Enhanced Ion Current Rectification in 2D Graphene‐Based Nanofluidic Devices

Furthering the promise of graphene‐based planar nanofluidic devices as flexible, robust, low cost, and facile large‐scale alternatives to conventional nanochannels for ion transport, we show how the nonlinear current–voltage (I–V) characteristics and ion current rectification in these platforms can be enhanced by increasing the system asymmetry. Asymmetric cuts made to the 2D multilayered graphene oxide film, for example, introduces further asymmetry to that natively inherent in the structurally symmetric system, which was recently shown to be responsible for its rectification behavior due to diffusion boundary layer fore–aft asymmetry. Supported by good agreement with theory, we attribute the enhancement to the decrease in the limiting current in the positive bias state in which counter‐ion trapping occurs within the negatively charged graphene oxide sheets due to increased film permselectivity as its cross‐section and surface charge distribution is altered on one end; these effects being shown to be sensitive to the electrolyte pH. Further, we show that an imbalance in the pH or concentration in the microreservoirs flanking the film can also increase asymmetry and hence rectification, in addition to displaying a host of other phenomena associated with the I–V characteristics of typical nanochannel electrokinetic systems.


Results and Discussion
In structurally/geometrically symmetric GO fi lms, it was recently found that ion current rectifi cation arises-quite unexpectedly given the absence of any apparent asymmetry in the system-from counter-ion trapping within the fi lm during the positive bias cycle that retards ion migration through the negatively-charged sheets, and their corresponding release during the negative bias cycle that leads to an enhanced electromigration fl ux through the sheets. [ 30 ] It is this counter-ion trapping and release that disrupts the electrokinetic fore-aft symmetry inherent in the structurally symmetric fi lm, particularly in the diffusion boundary layer, thus endowing it with the rectifi cation characteristics observed. It is also possible that the nonuniform electric fi eld that arises within the sheets due to the tortuosity in the spaces between them also contributes to the inherent asymmetry of the system, although this appears to be a secondary effect. We show here that it is possible to increase the degree of rectifi cation in the GO fi lm by introducing further asymmetry to the system in a variety of ways, which we examine in turn: the fi lm geometry (Section 3.1), solution pH (Section 3.2), and solution concentration (Section 3.3).

Geometrical Asymmetry
Reminiscent of symmetry breaking and rectifi cation in conical nanopores, [ 1,21,31,35,36 ] one way geometrical asymmetry can be introduced in a 2D planar structure such as the GO fi lms examined here, for example, is to cut the fi lm into a trapezoidal geometry such that one end is narrower than the other. Figure 1 a, in fact, shows that the rectifi cation factor F (the ratio of the currents measured for applied voltages with the same amplitude but opposite polarities | I (− V ) / I (+ V ) |, wherein I (− V ) and I (+ V ) are the reverse and forward currents measured at negative and positive bias voltages applied to the working electrode (WE), respectively) approximately doubles with the tapered geometry (the dependence of F on the degree of tapering will be investigated subsequently), at least initially for voltages up to ±2 V. Beyond this voltage, however, we observe the rectification behavior of the asymmetric fi lm to decrease despite the monotonic increase in the rectifi cation with applied voltage in its symmetric counterpart, and hence the rectifi cation enhancement to diminish considerably. As an aside, while swapping the working and counter electrodes with respect to the fi lm did not lead to any differences for the geometrically symmetric fi lm, [ 30 ] we observe in contrast in Figure 2 that effects of the geometric asymmetry in the fi lm (i.e., the saturation in the current at lower bias voltages and hence the lower limiting current values at the tapered end, the reason for which we elucidate below) are preserved, as would be expected. Nevertheless, we note that only the polarity of the current inverts; the magnitude of the current at a given voltage however remains similar, which is at pH 7 for geometrically symmetric (red squares) and asymmetric (black triangles) GO fi lms. The inset in (a) shows an extension to higher voltages for the symmetric case, indicating that a maximum in the rectifi cation factor also arises in this case above a critical gating voltage of approximately 6 V, whereas the inset in b) is a magnifi cation of the positive bias region, showing the earlier transition to the overlimiting region in the asymmetric case, as observed by the lower critical gating voltage of approximately 2 V.

Figure 2.
Effect of reversing the working and counter electrodes (WE and CE, respectively), with respect to the geometrically asymmetric fi lm (cross-sectional area ratio b / a = 3) on its I -V characteristics. The electrolyte concentration and pH was maintained at 0.1 × 10 −3 M and a value of 7, respectively. consistent with that shown previously for geometrically similar fi lms wherein the rectifi cation, and hence the underlying charge trapping mechanism responsible for giving rise to it, is insensitive to reversal of the electrodes. [ 30 ] To understand the observations above, in particular, the maximum and subsequent decay in the rectifi cation factor in the geometrically asymmetric fi lm, we fi rst examine the I -V characteristics of the system. As seen in Figure 1 b, the I -V characteristics for these systems are essentially nonlinear and similar to that typically observed for nanopore/nanochannel geometries due to the ion permselectivity endowed in the pores as a consequence of the overlap in the Debye layers when their lengths become comparable to that of the nanopore/nanochannel dimension above a critical electrolyte concentration. [ 1,[32][33][34] Briefl y, the I -V curves for these systems comprise a linear Ohmic region at low voltages followed by a limiting current region above a threshold voltage over which the current plateaus when the ion concentration at the reservoir-fi lm entrance vanishes. The current then starts to increase again beyond a critical gating voltage in what is known as the overlimiting current region due to the dominance of the electromigration fl ux over the diffusive fl ux in the nanopore/nanochannel, or in this case, the interstitial spaces between the GO sheets. The large current density that forms as a consequence of the convergence of the electric fi eld from the micrometer dimension reservoir into the nanopore/nanochannel can only be sustained through the formation of an electroneutral diffusion layer at the reservoir-pore/channel entrance/exit in both the diffusion-limited Ohmic and limiting current regions, [ 37 ] whereas an additional concentration polarization layer known as the secondary double layer rich in counter-ions forms in the overlimiting current region due to the strong electromigration fl ux. [ 38,39 ] From Figure 1 b, it can be seen that both the symmetric and asymmetric GO fi lms exhibit such typical nonlinear I -V characteristics although we note that the asymmetric fi lm not only possesses a lower limiting current I lim but also a shorter voltage range over which the limiting current behavior is observed, i.e., a lower critical gating voltage of around 2 V exists for the asymmetric fi lm above which the current increases sharply (in contrast to the critical gating voltage of approximately 6 V for the symmetric case, as observed in Figure 1 b, and the inset of Figure 1 a); this is possibly due to the stronger electromigration fl ux in the fi lm arising from the the increased intensity of the convective vortices in the secondary polarization layer [ 40,41 ] as a consequence of the fi eld focusing effect at the narrow end of the asymmetric fi lm. Given that the primary mechanism for the symmetry breaking and hence the observed rectifi cation behavior in the GO fi lm lies in the existence of the asymmetric diffusion boundary layers at both ends of the fi lm as a consequence of the counter-ion trapping and release, [ 30 ] it then becomes clear that the disruption in the diffusion boundary layer to form the secondary double layer above the critical gating voltage of 2 V is the reason for the observed decrease in the rectifi cation above this voltage in Figure 1 a. A corresponding decrease in the rectifi cation is not observed for the symmetric GO fi lm in Figure 1 a over the scan range of ±6 V because both its limiting current and critical gating voltage are considerably higher than its asymmetric counterpart, as seen in Figure 1 b.
Here, we adopt, for simplicity, the 1D model by Yossifon et al. [ 37 ] which captures the transport of ions through a nanochannel membrane fl anked by two microreservoirs-a confi guration that is similar to the present work given that the interstitial space between the sheets that make up the multilayered GO fi lm of height h (≈1 nm after swelling in water [ 30,42 ] ) can be approximated by n discrete parallel "nanochannels" with effective height h eff = nh . By matching the electric fi eld and fl ux at the nanochannel-reservoir interfaces at both entrance and exit ends, Yossifon et al. were able to capture the electric fi eld focusing effect that arises due to the convergence of the 2D fi eld in the radially symmetric reservoir into the nanochannel, which is assumed to have a height that is much smaller than the reservoir dimension. The holistic treatment of the system, which not just considers the ion transport through the nanochannel, but also that in the bulk reservoir region as well as in the boundary layers at the nanochannel-reservoir interface, in addition to a departure from an equilibrium treatment of the Debye layer (i.e., the Donnan theory), allows a more comprehensive insight into the nonlinear I -V characteristics (particularly in the overlimiting region) in permselective nanoporous membranes. This is a particularly important consideration given that such nonlinear I -V characteristics and the associated diffusion boundary layer play a central role in the GO fi lm and its rectifi cation behavior that we explore here. [ 30 ] Although the model does not capture the transient dynamics of the ion trapping and release within the GO sheets and hence the resulting asymmetry in the diffusion boundary layers, it provides a suffi ciently adequate framework for interpreting our observations given that we simply seek insight into the limiting current behavior.
By solving the Nernst-Planck equations that govern the transport of ions of a symmetric electrolyte with equal diffusivities D together with Poisson's equation in each of the three regions together with appropriately matched interface and farfi eld conditions, Yossifon et al. showed that it was possible to obtain the ionic fl ux entering the nanochannel and hence an expression for the limiting current. [ 32,37 ] Given our approximation of n nanochannels stacked in parallel to model the interstitial space between the sheets in the GO fi lm of width w and length L , the limiting current across the fi lm can simply be approximated by the sum of the limiting currents for each nanochannel in parallel, i.e., where η is the degree of permselectivity of the fi lm with η → ∞ for ideal permselectivity. In the above, c 0 is the concentration of the buffer solution in the bulk reservoir and L e is the thickness of the concentration polarization layer that comprises the Debye layer, the diffusion boundary layer, and the secondary double layer. [ 43 ] Yossifon et al . demonstrated that L e can be adequately approximated by the distance between the nanochannel-reservoir interface and the electrode, which, in this case, is around 2 mm. We note from Equation ( 1) that the limiting current is dependent on both the width of the fi lm w and hence its geometry at the entrance and exit, as well as the factor ( η + 1)/( η − 1), which is related to the volume charge density in the fi lm X = 2σ/ zFh eff (assumed uniform) through the ratio of the counterion to co-ion concentrations within the fi lm, i.e., η = c assuming that the GO fi lm is negatively charged. These, in turn, can be obtained from the equilibrium Donnan theory [ 44 ] We now proceed to use these relationships to understand the consequences of introducing geometrical asymmetry, in particular, through variations in the cross-sectional area and the surface charge distribution across the GO fi lm, on its I -V characteristics and rectifi cation behavior.
It can be seen from Figure 3 that the introduction of geometric fore-aft asymmetry by cutting the fi lm leads to a departure from linearity in the fi lm's I -V characteristics; the greater the asymmetry, captured through its cross-sectional area ratio b / a , the more nonlinear the behavior that is observed. That this effect is only seen for positive bias voltage and not in the negative bias state, and thus the rectifi cation that arises (the degree of rectifi cation increasing with increasing asymmetry), was attributed to a push versus pull mechanism postulated by Miansari et al. [ 30 ] In addition, we observe the limiting current in Figures 3 a and 4 a to decrease with increasing geometric asymmetry, although we note that the decrease in the nonlinearity observed and in the limiting current appears to asymptote to a constant value as the fi lm cross-section at the entrance and exit ends becomes increasingly divergent.
This trend can also be seen in the prediction afforded by Equation ( 1) . The surface charge density was obtained from the measured conductance across the fi lm, which, for n parallel nanochannels, is simply n times the conductance of a single nanochannel, given by [ 29,30 ] 2| | the fi rst term on the right representing the bulk conductance, which dominates at high ionic strengths, and the second term the double layer conductance (including the fraction of excess K + and H + ions within the nanochannel), which dominates at low ionic strengths. In the above, 7.63 10 s are the mobilities of the various ionic species in the system. [ 45 ] Briefl y, we fi rst calculate h eff by considering only the fi rst term on the right side of Equation ( 3) and measuring the conductance at high salt concentration (1 M KCl) such that the fi lm only exhibits bulk-solution like conductance, [ 30,42 ] from which n = h eff / h can be estimated. We then obtain approximate values for σ by considering the full expression given in Equation ( 3) by measuring the total conductance at low ionic concentrations (0.1 × 10 −3 M ) and dividing by n . As seen from Figure 4 a, relatively good agreement is obtained between the limiting current that is predicted with that observed experimentally. We note that although the limiting current is linearly dependent on the width of the fi lm, as suggested by Equation ( 1) , the effect of altering the cross-sectional area of the fi lm on the limiting current is much more complex given that X and hence h eff varies for different geometries, thus leading to different values for ( η + 1)/( η − 1).
The solution pH and hence the surface charge distribution within the fi lm can also infl uence the limiting current in the geometrically asymmetric GO fi lm ( b / a = 3), as seen from Equation ( 1) . To investigate this effect, we record the fi lm's I -V characteristics for acidic (pH = 2 and pH = 5) as well as basic (pH = 9) solutions ( Figure 5 ), corresponding to estimated η values of approximately 1.44, 4.10, and 6.33, or ( η + 1)/( η − 1) ≈ 5.54, 1.65, and 1.37, respectively. The increase in the fi lm's permselectivity, refl ected in the increase in the value of η with pH, is a consequence of the increase in the dissociation of the carboxylic acid groups in the GO sheets (COOH → COO − + H + ), which therefore leads to an increase in the number density of the COO − surface charges. [ 30 ] From Equation ( 1) , we thus expect the I -V curves to become more nonlinear and hence the limiting current to decrease monotonically with increasing solution pH. However, it can be seen from both Figures 4 b and 5 that the behavior is, in contrast, nonmonotonic. This is because the conductance did not signifi cantly change with increasing pH above the dissociation point of the carboxyl groups along the surface of the GO sheets (pK a ≈ 4.2), at which point the reduction in surface charge and the electrostatic repulsion associated with the  overlapping Debye layers in the nanochannels result in the collapse of the fi lm, [ 30 ] thus reducing its height and cross-sectional area in Equation ( 1) , and therefore suppressing further decrease in the conductance and hence decrease in the limiting current at pH 5. In fact, we observe this effect to slightly overcompensate at high pH such that there is a small increase in the limiting current (Figure 4 b) and corresponding decrease in the rectifi cation factor (Figure 5 b); the overcompensation becoming increasingly pronounced at higher voltages, consistent with our previously reported results for geometrically symmetric fi lms. [ 30 ] Parenthetically, we also note that Figure 5 a suggests that the departure from nonlinearity can still be observed even if the nanochannels do not possess large ion-selectivity at low pH values, although we observe the onset of nonlinearity at the limiting current to occur at larger currents and at higher applied voltages.

Solution pH Asymmetry
The above study examining the infl uence of the solution pH on the limiting current and hence the rectifi cation behavior of GO fi lms can be further extended by generating an asymmetric imbalance in the solution pH on the anodic and cathodic reservoirs surrounding a geometrically symmetric GO fi lm. Figure 6 shows the degree of rectifi cation to be very sensitive to variations in the solution pH in the reservoir that interfaces the narrow end (while being held constant at the wide end) compared to the case when the solution pH is varied in the reservoir at the wide end (and held constant at the narrow end), which is almost insensitive to the pH variation. This is because of the compounding effects of both the cross-sectional area and the surface charge distribution on the limiting current previously discussed in Section 3.1. More specifi cally, the rectifi cation ratio F is observed to continuously increase when the pH at the wide end is held at highly basic conditions (pH = 11) and the pH at the narrow end is gradually increased until the pH levels are symmetric across the fi lm. We postulate that this is a result of the decrease in I (+ V ) due to the opposing cation (K + ) diffusion from the high pH end to the low pH end of the GO fi lm. In contrast, F is observed to decrease again above pH 7 at the narrow end when the pH at the wide end is held under acidic conditions (pH = 2) due to a reversal in the direction of the cation diffusion, thus leading to a decrease in I (− V ) and hence the rectifi cation ratio ( Figure 6 ). Below, we will isolate these confounding effects to allow us to examine the effects of asymmetry in the solution pH alone by considering a geometrically symmetric GO fi lm.   To ascertain the effects of the asymmetry in the solution pH in isolation from that arising from geometrical asymmetry, we repeated these experiments but with a geometrically symmetric fi lm. Figure 7 records our observations when the solution pH in the reservoir on the grounded counter electrode (CE) end is similarly ramped from acidic (pH 2) to basic (pH 11) conditions for both cases when the solution pH in the reservoir on the working electrode (WE) end to which a positive or negative bias is applied is held constant either in acidic or basic state. Consistent with our observations in Section 3.1, we observe the permselectivity η to increase and hence ( η + 1)/( η − 1) to decrease from acidic to basic conditions, which generally leads to a decrease in the limiting current (Equation ( 1) ). Again, we however do not observe a monotonic decrease but rather an infl exion around pH 7, which can also be attributed to the collapse of the fi lm above the dissociation point discussed above and in Miansari et al. [ 30 ] In keeping with our observations for geometrically asymmetric fi lms, we also observe the reversal in the rectifi cation at low pH, again likely due to proton adsorption under the highly acidic conditions (Figure 7 d); we note the reversal is not observed when the conditions in the reservoir at the WE end were basic (Figure 7 c).

Solution Concentration Asymmetry
We now turn our attention to investigating the effects of asymmetry obtained by introducing an imbalance in the electrolyte concentration in the anodic and cathodic reservoirs, fi rst for a geometrically symmetric fi lm and subsequently for a geometrically asymmetric one.   as would be expected, when the concentration of the solution on the grounded CE and WE ends were 10 and 0.1 × 10 −3 M , respectively; the amount by which the rectifi cation increases with the applied voltage, however, remained similar for both cases. The reason for the increase in the rectifi cation with solution concentration asymmetry can be attributed to the increase not only in the limiting current but also in the threshold voltage at which the limiting current for the negative voltage bias occurs (Figure 8 b). This is a consequence of a reduction in the Debye length on the CE end as the electrolyte concentration is increased, thus leading to a diminution in the ion permselectivity of the fi lm. The decrease in η , corresponding to an increase in ( η + 1)/( η − 1) in Equation ( 1) then results in an increase in the value for I (− V ) . Similarly, the low electrolyte concentration at the WE end leads to a decrease in the limiting current, the corresponding threshold voltage and hence the value of I (+ V ) on the positive voltage bias state (Figure 8 b). As such, the degree of rectifi cation F ≡ | I (− V ) / I (+ V ) | increases with asymmetry in the electrolyte concentration.
Further, it can be seen from the low mV I -V characteristics in Figure 9 a that the asymmetric electrolyte concentration across the reservoirs gives rise to a fi nite current I net = I p + I n , wherein I p and I n are the ionic current contributions by the cations (K + ) and anions (Cl − ), respectively, even in the absence of an applied potential. Figure 9 b shows the dependence of this zero-volt current that is generated due to net ion diffusion through the interstitial spaces between the sheets that make up the GO fi lm [ 46,47 ] on the difference in the concentration in both reservoirs C max / C min ; the current was recorded by maintaining the low concentration end at 1 × 10 −3 M while varying the concentration on the other end from 1 × 10 −3 M to 1 M . We observe the current to increase drastically with increasing salinity difference. Likewise, the faster cation transport compared to that for anions in the cation-selective nanochannels comprising the GO fi lm-a consequence of its native negative surface charge and overlapping Debye layers [ 30 ] -gives rise to more cation accumulation on one end relative to the other end of the nanochannel, thus producing a potential at zero current, known as the reversal potential [ 48,49 ] V rev (Figure 9 a). The reversal potential is also present for a geometrically asymmetric fi lm. As seen in Figure 9 c, V rev increases with increasing geometrical asymmetry, i.e., increasing b / a values, due to the accumulation of more cations along the wide end of the GO fi lm compared to that at the narrow end such that one end of the fi lm is more positively charged relative to the other, thus producing a larger reversal potential. These observations are, to our best knowledge, the fi rst time electrical power generation has been shown in planar graphene-based nanofl uidic devices simply through the introduction of a salinity gradient across the fi lm, therefore offering an alternative to the membranes used in pressureretarded osmosis and reverse dialysis. [ 47,50,51 ] Further, it can be seen that both I net and V rev are dependent on the permselectivity of the fi lm and hence the solution pH, whose effect on the permselectivity has already been discussed in Sections 3.1 and 3.2, i.e., the permselectivity of the fi lm increasing with increasing pH. This, as a result, leads to an increase in the net ion fl ow across the fi lm I net as well as the reversal potential V rev , as seen in Figure 10 and Table 1 , consistent with that observed elsewhere. [ 52 ] The solution pH is seen to compound the increase in I net and V rev with larger concentration gradients. In addition to the enhancement in power generation P max = I net V rev , we also observe an enhancement in the degree of rectifi cation with increasing concentration gradient, as shown in Figure 11 .

Conclusion
In this work, we have demonstrated ways in which ion current rectifi cation in 2D graphene-based nanofl uidic rectifi ers can be enhanced simply by increasing the asymmetry already inherent in the diffusion boundary layer in these systemsshown in recent work to be due to counter-ion trapping within the sheets that make up the graphene oxide fi lms: by increasing the fi lm's permselectivity through symmetry-breaking of the surface charge distribution within the fi lm. For example, geometrically asymmetric cuts can be made to the fi lm-a broad 2D analogue of nanofl uidic rectifi ers comprising conical nanopores; the larger the difference in the cross-sectional areas between the two ends of the fi lm, the larger the departure from linearity in the current-voltage characteristics of the fi lm owing to the decrease in the limiting current as a consequence of  the increased permselectivity. This then leads to an enhancement in the rectifi cation given that the nonlinear behavior occurs only in the positive bias state in which counter-ion trapping within the fi lm occurs; moreover, the rectifi cation is also observed at lower voltage bias in the asymmetrically cut fi lm. These observations are supported by good agreement obtained between the experimental measurements for the limiting current and that predicted by a simple 1D model for ion transport across a permselective nanochannel membrane.
Additionally, we show the sensitivity of the surface charge distribution and hence the limiting current and rectifi cation factor to the solution pH due to the dissociation of carboxylic ions within the sheets of the graphene oxide fi lms, which increases with decreasing acidity of the solution. Further, we demonstrate that the fi lm's asymmetry and therefore rectifi cation behavior can also be increased by imposing a mismatch between the electrolyte pH or concentration in the reservoirs on both ends of the fi lm. In the latter, the salinity gradient gives rise to the existence of a fi nite current at zero applied potential, as well as a reversal potential, thus facilitating the possibility for osmotic power generation-the fi rst time this has been demonstrated in these graphene-based nanofl uidic devices to the best of our knowledge.
In summary, these simple ways of enhancing ion current rectifi cation as well as generating electrical power through salinity gradients add to the benefi ts of low cost, ease, and simplicity of synthesizing, chemically functionalizing, handling, integrating, and scaling up these fi lms for use in practical microdevices for a broad range of applications for biosensing, membrane separation, and energy storage and conversion, among others.

Experimental Section
Multilayered GO fi lms were prepared by vacuum fi ltration of a chemically exfoliated GO dispersion (known as the modifi ed Hummers' method [ 53,54 ] ). To prepare the freestanding fi lm, 100 mL of 0.05 wt% GO solution was fi rst fi ltered through a cellulose acetate fi lter membrane (47 mm diameter, 0.2 µm pore size; Whatman Ltd., Maidstone, UK). The GO fi lm was then air-dried and peeled off from the fi lter membrane, and cut using a blade into the desirable dimension-in this case, Figure 9. a) I -V characteristics of a geometrically symmetric fi lm subject to a concentration gradient at pH ≈ 7, showing the existence of a zero-volt current I net (black square along the y -axis) and reversal potential V rev (green circle along the x -axis). The KCl concentrations in the reservoirs at the WE and CE ends are shown in the legend above. b) Zero-volt current as a function of the imposed concentration gradient, characterized by the ratio between the concentration in one reservoir C min , fi xed at 1 × 10 −3 M , and the concentration in the other C max , which was increased from 1 × 10 −3 M to 1 M . c) Corresponding I -V characteristics of a geometrically asymmetric fi lm with varying ratios of the fi lm cross-sectional area b / a , showing the increase in the reversal potential V rev (green circles) with increasing geometric asymmetry; the concentration is 1 × 10 −3 M at both ends. a 3 × 3 mm rectangular geometrically symmetric fi lm and several trapezoidal geometrically asymmetric fi lms of 3 mm widths with varying end lengths. The thickness of the fi lms were measured using a digital micrometer caliper; at least fi ve different locations were measured and the averaged thickness was found to be approximately 30 µm.
To ensure that the ion transport occurs solely through the interlayer spacing of the GO fi lm, its top and bottom surfaces were fi rst covered with a layer of UV epoxy; the entire fi lm was then placed on a glass slide and immediately exposed to the UV irradiation. The ends of the fi lm were then connected to two reservoirs glued to both ends of the fi lm, as illustrated in Figure 12 . The reservoirs were then fi lled with potassium chloride (KCl) solutions at different pH and ionic strengths.
The I -V behavior of the system was observed using a sourcemeter unit (SMU; Model 6430, Keithley Instruments Inc., Cleveland, OH) connected to two Ag/AgCl reference electrodes that were inserted into each half-cell solution; all measurements were conducted within a Faraday cage. The pH of the solution was adjusted by adding potassium hydroxide (KOH) or hydrochloric acid (HCl). To ensure that the GO fi lm is fully hydrated and swelled before conducting any measurements, both reservoirs were fi lled with DI water for approximately 2 d prior to Figure 10. Low voltage I -V characteristics for a geometrically asymmetric fi lm ( b / a = 3) at a) pH = 7 and b) pH = 3 solutions in which different KCl concentrations are imposed across the reservoirs at the WE and CE ends, as shown by the legend below the plots. The zero-volt currents I net for the different cases are represented by the black squares along the y -axis and the reversal potential V rev by the green circles along the x -axis.   their fi lling with the electrolyte solution at the requisite concentration, after which the system was maintained for a further 12 h. The electrical conductance across the nanochannels was then calculated hourly to obtain the I -V curves until no detectable changes were observed, i.e., steady-state was attained while ensuring the fi lm remained fully wetted.