1.5 points higher than that of KCl and LiCl solutions. Therefore, the distinctly high rectification ratio found in KF electrolyte can also be attributed to the elevated pH. Finite-element simulation was performed to elucidate the underlying mechanism of the concentration-gradient-depend2196

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Figure 5. Eliminating the geometry-induced ICR via a reversely applied concentration gradient. The total ion concentration profile along the pore axis (z axis) is calculated at +1 and −1 V. The tip concentration was fixed at 10 mM, and the base concentration is (a) 10, (b) 100, (c) 300, and (d) 1000 mM. With the increasing in the reverse concentration gradient, the total ion concentration profiles at −1 and +1 V approach identical values, indicating a gradually eliminated ICR.

Figure 6. Model calculation qualitatively predicts the trends in rectification inversion. (a) For KCl, LiCl, and KF, the degree of ICR initially decreases with the increasing reverse concentration gradient. Under the highest concentration gradient of 1000-fold, rectification inversion is observed, in agreement with the experimental results shown in Figure 3c. (b) This trend is also dependent on the nanopore tip diameter.

negative potential, the electromigration of counterions is in the same direction as the diffusive current. Thus, the ion concentration profile in the nanopore at −1 V is always higher than that at +1 V, which is responsible for the ICR. This effect shares the same physical basis with previously discovered concentration-gradient-induced rectified ion transport through cylindrical nanochannels.29 Because the diffusive ion current driven by the forward concentration gradient is parallel to the geometry-induced preferential ion transport direction, no rectification inversion is found in this configuration. In the presence of a 1000-fold reverse concentration gradient (Figure 4a), however, the diffusive current is opposite to the geometry-

reverse concentration gradients. The model conical nanopore is 12 μm long with a tip diameter of 45 nm, in accordance with that used in the experiment. The surface charge density is −60 mC m−2. In the absence of a concentration gradient (Figure 4b), the ion depletion at +1 V and ion accumulation at −1 V in the pore interior are apparently observed; these mirror the ionic conductance in response to the electrical potential and result in classical ICR because of geometrical asymmetry. Upon application of a 1000-fold forward concentration gradient (Figure 4c), the diffusive ion flow dominates the ion distribution in the nanopore, which brings in a considerable number of counterions from the high-concentration bath. At a 2197

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induced preferential direction. In this case, at positive potential, the diffusive flow facilitates counterion migration into the nanopore from a high-concentration bath, resulting in a high conducting state. At negative potentials, diffusive flow prohibits the counterions form flowing into the nanopore, leading to a low conducting state. Therefore, the rectification inversion is observed. Further calculation results prove that the geometry-induced ICR can be counteracted by the reversely applied concentration gradient. As depicted in Figure 5, the tip concentration was fixed at 10 mM, with the base concentration increasing from 10 to 1000 mM and the ion concentration distribution at negative and positive potentials gradually approaching equal values, indicating a nonrectifying state under a high concentration gradient. As shown in Figure 6a, the simulation results qualitatively predict the trends in the concentration-gradient-dependent ICR and rectification inversion in all three types of monovalent inorganic salts. Slight differences in the rectification factor among the three types of electrolyte are still found in both the experimental and theoretical results. As summarized in Table S5, in the KCl electrolyte the cations and anions bear nearly symmetric mobility in solution (D+ ≈ D−). In LiCl solution, the anions diffuse faster than the cations (D+ < D−), but in KF solution, the cations diffuse faster than the anions (D+ > D−). The differences in the rectification factor can be attributed to the inherent asymmetric ion mobility between the cations and anions. This suggestion is in agreement with our previous work that in negatively charged nanopores the diffusive ion flux can be enhanced if the counterion mobility is evidently higher than that of the co-ions, such as in KF.38 The physical model provided here concerns only the electrostatic interactions between the charged channel wall and the mobile ions in solution. It fails to quantitatively predict the surprisingly high ICR phenomenon in KF electrolyte, which verifies our speculation that other working principles may exist in such nanofluidic system. The concentration-gradient-dependent ICR is also influenced by the nanopore tip diameter (Figure 6b). The concentration gradient needed to fully counteract the geometry-induced ICR varies from 2.8 to 2.5 (log(CH/CL)) with the nanopore tip diameter changing from 30 to 100 nm. The modulation of ICR in a structurally asymmetric nanofluidic system originates from the cooperation and competition between the geometry-induced preferential direction for ion transport and the diffusive ion flow driven by the concentration gradient. It can be smoothly extended to, for example, positively charged nanofluidic channels. The ICR modulation mechanism proposed in this article may have implications in understanding the function of rectifying ion channels and ion pumps in response to the membrane potential associated with the transmembrane ion concentration difference.39 Both experimental and theoretical results suggest that the ion transport through the asymmetrical electrical double layer (EDL) in relation to the surface charge and the electrolyte concentration gradient is essential to the ICR and rectification inversion. However, it is worthwhile to mention that even at the lowest concentration in this work (1 mM) the local Debye length (∼10 nm) extends only a fraction of the length along the tip radius (less than 45%). Therefore, the requirement for the EDL overlap is not necessary to obtaining the ICR, in agreement with previous discoveries by Jacobson40 and White.18

We have noted that Siwy et al. have described similar experiments with electrolytes of different concentration placed on either side of the nanopore.41 The ICR inversion they described is caused by the reverse in the concentration gradient. This is different from the present work, in which we demonstrate that the geometry-induced ICR can be regulated by the concentration gradient. The forward concentration difference enhances the degree of ICR, and the reversely applied concentration gradient results in the ICR inversion. In addition, their interpretation with respect to the ICR inversion is available only if the electrolyte concentration on one side of the nanopore is extremely low (10−6 M) so that the total transmembrane current is carried separately by cations or anions from the high-concentration side. With a lower concentration difference (for example, 2- to 100-fold) across the nanopore, this interpretation is invalid because the ion migrations on both sides become comparable. In our present work, we provide a general description of the concentrationgradient-dependent ICR and its inversion. The contribution from the ion migration on either side can be accurately calculated with the theoretical model. The previous assumption is no longer necessary. In conclusion, we have reported a previously unobserved but fundamentally important ICR effect in charged asymmetrical nanofluidic system with ion diffusion. In particular, when the concentration gradient is reversely applied, an unusual rectification inversion is observed. Simulation results qualitatively describe the ICR behavior in the conical nanopores suggested by the experimental data and demonstrate the cooperation and competition between geometry-induced asymmetric ion transport and concentration-gradient driven ion flow. The present study improves our understanding of the ICR in asymmetric nanofluidic channels associated with the ion concentration difference. The diffusive and ion-rectifying nanofluidic systems have promising use in constructing highefficiency bioinspired energy-conversion devices.

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ASSOCIATED CONTENT S Supporting Information * The experimental setup. I−V curves measured in KCl, LiCl, and KF electrolytes under different concentration gradients. Details of the model calculation. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected], [email protected].

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ACKNOWLEDGMENTS We thank the Materials Research Group of GSI (Darmstadt, Germany) for providing the single-ion irradiated samples. This work was financially supported by the National Research Fund f o r Fun d am e n t a l Ke y P r o j e c t s ( 20 1 1C B9 35 7 00 , 2010CB832904, 2010CB934700, and 2009CB930404) and the National Natural Science Foundation of China (90923004, 91127025, 20920102036, 20974113, 21121001, and 21103201). The Chinese Academy of Sciences is gratefully acknowledged.

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