Effect of Surface Charge on the Resistive Pulse Waveshape during

Jan 10, 2014 - associated with translocation of charged nanoparticles through a conical-shaped, charged glass nanopore. In contrast to single-peak res...
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Effect of Surface Charge on the Resistive Pulse Waveshape during Particle Translocation through Glass Nanopores Wen-Jie Lan,† Clemens Kubeil,‡ Jie-Wen Xiong,† Andreas Bund,‡ and Henry S. White*,† †

Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112, United States Electrochemistry and Electroplating Group, Technische Universitaet Ilmenau, 98693 Ilmenau, Germany

‡

S Supporting Information *

ABSTRACT: This paper describes a fundamental study of the effect of electrostatic interactions on the resistive pulse waveshape associated with translocation of charged nanoparticles through a conical-shaped, charged glass nanopore. In contrast to single-peak resistive pulses normally associated with resistive-pulse methods, biphasic pulses, in which the normal current decrease is preceded by a current increase, were observed in the current−time recordings when a high negative potential (lower than −0.4 V) is applied between the pore interior and the external solution. The biphasic pulse is a consequence of the offsetting effects of an increased ion conductivity induced by the surface charge of the translocating particle and the current decrease due to the volume exclusion of electrolyte solution by the particle. Finite-element simulations based on the coupled Poisson−Nernst−Planck equations and a particle trajectory calculation successfully capture the evolution of the waveshape from a single resistive pulse to a biphasic response as the applied voltage is varied. The simulation results demonstrate that the surface charges of the nanopore and the particle are responsible for the voltage-dependent shape evolution. Additionally, the use of high ionic strength solution or high pressures to drive particle translocation was found to eliminate the biphasic response. The former is due to the screening of the electrical double layer, while the latter results from the solution flow preventing formation of an equilibrium double layer ion distribution within the nanopore, similar to the previously reported elimination of ion current rectification when solution flows through a nanopore.

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INTRODUCTION Conical-shaped nanopores are widely employed in fundamental studies of mass transport in confined volumes, as well as in single-particle resistive pulse analyses, and as platforms for protein ion channel measurements.1−3 In this report, we demonstrate that conical nanopores exhibit unusual resistive pulse waveshapes when used to study the translocation of charged particles. We show that these waveshapes reflect electrostatic interactions between the moving particle and the nanopore surface. A unique characteristic associated with charged conical pores is ion current rectification (ICR), which describes the potentialdependent asymmetric current response in charged conical nanopores.4 In nanopores that exhibit ICR, the experimentally measured current flowing through the nanopore is found to be different at potentials with the same magnitude but opposite polarity.5−12 The nonohmic ICR response of conical nanopores originates from the surface charge that induces potential-dependent ion depletion and enrichment within the nanopore interior.13−16 Briefly, the nanometer-scale pore opening of a negatively charged nanopore is highly cation selective when immersed in a low ionic strength solution (e.g., potassium chloride, KCl). When a negative potential is applied inside the pore, the potassium ions (K+) translocate from the external bulk solution to the pore interior, while chloride ions (Cl−) are electrostati© 2014 American Chemical Society

cally rejected by the glass surface from translocating in the opposite direction. The anion rejection leads to an increase in ionic concentrations within the pore interior, resulting in an increase in nanopore conductivity. Conversely, when a positive potential is applied, the transport of Cl− from external to internal solution is again blocked by the surface charges, and thus, Cl− is depleted within the pore interior, resulting in a decrease in the nanopore conductivity. The accumulation and depletion of ions in the nanopore are reflected by corresponding higher and lower ionic currents at, respectively, negative and positive potentials. Recently, Sa and Baker reported experiments and theory demonstrating that ion current through a conical quartz nanopipette can be reversibly altered if the nanopipette is physically brought in close proximity to an electrically charged substrate.17,18 They demonstrated that when the distance between the pipet and the external surface charge is comparable to the thickness of the electrical double layer, the charge from the external surface can alter the distribution of current-carrying ions near the nanopore and, thus, influence the i−V response of the nanopore. Received: December 11, 2013 Revised: January 9, 2014 Published: January 10, 2014 2726

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Herein, we describe the dependence of the waveshape of particle-translocation current pulses on the surface charges carried by the particle and the nanopore. Our experiments employ single conical nanopores embedded in a thin glass membrane (50−100 μm).19−21 We conducted the experiments using a nanopore with a 215 nm radius orifice connecting two reservoirs of aqueous 0.01 M KCl, Figure 1, both maintained at

Figure 1. Schematic illustration of negatively charged polystyrene (PS) particles translocating through a glass nanopore (not drawn to scale) in a KCl solution. A voltage (V) and a pressure (ΔP = Papp − Patm) gradient are used to control the particle translocation and the corresponding resistive pulse shape.

pH 7.4 by 1 mM phosphate buffer. A negative pressure was applied to the internal solution to engender a flow from the external solution into the nanopore. A voltage was applied across the pore using two Ag/AgCl electrodes and the passages of the 160 nm radius −COOH charged polystyrene (PS) particles were continuously monitored. The signs of both pressure and potential are defined as the value inside the nanopore relative to the value in the external solution. Typically, the steady current flowing through a nanopore is briefly disturbed when a particle translocates through the pore, creating a decrease in the current, or a resistive pulse.22−24 In this article, we demonstrate, both experimentally and computationally, that the shape of i−t current pulses observed during particle translocation gradually changes from a single resistive peak to a biphasic pulse in which a current increase is followed by a current decrease, as the applied voltage across the nanopore is varied from positive to negative values. Finiteelement simulation based on the coupled Poisson−Nernst− Planck equations reveals the mechanism behind the shape evolution.

Figure 2. Current−time (i−t) recordings corresponding to the translocation of 160 nm radius, negatively charged PS particles through a 215 nm radius nanopore in a 0.01 M KCl solution while switching the applied voltage between (a) 0.4 V and (c) −0.4 V (the i−t traces for the two voltages are presented separately because of the large difference in baseline currents). A pressure of −4 mmHg was applied to drive the particles from the bulk solution into the nanopore. (b, d) Enlarged i−t recordings for single nanoparticle translocations in (a) and (c), respectively. The signs of applied voltage and pressure in this article refer to the values inside the pore relative to those in the external solution.

laboratory has previously shown that the pulse asymmetry is due to a convolution of the influences of the geometries of the conical nanopore and the spherical nanoparticle on the ion fluxes.25,26 At the negative applied voltage, however, biphasic pulse shapes were observed in the i−t recordings, as shown in Figure 2c. An expanded i−t trace for a single nanoparticle translocation, Figure 2d, shows that the ionic current through the nanopore initially experiences a slight increase (∼0.5%) and then rapidly decreases to a value that is ∼80 pA lower (∼1% decrease) than the baseline current, followed by a slow increase back to the baseline. The direction of particle translocation can be readily distinguished from the asymmetric pulse shape produced by conical pores, an advantage over cylindrical pores which generate symmetric square-wave pulses that are independent of translocation direction.27 The asymmetric pulse in Figure 2d shows that the negatively charged particles translocated from the external solution to the pore interior, opposite to the direction of electrophoresis, indicating the dominating driving force is pressure-driven or electroosmotic flow. The biphasic

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RESULTS AND DISCUSSION Biphasic Resistive Pulses for Particle Translocation through Conical Nanopores. Figure 2 shows typical i−t recordings for translocation of 160 nm radius charged PS particles under a −4 mmHg applied pressure while switching the voltage back and forth between −0.4 and 0.4 V. The 215 nm pore used in this experiment shows a slight current rectification, as indicated in Figure 2 by the different baseline currents at positive and negative voltages used to measure the i−t response (∼6.1 nA at +0.4 V vs ∼ −7.7 nA at −0.4 V). At the positive potential, the translocation of particles from external solution to the pore interior generates asymmetric triangular-shaped current pulses, Figure 2a,b, as anticipated in resistive-pulse analysis using a conical-shaped pore. Our 2727

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similarity in the trend of waveshape indicates that the nanopore undergoes the same conductivity change during particle translocation at negative potentials, regardless of the force driving the particle through the nanopore. In contrast, singlepeak pulses are always observed for particle translocations at positive potentials (Figures 2a and 3c,d). Surface Charge Effects on the Translocation Pulse Waveshape. An increase in nanopore current induced by DNA translocation has been previously reported by several groups and attributed to an increase in electrical conductivity of the pore resulting from the charge of DNA and its mobile counterions.28−31 Analogously, the translocation of soft hydrogel particles through a nanopore results in a current increase due to higher conductance of the hydrogel particles relative to the bulk solution.32,33 Likewise, we believe the introduction of excess ions to the pore interior by a translocating charged particle is responsible for the current increase observed in the biphasic pulses. Qualitatively, a translocating charged particle has two competing effects on the nanopore current. First, volume exclusion of electrolyte in the nanopore effectively hinders the transport of electrolyte ions (K+ and Cl−), thereby decreasing the current. This mechanical effect is voltageinsensitive.25 Second, the surface charge carried by the moving particle exerts an influence on the ionic distributions within the pore via electrostatic interactions. This surface charge effect is more pronounced as the particle is in close proximity to the pore orifice, since the electric field across the conical-shaped pore is highly confined at the orifice (i.e., sensing zone). Thus, a redistribution of ions at the pore orifice occurs during particle translocation. The particle-induced ion redistribution, however, is complicated by the electrical double layer associated with the charge on the nanopore surface and influenced by the applied voltage and ion concentrations of the contacting solutions. In the absence of a particle, ion depletion and accumulation inside the negatively charged pore occurs at positive and negative potentials, respectively, as expected for a pore that exhibits ICR (vide supra). Qualitatively, when a negatively charged particle enters the pore orifice from the bulk solution, the negative surface charge carried by the particle enhances the effect of ion depletion at positive potentials, further decreasing the nanopore conductivity and observed ionic current. Thus, a single resistive peak is always anticipated. In contrast, at negative potentials, the presence of the negatively charged particles enhances ion accumulation, thus, increasing pore conductivity and the current flowing through the pore. Similar to nanopores having high ICR ratios (defined as the ratio of the ion current at a negative potential to that at the same positive potential) at high voltages, the surface effect from the translocating particles is more pronounced at high negative potentials. As the effect becomes strong enough to override the volume-exclusion effect, an increase in the nanopore conductivity occurs, as reflected by a current increase in the i−t recording. As the particle travels further into the pore, the particle-induced ion accumulation becomes weaker at the orifice. The exclusion effect then dominates the current and generates a current decrease. Finally, the current slowly returns to the baseline as the particle leaves the sensing zone of the nanopore. Analogous to ICR, the effect of the particle surface charge is highly voltage-dependent. For instance, at lower voltages, the surface charge-induced ion accumulation is insignificant compared to the volume exclusion effect. Therefore, it is not surprising that the current pulses at −0.2 V only show a single

pulses observed during particle translocation represent a significant departure from the typical single-peak resistive pulses predicted by the physical blockage of the ion flux through the pore. Further studies suggest that the pulse shape depends on the magnitude of the applied potential, as well as the polarity. Figure 3a shows that particle translocation results in current

Figure 3. i−t recordings in a 0.01 M KCl solution corresponding to the translocation of 160 nm radius negatively charged particles through a 215 nm radius nanopore under negative (a, b) and positive (c, d) applied voltages at a pressure of −4 mmHg. Regions of the i−t trace where no data is shown correspond to periods where the applied voltage is stepped to a value different from the values shown on the plot.

pulses with a single peak at a less negative potential (−0.2 V). As the potential is increased to −0.3 V (Figure 3b), however, a small fraction of particle translocations lead to biphasic pulses, while the shape of other pulses remains unchanged. We consider Figure 3b as an intermediate state between the single pulses observed at −0.2 V (Figure 3a) and the more pronounced double pulses observed at −0.4 V (Figure 2c). The individual differences between pulse waveshapes observed at −0.3 V may reflect the difference in surface charges carried by particles, vide infra. A similar shape evolution of the current pulse for a different nanopore in the absence of an applied pressure is presented in Figures S1 and S2 of the Supporting Information. Although these latter particle translocations may be driven by the electroosmotic flow or particle diffusion, the 2728

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Figure 4. Simulated voltage-dependent distributions of electric conductivity (left column) and current-position (i−z) curves (right column) as a 160 nm radius nanoparticle translocates through a 215 nm radius nanopore in a 0.01 M KCl solution. z = 0 corresponds to the location of the pore orifice. Values of z > 0 μm correspond to the external solution, while values of z < 0 μm correspond to the nanopore interior. The surface charges at the pore wall and particle surface were set equal to −0.005 and −0.015 C/m2, respectively.

resistive peak. The above qualitative explanation is supported quantitatively by the finite-element simulation presented in the next two sections. Finite-Element Simulations: Description of the Model. Finite-element methods have been intensively used to simulate mass transfer in nanopores. Previous simulations of ICR conclusively demonstrate a potential-dependent ion depletion and accumulation inside the nanopore, arising from the surface charges on the pore walls and a finite amount of electrolyte ions in the solution.13 Herein, the finite-element method is used to solve the coupled Poisson−Nernst−Planck (PNP) partial differential equations that relate surface charge with the ionic fluxes and corresponding conductivity distribution within a conical-shaped nanopore, with the purpose of simulating the experimentally observed pulse evolution. The Nernst−Planck equation, eq 1, describes the fluxes of the ionic species. Ji = −Di∇ci −

ziF Dici∇Φ + ci u RT

∇2 Φ = −

F ε

∑ zici i

(2)

where ε is the dielectric constant of the solution. In employing the Nernst−Planck equation to compute the ionic current we simplified the model by ignoring the convective transport of the ions driven by the applied transmembrane pressure and electroosmosis. This treatment is appropriate for modeling transport behavior in nanopores at small applied pressures. We will show, in the following section, that the simplified PNP equations are able to capture the pulse characteristics observed in the experiments. Regardless, we are aware that quantitatively accurate prediction of nanopore current may require the simultaneous computation of the complete version of PNP and Navier−Stokes equations.13 We solved the equations in a 2D axial symmetric geometry (with appropriate boundary conditions, Figure S3) that mimics the 3D conical shape of the nanopore. The surface charge density on the pore wall was set to be −0.005 C/m2, assuming the glass surface charge has been partially covered by the neutral −CN or −C4H9 groups during silanization.18 To predict the surface effect on the pulse waveshape, we performed the finite-element simulation of ion fluxes as a function of the nanoparticle’s position within the nanopore. A 160 nm radius charged particle was introduced into the 2D nanopore geometry and then moved incrementally in Δzlength steps along the centerline axis of the pore, Figure S3, from a position in the external solution far away from the pore orifice (z = 10 μm) to a position deep inside the pore (z = −10 μm).

(1)

Ji, Di, ci, and zi are, respectively, the flux, diffusion constant, concentration, and charge of the species i. Φ and u are the local electric potential and fluid velocity, while F, R, and T are the Faraday’s constant, the gas constant, and the absolute temperature, respectively. Ji, ci, Φ, and u are position-dependent quantities. In eq 1, the three terms in the right-hand side represent the ion flux contributed from diffusion, migration, and convection. The relationship between the electric potential and ion concentrations is described by the Poisson equation, eq 2, 2729

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The simulation of the ion fluxes and current was performed at steady state, assuming that the electrolyte redistribution is much faster than the particle movement. The distance an ion diffuses is proportional to the square root of the diffusion coefficient D (∼ 2 × 10−9 m2/s). Assuming the ions diffuse across a distance equal to the pore orifice radius (δ = 215 nm) during the redistribution, we approximate the time duration needed for this diffusion using the Einstein relationship34,35 δ 2 = 2Dt

potential (−0.2 V) and a positive potential (0.4 V), in good agreement with the experiments. The surface charge effect is weaker at lower negative potentials, as indicated from the greatly reduced ionic conductivity (compare column ii in Figure 4a,c). The volume exclusion effect thus becomes the dominating effect again, resulting in a current decrease in Figure 4d. In contrast, at positive potentials (0.4 V), the presence of the charged particle enhances the ion depletion and decreases the electric conductivity around the pore’s mouth (Figure 4e), thus, creating a synergetic current decrease along with the volume exclusion effect, as shown in Figure 4f. Both our experiments and simulation suggest that the nanopore current during particle translocation is highly dependent on the direction and magnitude of the potential. Furthermore, the voltage-dependent simulation conducted over a broader voltage range (−0.1 to −1 V) shows a more substantial change in the shape of current pulses in comparison to the experiments. Figure 5 shows that, as the voltage becomes more negative, the shape of the simulated current pulse changes from an upward (decreasing) single peak at −0.1 and −0.3 V to

(3)

t is computed to be ∼10 μs, which is 2 orders of magnitude smaller than the particle translocation (∼2 ms, Figure 2d), justifying the assumption of a steady-state mode. Simulation of Biphasic Pulses and Shape Evolution in Nanopore Translocation. Figure 4a shows the simulated 2D distribution of the electric conductivity (κ, ohm−1·m−1) at a 215 nm radius pore orifice with a 160 nm radius nanoparticle located at different positions along the pore axis at an applied potential of −0.4 V. The conductivity was obtained by multiplying the ionic concentration by the ion mobility (assumed to be a constant for each ion and the Faraday's constant). When the particle is placed far away from the orifice, the electric conductivity around the nanopore is slightly higher than the value in the bulk solution (0.15 ohm−1·m−1), column i in Figure 4a, indicating a minor current rectification produced by the surface charge of nanopore, in accordance with previously published reports.13,36 As the particle is moved manually toward the pore orifice along the central axis (column ii), the electric conductivity at the pore orifice increases dramatically compared to column i. This increased electric conductivity, due to the enhanced ion accumulation induced by the negative surface charges carried by the particle, overrides the volume exclusion effect that decreases the current and results in a current increase in the corresponding currentposition (i−z) curve, Figure 4b. As the particle continues moving toward the pore interior (column iii in Figure 4a), despite an obvious ion enhancement between the position where the particle is situated and the pore interior, the electric conductivity at the pore orifice that dominates the overall nanopore conductance decreases, leading to a decrease in the i−z recording (Figure 4b, iii). When the particle moves further into the pore, both surface and the volume exclusion effects weaken significantly and the current gradually returns to the baseline (iv). As shown in Figure 4b, finite-element simulations successfully predict the “double-peak” resistive current pulse observed in the experiments. The conversion of simulated i−z curves to the experimentally recorded i−t curves requires knowing the particle velocity, which is complicated by the electrophoresis, electrostatic interaction between particle and nanopore, the pressure-driven flow, and the electroosmotic motion. Previous reports from our laboratory show that the conversion from i−z to i−t curves does not change the pulse shape.25,37 As a result, the simulated i−z curves appropriately reflect the experimental particle-mediated current fluctuation within a nanopore. The simulation supports our physical explanation in which the opposing effects of particle surface charge-enhanced ion accumulation and volume exclusion are combined to give rise to the biphasic current pulses. Figure 4c−f shows electric conductivity distributions and the resulting current−position (i−z) curves with varying potentials. Simulation results indicate that the particle translocation creates a current decrease in the baseline at both a lower negative

Figure 5. Simulated i−z traces corresponding to the translocation of a 160 nm radius nanoparticle through a 215 nm radius nanopore in a 0.01 M KCl solution at applied voltages of −0.1, −0.3, −0.5, and −1 V. 2730

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a biphasic pulse at −0.5 V and eventually to an almost downward (increasing) single peak at −1 V. Additional simulations that provide a more detailed shape evolution between −0.3 and −0.4 V, presented in Figure S4, indicate that the response from a single peak to a biphasic pulse occurs over a potential window smaller than 50 mV. Simulation of the Dependence of Waveshape on Surface Charge. Computational results suggest that the trend from a single decreasing peak to a biphasic peak can also be obtained by tuning the surface charge density on the particle. As shown in Figure 6a, for a 215 nm radius nanopore (with a

negative surface charge on the pore not only dictates the baseline current (increasing when the surface charge becomes more negative) at a voltage of −0.4 V, but also controls the shape of the translocation pulse. As the pore is more negatively charged, the “double-peak” characteristic becomes more evident. When the pore surface is positively charge, a single current decrease is observed due to the ion depleting effect associated with the positive charges. Moreover, the simulation also indicates that the surface charge on the moving particle has a negligible effect on larger nanopores (data not shown), similar to the previous observation of a weaker ICR in larger nanopores.6 Surface Charge Effect on the Percentage Pulse Height at Positive Potentials. We previously reported the simulation of the nanopore translocation pulses by solving the Nernst− Planck equation with electroneutrality, assuming no charge on the particle and nanopore.25 The electroneutrality simulations successfully captures the asymmetric triangular shape of the current pulses; however, they only take into account of the volume exclusion effect, thus resulting in a pulse height that is related to the ratio of particle radius over pore radius and independent of the applied positive voltages. Here, we demonstrate that a more advanced form of the Nernst−Planck equation (coupled PNP equations without electroneutrality) is required to predict the surface charge effect and the resulting percentage change in pulse height. We studied by both experiment and simulation, the change of the pulse height as a function of applied positive voltage. As shown in Figure 7a−f, the percent decrease in the experimental single-peak current pulse increases from less than 5% at 0.05 V to ∼7% at 0.6 V. The corresponding PNP simulations predict a similar qualitative trend, but with a more substantial voltagedependent change in percentage current decrease (∼10% at 0.05 V to ∼25% at 0.6 V). We attribute the increase in pulse height at positive voltages to the ion depletion effect associated with the negative charges at the pore orifice and introduced by the particle. The current flowing through the nanopore therefore decreases as the ions are depleted at positive potentials. Because the volume exclusion effect is not voltagedependent, the translocation current decreases more noticeably at higher positive potentials due to a stronger surface chargeinduced conductivity decrease. Elimination of Surface Effect by High Ionic Strength Solution and Pressure-Driven Flow. Having determined that surface charges on the particle and the nanopore influence the translocation pulse waveshape, we further explored this dependence by varying the ionic strength and pressure-driven flow,36 two variables that affect the ion distribution inside the nanopore orifice. Particle translocation experiments were carried out at a higher electrolyte concentration (0.1 M KCl vs. 0.01 M in the previously described experiments) in order to screen the electrical double layers associated with the charged pore and charged particles (the Debye length, κ−1, is ∼1 nm in the 0.1 M KCl solution). Under the high ionic strength condition and at −0.4 V, the resulting i−t recording of translocation events yielded only normal resistive peaks, as shown in Figures 8a,b and S5 for two different types of negatively charged particles (−COOH modified 160 nm radius and nonfunctionalized 120 nm radius PS particles). These results are in contrast to the biphasic events observed at 0.01 M KCl solutions at −0.4 V and indicate that volume exclusion governs the shape of the i−t pulse at higher electrolyte concentrations. In simulations performed assuming a 0.1 M

Figure 6. Simulated surface charge-dependent i−z traces corresponding to the translocation of a 160 nm radius nanoparticle through a 215 nm radius nanopore at a negative applied voltage of −0.4 V. (a) Surface charge at the particle was varied between 0.01 and −0.025 C/ m2, while the surface charge at the pore wall was fixed at −0.005 C/m2. (b) Surface charge at the pore wall was varied between 0.005 and −0.015 C/m2, while the surface charge at the particle was maintained at −0.015 C/m2. A 0.01 M KCl solution was assumed in the simulation.

surface charge density of −0.005 C/m2) at a constant potential of −0.4 V, the change in the particle surface charge from 0.01 to −0.025 C/m2 results in a continuous evolution of the waveshape from a single resistive pulse to a biphasic pulse shape. The simulation demonstrates that the particle-mediated nanopore conductivity can be effectively manipulated by the particle surface charge. As the surface of the particle becomes more negatively charged, the ion accumulation becomes more prominent and the current increase is more noticeable. On the other hand, a positively charged or a neutral particle creates a single pulse with a higher percentage current decrease. Previous reports demonstrate that the pore surface charge plays an important role in producing ICR.13,14 In the simulation of particle-mediated nanopore conductivity, Figure 6b, the 2731

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Figure 7. Normalized i−t recordings of a 200 nm radius nanopore in a 0.01 M KCl solution in the presence of negatively charged 160 nm radius PS particles at different applied voltages: (a) 0.05, (b) 0.1, (c) 0.2, (d) 0.3, (e) 0.4, and (f) 0.6 V. The particles were placed in the external solution only. No pressure was applied across the nanopore. The percentage pulse height increases with increasing positive voltage. (g) Simulated normalized i−z traces as a function of the applied voltage. The surface charges at the pore wall and particle surface were set equal to −0.005 and −0.015 C/m2, respectively. The simulation result is in qualitative agreement with the experimental data shown in a−f.

Figure 8. (a, b) i−t recordings of negatively charged 160 nm radius particles translocating through a 215 nm radius nanopore at −0.4 V and −10 mmHg in a 0.1 M KCl solution. (c, d) Corresponding simulated 2D conductivity distribution and i−z curves as the particle enters the pore.

KCl concentration, we observed a greatly reduced ion accumulation effect in Figure 8c, resulting in a single resistive pulse event signature (Figure 8d) that is in agreement with the experiment. The elimination of biphasic pulses can also be realized by applying a higher pressure gradient across the nanopore. As previously reported, the increasing pressure-engendered flow, which is proportional to the applied pressure,37 disrupts the equilibrium ion distributions within the nanopore.36 Analogously, high flow rates remove the ion build-up within the pore interior responsible for the biphasic pulses, resulting in a singlepeak resistive pulse, Figure 9. This experimental observation, however, is complicated by two factors. First, particle velocity increases with an increase of pressure-driven flow, and the instrumental low-pass filtering influences the waveshape.37 A consequence of this filtering effect is a decrease in the current pulse magnitude with increasing pressure. Second, in the simulations described above, the ion redistribution is assumed to occur rapidly relative to the motion of the particle. As the particle velocity increases proportionally with the increasing

pressure, the ion redistribution might become slow relative to the velocity of particle translocation,38 in which case a steadystate assumption is no longer valid and the conductivity increase may not occur. Accurate interpretation or simulation of this complex observation is beyond the scope of this present work and still requires further investigation.

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CONCLUSIONS In summary, we demonstrate that surface charges on the nanoparticle and nanopore play an important role in determining the shape of resistive pulses generated by the translocation of particle through a glass nanopore. As the potential applied across the nanopore membrane scans more negative, we observe a shape evolution from a conventional resistive pulse to a biphasic shape that contains a small but significant current increase prior to a steep decrease in current. Finite-element continuum modeling reveals that the current 2732

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prepared using water (18 MΩ·cm) from a Barnstead E-pure water purification system. Acetonitrile (HPLC grade, J. T. Baker) was stored over 3 Å molecular sieves. −COOH functionalized (160 nm radius, PC02N Lot 9172) and nonfunctionalized (120 nm radius, PS02N Lot 5708) polystyrene particles (Bangs Laboratories, Fishers, IN) were dispersed in the KCl solutions as received. Glass Nanopore Membranes (GNMs) Fabrication and Surface Modification. GNMs were fabricated according to a previous report from our lab.19 The GNM was silanized with Cl(Me)2Si(CH2)3CN or Cl(Me)2Si(CH2)3CH3 on the exterior and interior glass surfaces. The radii of the small orifices of the nanopores were determined from the ionic resistance (R) of the pores in a 1.0 M KCl solution. The ionic current was measured as a function of the voltage scanned between internal and external Ag/AgCl electrodes. The radius (ri) was calculated from the slope of the i−V curve using the expression ri = 18.5/ R.39 The orifice radii of the nanopores used in this study is ∼200 nm, with a relative uncertainty of ∼10%. Cell Configuration and Data Acquisition. A Dagan Cornerstone Chem-Clamp potentiostat was interfaced to a computer through a PCI 6251 data acquisition board (National Instruments). Current−time (i−t) data were recorded by inhouse virtual instrumentation written in LabVIEW (National Instruments) and recorded at a sampling frequency of 100 kHz. A 3-pole Bessel low-pass filter was applied at a cutoff frequency of 10 kHz. The GNM was filled and immersed in KCl solutions (pH 7.4) and polystyrene nanoparticles were homogeneously dispersed into the external solution. A potential difference was applied across the nanopore using Ag/AgCl electrodes placed directly in contact with the internal and external solutions. The pressure was applied using a 10 mL gastight syringe and was measured by a pressure gauge (Traceable Pressure Meter, Fisher Scientific, model 06−662−69). Computational Analysis and Finite-Element Simulations. The i−t recordings were plotted with Igor Pro software 6.0.2.4 (WaveMetrics, Lake Oswego, U.S.A.). The finiteelement simulations were carried out with COMSOL Multiphysics 3.5a (COMSOL Inc.) on a high-performance desktop computer (16 GB RAM). In the simulations, the opening radius, length of the nanopore, and the half-cone angle of the conical-shaped pore were set to be 215 nm, 20 μm, and 10°, respectively, corresponding to the estimated nanopore geometry used in the experiments. The surface charges on the nanoparticle and the pore walls were varied, respectively, from −0.025 to +0.01 C/m2 and from −0.015 to +0.005 C/m2 in order to investigate the effect of surface charge on the ionic current through the nanopore. The ionic current (A or C·s−1) through the nanopore is computed by integrating the total ion fluxes (mol·m−2·s−1) toward the two semi-infinite boundaries in the z direction (with area in the unit of m2) and multiplying the integrated fluxes (mol·s−1) by Faraday’s constant (C·mol−1). The relative error of the calculated ionic current between the two electrodes is typically smaller than 0.1%. Details of the finite-element simulation model are provided in the Supporting Information.

Figure 9. Pressure-dependent i−t recordings of 160 nm radius negatively charged particles translocating through a 215 nm radius nanopore under a −0.4 V applied voltage in a 0.01 M KCl solution.

increase is due to the particle-enhanced ion accumulation that overrides the electrolyte volume-exclusion effect as the particle enters the pore. At positive potentials, on the contrary, the ion depletion effect associated with the negative charges on the particle facilitates the current decrease produced by the volume exclusion, thus, resulting in a higher percentage pulse height. The findings of “double-peak” current pulses and increasing pulse height generated by particle translocation suggest that the nanopore current can be manipulated in both directions. We and others have previously demonstrated that surface chargeinduced ICR is highly related to the ionic strength of the bulk solution and the applied transmembrane pressure.4,6,13,36 Analogously, the surface charge effect on nanoparticle translocation can be eliminated by the increase of electrolyte concentration or pressure-driven flow. We anticipate that the results presented above will enable a better understanding of the fundamental aspects of surface charge effect on particle transport in a confined nanopore or a nanochannel. Furthermore, as the pulse shape is very sensitive to the surface charges on the nanoparticle and nanopore, our findings may also have potential applications in measuring the surface charge of individual particles or nanopores via comparing experimentally measured parameters of translocation pulse with computational predictions.

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EXPERIMENTAL SECTION Chemicals. KCl, K2HPO4, KH2PO4 (Mallinckrodt), 3cyanopropyldimethylchlorosilane (Cl(Me)2Si(CH2)3CN), and n-butyldimethylchlorosilane (Cl(Me)2Si(CH2)3CH3; Gelest Inc.) were used as received. All aqueous solutions were

ASSOCIATED CONTENT

S Supporting Information *

Additional i−t recordings for particles translocating through a nanopore, the description of the finite-element simulation model, and voltage-dependent simulation of current pulses. 2733

dx.doi.org/10.1021/jp412148s | J. Phys. Chem. C 2014, 118, 2726−2734

The Journal of Physical Chemistry C

Article

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge financial support from the National Science Foundation (CHE-0616505). REFERENCES

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dx.doi.org/10.1021/jp412148s | J. Phys. Chem. C 2014, 118, 2726−2734