Figure 2 shows typical current signals under various applied voltages, when KCl solution (0.05 M, pH = 7) is filled in the micro-channel with a diameter of .

Fig. 2.

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	Fig. 2. (color online) Current value curve with time, 0.05-M KCl solution, pH = 7, diameter of channel . (a) The current decays with time. Pausing about 2 minutes between 10 mV and 20 mV, and 20 mV and 40 mV. (b) The relationship between steady state current and external applied voltage. The solid line is curve fitted.

In Fig. 2(a), it can be clearly observed that under 10 mV, the current had a greater positive value initially, followed by a quickly decreasing. After a few seconds, a steady state was achieved. The steady current was negative at approximately −3.8 nA. When the external voltage is 20 mV, the current signal exhibits a larger initial value and a positive steady state at 1.6 nA. Furthermore, when the external voltage was increased to 40 mV, the initial current becomes even larger. The steady state current is 4.1 nA. The current always exhibits larger value in the initial phase, and then quickly decreased to a steady state as shown in Fig. 2(a).

The variation of steady state currents ( ) with applied voltage (U) is plotted in Fig. 2(b). When U is lower than a critical voltage ( ), i.e., 18 mV, the steady current is negative. The current is in the opposite direction of the external voltage. When U is larger than 18 mV, the becames positive, i.e., in the same direction of the external voltage. Besides, generally say, increases U monotonically. The relation between the steady current and external applied voltage U, as shown in Fig. 2(b), can be approximately expressed by an exponential function as follows:

Figure 3 displays the six typical current signals recorded during the experiments.^[22] These six typical current signals can be attributed to two different mechanisms, depending on the applied parameters.

Fig. 3.

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Fig. 3. (color online) Typical models of current signal curves at the initial stage. The current signals in panels (d), (e), and (f) are the reversal response of panels (a), (b), and (c), respectively. [(a) and (b)]: A typical exponential decay of I, where 0.05-M KCl, external voltage is 100 mV, 20 mV, respectively, pH = 7, the channel diameter is . (c): A typical oscillating decay of I, where 0.2-M KCl, at 25 mV, and pH = 7, . [(d) and (e)]: A typical exponential decay of , where 0.05-M KCl, external voltage is 200 mV, 300 mV, respectively, and pH = 7, . (f): A tyical oscillating decay of , where 0.2-M KCl, external voltage is 20 mV, pH = 7, .

As shown in Figs. 3(a), 3(b), 3(d), and 3(e), initially, the magnitudes of currents increases rapidly to a peak value. After that, the current magnitude monotonically decreases with time respectively. The evolution of current can be divided into three stages: (i) initiation stage; (ii) attenuation stage; and (iii) steady-state stage. This phenomena was also observed by Morrow and McKenzie,^[19] as soon as the power source was switched on. They attributed this phenomenon to the necessity of time cost to achieve the applied voltage value. However, their theory cannot explain the peak of current. Actually, the current characters shown in Figs. 2(a) and 3 can be better understood with the overpotential theory^[24] and the EDL theory^[25] in the three-electrode monitoring system.

During the experiments, the Pt electrodes will be polarized so long as there is electric current passing through the electrodes, which produces overpotentials on the electrodes. The potentials of the electrodes will exhibit deviation from the original equilibrium one ( ). The potential of the cathode is lower than that of the theoretical equilibrium value ( ), and the anode potential is larger than the anode potential at theoretical equilibrium ( ), where is the potential of cathode, is the potential of anode, and is the overpotential. This deviation from the equilibrium electrode potential is defined as the overpotential (Pt), and therefore the practical electrode potential is not equal to the theoretical value.

Generally say,^[26] overpotentials can be grouped into three categories: activation, concentration, and resistance. Since Pt electrodes have very stable physical and chemical properties, the activation overpotentials around the interface of Pt electrodes are negligible.^[27] Therefore, the overpotentials around the interface of Pt electrodes are primarily determined by the concentration and resistance overpotentials.^[28] Both of them can results in a peak current: the former one can generated peak current by polarization overpotential, while the latter one is always accompanied with the peak current in the “switch on” process. Since in the experiments, the measurement is normally conducted after the electrodes was immersed in the solution, the initial polarization has been finished. Therefore, the peak current should be aualitatively dominated by the resistance overpotentials.

If the initial overpotential is not sufficiently strong (probably due to the low ionic concentration), after the peak current is generated, a screening region will be formed gradually by the accumulation of these opposing charges near the electrodes. This screening region is also denoted as the EDL of the electrode pole.^[27] Then, a shield electric field ( ) along the micro-channel in the opposite direction to the external electric field ( is established. The slowly increasing accumulation of charges causes stronger shielding field . Consequently, the actual electric field intensity ( ) between the two electrodes gradually decreases, and the current is reduced with the square root of time as described by the Cottrell equation:^[29] , where n is the number of electrons transferred per molecule, F is the Faraday constant, S is the area of the electrode surface, C_R is the concentration of the reduced species R, and D_R is the diffusion coefficient of R. Eventually, the charges accumulated on the two electrode surfaces will achieve a saturation state, and so does the current.

While 0.2-M KCL solution is applied, the monotonic decaying process is replaced by an turn-over decaying process, as plotted in Figs. 3(c) and 3(f). Probably due to the higher concentration, a larger initial overpotential and faster charge accumulation can be predicted. A strong is generated. While the overpotential is finished, the external electric field is not sufficiently strong to overcome the high . The overall electric field intensity will be in the direction of and opposite to the external electric field. The turn-over phenomenon of current can be observed.

The six typical current response occurs not certainly in the measurements, but probably. Therefore, statistical analysis were proceeded on the 6 typical current signals to evaluate the probability of each case. The experiments were conducted in both 5- and 10- micro-channels. In the 5- micro-channel, a total of 273 measurements that show negative Is are statistically investigated. While in the 10- micro-channel, 353 measurements are statistically investigated. The probability histograms are plotted in Fig. 4.

Fig. 4.

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	Fig. 4. (color online) Histograms of the probabilities of six typical current signals corresponding to Figs. 3(a)–3(f) respectively. The green histograms with vertical stripes represent the probabilities of six current signal in the micro-channel with 5- diameter, and the orange histograms with horizontal stripes are for the 10- diameter micro-channel.

From Fig. 4, it can be observed:

(i) In the 5- micro-channel, among the six types of current signals, the phenomenon shown in Fig. 3(a) has the highest probability upto 69.96%. The curves shown in Fig. 3(d) has less chances at 27.11%. Relatively, the total probability of both Figs. 3(c) and 3(f) are 0.3662%.

(ii) In the 10- micro-channel, the probability of case (a) is decreased, while the probabilities of other cases are increased. The overall probability related to monotonic decaying process is slightly decreased in the 10- micro-channel, and the corresponding decaying process with turn-over phenomenon becomes more observable. Or in other words, in the micro-channel with smaller diameter, the turn-over phenomenon of current becomes rare and the current is more “controllable”.

Since the movement of bulk ions in our micro-channel system is primarily determined by three mechanisms, which are electrophoresis, electroosmotic flow and diffusion. Both the electrophoresis and diffusion are dominated by the length scale of micro-channel, not the diameter. Only the electroosmotic flow is strongly affected by the diameter of micro-channel. At the initial stage, due to overpotential, the EDL moves faster than at the steady state. And so does the bulk flow (out of EDL) of EOF. After the overpotential is finished, the steady state voltage cannot provide such a fast EOF, and there exists a deceleration of EDL. The EDL can be decelerated immediately due to electric field, but the bulk flow and the related ions movement cannot respond immediately. This may induce a disordered EOF, and the corresponding lag or oscillation of ion transport. In a smaller micro-channel, due to the stronger influence of viscosity, the ions movement in bulk flow can be decelerated faster than in a larger micro-channel. Therefore, the convective transport of ions by the inertial effect of bulk flow can be more controllable in smaller micro-channels and prohibit the generation turn-over phenomenon of current. This could explain why in the 10- micro-channel, the occurrence probability of decaying process with turn-over phenomenon is higher.

To investigate whether the current-reversal phenomenon occurred in a particular aqueous solution, four kinds of solutions were compared, which are DI Water, KCl (1.0 M), Tris (10 mM), and TBE. The TBE buffer is composed of Tris (hydroxymethyl) aminomethane, boric acid (Borate), and disodium ethylene diamine tetraacetic acid (EDTA-2Na) in a certain proportion. At the concentration of TBE, the concentration of Tris (hydroxymethyl) aminomethane, boric acid (Borate), and EDTA-2Na are 0.09 M, 0.09 M, and 0.002 M respectively.

Figure 5 shows the steady current values for the four aqueous solutions under 0 mV to 300 mV. It can be clearly seen, initially, all of the steady current values were negative. The currents increased gradually with voltage with different slopes. Due to the different initial steady current values and slopes of –U curves, the critical voltages in the four cases were 47 mV, 73 mV, 60 mV, and 94 mV, respectively. From Fig. 5, the phenomena of current reversal were observed in all the four aqueous solutions in the 5- diameter micro-channel driven by an electric field force. This indicates that the current-reversal phenomenon is not belong to a specific solution, but commonly existed.

Fig. 5.

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	Fig. 5. (color online) Steady current values of four solutions varying with external applied voltage. ■, •, ▴, and ⋆ represent DI water, 1× TBE, 1-M KCl, and 10-mM Tris, respectively. Diameter of channel .

To investigate the influence of the external applied voltage and its operation sequence on the current-reversal phenomenon, two kinds of voltage operation sequences were systematically studied as a comparison. That is, the external applied voltages were set to either increase from 0 mV to 400 mV or decrease from 400 mV to 0 mV.

In Fig. 6, the variations of steady current with voltage under different operation sequences are plotted, for all the four aqueous solutions. A hysteresis phenomenon can be found when changing the operation sequence. When a larger external voltage is applied, the difference of current values in different operation sequence becomes larger too. It is also found: 1) For each solution, the –U curve basically follows the exponential relationship in Eq. (1), no matter in which operation sequence; 2) The value in the increasing process was a little bit larger than that of the decreasing process, i.e. there is hysteresis phenomenon between the two operation sequences.

Fig. 6.

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	Fig. 6. (color online) Steady current varying with external applied voltage. ■ and represent the applied voltage change sequence for an increasing and decreasing process, respectively. (a) 1× TBE, (b) 1-M KCl, (c) 10-mM Tris, and (d) DI water. Diameter .

The hysteresis of current can be attributed to the charge accumulation on electrode surface. When the applied voltage was increased, more charges were accumulated on the electrode surface. An equilibrium state of electric field in micro-channel is rapidly established. While the applied voltage was decreased, the surface charges cannot stay around the electrodes and diffused back to the bulk solution. However, since the charge accumulation on the electrode surfaces that determined by electrostatic force is much faster than that of ions diffused back to bulk solution (on the time scale of 10³ s–10⁴ s), much more time is required to establish a new equilibrium state. The residue charges around electrodes generate opposite electric field relative to the applied external one. It results in a smaller overall electric field in the micro-channel, and so does the smaller current values. This is why hysteresis phenomenon of current can be observed.

Consequently, the of the increasing sequence was smaller than that of the decreasing process, as shown in Table 2. For the four solutions, i.e., 1× TBE (Fig. 6(a)), 1-M KCl (Fig. 6(b), 10-mM Tris (Fig. 6(c), and DI water (Fig. 6(d), in the increasing process were 92, 73, 66, and 47 mV, respectively, while the in the decrease process were 94, 76, 69, and 48 mV, respectively. However, the difference is very small. The relative difference is no more than 4.5% in all the four cases. Therefore, the operation sequence of applying voltage should not have a significant effect on the measurement of current reversal phenomenon.

Table 2.

Table 2.

Table 2. Critical voltages under the two opposite operation sequences of the voltage. . Critical voltage ( ) Solution Increasing/mV Decreasing/mV Difference/mV Average/mV Percentage a /% 1× TBE 92 94 2 93 2.15 1-M KCl 73 76 3 74.5 4.03 10-mM Tris 66 69 3 67.5 4.44 DI Water 47 48 1 47.5 2.11 a .

Table 2. Critical voltages under the two opposite operation sequences of the voltage. .

Case (a): In micro-channel

KCl electrolyte with various concentrations was selected to investigate how the current-reversal phenomenon was affected by the ionic concentration. The experiments were conducted in the 5- micro-channel.

Figure 7(a) shows the –U relations under different ionic concentrations by ensemble averaging. Since in single-biomolecule detection, the buffer concentration is usually lower than 1 M, the selected ionic concentrations were 0.2 M, 0.5 M, and 1.0 M, respectively. It can be seen, in all the three concentrations, the initial current values are negative. As the concentrations of KCl aqueous solution is increased, i.e., 0.2 M, 0.5 M, and 1.0 M, the values of in the increasing process of applied voltage were 52, 31, and 20 mV, respectively. Therefore, with increasing ionic concentration of the KCl solution, the critical voltage was reduced, which revealed that the screening electric field produced was smaller with larger ionic concentration.

Fig. 7.

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	Fig. 7. (color online) The ensemble averaging steady current versus applied voltage and the corresponding critical voltages, for various ionic concentrations of KCl solution. Here, pH = 6. (a) –U relation in 5- micro-channel. (b) –U relation in 500-nm submicro-channel. (c) The relation between ionic concentration and critical voltage in the channels with different diameter.

Case (b): 500-nm-diameter channel

The influence of the KCl concentration on the current-reversal phenomenon is also investigated in the 500-nm channels, as shown in Fig. 7(b). Three concentrations of the KCl solution are considered, which are 0.2 M, 0.5 M, and 1.0 M, respectively.

It can be seen, the –U relation is less exponential at lower concentrations. At the concentration of 0.2 M, the –U relation approaches approximately linear. As the concentration is increased, the –U becomes consistent with the exponential equation (1) . For each working condition, was negative at the beginning and then reversed to a positive value as the voltage is increased.

Case (c): UC versus ionic concentration

The relations between critical voltages and concentrations in the two channels are plotted in Fig. 7(c). It can be seen in both cases, the critical voltage decreased with increasing concentration (C) of solution. In the meanwhile, at same concentration, the critical voltages in 500-nm channel is always higher than in the 5- channel. The influence of channel diameter will be discussed in details later.

The main reason for this phenomenon could also be the electrical double layer (EDL) on the electrodes. The EDL thickness (Debye length) is thinner at higher ion strength and thicker at lower ion strength, and the strength of the screening electrical field increases with increasing EDL thickness. The thickness of EDL changes with the ionic concentration.^[30,31] For a monovalent electrolyte at 25 °C (298 K), the Debye length (k ⁻¹, k is the Debye–Hückel parameter) of the aqueous solution can be described with the following equation:^[32] . where C is the solution concentration. For the solution with same ions, when the solution concentration is lower, the thickness of the EDL of the electrode surface is greater and the zeta-potential is higher.^[33] The shielding field caused by the accumulated charges is stronger. As a result, a great amount of applied voltage is required to counteract the effect of the shielding field, and the critical voltage is larger.

In the practical applications of micro-nanofluidic technology, especially for studying single biological molecules, the pH value of the solution is a critical factor. For example, the pH value of buffer solution is usually set as alkalescent environment to ensure the activity of DNA molecules.

Figure 8 shows how the steady current value and the critical voltage are affected by pH values. During our experiments, the pH values of solutions, such as pH = 2, 4 (acidic), pH = 9, 11 (alkali), as well as the neutral condition pH = 7, were selected. Extreme conditions such as pH = 1 or 12 were not chosen because these values are not commonly used in practical applications and may damage the electrode.

Fig. 8.

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	Fig. 8. (color online) (a) Steady current versus applied voltage under various pH values. (b) Critical voltage versus pH value. 1.0-M KCl solution. .

It can be seen in Fig. 8(a) that under different pH values, all the –U curves matches well with Eq. (1), despite the different fitting coefficients. The steady currents were first negative and then reversed to positive as the external applied voltage is increased. The critical voltage was not a constant, but decreased with the increasing pH value by a linear relationship approximately, as shown in Fig. 8(b). This could be attributed to the charges absorbed onto the electrode surface^[24,25] and induce different surficial potential which were significantly affected by the pH value. In principle, once a solid-oxide material is immersed into electrolytic solution, the solid-liquid surface then forms an electrically charged layer. This layer can be due to two mechanisms:^[34,35] (a) amphoteric dissociation of surface MOH groups, i.e., or ; (b) adsorption of metal hydroxo complexes derived from the hydrolysis products of material dissolved from the solid, i.e., from amphoteric dissociation of . Here, M stands for a metallic element. Both mechanisms can partially qualitatively explain the relationship between the pH value and surface charge.

When the amount of net surface charge is equal to zero, the pH value is defined as the isoelectric point (IEP) or the zero point of charge (ZPC).^[36] The ZPC has been widely employed to indicate that there is no surface charge of a metal oxide immersed into solution, or to reveal that the concentrations of the anion and cation of hydroxyl complexes are equal and electrically neutral. During our experiments, when the platinum (Pt) electrode was immersed into the electrolytic solution, there was a chemical reaction equilibrium between the metal (Pt) and metal oxide (PtO) on and near the electrode surface. The reaction can be described by the following equation:^[37,38] . Kruyt et al.^[39] has found that the ZPC of PtO is approximately equal to 14. Thus, it can be reasonably speculated that the net charge adsorbed onto the electrode surface should be reduced as the pH value increases Recently, Morrow and McKenzie^[19] found that in pure water, a large number of anions were gathered around and onto the anode and then the nearby hydronium ions ( ) were consumed. This increases the local pH value. In the meanwhile, the surrounding the cathode resulted in the environmental pH value decreasing. They have also observed that both the maximum and minimum pH value on each electrode linearly changed with the external applied voltage. Therefore, it can be inferred that because of the influence of solution pH, the adsorption ability of the anode surface is weaker than that of the cathode, and the amount of surface charge on the anode is lower than that on the cathode.

In micro-nanofluidics, as the inner diameter of channel is decreased, the surface-to-volume ratio increases. The scale effect and surface effect becomes stronger.

To evaluate the role of the channel diameter on the current-reversal phenomenon, three channel diameters, i.e., 200 nm, 500 nm, and , were employed. Figure 9 shows the –U relations in 0.5-M and 1-M KCl electrolytes in the three channels. From Fig. 9(a), it can be seen that in the channels with diameters of 200 nm, 500 nm, and , of 0.5-M KCl solution were 123 mV, 60 mV, and 30 mV, respectively. While, for the 1-M KCl solution as shown in Fig. 9(b), were 116 mV, 51 mV, and 20 mV respectively. Apparently, the critical voltages decrease with the increasing channel diameter. This implies the influence of surface electrochemistry becomes important.

Fig. 9.

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	Fig. 9. (color online) Steady current versus voltage for various channel diameters. The concentrations of the electrolyte KCl are (a) 0.5 M and (b) 1 M. ■, , and represent channel diameters of 200 nm, 500 nm, and , respectively.

This might be related to electroosmosis,^[40,41] since electroosmotic flow can cause an opposite convection of ions and inhibit the ions transport by electrophoresis. With the decreasing of the channel diameter, the electroosmotic flow might be strengthened; thus, to counter balance the opposite electric field, the external electric field needs to be comparatively stronger. As a result, the increases with the decreasing diameter of the channel. The in 10- micro-channel was also studied. Since the critical voltage is negligibly affected by the solution concentration, the data is not shown.

From Fig. 9, it can be clearly observed that, no matter what the size of the channel diameter is, the current-reversal phenomena occurred in all the investigated cases. Also, the variations of the steady current versus applied voltage were highly similar and consistent with Eq. (1). For the 500-nm-diameter channel: a = 0.11634 nA, b = −0.35934 nA, and k = −110.54472 mV, while for the 200-nm-diameter channel: a = 0.10392 nA, b = −0.34016 nA, and k = −105.8402 mV. These results indicate that the current-reversal phenomenon was not occasionally occurs in a particular channel.