Article pubs.acs.org/JPCC
Ion Current Oscillation in Glass Nanopipettes Xiao Long Deng, Tomohide Takami,* Jong Wan Son, Tomoji Kawai, and Bae Ho Park* Division of Quantum Phases and Devices, Department of Physics, Konkuk University, Seoul 143-701, Republic of Korea S Supporting Information *
ABSTRACT: Ion currents detected by glass nanopipettes in solutions depended on the diameters of pipettes and ion species in the solutions. The ion current oscillation with frequency of 2.7 mHz was observed using the pipet with inner diameter of 50 nm in 0.1 M KCl solution. However, nonoscillatory currents were observed using the same pipet in 0.1 M KOH and HCl solutions or using pipettes with inner diameters of 15 nm, 500 nm, and 0.7 mm in 0.1 M KCl solution. Oscillation of the double layer thickness due to the change of ion concentration in the nanopipette perturbs the path of the ion current through the bulk layer, which results in the nonlinear current oscillation.
G
reaction was explained by Noyes et al.,19 a simplified mechanism named “Oregonator” was also proposed.20 It is an activator/inhibitor system, in which HBrO2 activator produces intermediate species but catalyst MOX inhibitor reacts with them, resulting in oscillation of the concentrations of activator, inhibitor and intermediate species. In this paper, we measured the time dependent ion current flowing through a glass pipet with inner diameter (i.d.) of 15 nm, 50 nm, 500 nm, and 0.7 mm in 0.1 M KCl solution. The oscillating behavior was observed with 50 nm i.d. pipet while nonoscillatory behaviors were observed using pipettes with other sizes. For comparison, we also measured the time dependent ion current with 50 nm i.d. pipet in 0.1 M KOH and HCl solutions which revealed nonoscillatory behaviors. Therefore, the oscillatory behavior was elucidated by competitive adsorption of H+ and OH− ions present in the KCl solution with inner surface of glass pipet with 50 nm i.d.. The pipettes used in this study were obtained from F. Iwata at Shizuoka University, and the detailed fabrication process was described in a previous paper.21 The low ion current detection system used in this study is similar as depicted in our previous report.22 The 10 mL prepared solution of 0.1 M was put into the glass dish with diameter of 50 mm. The same amount of distilled water was filled in each pipet. The signals obtained from the 0.1 mm Ag electrode in pipet were converted to
lass pipettes with diameters of submicro or nanoscale play important roles in the investigation of local characteristics in solutions.1−3 Pipettes are typically used for the electrophysiological measurements4−6 and injection7 separately or both tasks concurrently.8 On the other hand, considerable attention has been attracted by the mass transfer characteristics through the charged nanopipettes, such as ion current rectification,3,9 ion transfer at the tip of nanopipette,10 and nanopore resistive-pulse sensing.11 Recently, ion current oscillations were observed with nanopores due to the dynamic precipitation in the pore caused by the weakly soluble salts.12,13 These indicate that the mass transports through nanopores are greatly different from those through micropores. It seems that the nanopores have the larger surface-to-volume ratios and thus the ions passing through the nanopores are strongly influenced by the properties of nanopore walls.13 In particular, the counterions and co-ions were accumulated and excluded by the charged nanopore walls, respectively.14 Therefore, it is required to investigate the effect of pipet size and ion species on the ion current measured through glass pipettes in solutions. Oscillations have also been observed in the reactions which have been extensively used in the chemical demonstrations.15,16 The best understood model for the oscillating chemical reaction is the Belousov−Zhabotinsky (BZ) reaction17 which serves as classical example of nonequilibrium thermodynamics. The oscillating BZ reaction is expected to be a useful model for biological fluctuations.18 The overall BZ reaction is the ceriumcatalyzed oxidation of malonic acid by bromated ions in diluted sulfuric acid. Although the complete mechanism of the BZ © 2012 American Chemical Society
Received: November 15, 2011 Revised: June 18, 2012 Published: June 19, 2012 14857
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voltage by an I−V converter. The Ag/AgCl counter electrode with 1 mm diameter was used to simultaneously apply 0.066 V AC voltage with a lock-in amplifier and 0.100 V DC voltage with a UM-1 battery accompanied by a voltage controller. The pipet touched the surface of the solution, then sank by 1 mm, and was kept at this position for all experiments. For investigating the size dependence of steady current, the ion current values were read at 2000 s in the time-dependent ion current curves. Figure 1 shows the schematic diagram of ion distribution around the tip of the glass pipet when a positive external bias is
Figure 2. Ion current observed with glass pipet in 0.1 M KCl solution versus inner diameter of the glass pipet. The ion current values were read at 2000 s in time-dependent ion current curves.
sinks by 1 mm in the solution, reaching the saturation, and then decreasing rapidly with time as shown in Figure 3a. The time dependent ion current measured using a 50 nm i.d. pipet in Figure 3b shows a very interesting behavior which is different from the others. The initial trend is similar as that measured using a 15 nm i.d. pipet but after reaching saturation, the ion current exhibits oscillating behavior. The time dependent ion current measured using a 500 nm i.d. pipet is shown in Figure 3c. It reveals the similar phenomenon as that measured using a 15 nm i.d. pipet except for slow decay after saturation. As the i.d. increases to 0.7 mm, the ion current saturates very fast and then keeps the constant value as shown in Figure 3d. All of these phenomena except the oscillation measured using 50 nm i.d. pipet can be explained by size effect of the pipet. As the i.d. increases, more amount of ions move into the pipet in the same time. Then, the final current level becomes higher, which is consistent with the data in Figure 2. However, for the pipettes with i.d. smaller than 500 nm, ionic motion is constrained by the negatively charged pipet surface so that the current exhibits a little suppression after saturation. The pipet with smaller size may result in the stronger constraint and more suppressed current. As shown in Figure 4, both thin Stern layer and Gouy−Chapman layer are usually formed at the negatively charged surface inside the pipet. The thickness of the double layer (3 to 30 nm) consisting of a Stern layer and a Gouy− Chapman layer is inversely proportional to the square root of ion concentration (10−2 to 10−4 M).23 Therefore, it seems that the double layer is formed on the inner surface of pipet based on our 0.1 M KCl bulk solution. In our experiment, the external electric field and the ion concentration gradient are the main driving force of ion currents. The pipet was filled with pure distilled water as internal electrolyte and 0.1 M KCl was used as the bulk solution. So we suppose that the concentration of the inside electrolyte is properly low to result in the appropriate thickness of the double layer. According to the report of Daiguji et al.,24 the silicon−based nanopipette has the surface charge density of about −10−3 C/m2. In our work, we can use the similar model to estimate the double layer thickness after simplifying the conical pipet to the nanotube in a very short shank range. The ionic density difference between K+ and Cl− inside the channel which is independent of the potential bias is determined by the surface charge density. The total charge of ions can be calculated due to the requirement of electroneutrality, which is equal to the surface charge on the wall:
Figure 1. Schematic diagram of ion distribution around the tip of the negatively charged glass pipet under external bias. The + sign indicates the positive voltage applied to the Ag/AgCl counter electrode outside the pipet. The arrows denote the directions of ion movement.
applied to the Ag/AgCl counter electrode. In KCl solution, the K+ and Cl− ions move into and out of the pipet, respectively, due to the external electric field. However, because the pipet was filled with pure distilled water, a certain amount of K+ and Cl− ions diffuses into the pipet due to the difference of the ion concentration. The external electric field and the ion concentration gradient are the main driving force of ion currents. Since the surface of the glass pipet is negatively charged at neutral pH, when the size of the pipet is very small, the ions selectively pass through the pore.3,14 The small size negatively charged pipet leads to small amount of ions moving into it as well as the attractive and repulsive forces on K+ and Cl−, respectively, resulting in the low ion current. As the size increases, the surface charge effect is reduced and the total amount of ions through the pore increases resulting in the larger ion current. Figure 2 shows the dependence of ion current observed in 0.1 M KCl solution on i.d. of pipettes from 15 to 500 nm, respectively. The ion current increases with the i.d. of the pipet, which confirms the above arguments. The time dependences of ion currents measured with different size pipettes in a 0.1 M KCl solution were also investigated as shown in Figure 3. For a 15 nm i.d. pipet, the ion current exhibits the behavior as following: suddenly increasing while the pipet touches the solution surface and 14858
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Figure 3. Time-dependent ion current measured using glass pipet with inner diameter of (a) 15 nm, (b) 50 nm, (c) 500 nm, and (d) 0.7 mm in 0.1 M KCl solution.
Δn = −
2σ eL
nanopipette. Then the equivalent concentration c can be estimated as follows:
Here σ is the surface charge density and L is the height of the channel which is equal to the inner diameter d of the tip of
c=
Δn 2σ =− NA edNA
c=−
−19
−1.6 × 10 1 M = 48.16d
2 × 10−3 × 10−3 M 23 −9 × 6.02 × 10 × d × 10
As we mentioned before the thickness of the double layer (TD)23 can be obtained as follows: TD =
0.3 c
Then we can get the thickness TD =
0.3 = 2.08 d 1/48.16d
According to this formula, we can assess the layer thickness of nanopipettes with different radius. For the 15 nm pipet the thickness is about 8.1 nm which is very close to the radius. For the 50 nm pipet the thickness is 14.7 nm which is about half of the radius that means the freely moving bulk region appears. For the pipet sizes of 250 and 500 nm the thickness is 32.9 and 46.5 nm which are much smaller than the pipet size. Therefore, for the 15 nm i.d. pipet, the double layer is overlapped resulting
Figure 4. Schematic diagram of double layer consisting of Stern layer and Gouy−Chapman layer, formed inside the tip of the negatively charged pipet. The yellow color indicates glass pipet. The signs + and − denote cation and anion, respectively. The thicknesses of Stern and Gouy−Chapman layers are denoted by δ and λ, respectively. 14859
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Figure 5. Time-dependent ion currents measured using glass pipet with inner diameter of 50 nm in 0.1 M solutions of (a) KOH and (b) HCl.
concentration and the absolute value of each ionic valence are the same for the KCl, KOH, and HCl solutions, the ion species will be the only factor to affect the current behavior in these solutions. The adsorption between negatively charged surface and hydrogen ions is stronger than relatively unstable adsorption between that and potassium ions.26 For the KOH solution, the K+ ions can move into the pipet and relatively small part of them will react with the negative charges on the surface. However, the OH− ions migrate into the pipet reacts again with the surface leading negatively charged one, and thus more K+ ions will be attracted by the surface resulting in the decrease of the K+ ion concentration. Finally, the system achieves the equilibrium with a lower current as shown in the Figure 5a. For HCl solution, the H+ ions will be driven into the pipet interior and part of them will combine with SiO− or −OH resulting in the neutral glass surface and thus decreasing the attractive force on the remaining H+ ions. Then more H+ ions will be attracted by the electrode inside the pipet resulting in the high conductivity due to the increase of H+ ion concentration. The ion current will be enhanced by H+ ions resulting in higher level measured in the HCl solution as shown in Figure 5b. In the acid or alkali solution, the OH− or H+ ions will be suppressed, respectively, due to repressed dissociation of water.27 Hence, in the acid or alkali solution, there is no obvious oscillation of H+ and OH− ions concentration. On the other hand, there are both H+ and OH− ions in the neutral KCl solution keeping an equal concentration due to the dissociation of water.27 Therefore, the ion current will exhibit current oscillation due to the oscillation of H+ and OH− ions concentration in time as a result of chemical kinetics.15,28 However, we should note that the main contribution to the current is from K+ ions but the oscillation is due to the fluctuation of H+ and OH− ions. This can be confirmed by the following estimation. The diffusion coefficient of K+ and H+, DK+ and DH+ are 1.96 × 10−9 and 9.34 × 10−9 m2/s.29 We can simply estimate the influence generated by the H+ and OH− ions. As we know, the average of the current at the steady state is around 1.8 nA and the fluctuation of the current is around 0.05 nA. The ionic current is proportional to flux which can be calculated as follows according to the report given in ref 24:
in absence of freely moving bulk region inside the nanochannel and thus decrease of ion current after reaching saturation, as shown in Figure 3a. However, for i.d. not less than 50 nm, the freely moving bulk region appears and generates different behaviors. As i.d. increases, the freely moving bulk region expands and thus decrease rate of ion current after saturation is reduced. For i.d. larger than 500 nm, there is almost no influence from the negatively charged pipet surface so that current reaches constant saturation value just like in the solution without pipet. In order to understand the mechanism for the peculiar oscillating behavior measured using the 50 nm i.d. pipet, additional experiments were performed. The time dependent ion currents were also measured in 0.1 M KOH and HCl solutions, respectively. Figure 5a exhibits the result measured in 0.1 M KOH solution. The ion current reaches the saturation after the pipet arrives at the suitable position. Then the current reduces with a relative large slope and finally is kept stable at a lower value. However, the current measured in a 0.1 M HCl solution shows a different tendency. The current increases gradually and then is kept stable at a higher level, as shown in Figure 5b. The oscillations with different frequencies in the concentration of 0.01 and 1.0 M KCl solutions were also observed using 50 nm pipettes, as shown in the Figure S1 and Figure S2 in the Supporting Information. We should note that the double layer thickness is estimated by inside electrolyte concentration instead by the concentration outside the pipet such as 0.01, 0.1, and 1.0 M. However, the outside solution concentration affects the ionic motion inside the pipet due to the difference in electric field and diffusion, and thus current oscillation behavior. The current oscillation measured in the KCl solution as shown in Figure 3b is very similar to the oscillatory BZ reaction. This oscillating effect is nonequilibrium. The KOH and HCl worked as the inhibitor and activator in this study, respectively, which decrease and increase the cation concentrations inside the pipet. The negatively charged glass surface arises from the dissociation of surface silanol group Si−OH; from adsorption of hydroxyls; and from cation exchange,25 which indicates the negative charges of the glass surface derived from the group of SiO− or −OH. In this study, we apply a positive voltage to the Ag/AgCl electrode outside a pipet resulting in the cations such as K+ and H+ moving into the pipet from the solution. And the region near the pore opening of the pipet is cation-selective, which will repel the negative Cl− and OH − ions from the pipet. Because the solution
⎛ z en Δϕ ⎞ Ji = −Di⎜ i i ⎟ ⎝ kTLx ⎠ 14860
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Figure 6. Schematic diagram showing relation between inner surface states of pipet and oscillating ion current. The yellow color indicates glass pipet. The letter H indicates adsorbed H+ ion at the inner surface of pipet. The darker blue color indicates that cations are more constrained by the negatively charged surface of pipet.
Here ni, Di, zie are the number density, diffusion coefficient and charge of i species, respectively. ΔΦ, k, and T are the potential bias, Boltzmann constant, and temperature, and Lx is the length of the conical pipet, respectively. The potassium ion concentration nK+ can be estimated as nK+ =
circular cross-section that is substantially longer than its diameter.30 The equation can be described as follows: Q=
JK +
=
r
π ΔP 2 πr 4 (r − y 2 )y d y = ΔP 2μl 8μl
where Q is the volumetric flow rate, ΔP is the pressure drop, l is the length of pipe, μ is the dynamic viscosity, and r is the inner radius of pipet. In our system, according to the van’t Hoff law, ΔP can be expressed as:
1 M = 4 × 10−4 M 48.16d
And we can get the ratio of the flux JH +
∫0
D H +n H + = 1 × 10−3 D K +n K +
ΔP = RT Δc where Δc is the difference in concentrations between in and out of the pipet, R is molar gas constant and T is Kelvin temperature. Moreover, the ionic conductance in double layer σd is smaller than that in bulk layer σb according to the results we got in the KOH and HCl solutions. Then, the HagenPoiseulle equation can be modified as follows to estimate the ion current I due to the electrical double layers and bulk layer:
The ratio of the current fluctuation over the average current can be obtained as iH+ 0.05 = = 3 × 10−2 iK+ 1.8
These two ratios are just about 1 order of magnitude difference, and not too significant deviation. That means the current fluctuation generated by H+ and OH− ions is possible. Figure 6 shows the schematic diagram of ion current oscillatory mechanism. As mentioned before, the H+ ions can be attracted by the negatively charged surface making the neutral glass surface and reducing the attraction of cations. The behavior is similar as in the HCl solution which shows the increase of current. At the same time, the OH− ions are increased due to the direction of the chemical reaction of water dissociation. The OH− ions react with the H+ adsorbed glass surface and then the negatively charged surface results in the decreased current like in the KOH solution. After achieving the minimum, the H+ ions eliminate the OH−ions and become the dominant ions driving the current as the same as the HCl solution. The cycles induce the current oscillation in a small range due to the low concentration of H+ and OH− from the water ionization. That is, the KCl solution in this study works as nonlinear system which can be considered as the combination of KOH and HCl solution with competitive contribution between OH− and H+ to maintaining the chemical equilibrium. The nonlinear oscillating behavior can be explained using the Hagen−Poiseuille equation, which is widely used in the fluid dynamics based on the assumption that the flow is laminar viscous and incompressible and the flow is through a constant
I = σb =
∫0
r − TD
r
2πyv dy+σd
∫r−T 2πyv dy D
π RT Δc {σdr 4 + (σb − σd)(TD − r )2 8μ l (r 2 + 2rTD − TD 2)}
where ν can be defined as ν = (ΔP/4μl)(r2 − y2). The first term (σdr4) in the brace is just the constant for the fixed radius, but the second term ((σb − σd)(TD − r)2(r2 + 2rTD − TD2)) in the brace indicates that the ion current will be varied as the change of double layer thickness. In other words, time-dependent TD due to dynamic change of ionic concentration inside the pipet may result in nonlinear oscillation of ion current. It is easy to understand that the ion current will achieve minimum (σdr4) when there is no bulk layer (TD = r) and maximum (σbr4) when there is only bulk layer (TD = 0). In summary, we investigated the dependence of ion current measured in the 0.1 M KCl solution on the size of glass pipet. It was significantly interesting that the oscillating behavior was observed using the 50 nm pipet during the time-dependent ion current experiment. The oscillatory behavior was explained by comparing with the very distinguishing behaviors observed in 0.1 M KOH and HCl solutions, respectively, under the same 14861
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experimental conditions. Competitive roles of H+ and OH− ions in 50 nm pipet containing KCl solution may induce oscillatory current behaviors.
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ASSOCIATED CONTENT
* Supporting Information S
Oscillations in the concentration of 0.01 and 1.0 M KCl solutions using 50 nm pipettes. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: (T.T)
[email protected]; (B.H.P) baehpark@ konkuk.ac.kr. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to Professor Futoshi Iwata of Shizuoka University for providing submicropipet probes. This work was supported by the Basic Science Program through the NRF of Korea funded by the MEST (2010-0024525), the KOSEF NRL Program grant funded by the Korea Government MEST (20080060004), and the WCU Program through the KOSEF funded by the MEST (R31-2008-000-10057-0).
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