An Alternating Current Electroosmotic Pump Based on Conical

An Alternating Current Electroosmotic Pump Based on Conical Nanopore Membranes Xiaojian Wu, Pradeep Ramiah Rajasekaran, and Charles R. Martin* Department of Chemistry, University of Florida, Gainesville, Florida 32611-7200, United States S Supporting Information *

ABSTRACT: Electroosmotic flow (EOF) is used to pump solutions through microfluidic devices and capillary electrophoresis columns. We describe here an EOF pump based on membrane EOF rectification, an electrokinetic phenomenon we recently described. EOF rectification requires membranes with asymmetrically shaped pores, and conical pores in a polymeric membrane were used here. We show here that solution flow through the membrane can be achieved by applying a symmetrical sinusoidal voltage waveform across the membrane. This is possible because the alternating current (AC) carried by ions through the pore is rectified, and we previously showed that rectified currents yield EOF rectification. We have investigated the effect of both the magnitude and frequency of the voltage waveform on flow rate through the membrane, and we have measured the maximum operating pressure. Finally, we show that operating in AC mode offers potential advantages relative to conventional DCmode EOF pumps. KEYWORDS: electroosmotic flow rectification, ion-current rectification, AC electroosmotic pump, nanofluidic diode, conical nanopore, high pressure

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anoionics deals with ion transport in spatially confined solutions where the charge and chemistry of the surface affect the properties of the solution.1−5 Nanopores with charged pore walls offer a convenient way to study nanoionic phenomena,1,4,6 as do glass pipettes with tip openings less than ∼70 nm.7−9 Studies with conically shaped pipettes, and correspondingly conical pores in thin membranes, have shown that these devices can act as diodes for ionic currents passing through the device.1,4,9−11 Ion-current is rectified because, in analogy to a solid-state diode, the ionic conductivity in the solution-filled tip changes with the direction of current passing through the tip.9,12 We have shown that ion-current rectification leads to another rectification phenomenon: electroosmotic flow rectification.13,14 Electroosmotic flow (EOF) is of considerable practical interest because it is used to pump solutions through microfluidic devices15−17 and capillary electrophoresis columns.18 EOF rectification means that, at constant driving force, the flow rate in one direction through the membrane is higher than the rate in the opposite direction. Conical pores, like those studied here (Figure 1), have a larger diameter base opening at one face and a smaller diameter tip opening at the other. EOF is rectified such that the flow rate in the direction base-to-tip is higher than in the direction tip-to-base.13,14 EOF rectification has more recently been observed in a conical glass nanopipet,19 and theoretical analysis of this phenomenon have also appeared.20,21 © 2016 American Chemical Society

Figure 1. (A) Schematic illustration of a PET membrane with conically shaped pores. Dimensions are not to scale. Scanning electron micrographs of (B) the base opening of a pore in a PET membrane and (C) a gold replica of a conical PET pore.

Typically, EOF is driven through a device in direct current (DC) mode by applying a constant voltage between electrodes in solutions in contact with either end of the device. However, we recently suggested that because of EOF rectification, net Received: February 5, 2016 Accepted: April 5, 2016 Published: April 5, 2016 4637

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ACS Nano flow base-to-tip (Figure 1) should be observed in alternating current (AC) mode where a symmetrical sinusoidal voltage waveform is applied across the membrane.14 This is because in one voltage half cycle a high flow rate in the direction base-totip would be observed, whereas the opposite half cycle would yield a lower flow rate tip-to-base, hence, net flow base-to-tip.14 For reasons to be discussed below there is considerable practical interest in developing such AC EOF pumps.22−25 We have found that net flow through a conical-pore polyethylene terephthalate (PET) membrane in the direction base-to-tip can be achieved by operating in AC mode. The effects of magnitude and frequency of the voltage waveform on flow rate were investigated. A maximum flow of 5 μL min−1 was achieved with a root-mean-square voltage23 of 3.5 Vrms at a frequency of 20 Hz. In addition, we have found that this nanoionic pumping device can generate pressures as high as 200 kPa, which is more than 2 orders of magnitude higher than an alternative AC EOF pump.23 Finally, we have shown that AC operation suppresses the water electrolysis reactions that accompany DC mode. Suppressing water electrolysis is important because it can yield gas bubbles that can block solution transport and unwanted pH changes.16,26−28 We report the results of these investigations here.

Figure 2. Schematic cutaway of the electroosmotic flow cell. The PET membrane was sealed between the chambers using O-rings. A dye solution plug was placed in the inlet tube, separated from the buffer solution front by a small air gap. The dye was used to visualize fluid flow.

in contact with the tip is like an electronic diode made from a semiconductor p−n junction.37 In both cases, voltage of one polarity applied across the device results in accumulation of charge carriers at the junction yielding a high conductivity state. Voltage of the opposite polarity results in depletion of charge carries at the junction, yielding a low conductivity state. For the conical nanopores used here, the charge carriers are ions of the electrolyte filling and bathing the pore. Voltages of one polarity cause ions to accumulate in the tip region within the pore, giving the high ionic conductivity state. The opposite polarity causes ion depletion and the low conductivity state. Yan et al. have recently presented detailed simulations of the enrichment and depletion regions within a conical nanopore.35,36 Enrichment and depletion can be demonstrated by measuring a current−voltage (I−V) curve associated with ion transport through the nanopore.1,4 Such I−V curves are nonlinear (Figure 3A).10,11 The lower slope observed at positive voltages results from ion depletion; accumulation occurs at negative voltages. The solution conductivity in the pore can be calculated by dividing the current at any point along the I−V curve by the voltage at that point.9 As expected, the conductivity is higher at negative voltages than at positive ones (Figure 3B). Note that the conductance changes in a narrow potential window around 0 V, and is constant at large negative and positive voltages. We will discuss this point further (vide inf ra). This voltage-dependent change in ionic conductivity also causes EOF rectification.13,14 The low conductivity state (positive voltages in Figure 3A,B) is the high electroosmoticflow-rate state, and this corresponds to flow in the direction base-to-tip. The reasons for this have been discussed in detail.13,14,21,38 The objective of these studies was to show that accumulation and depletion also occur when a sinusoidal voltage waveform is applied across the membrane and that this yields net flow base-to-tip. AC Ion Current Rectification. To observe net flow with a sinusoidal voltage, the resulting AC ion-current must be rectified. This is demonstrated in Figure 4, which shows a typical applied voltage waveform (Figure 4A) and the resulting AC ion current (Figure 4B). In analogy to the I−V curves in Figure 3A, lower currents are observed in the positive halfcycles than in the negative half cycles.

RESULTS AND DISCUSSION Membranes Studied. The track-etch method used to prepare the conical-pore PET membranes has been described previously.10,29,30 The membranes used were 12 μm thick and contained 107 pores/cm2. The diameter of the base, 420 ± 30 nm, was determined from electron micrographs like that shown in Figure 1B. The diameter of the tip, 22 ± 2 nm, was determined using an electrochemical method.29,30 The shape of the pore can be imaged by depositing gold within the pore, dissolving the membrane, and collecting the gold replicas by filtration (Figure 1C).31,32 The length of the gold replica is 12 μm, which is equivalent to the membrane thickness. A cone angle of 1.8° was determined from an expanded version of Figure 1C using ImageJ software. A value of 1.9° was calculated from the measured tip diameter, base diameter, and pore length.33 A control membrane containing cylindrical pores with constant diameter of 410 ± 40 nm through the membrane thickness was also prepared.30,34 Flow Rate Measurements. The flow cell (Figure 2) sandwiched the PET membrane between inlet and outlet chambers with the base side (Figure 1) facing the inlet chamber. A glass capillary tube sealed to each chamber allowed for solution flow through the cell. EOF was driven by using a function generator to apply a sinusoidal voltage waveform between Pt electrodes placed on either side of the membrane (Figure 2). EOF was manifested by movement of the solution in the inlet tube toward the inlet chamber (Figure 2). This was visualized by adding a dye-solution plug, separated from the buffer solution front by an air gap of ∼6 mm. The position of the dye plug was measured using a scale attached to the inlet tube. This was accomplished by periodically imaging the position of the dye plug on the scale. The volume of fluid pumped was calculated from the displacement of the plug and the tube inner diameter. A short video of the fluid movement process is available in the Supporting Information.30 EOF and Ion-Current Rectification. The theories of EOF9,13,14,20,21 and ion-current9,12,35,36 rectification have been discussed previously. In short, as noted above, the ionic junction between the electrolyte-filled pore tip and the solution 4638

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the charge passed during a half-cycle by the duration of that half-cycle. AC ion-current rectification ratios were measured in this way for different voltages in the range from 0.7 to 3.5 Vrms at a frequency of 20 Hz; rac was found to be independent of voltage with an average value of 2.25 ± 0.06 (Figure S3). That rac is independent of voltage suggests that the extents of ion accumulation and depletion are independent of voltage over this range. This is supported by the membrane conductance data in Figure 3B, where, for both positive and negative voltages in this range, conductance is independent of voltage. Voltage Dependence of Flow Rate. That net flow baseto-tip occurs with a sinusoidal voltage waveform can be verified by watching the displacement of the dye plug (Figure 2) as the wave is repetitively applied across the membrane.30 By measuring this displacement as a function of time, we can calculate the volume of solution pumped at that time. Figure 5A

Figure 3. (A) Current−voltage curve associated with ion transport through the conical nanopore membrane. (B) Ionic conductance vs applied voltage for the membrane in panel A.

Figure 5. (A) Volume pumped vs time at the indicated values of Vrms, frequency of 20 Hz. (B) Volumetric flow rate vs Vrms.

Figure 4. (A) Applied sinusoidal voltage waveform with magnitude of 2.8 Vrms and frequency of 20 Hz. (B) Resulting ion current.

shows the effect of amplitude of the sinusoidal voltage, Vrms, on the volume pumped. At each Vrms, the volume pumped increased linearly with time indicating a constant flow rate through the membrane. No flow was observed with a membrane containing cylindrical pores, and no flow was observed in the absence of the applied waveform. The volumetric flow rate, QEOF, at any Vrms can be obtained from the slopes of the lines in Figure 5A. QEOF, again base-totip, was found to increase linearly (R2 = 0.992) with Vrms (Figure 5B). This is because the voltage drop across the membrane increases with Vrms, and EOF velocity increases with voltage drop or electric field strength.38 For reasons to be

With I−V curves (Figure 3A), the extent of ion-current rectification can be quantified by the rectification ratio, ric, which is the current at any value of negative applied voltage divided by the current at the same value of positive voltage.9,13 The rectification ratio is important because we have shown that the extent of EOF rectification increases with increasing ric.13 We define here the corresponding AC rectification ratio, rac, as the average current during a negative half-cycle divided by the average current during the corresponding positive half-cycle (Figure 4B). The average currents were calculated by dividing 4639

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operation offers important advantages relative to power consumption and suppression of unwanted redox reactions at the electrodes.16,42 In DC mode, the current is carried through the electrode/solution interfaces by driving redox reactions at the electrode surfaces. When water is the solvent, the cathode reaction is water reduction to yield hydrogen gas and hydroxide (eq 1)

discussed below, the maximum voltage used in these studies was Vrms = 3.5 V, yielding the maximum flow rate, 5 μL min−1. Frequency Dependence of Flow Rate. QEOF decreased monotonically with increasing frequency over the range studied here (Figure 6A), asymptotically approaching zero at the

2H 2O + 2e− → H 2(g) + 2OH−

(1)

The anode reaction is water oxidation to yield oxygen gas and hydronium ion (eq 2) 2H 2O → O2 (g) + 4H+ + 4e−

(2)

These reactions can produce unwanted pH changes and generate gas bubbles that can block flow.16,27,28 In addition, since it takes energy to split water, these reactions mean DC operation wastes energy. In AC operation, these unwanted redox reactions are suppressed because the current is preferentially carried by charging and discharging the electrical double layers at the electrode/solution interfaces during each half-cycle. In electrochemical parlance, AC operation replaces the Faradaic current from the unwanted redox reactions (eqs 1 and 2) by double layer charging currents that do not require redox reactions. Furthermore, since water does not need to be split, power consumption should, in principle, be lower with AC operation. To prove that AC operation suppresses the unwanted redox reactions, the pH of both the inlet and outlet chambers (Figure 2) was measured while driving EOF with a voltage of 3.5 Vrms at a frequency of 20 Hz. The pH values were measured using a glass electrode immersed into each solution. Analogous experiments were conducted in DC mode, where EOF was driven using a constant DC voltage of 3.5 V. For both experiments, the inlet and outlet solutions were 25 mM KCl buffered with 1 mM Na2HPO4 at pH 7.4. As shown in Figure 7, in DC operation the pH of the outlet chamber increases with time, due to water reduction (eq 1),

Figure 6. (A) Volumetric flow rate vs the frequency of the voltage wave at 2.8 Vrms. (B) AC ion-current rectification ratio vs the frequency at 2.8 Vrms.

highest frequencies. Hence, if high flow rates are desired, low frequency modulation is best. However, for reason to be discussed below, we cannot measure flow at frequencies lower than about 20 Hz. Because of the falloff of flow with frequency, there is no advantage to high frequency pumping with this device. Since EOF results from ion-current rectification, these data suggest that rac should likewise decrease with increasing frequency. To prove this, we measured rac (Figure 6B) over a larger frequency range than that used in the flow studies. We see that rac also decreased monotonically with increasing frequency. This reinforces the point that EOF rectification follows ion-current rectification.13 Similar results were obtained in studies of ion-current rectification in conical glass pipettes.39,40 Those authors suggested that rectification fails at high frequency because the ionic redistribution needed for accumulation and depletion cannot keep up with the voltage waveform at high frequencies.39−41 Advantages of AC EOF Pumping. While EOF pumps based on conventional DC operation are commercially available, there is considerable interest in developing analogous AC electroosmotic pumps.16,22−24,42 This is because AC

Figure 7. pH of the inlet and outlet chambers vs time while driving EOF with 3.5 V DC (open symbols), and 3.5 Vrms (20 Hz) (solid symbols).

and the pH of the inlet chamber decreases due to water oxidation (eq 2). In addition, vigorous bubble formation was observed at the Pt electrode surfaces in DC mode. In contrast, in AC mode there is no change in pH of either solution over the time window studied, and no bubbles were observed. These 4640

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where η is the viscosity of the fluid, θ is the half-cone angle of the pore, and rT is the radius of tip opening. As discussed above, ΔPmax is obtained when Qp is equal to QEOF, such that the net flow is zero, giving

results show that AC operation suppresses Faradaic electrochemistry, an important goal for AC EOF pumps.16,42 However, when voltages greater than about 5 Vrms are used, the unwanted Faradaic current returns, as evidenced by the appearance of gas bubbles on the electrode surfaces. The Faradaic current returns because the rates of the redox reactions (eqs 1 and 2) increase exponentially with voltage. Hence, at high voltages Faradaic currents are essentially unavoidable. In our experiment, the gas bubbles obtained at higher voltages interfere with the flow measurement. This is because the pressure increase in both half-cells obviates the need for the inlet cell to suck solution through the inlet tube. EOF may still be occurring at higher voltages, but it cannot be measured with this device. This is why a maximum of 3.5 Vrms was used in these studies. The unwanted Faradaic reactions also return at frequencies lower than 20 Hz. This is because the AC impedance increases with decreasing frequency, which allows current to flow through the charge-transfer resistance yielding the unwanted Faradaic reactions.43 This is the reason the lowest frequency used in these studies was 20 Hz. Measurement of Maximum Pressure. At this time, the only other AC EOF pumping technology uses arrays of asymmetric microelectrodes to drive EOF.22,42,44,45 The maximum pressure produced against an external load, ΔPmax, was used as a figure of merit by which to compare our pump with those devices. ΔPmax was measured by pumping into a closed end-capillary containing a trapped column of air (see Methods). Pumping compresses the air and develops a backpressure that ultimately stops flow. ΔPmax is related to the length of this compressed air column, L, and the length before compression, L0, by46 ΔPmax =

⎛ L0 ⎞ ⎜ − 1⎟(100 kPa) ⎝L ⎠

Q EOF = Q P =

3ΔPπrT3 8η cot θ

(5)

Rearranging eq 5 gives ΔPmax =

8ηQ EOF cot θ 3πrT3

(6)

We see that ΔPmax increases linearly with QEOF, and from Figure 5B, we know that QEOF is linearly related to Vrms. This is the reason ΔPmax increased linearly with Vrms (Figure 8). A maximum pressure of 200 kPa was obtained at 3.5 Vrms, which is over 150 times higher than the best result (1.3 kPa) achieved with existing AC EOF pumping technology.23 This is because in our device ΔPmax is inversely proportional to third power of the tip radius, rT (eq 6), which for these membranes in only 22 ± 2 nm. Equation 6 clearly shows the advantage of using a conical nanopore device to drive EOF. Finally, eq 6 also allows us to calculate the theoretical maximum pressure from the known pore characteristics and experimental flow rate (Figure 5B) at each applied voltage. The theoretical maximum pressure values are also shown in Figure 8 (open triangles). The error bars on the theoretical points were obtained by doing a propagation of error analysis from the known standard deviations for the experimental parameters in eq 6. The error in the cone angle was obtained from the standard deviations of the base and tip diameters. The theoretical maximum pressures were found to be in good agreement with the experimental values. This is because we know the base and tip diameters with good accuracy and precision.

(3)

Over the voltage range studied here, ΔPmax increased linearly with Vrms (Figure 8). This can be explained by noting that for a membrane with conically shaped pores, pressure driven flow, QP, is related to the pressure difference across the membrane, ΔP, by7 QP =

3ΔPmaxπrT3 8η cot θ

CONCLUSIONS We have described a nanoionics-based AC EOF pump operated by applying a sinusoidal voltage waveform across a membrane containing conically shaped pores. AC mode suppresses the water oxidation and reduction reactions (eqs 1 and 2) that occur in conventional DC-mode operation. This minimizes energy consumption and suppresses bubble formation, and solution pH remains constant. Our membrane-based AC EOF pump produced a maximum operating pressure significantly higher than that produced by a competing AC EOF technology.23

(4)

METHODS Materials and Reagents. Ion-tracked poly(ethylene terephthalate) (PET) membranes (12 μm thick, 107 tracks/cm2) were obtained from GSI (Darmstadt, Germany). Commercial gold electroless plating solution (Oromerse Part B) was obtained from Technic, Inc., USA. Purified water was obtained by passing house-distilled water through a Barnstead E-pure model D4641 water purification system. All other chemicals were of reagent grade and were used as received from Sigma-Aldrich, unless otherwise noted in the Supporting Information. Nanopore Fabrication. A two-step chemical etching method29 was used to fabricate conically shaped nanopores in the ion-tracked PET membranes. Briefly, the first-step was asymmetric etching, where the etching solution (9 M NaOH) was placed on one side of the membrane, while the stopping solution (1 M KCl and 1 M HCOOH) was placed on the opposite side. The membrane was etched for 30 min to yield conically shaped pores. The second-step was symmetric

Figure 8. Experimental (solid squares) and theoretical (open triangles) maximum pressures obtained as a function of Vrms, frequency of 20 Hz. 4641

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ACS Nano etching, where the membrane was immersed into etching solution (9 M NaOH) for a desired time to control the size of pore tip opening. A second-step etching time of 20 min was used in this study to produce a tip diameter of 22 ± 2 nm. Gold Replicas. Gold replicas of the nanopores were deposited into pores using an electroless plating method described in detail previously.33,47,48 Plating was performed overnight in order to fill the pores and obtain complete coverage of all surfaces. The plating process created a thin film of gold on both faces of the membrane in addition to the gold replicas. Current Measurement. Current−voltage curves were measured with a Keithley 6487 picoammeter/voltage source (Cleveland, OH). The potential across membrane was stepped in 200 mV increments every 2 s from −5 to +5 V with respect to the electrode in the tip solution, and the resulting current was measured at each value of potential. AC current responses were obtained by applying sinusoidal waves across the membrane with a function generator (4040, B&K Precision Corp., Yorba Linda, CA). The resulting AC current was measured by a data acquisition system (Digidata 1440A, Molecular Devices, Sunnyvale, CA). Both current−voltage curve and AC data were obtained using 25 mM KCl solution buffered with 1 mM Na2HPO4 (pH 7.4) with two Ag/AgCl wires as electrodes. Flow Rate Measurement. The PET membrane was sealed between two chambers of an acrylic flow cell (Figure 2), positioned such that the base side was facing the inlet chamber and the tip side was facing the outlet chamber. A capillary tube with inner diameter of 0.73 mm was attached with an airtight seal to each chamber (Figure 2). The area of the membrane exposed to the solution was 1.27 cm2. EOF was driven through the membrane using a function generator (4040, B&K Precision Corp., Yorba Linda, CA). In total, each chamber and tube contained ∼5 mL of phosphate buffer solution. EOF was manifested by movement of the solution in the inlet tube toward the inlet chamber (Figure 2). This was visualized by adding a dye-solution plug, separated from the buffer solution front by an air gap of ∼6 mm. The position of the dye plug was measured using a scale attached to the inlet tube. This was accomplished by periodically imaging the position of the dye plug on the scale. The volume of fluid pumped was calculated from the displacement of the plug and the tube inner diameter. Maximum Pressure Measurement. The maximum pumping pressure was measured by connecting a capillary tube to the outlet chamber of the pump as before.46 With the pump off, this tube was filled with air at ambient pressure, 1 atm. The open end of the tube was then sealed with epoxy trapping the air. When the pump was turned on, the solution in this dead-end tube moved forward, compressing the air plug. This caused the length of the plug to decrease. Eventually, the air plug could be compressed no further, and flow stopped. In this configuration, the maximum pressure, ΔPmax, is given by eq 3,46 where L0 and L are the initial and final lengths of the air plug. Scanning Electron Microscopy. Electron micrographs were obtained using a Hitachi S-4000 filed-emission microscope (FESEM). FESEM was used to image the conically shaped and cylindrical shaped pores in the PET membrane as well as the gold replicas deposited within these pores. To image the gold replicas, the PET template had to be removed. This was accomplished by dissolving the PET in 1,1,1,3,3,3-hexafluoroisopropanol (HFIP).48 ImageJ software from NIH was used to obtain the dimensions of the gold cones.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]fl.edu. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The work was supported by the Nanostructures for Electrical Energy Storage (NEES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DESC0001160. REFERENCES (1) Cheng, L. J.; Guo, L. J. Nanofluidic Diodes. Chem. Soc. Rev. 2010, 39, 923−938. (2) Daiguji, H. Ion Transport in Nanofluidic Channels. Chem. Soc. Rev. 2010, 39, 901−911. (3) Schoch, R. B.; Han, J.; Renaud, P. Transport Phenomena in Nanofluidics. Rev. Mod. Phys. 2008, 80, 839−883. (4) Siwy, Z. S.; Howorka, S. Engineered Voltage-Responsive Nanopores. Chem. Soc. Rev. 2010, 39, 1115−1132. (5) Sparreboom, W.; Van den Berg, A.; Eijkel, J. C. Principles and Applications of Nanofluidic Transport. Nat. Nanotechnol. 2009, 4, 713−720. (6) Haywood, D. G.; Saha-Shah, A.; Baker, L. A.; Jacobson, S. C. Fundamental Studies of Nanofluidics: Nanopores, Nanochannels, and Nanopipets. Anal. Chem. 2015, 87, 172−187. (7) Lan, W.-J.; Holden, D. A.; Liu, J.; White, H. S. Pressure-Driven Nanoparticle Transport across Glass Membranes Containing a Conical-Shaped Nanopore. J. Phys. Chem. C 2011, 115, 18445−18452. (8) Laohakunakorn, N.; Thacker, V. V.; Muthukumar, M.; Keyser, U. F. Electroosmotic Flow Reversal Outside Glass Nanopores. Nano Lett. 2015, 15, 695−702. (9) White, H. S.; Bund, A. Ion Current Rectification at Nanopores in Glass Membranes. Langmuir 2008, 24, 2212−2218. (10) Apel, P. Y.; Korchev, Y. E.; Siwy, Z.; Spohr, R.; Yoshida, M. Diode-Like Single-Ion Track Membrane Prepared by ElectroStopping. Nucl. Instrum. Methods Phys. Res., Sect. B 2001, 184, 337− 346. (11) Siwy, Z.; Heins, E.; Harrell, C. C.; Kohli, P.; Martin, C. R. Conical-Nanotube Ion-Current Rectifiers: The Role of Surface Charge. J. Am. Chem. Soc. 2004, 126, 10850−10851. (12) Cervera, J.; Schiedt, B.; Neumann, R.; Mafe, S.; Ramirez, P. Ionic Conduction, Rectification, and Selectivity in Single Conical Nanopores. J. Chem. Phys. 2006, 124, 104706−104709. (13) Jin, P.; Mukaibo, H.; Horne, L. P.; Bishop, G. W.; Martin, C. R. Electroosmotic Flow Rectification in Pyramidal-Pore Mica Membranes. J. Am. Chem. Soc. 2010, 132, 2118−2119. (14) Bishop, G. W.; Lopez, M. M.; Ramiah Rajasekaran, P.; Wu, X.; Martin, C. R. Electroosmotic Flow Rectification in Membranes with Asymmetrically Shaped Pores − Effects of Current and Pore Density. J. Phys. Chem. C 2015, 119, 16633−16638. (15) Pu, Q.; Liu, S. Microfabricated Electroosmotic Pump for Capillary-Based Sequential Injection Analysis. Anal. Chim. Acta 2004, 511, 105−112. (16) Wang, X.; Cheng, C.; Wang, S.; Liu, S. Electroosmotic Pumps and Their Applications in Microfluidic Systems. Microfluid. Nanofluid. 2009, 6, 145−162. (17) Whitesides, G. M. The Origins and the Future of Microfluidics. Nature 2006, 442, 368−373. (18) Lee, C. S.; Blanchard, W. C.; Wu, C. T. Direct Control of the Electroosmosis in Capillary Zone Electrophoresis by Using an External Electric Field. Anal. Chem. 1990, 62, 1550−1552. (19) Laohakunakorn, N.; Gollnick, B.; Moreno-Herrero, F.; Aarts, D. G.; Dullens, R. P.; Ghosal, S.; Keyser, U. F. A Landau-Squire Nanojet. Nano Lett. 2013, 13, 5141−5146.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b00939. Experimental details of fabrication and characterizations (PDF) Video S1: short video of the fluid movement process (MPG) 4642

DOI: 10.1021/acsnano.6b00939 ACS Nano 2016, 10, 4637−4643

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DOI: 10.1021/acsnano.6b00939 ACS Nano 2016, 10, 4637−4643