Voltage-Induced Modulation of Ionic Concentrations and Ion Current

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Voltage Induced Modulation of Ionic Concentrations and Ion Current Rectification in Mesopores with Highly Charged Pore Walls Chih-Yuan Lin, Li-Hsien Yeh, and Zuzanna S. Siwy J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03099 • Publication Date (Web): 05 Jan 2018 Downloaded from http://pubs.acs.org on January 6, 2018

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The Journal of Physical Chemistry Letters

Voltage Induced Modulation of Ionic Concentrations and Ion Current Rectification in Mesopores with Highly Charged Pore Walls Chih-Yuan Lin,1,2 Li-Hsien Yeh,3,* Zuzanna S. Siwy1,4,5,* 1

Department of Physics and Astronomy, University of California, Irvine, California 92697, United States

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Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan

Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan

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Department of Biomedical Engineering, University of California, Irvine, California 92697, United States

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Department of Chemistry, University of California, Irvine, California 92697, United States

* Corresponding authors: E-mail: [email protected] (Li-Hsien Yeh), [email protected] (Zuzanna S. Siwy)

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Abstract It is believed that ion current rectification (ICR), a property which assures preferential ionic transport in one direction, can only be observed in nanopores when the pore size is comparable to the thickness of the electric double layer (EDL). Rectifying nanopores became the basis of biological sensors and components of ionic circuits. Here we report that appreciable ICR can also occur in highly charged conical, polymer mesopores whose tip diameters are as large as 400 nm thus over 100-fold larger than the EDL thickness. A rigorous model taking into account the surface equilibrium reaction of functional carboxyl groups on the pore wall and electroosmotic flow is employed to explain that unexpected phenomenon. Results show that the pore rectification results from the high density of surface charges as well as the presence of highly mobile hydroxide ions, whose concentration is enhanced for one voltage polarity. This work provides evidence that highly charged surfaces can extend the ICR of pores to the sub-micron scale, suggesting the potential use of highly charged large pores for energy and sensing applications. Our results also provide insight into how a mixture of ions with different mobilities can influence current-voltage curves and rectification.

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Keywords: Ion Transport, Fluidic Diode, Debye Length, Charge Regulation

Since the first experimental observation in a conically shaped glass nanopipette by Wei et al. in 1997,1 ion current rectification (ICR) has been extensively investigated because of its widespread applications ranging from energy and environmental2-5 to sensing fields.6-9 ICR indicates that ion currents for one voltage polarity are significantly higher than currents for the opposite voltage polarity, even though a pore is studied in symmetric electrolyte conditions. The ICR effect has been observed in several different nanopore systems including conical nanopores,1, 10-16 funnel-shaped nanopores,17-18 asymmetric hourglass nanopores,19-20 and nanopores with surface charge patterns.21-25 All these nanopore systems rectified, because at least one of their openings was of nanoscale dimensions and comparable to the thickness of the electric double layer (EDL), called the Debye length. It is generally recognized that appreciable ICR is rarely observed for pores whose opening is more than 10 times larger than the EDL thickness.13 Even though there have been few studies reporting ICR at sub-micro and even micro scale systems, these experiments were performed under asymmetric solutions set-up, and the mechanism of rectification originated from electroosmotic flow (EOF).26-29 Depending on voltage polarity, EOF would fill a pore with a solution of higher or lower conductivity, leading to asymmetric current-voltage curves.26-29 Here we show that highly charged surfaces of the pore wall can induce ICR even in ~400 nm in diameter conically shaped mesopores placed in contact with symmetric electrolyte solutions. The finding of ICR on the mesoscale is important, because fabrication of larger pores is more accessible than of nanoscale structures. Many materials can be patterned at the meso- and microscales, opening a possibility to create rectifying pores of different

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chemistries. In addition, modification procedures with DNA30-32 and other polyelectrolytes23, 33-36

have already been established providing tools to render pore walls highly charged.

Experiments presented in this manuscript were carried out with single conically shaped pores fabricated in 12 µm thick polyethylene terephthalate (PET) films prepared by the track-etching technique described before.37-38 Opening diameter of all pores examined was between 400 nm and 500 nm. Etched PET pores contain functional carboxyl groups (~COOH) on the walls,37 thus at pH values above pK a of the group, the pores carry negative surface charge. Measurements were performed in KCl, because mobilities of potassium and chloride ions are nearly identical, making it an ideal electrolyte for understanding origin of ICR. The pores were studied in KCl concentrations between 1 mM and 1 M, thus at conditions at which the Debye screening length was < 10 nm, thus at least 40 times smaller than the pore radius.

Figure 1 shows experimental data of current-voltage curves for a single mesopore with openings of 430 and 1100 nm at two pH values, pH 6 and pH 11. At pH 6 the pore behaved as an Ohmic resistor for all KCl concentrations examined; a similar set of linear I-V curves was recorded at pH 3 when the pore wall can be considered neutral (Figure S1). The results indicate that at lower pH values the pore’s transport properties remain unaffected by the changing pore wall characteristics. The same pore, however, started to rectify at 10 mM KCl once pH of the solution was increased to pH 11. The I-V asymmetry was quantified by calculating rectification ratio defined as a ratio of currents at -2V and +2V. Rectification as high as 10 was observed (Figure 1d). The experimental finding of ICR were confirmed using few other independently prepared pores with the tip opening diameters exceeding 400 nm (Figure S2). A set of I-V curves for three different values of pH is shown in Figure S3. We hypothesized that the ICR at pH 11 can result from a higher surface charge density at the basic conditions compared to pH 6. Indeed, even though pK a of the pore wall was 4


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reported to be ~ 4,39 the titration curve of PET track-etched pores at a wide range of pH values suggested there could still be an increase of surface charge density at the range of pH beyond pH 9.40 The effect of surface charge on ion current is also visible in the recordings performed at 100 mM KCl, pH 11; the sigmoidal shape of the current-voltage curve suggests that the pore transport properties might be affected by concentration polarization.41-42 The effects of concentration polarization for the 400 nm pore in 100 mM KCl and rectification in 10 mM KCl are certainly surprising, because surface charges in a pore that is 400 nm in diameter are expected to have a negligible effect on the pore conductance. The set of data shown in Figure 1 suggested that highly charged pores may exhibit unique ion transport phenomena that have not been reported or well understood before.

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Figure 1. High density of surface charges on the pore wall can cause ICR in mesopores 5



whose tip opening diameters are significantly larger than the EDL thickness. (a-c) Current-voltage curves of a single conically shaped PET pore with the tip diameter of 430 nm recorded in (a) 1 mM, (b) 10 mM, and (c), 100 mM KCl solutions under two pH conditions. (d) Rectification ratio, calculated as the ratio of ion currents at ± 2V for the same PET pore in three KCl concentrations at two pH values (a)-(c). The base diameter of this pore was 1100 nm. The error bars shown represent a standard deviation, calculated based on three consecutively recorded current-voltage curves.

In order to probe the origin of rectification, we looked at the concentration dependence of ionic currents at -2V and +2 V. Figure 2 shows that similar to previous findings for rectifying nanoscale pores, magnitudes of ion current for voltages of both polarities depend on salt concentration in a non-linear fashion. Positive currents exhibit first a decrease with the KCl concentration decrease, followed by ion current saturation at ~10 mM KCl. Leveling off of the current at dilute solutions indicates that ionic concentrations in the pore become dominated by the surface charge of the pore wall.43 Negative, larger currents also tend to saturate but at higher concentrations than positive currents, already at ~100 mM KCl for the pore show in Figure 2. Higher magnitude of negative currents at diluted solutions suggests that the applied voltage might lead to accumulation of ions in the pore volume.

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Figure 2. Magnitudes of ion current at -2V and +2V as a function of KCl concentration at two pH conditions pH 11 (left) and pH 6 (right). This is the same mesopore as shown in 6


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Figure 1. The red and black lines are smoothed curves connecting the experimental data points.

The experimental results shown in Figures 1,2 suggest that the ICR effect observed might indeed stem from high surface charge density created at basic conditions above pH 10. In order to support the hypothesis, we modeled ion current in a conically shaped mesopore by numerically solving the multi-ion Poisson-Nernst-Planck (PNP) and Navier Stokes (NS) equations44 to account for the effect of electroosmosis. Surface charge density was calculated via incorporation of the surface equilibrium reaction of carboxyl groups on the pore wall as well as the presence of H + and OH − (see details in Materials and Method); the site density of carboxyl groups was assumed 1 per nm2. A pore of the same geometrical parameters as

examined in Figures 1-2 was considered. Figure 3a,b shows current-voltage curves obtained from the model; as recorded in our experiments, the model predicted an Ohmic behavior at pH 6 and ICR at pH 11. The modeling also confirmed that the two pH conditions led to significantly different effective surface charge densities of the pore wall: ~ −160 mC/m 2 at pH 11, and ~ −41 mC/m 2 at pH 6, as shown in Table S1 (Supporting Information). The estimated charge density of −160 mC/m 2 implies that at pH 11 the functional carboxyl groups on the pore wall are nearly fully deprotonated. Figure S4 shows comparison of ICR as predicted for the considered here mesopore as well as a nanopore with the tip opening of 10 nm; base opening of the smaller pore was 680 nm to assure the same opening angle of the two pores. Both pores had the density of carboxyl groups of 1 per nm2. The dependence of rectification on pH for the two pores is qualitatively similar and increases with the increase of pH. Note, however, that rectification of the mesopore is very weak for pH values below 10 and exhibits a large increase at pH 11, as observed in our experiments (Figure S3). The nanoscale structure, on the other hand, displays 7



rectification ratios above 3 for all pH values above pH 7. We also considered the same mesopore with a higher density of carboxyl groups of 1.5 per nm2 (Figure S4); in this case significant ICR could be observed already at pH 9, pointing to the important role of surface charge density in ion current rectification. 120

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multiple ions 2 − 40 mC/m 2 −160 mC/m

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Figure 3. Numerical modeling of ion current and ICR by the coupled multi-ion PNP and NS equations together with the protonation/deprotonation kinetics of carboxyl groups. (a) (b)

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Current-voltage curves of an 11 µm long pore with opening diameters of 430 and 1100 nm for two levels of pH at the background KCl concentration of Cb = 1 mM, (a), and 100 mM, (b). (c) Axial variations in the cross-sectionally averaged sum of concentrations of all ions (i.e. total concentration of charge carriers) for the two levels of pH, Cb = 1 mM. Solid lines: V = −2 V , dashed lines: V = +2 V . (d) and (e) Axial variations in the cross-sectionally

averaged concentrations of cations ( K + and H + ), and anions ( Cl − and OH − ), respectively. Modeling for pH 11 is shown. Dash-dotted and dotted lines in (d) and (e) denote the results at the voltage V = −2 V and +2 V , respectively. Blue regions highlight the pore interior where the axial position of 0 nm on the x-axis denotes the tip opening of the conical pore. The simulation parameters include: pK a = 3.8 , N s = 1 sites/nm 2 , Dtip = 430 nm , and Cb = 1 mM . (f) Current-voltage curves for various situations with adopting constant charge density on the pore wall.

In order to elucidate the mechanism behind the rectifying current-voltage curves of mesopores at pH 11, we plotted the spatial variations of the sum of all ionic concentrations together with distributions of individual ions (Figure 3c-e). The effect of rectification can already be appreciated from the plots of the summed ionic concentrations. For negative voltages in our electrode configuration, the total concentration of charge carriers is significantly higher than the total concentration at positive voltages. Ion current is related with the number of ions available for transport, thus negative currents are larger than positive currents. Note that due to the presence of surface charges on the pore wall, the total concentration of charge carriers for both voltage polarities exceeds the bulk value. The modeling also revealed that at negative voltages, concentrations of both positive and negative ions ( OH − ) are enriched, similar to earlier findings for nanoscale pores.45-47 The large increase of local OH − concentration for one voltage polarity (Figure 3e) prompted us to ask a question on the contribution of OH − to the current and rectification. In neutral pH conditions, the influence of protons and hydroxides is rarely discussed, because

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their concentration is significantly lower than that of the supporting electrolytes. In our experiments however at pH 11, OH − ions are present at the concentration of 1 mM thus comparable to the concentration of potassium and chloride ions. Hydroxide ions are characterized by ~2.5 higher mobility than chloride ions (see Supporting Information for values of diffusivities of all ions); thus one might expect their contribution to ion transport is not negligible. Figure 3e confirms that this is indeed the case: in the pore the concentration of

OH − is several times higher than the concentration of Cl − . We believe the larger enhancement of OH − concentration is caused by the ions’ high mobility. Moreover, voltage modulation of hydroxide ions concentrations is much stronger than that of even of counterions, both K+ and H+. At −2 V , concentration of OH − exceeds the bulk concentration by a factor of 6, while at +2V, concentration of OH − is strongly depleted to a level below 0.05 mM. Note that the peak of OH − concentration is located closer to the large opening of the pore, most probably due to the effect of concentration polarization.41-42 In order to probe whether the presence of the highly mobile ions is necessary for rectification, we considered two additional situations. (i) In the first case, the surface charge density was set constant and equal to −160 mC/m 2 , i.e. equal to the density predicted for pH 11 (Table S1); the electrolyte was binary and composed only of K + and Cl − . (ii) In the second case, the surface charge density was also kept constant at −160 mC/m 2 , but the presence of OH − and H + was considered at set concentrations equal to these at a bulk solution of pH 11. The modeling confirms that the presence of the highly mobile OH − and its accumulation for negative voltages is crucial for the rectification to occur (see green solid line in Figure 3f), because the high surface charge density of -160 mC/m2 alone produced a linear current-voltage curve (the first case, shown as orange dotted line in Figure 3f). Figure 3f also shows an I-V curve for a less charged pore; even in the presence of highly mobile OH − ions,

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no rectification occurs (see the green dashed line in Figure 3f), pointing to the importance of the highly charged pore wall for ICR. In order to understand the role of mobile ions to current-voltage curves and rectification, a series of simulations was performed assuming a presence of a hypothetical anion with a mobility that was varied between a value that was equal to the mobility of chloride ions, and a value of hydroxide ions. An additional I-V curve calculated when the anion’s mobility exceeded the mobility of Cl- by a factor of 4 was included as well. The concentration of the anion was again assumed 1 mM. The electrolyte also contained 1 mM KCl and protons at a concentration equivalent to pH 11. A set of current-voltage curves for a pore with openings of 430 and 1100 nm, and surface charge density of -160 mC/m2 is shown in Figure S5. A significant ICR was obtained only in the case when the mobility of the anion exceeded the mobility of Cl − by a factor of 2 (Figure S5a). A similar set of modeling was performed for the same pore but with positive surface charges of +160 mC/m2, at 1 mM KCl, and the presence of 1 mM positively charged co-ion with mobility that was varied between the value of K+ and the mobility of protons. Hydroxide ions were present as well at a concentration equivalent to pH 3. Current-voltage curves found for this case corroborated our hypothesis on the importance of co-ions mobility in ICR of mesopores (Figure S5b). The modeling confirmed that rectification of mesopores is dependent on the presence of highly mobile co-ions, and can be tuned by the co-ions' mobility. Finally we considered a situation in which a negatively charged pore was in contact with 1 mM KCl, and 1 mM of a hypothetical cation whose mobility exceeded the mobility of potassium ions by a factor of 2.5. The obtained I-V curve was in this case linear (Figure S5c), confirming our hypothesis that in highly charged mesopores it is the highly charged co-ions, not counterions, which can induce rectification.

In conclusion, we have demonstrated both experimentally and theoretically that

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mesopores whose opening diameter is even 100 times larger than the EDL thickness can exhibit ICR if the following conditions are fulfilled. First, the surface charge density of the pore wall has to be high, in the example shown here −160 mC/m 2 . The second condition considers presence of highly mobile co-ions, whose mobility significantly exceeds the mobility of other ions. Numerical modeling shown here revealed that voltage-induced enrichment of the highly mobile ions is more significant than the enrichment of slower ions of the same charge, and necessary for ICR. As an example, a negatively charged mesopore that exhibits an Ohmic behavior in a binary electrolyte, can rectify if a salt with highly mobile anions is added. This situation could be, for example, realized using a mixed electrolyte containing a solution of ionic liquids, composed of large ions with low mobility, and a solution of an inorganic salt. This manuscript suggests that highly charged (e.g. DNA-modified and polyelectrolyte-coated) pores can open up a new avenue to extend ICR-based devices up to the sub-micron and even micro scale for energy, biosensing, and environmental applications. Examination of ionic rectification in mixtures of electrolytes has not been yet studied extensively and can lead to new discoveries of ionic selectivity and complex voltage-regulated ionic concentrations.

Materials and Methods Preparation of Single Conically Shaped Pores. Single conical pores were fabricated in the tracked polyethylene terephthalate membranes of 12 µm thickness (GSI, Darmstadt, Germany) by the asymmetric etching technique, as described previously.37-38 Wet solution etching process decreased the film thickness by about 1 µm, and the resultant pore length reported here was 11 µm. The pore geometry was characterized after etching on the basis of measuring current-voltage curves in 1 M KCl solution, which relates the resistance and geometry of a cone-shaped pore with the etching time.37 The pore shown in the main manuscript had tip and

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base opening diameters equal to 430 and 1100 nm, respectively. Ion Current Measurement. Single-pore membranes were mounted between two chambers of a homemade conductive cell. Current-voltage characteristics were carried out with a Keithley 6487 picoammeter/voltage source (Keithley Instruments, Cleveland, OH) and two pellet Ag/AgCl electrodes (A-M Systems, Sequim, WA). The voltage was changed between −2 V and +2 V with 0.1 V steps. The sign of voltage in all I-V curves indicates the electric potential at the wide opening of the pore versus the electrode at the pore tip, which was the ground. Theoretical Modeling. The ion transport properties of a single mesopore was modeled by solving the coupled multi-ion PNP and NS equations using the commercial COMSOL Multiphysics 4.3a on a high-performance cluster. Simultaneously solving the NS equation assures that the EOF effect, expected to influence ionic transport for highly charged mesopores,48-50 is considered. It is known that the walls of track-etched PET pores carry functional carboxyl groups, capable of undergoing the surface dissociation reaction, ~ COOH ↔ ~ COO − + H + with an equilibrium constant of K a . This implies that the pore surface charge density, σ s , is not a constant value, but rather depends on the local pH on the pore wall. To account for this effect, we assumed that the pore surface charge density can be described by51



 Ka , +  Ka + [H ]s 

σ s = − ( eNs ×1018 ) 

(1)

where e is the elementary charge; N s is the total site density of carboxyl groups on the pore wall; [H + ]s = 10− pHs and pHs are the surface molar proton concentration and the local pH on the pore wall, respectively. Note that the surface pH is different from the bulk value of pH, and is obtained through numerical modeling of the problem considered.44 The multi-ion PNP-NS coupled with equilibrium surface reactions has been verified suitable for describing 13



ion transport in a charge-regulated nanopore in our previous study.44 Details of the model can be found in the Supporting Information. To capture underlying physical insights from the problem considered, we assumed: pK a = 3.8 , N s = 1 sites/nm 2 ,39 and a conically shaped pore having tip opening diameter Dtip = 430 nm in the modeling.

Acknowledgements This research was supported in part by the National Science Foundation (CHE 1306058), and the Ministry of Science and Technology of the Republic of China (MOST 103-2221-E-224-039-MY3, 105-2221-E-224-058-MY3, and 106-2918-I-224-003) for L.H.Y. C.Y.L. acknowledges financial support from the Ministry of Science and Technology of the Republic of China (106-2917-I-002-015). We acknowledge GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany for providing tracked membranes.

Supporting Information Available: Additional experimental results and details of theoretical modeling.

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Voltage-Induced Modulation of Ionic Concentrations and Ion Current

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