pubs.acs.org/Langmuir © 2009 American Chemical Society
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Logic Gates Using Nanofluidic Diodes Based on Conical Nanopores Functionalized with Polyprotic Acid Chains Mubarak Ali,† Salvador Mafe,‡ Patricio Ramirez,*,§ Reinhard Neumann, and Wolfgang Ensinger† †
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Technische Universit€ at Darmstadt, Fachbereich Material-u. Geowissenschaften, Fachgebiet Chemische Analytik, Petersenstrasse 23, D-64287 Darmstadt, Germany, ‡Departament de Fı´sica de la Terra i Termodin amica, Universitat de Val encia, E-46100 Burjassot, Spain, §Departament de Fı´sica Aplicada, Universidad Polit ecnica de Valencia, E-46022 Valencia, Spain,, and GSI Helmholtzzentrum f€ ur Schwerionenforschung GmbH, Planckstrasse 1, D-64291 Darmstadt, Germany Received July 29, 2009. Revised Manuscript Received September 4, 2009
Single-track conical nanopores functionalized with polyprotic acid chains have pH-sensitive fixed charge groups and show three levels of conductance that allow integrating several functions on a single nanofluidic diode. Nanometerscaled pores have previously been employed in separation and sensing but not in logic devices, despite the fact that biological ion channels with pH-dependent fixed charges are known to be responsible for information processing in biophysical structures. As a preliminary application, we propose a logic gate scheme where binary and multivalued logical functions are implemented.
Introduction Nanofluidic structures are potentially useful to implement a variety of functions because they show rich individual characteristics and allow high packing densities. Nanopores, nanopipettes, and nanoelectrodes constitute a new generation of devices designed for single-molecule sensing and molecular separation.1-11 Nanofluidic diodes based on asymmetric nanopores with only one type of charge, and bipolar diodes and transistors, composed by regions of different charge juxtaposed in series, have been reported.12-14 Recently, we have demonstrated a nanofluidic diode with amphoteric chains (lysine or histidine) functionalized on the pore surface that shows a broad range of rectification properties.15 The experimental characterization and modeling of particular nanofluidic devices are receiving much attention, but it is also necessary to devise applied schemes based on these nanostructures. In this letter, we demonstrate theoretically and experimentally that single-track conical nanopores functionalized with polyprotic acid chains show three levels of conductance that can be tuned externally (because of the pH-sensitive fixed charges). The selectivity and rectification properties are dictated
Experimental Section
*Corresponding author. E-mail:
[email protected]. (1) Siwy, Z.; Fulinski, A. Phys. Rev. Lett. 2002, 89, 198103. (2) Lee, S.; Zhang, Y. H.; White, H. S.; Harrell, C. C.; Martin, C. R. Anal. Chem. 2004, 76, 6108. (3) Lebedev, K.; Mafe, S.; Stroeve, P. J. Phys. Chem. B 2005, 109, 14523. (4) Zhang, Y. H.; Zhang, B.; White, H. S. J. Phys. Chem. B 2006, 110, 1768. (5) Umehara, S.; Pourmand, N.; Webb, C. D.; Davis, R. W.; Yasuda, K.; Karhanek, M. Nano Lett. 2006, 6, 2486. (6) Dekker, C. Nat. Nanotechnol. 2007, 2, 209. (7) Ku, J. R.; Lai, S. M.; Ileri, N.; Ramirez, P.; Mafe, S.; Stroeve, P. J. Phys. Chem. C 2007, 111, 2965. (8) Murray, R. W. Chem. Rev. 2008, 108, 2688. (9) Ali, M.; Yameen, B.; Neumann, R.; Ensinger, W.; Knoll, W.; Azzaroni, O. J. Am. Chem. Soc. 2008, 130, 16351. (10) Healy, K.; Schiedt, B.; Morrison, A. P. Nanomedicine 2007, 2, 875. (11) Umehara, S.; Karhanek, M.; Davis, R. W.; Pourmand, N. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 4615. (12) Siwy, Z.; Heins, E.; Harrell, C. C.; Kohli, P.; Martin, C. R. J. Am. Chem. Soc. 2004, 126, 10850. (13) Vlassiouk, I.; Siwy, Z. Nano Lett. 2007, 7, 552. (14) Kalman, E. B.; Vlassiouk, I.; Siwy, Z. Adv. Mater. 2008, 20, 293. (15) Ali, M.; Ramirez, P.; Mafe, S.; Neumann, R.; Ensinger, W. ACS Nano 2009, 3, 603.
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by the nanometer-sized tip region, and the intrinsic (geometric and electrostatic) asymmetries of the device permit one to obtain different functions with a single nanofluidic diode. As a preliminary application, we consider a logic gate scheme where the AND and NOT gates are implemented using chemical inputs. These allow tuning the electrostatic interaction between the ionic permeants and the charged groups on the nanopore surface. The surface functionalization with polyprotic acid chains permits a multilevel response and the implementation of multivalued logic gates. Arrangements of several nanopores subjected to different electrical inputs can give other logical gates. Nanometer-scaled pores have previously been demonstrated in separation and sensing applications2,5,7,8,10,11,16-18 but not in logic devices despite the fact that biological ion channels with pHdependent fixed charges are known to be responsible for information processing in biophysical structures.19 Because an expanding list of chemically and electrochemically switchable nanopores have experimentally been demonstrated,2,9,10,12-18,20,21 this study can stimulate future particular realizations by showing the essential characteristics of the concept.
Polymer foils of polyethylene terephthalate (PET) (Hostaphan RN 12, Hoechst) of 12 μm thickness were irradiated at the linear accelerator UNILAC (GSI, Darmstadt) with single swift heavy ions (Pb, U and Au) having an energy of 11.4 MeV per nucleon. N-(3-dimethylaminopropyl)-N0 -ethylcarbodiimide hydrochloride (EDC, 98%, Fluka), pentafluorophenol (PFP, 99+ %, Aldrich) and 3-aminopropylphosphonic acid (APPA; 99%, Aldrich) were used as received for the chemical modification. The surfactant (16) Chun, K.-Y.; Mafe, S.; Ramirez, P.; Stroeve, P. Chem. Phys. Lett. 2006, 418, 561. (17) Cheng, L.-J.; Guo, L. J. ACS Nano 2009, 3, 575. (18) Ali, M.; Schiedt, B.; Healy, K.; Neumann, R.; Ensinger, W. Nanotechnology 2008, 19, 085713. (19) Hille, B. Ion Channels of Excitable Membranes; Sinauer Associates: Sunderland, MA, 2001. (20) Spohr, R. Radiat. Meas. 2005, 40, 191. (21) Cervera, J.; Schiedt, B.; Neumann, R.; Mafe, S.; Ramirez, P. J. Chem. Phys. 2006, 124, 104706.
Published on Web 09/28/2009
DOI: 10.1021/la902792f
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Dowfax* 2A1 (Dow Chemical) was used as received without further purification. The fabrication of asymmetric conical nanopores in PET was accomplished by asymmetric surfactantcontrolled etching of single ion-tracked membranes.22 Briefly, the heavy ion-irradiated membranes were sensitized with ultraviolet irradiation for 35 h from one side only. Then the membrane was placed in a conductivity cell in which it served as a dividing wall between the two compartments. The pure etchant (6 M NaOH) was filled on the UV-sensitized side while the other half of the cell, adjoining the non-UV treated side of the membrane was filled with protecting solution (4 M NaOH + 0.03% v/v surfactant). The etching process was carried out at 60 °C. During the etching process, a voltage of -1 V was applied across the membrane in order to observe the current flowing through the nascent nanopore. The current remains zero as long as the pore is not yet etched through, and after the breakthrough a continuous increase of current is observed. The etching process was stopped when the current was reached at a certain value and the pore was washed first with 1 M HCl in order to neutralize the etchant, followed with deionized water. The etching procedure results in the generation of carboxyl groups on the wall of the nanopore. These carboxyl groups were converted into amine-reactive pentafluorophenyl esters via PFP and EDC coupling chemistry. For activation, an ethanolic solution, containing 0.1 M EDC and 0.2 M PFP, was placed on both sides of the track-etched singlenanopore membrane, which was mounted between the two halves of a conductivity cell. The activation was carried out for 1 h at room temperature. After washing with ethanol several times, the solution was replaced with 50 mM APPA on both sides of the membrane and left for overnight. Then, the modified membrane was washed thoroughly first with ethanol followed by careful rinsing with deionized water. Figure 1 schematically shows the pore surface carboxyl groups (a) converted into amine-reactive PFP-esters (b) and subsequently coupled with APPA leading to the terminated phosphonic acid groups (c). Figure 1d shows the pH dissociation equilibrium that gives the nanopore surface charge. The single-nanopore membrane modified with APPA was mounted between the two halves of the conductivity cell filled with the electrolyte solution, and the pH was adjusted by dilute HCl or KOH solutions. An Ag/AgCl electrode was placed into each half-cell solution, and a picoammeter/voltage source (Keithley 6487, Keithley Instruments, Cleveland, OH) was used to apply the desired transmembrane potential. To measure the resulting ion current flowing through the nanopore, a scanning triangle voltage from -2 to +2 V on the tip side was applied (the base side of the pore remained connected to the ground electrode).
Results and Discussion Figure 1e shows the current-voltage (I-V) curve of the conical nanopore separating two identical electrolyte solutions (0.1 M KCl) for a broad set of pH values. The pKa values of the attached pH-responsive groups are 4.5 and 7.7 approximately.23 At low pH, both ionizable hydroxyl groups of the terminated phosphonic acid (-PO3H2) are protonated, which imports neutral charge to the pore surface. The nanopore is now nonselective to ions (anions and cations), leading to the loss of rectification. By increasing the pH, ionization starts, and at pH 5 one of the hydroxyl group is ionized, and a monoanion form of the phosphate (-PO3- H) group is achieved (partly charged pore). The net pore fixed charge is then negative, and the nanopore is now selective to cations. There is a high-conducting (“on”) state for V > 0 and a low-conducting (“off”) state for V < 0. At pH > 8, (22) Ali, M.; Bayer, V.; Schiedt, B.; Neumann, R.; Ensinger, W. Nanotechnology 2008, 19, 485711. (23) Zhang, J.; Kirkham, J.; Robinson, C.; Wallwork, M. L.; Smith, D. A.; Marsh, A.; Wong, M. Anal. Chem. 2000, 72, 1973.
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Figure 1. Scheme of the nanopore carboxyl groups (a) converted into amine-reactive PFP-esters (b) and subsequently coupled with APPA leading to the terminated phosphonic acid groups (c). The polyprotic acid dissociation equilibria dictate the nanopore surface charge (d) and the current-voltage curve in an electrolyte (0.1 M KCl) solution (e).
the phosphate group (-PO32-) is double-charged and the (now fully charged) pore shows enhanced rectification properties (see Figure 1e). Note also that, at a given positive voltage, three welldefined conductance levels (0.37 nS at pH ≈ 3, 1.06 nS at pH ≈ 5, and 1.57 at pH ≈ 10) can be identified corresponding to the ionization equilibria of the two ionizable hydroxyl groups of polyprotic acid shown in Figure 1d. There are several methods to estimate the conductance of a nanopore.21,24,25 Here, all values were measured at V = 1 V and obtained as the average of six individual experimental points of the respective I-V curves. Remarkably, at V = -1 V, the pH dependence of the two conductance levels now available is reversed (see Figure 1e): 0.41 nS at pH ≈ 3 and 0.15 nS at pH ≈ 10. These different conductance levels allow implementing binary and multivalued logic gates by using potential and pH as input values, as it will be shown later. The experimental results can be described theoretically in terms of a continuous model based on the Poisson and Nernst-Planck equations:21,25-28 r2 φ ¼
F ðcCl - - cK þ Þ ε
r 3 JBi ¼ -r 3 ½Di ðrci þ zi ci rφÞ ¼ 0,
ð1Þ
i ¼ K þ , Cl -
ð2Þ
(24) Stein, D.; Kruithof, M.; Dekker, C. Phys. Rev. Lett. 2004, 93, 03590. (25) Ramirez, P.; Apel, P. Y.; Cervera, J.; Mafe, S. Nanotechnology 2008, 19, 315707. (26) Cervera, J.; Schiedt, B.; Ramirez, P. Europhys. Lett. 2005, 71, 35. (27) Constantin, D.; Siwy, Z. S. Phys. Rev. E 2007, 76, 041202. (28) Gracheva, M. E.; Leburton, J. P. Nanotechnology 2007, 18, 145704.
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Figure 2. Comparison between the experimental (a) and theoretical (b) current-voltage curves at three relevant pH values: 3 (uncharged pore), 5 (partly charged pore), and 10 (fully charged pore). The AND (c) and NOT (d) binary logic gates, together with the multivalued logic function (e), are obtained with a single nanopore using the pH dependence of the conductance levels.
where JBi, ci, Di, and zi are the flux density, the local concentration, the diffusion coefficient, and the charge number of ion i (i=K+ and Cl-), with φ and ε being the local electric potential and the electrical permittivity of the solution within the pore, respectively. Despite the nanometer scales involved in the problem, relatively simple continuum theories1,2,7,13-17,21,25,27-30 can correctly predict the observed behavior, as shown in Figure 2a,b for three relevant pH values: 3 (uncharged pore), 5 (partly charged pore), and 10 (fully charged pore). The comparison between theory and experiment allows for the determination of the nanopore surface charge by using the following procedure. First, the radius of the wide pore opening, aR, is determined by FESEM using a polymer foil containing approximately 107 pores cm-2, which was etched simultaneously with the sample containing the single pore under the same conditions.15 Second, the radius of the pore tip, aL, is calculated from the (linear) fitting of the linear I-V curve for the uncharged nanopore. The values obtained in our case were aR = 100 nm and aL=9 nm. Once the pore radii have been calculated, (29) Ramirez, P.; Mafe, S.; Alcaraz, A.; Cervera, J. J. Phys. Chem. B 2003, 107, 13178. (30) Ramirez, P.; Mafe, S.; Aguilella, V. M.; Alcaraz, A. Phys. Rev. E 2003, 68, 011910.
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the only free parameter of the model is the surface charge σ (in elementary charges per square nanometer). The values of σ in Figure 2(b): 0 (uncharged pore), -0.2 e/nm2 (partly charged pore), and -0.4 e/nm2 (fully charged pore) are in agreement with the reaction schemes of Figure 1d and similar to those found previously for other conical nanopores.25 In this preliminary study, we explore now the implementation of a logic gate scheme with the conical nanopore acting as a nanofluidic diode by using the experimental data of Figure 2a as the input parameters. Figure 2 shows the AND (c) and NOT (d) binary logic gates together with a multivalued logic function (e). Note that all these functions can be implemented with a single nanopore using the pH dependence of the conductance levels. The input logic values are given by electrolyte solutions of characteristic pH values selected from the experimental results of Figure 2a. The pH values 3 and 10 were chosen here because they show welldefined, separated conductance levels. The low and high pH values constitute the inputs, and the respective low and high conductance values constitute the outputs. The low pH and (31) Casasus, R.; Climent, E.; Marcos, M. D.; Martı´ nez-Manez, R.; Sancenon, F.; Soto, J.; Amoros, P.; Cano, J.; Ruiz, E. J. Am. Chem. Soc. 2008, 130, 1903.
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Figure 3. The OR (a) and AND (b) gates are now obtained with arrangements of two nanopores. The output voltages Vout in the truth tables are obtained in each case by solving the respective circuits with the values of the nanopore resistance obtained from the experimental I-V curve of Figure 2a.
conductance values correspond to the logic “0”, and the high pH and conductance values correspond to the logic “1”. The use of different electrolytes31 incorporating, e.g., divalent or large ions could add flexibility to the resulting logical gates. Also, a specific conductivity cell in which the inputs could be better controlled would be desirable for more elaborated applications but it is not crucial to show the proof-of-principle. The NOT gate is based on the conical nanopore rectification: the pH dependence obtained for V < 0 is reversed with respect to the case V > 0. The multivalued function operates with low, medium, and high pH inputs corresponding now to the logics “0”, “1”, and “2”, respectively, and selects the low (0) output when (at least) one of the two input values is low, a medium (1) output when both inputs are medium, and the high (2) output otherwise. The multivalued logic is a direct extension of the above case and allows for higher information densities than the binary logic. It is realized here by functionalizing the conical nanopore surface with the polyprotic chains. Remarkably, amphoteric nanopores functionalized with amino acid chains show also a broad range of rectification properties15 and could also permit to implement other logical functions. Other gates can also be obtained with arrangements of two nanopores. Figure 3 shows the OR gate (a) and the AND gate (b) together with the calculated truth tables obtained for the partly (pH=5) and fully (pH=10) charged pores. V1 and V2 are the input voltages: -0.1 V (logic input “0”) and 2 V (logic input “1”). Logic outputs “0” and “1” are defined here as those lower than 1 V and higher than 1 V, respectively. We have taken R=2.73 GΩ, corresponding to the electrical resistance of the uncharged pore, calculated from Figure 2a for σ=0 at pH=3. In each case, the output voltage Vout is obtained by solving the respective circuits with the values of the nanopore resistance obtained from the experimental I-V curve of Figure 2a. As expected, the logic outputs “0” and “1” are better defined for the fully charged pore (pH=10) than for the partly charged pore (pH=5), especially in the case of the OR gate. As in previous designs (32) Kim, D.-H.; Lee, H.; Song, C.-K.; Lee, C. J. Nanosci. Nanotechnol. 2006, 6, 3470. (33) Rinaldi, R.; Cingolani, R. Physica E 2004, 21, 45. (34) Nitahara, S.; Terasaki, N.; Akiyama, T.; Yamada, S. Thin Solid Films 2006, 499, 354. (35) Bachtold, A.; Hadley, P.; Nakanishi, T.; Dekker, C. Science 2001, 294, 1317.
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of logic gates with nanostructures (see, e.g., refs 32-34 for molecular and SAM arrays, refs 35 and 36 for carbon nanotube transistors, and refs 37 and 38 for nanowire devices), the logics “0” and “1” are only approximately defined. However, we believe that there is wide margin to further improve the nanopore rectification properties, as shown in previous experimental and theoretical studies.8,13,17,21,25,27-39 Moreover, the usual problems associated with the irreversibility phenomena and aging of nanostructures33 should not be a serious concern here. On the contrary, the time response could be a limitation for nanofluidic diodes because they operate on the ionic time scale. To achieve an efficient time modulation, the external tuning should involve times larger than the typical relaxation time characteristic of the nanopore. An upper bound (because of the effect of the applied potential) for this time is the diffusion constant τ=L2/Di, where L is the length of the pore and Di =10-10 - 10-9 m2/s is the ionic diffusivity. This gives times τ on the order of 1 s for typical synthetic nanopores of thickness L = 10 μm. This time could be decreased by several orders of magnitude in the case of biological ion channels19,40,41 and solid state synthetic nanopores,6,42,43 where L=10 nm. However, the effective operating time could still be significantly higher than expected because of the external connections (this is also the case of nanostructures connected to external wires with high parasitic capacitances; see ref 35 as well as the typical response times reported in refs 32, 34, and 36). Despite this limitation, it is clear that the functionalization of polyprotic acid chains on the surface of a conical nanopore gives three well-defined conductance levels that can be tuned by simply changing the pH of the external environment. The integration of a multilevel response on a unique conical nanopore acting as a (36) Javey, A.; Wang, Q.; Ural, A.; Li, Y.; Dai, H. Nano Lett. 2002, 2, 929. (37) Park, W. I.; Kim, J. S.; Yi, G.-C.; Lee, H.-J. Adv. Mater. 2005, 17, 1393. (38) Huang, Y.; Duan, X.; Cui, Y.; Lauhon, L. J.; Kim, K.-H.; Lieber, C. M. Science 2001, 294, 1313. (39) Ramirez, P.; Gomez, V.; Cervera, J.; Schiedt, B.; Mafe, S. J. Chem. Phys. 2007, 126, 194703. (40) Alcaraz, A.; Ramirez, P.; Garcia-Gimenez, E.; Lopez, M. L.; Andrio, A; Aguilella, V. M. J. Phys. Chem. B 2006, 110, 21205. (41) Garcia-Gimenez, E.; Alcaraz, A.; Aguilella, V. M.; Ramirez, P. J. Membr. Sci. 2009, 331, 137. (42) Radenovic, A.; Trepagnier, E.; Csencsits, R.; Downing, K. H.; Liphardt, J. Appl. Phys. Lett. 2008, 93, 183101. (43) Abgrall, P.; Nguyen, T. Anal. Chem. 2008, 80, 2326.
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nanofluidic diode allows both binary and multivalued logic gates, as those implemented on the basis of enzymes with biochemical input signals44-47 and nanogated hybrid architectures.31,48,49 In conclusion, we have given preliminary but plausible arguments linking predefined output signals (Figure 2a) with chemical stimuli acting as input signals, both in the case of binary (Figure 2c) and multivalued (Figure 2f) logics, for the case of a novel conical nanopore functionalized with polyprotic acid chains that shows three levels of conductance. Theoretical calculations
concerning the pH and voltage dependences of the conductance (Figure 2b) give additional support to the basic concepts involved. Moreover, simple arrangements of two nanopores are suggested (Figure 3) and the calculations made using the experimental nanopore conductances as the input values for the respective electrical circuits give further evidence of the validity of the ideas proposed. Finally, we emphasize that other experimental systems (e.g., an amphoteric nanopore) could also be used to implement these ideas. We believe that all the above facts could constitute a proof-ofprinciple for a new logical scheme based on fixed-charge nanopores.
(44) Ferreira, R.; Remon, P.; Pischel, U. J. Phys. Chem. C 2009, 113, 5805. (45) Pita, M.; Katz, E. J. Am. Chem. Soc. 2008, 130, 36. (46) Pita, M.; Kr€amer, M.; Zhou, J.; Poghossian, A.; Sch€oning, M. J.; Fernandez, V. M.; Katz, E. ACS Nano 2008, 2, 2160. (47) Motornov, M.; Zhou, J.; Pita, M.; Gopishetty, V.; Tokarev, I.; Katz, E.; Minko, S. Nano Lett. 2008, 8, 2993. (48) Aznar, E.; Casasus, R.; Garcı´ a-Acosta, B.; Marcos, M. D.; Martı´ nezMan~ez, R.; Sancenon, F.; Soto, J.; Amoros, P. Adv. Mater. 2007, 19, 2228. (49) Aznar, E.; Coll, C.; Marcos, M. D.; Martı´ nez-Man~ez, R.; Sancenon, F.; Soto, J.; Amoros, P.; Cano, J.; Ruiz, E. Chem.;Eur. J. 2009, 15, 6877.
Acknowledgment. We acknowledge Drs. Basit Yameen (MPIP) and Omar Azzaroni (INIFTA) for fruitful and enlightening discussions about the use of polyprotic acid groups. M.A. thanks HEC of Pakistan, on receiving partial financial support. P. R. and S.M. acknowledge the support from Ministry of Science and Innovation of Spain, Program of Materials (Project No. MAT2009-07747), and FEDER.
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