Electrokinetic Phenomena in Organic Solvents | The Journal of

Article Cite This: J. Phys. Chem. B 2019, 123, 6123−6131

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Electrokinetic Phenomena in Organic Solvents Rachel A. Lucas,† Chih-Yuan Lin,† and Zuzanna S. Siwy*,†,‡,§ †

Department of Physics and Astronomy, ‡Department of Chemistry, and §Department of Biomedical Engineering, University of California, Irvine, California 92697, United States

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S Supporting Information *

ABSTRACT: Solid/liquid interfaces play a key role in separation processes, energy storage devices, and transport in nanoscale systems. Nanopores and mesopores with well-defined geometry and chemical characteristics have been a valuable tool to unravel electrochemical properties of interfaces, but the majority of studies have been focused on aqueous solutions. Here, we present experiments and numerical modeling aimed at characterizing effective surface charge of polymer pores in mixtures of water and alcohols as well as in propylene carbonate and acetone. The charge properties of pore walls are probed through analysis of current−voltage curves recorded in the presence of salt concentration gradients. The presence and direction of electro-osmotic flow lead to asymmetric current−voltage curves, with rectification characteristics determined by the polarity of surface charge. The results suggest that the effective surface charge of the pore walls depends not only on the type of solvent but also on the concentration of the electrolyte and voltage. We identified conditions at which polymer pores that are negatively charged in aqueous solutions become positively charged in propylene carbonate and acetone. The findings are of importance for nonaqueous separations, fundamental knowledge on solid/liquid interfaces in organic media, and preparation of porous devices with tunable surface charge characteristics.

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INTRODUCTION Surface charges of molecules and within biological cells play a key role in many physiological processes.1,2 As an example, charges of lipids in a cell membrane and in transmembrane proteins are important for functioning of biological channels3 and cellular uptake of particles and molecules.4 Charges on a cell membrane also determine localization of certain proteins, which further influence cell signaling.5 In another example, local positive charges in aquaporins help salt rejection by preventing cations to pass through.6 Transport properties and function of man-made micropores and nanopores are also affected by surface characteristics. A pore or channel with finite surface charges induces electrokinetic phenomena, such as electro osmosis and streaming potential among others.7,8 On a nanoscale, charges on the pore wall can lead to ionic selectivity so that a nanopore with negative surface charges will predominantly transport positively charged ions.7,9 In conically shaped nanopores, presence of surface charges leads to breaking of the system’s electrochemical symmetry and ion current rectification (ICR).10−19 ICR is the preferential transport of ionic current at one voltage polarity over transport at the opposite polarity. The nonlinear current−voltage curves are very sensitive to even small changes of surface charge; thus, ICR has been exploited for many applications such as biosensing, desalination, and energy production.16,20−23 Patterns of surface charges on the nanopore walls are the basis for preparation of ionic diodes and ionic transistors.24,25 Ion transport through pores is therefore linked with electrochemical properties of the pore walls and can be used © 2019 American Chemical Society

as a probe of the wall charges. The majority of electrokinetic experiments with micro- and nanoscale pores and channels have been performed in an aqueous environment, to mimic conditions of biological systems. Nonaqueous media are however important in many applications including separation of drug molecules and other compounds26−29 as well as in energy storage devices such as batteries and capacitors.30−35 It would therefore be crucial to understand how electrochemical properties of a surface change when it is exposed to nonaqueous solutions. Consequences of the modified surface characteristics on ionic transport in nano- and mesostructures need to be understood as well. It is known from the literature that pKa of chemical groups depends on the solvent,36−39 so that a surface can be characterized by effective charge density that is modulated by the medium it is exposed to. Nonaqueous capillary electrophoresis,40 as well as ionic conductance experiments through porous media37 and zeta potential measurements of particles41 provided evidence that pKa values changed with the change of the solvent and solvent mixtures. Surface properties in mixtures of solvents depend on the relative ratio of the solvents and can be further modulated by the addition of salt. The role of salt is typically described by the screening effect as the salt concentration increases, the zeta potential of the surface decreases. There was also a surprising experiment reported, which showed that Cs+ ions had an ability to invert Received: May 25, 2019 Revised: June 18, 2019 Published: June 19, 2019 6123

DOI: 10.1021/acs.jpcb.9b04969 J. Phys. Chem. B 2019, 123, 6123−6131

Article

The Journal of Physical Chemistry B

Figure 1. (a) Current−voltage curves of a single polymer cylindrically shaped pore with an opening diameter of 700 nm before and after modification with a positively charged polyelectrolyte (PAH), which changed the surface charge from negative to positive. LiClO4 (10 mM) was present on the side of the membrane in contact with the ground electrode, while 100 mM LiClO4 was placed on the opposite side of the membrane. (b) Scheme of the experimental setup and expected current−voltage curves for a pore with negative and positive surface charges.

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MATERIALS AND METHODS Preparation of Pores. Single pores in 12 μm thick PET films were prepared by the track-etching technique.51 Briefly, the technique entails irradiation of the films with single energetic heavy ions, for example, Au or U, followed by wet chemical etching. Films used in this research were irradiated at the Institute for Heavy Ions Research in Darmstadt Germany. Wet chemical etching was performed in 2 M NaOH at 50 °C, thus at conditions which were shown to produce cylindrically shaped PET pores.52,53 After preparation, each pore was characterized by its current−voltage curve recorded in 1 M KCl. The resistance determined from the measurement was used to estimate the effective pore opening diameter assuming that the pores were filled with bulk solution.53 Recordings in 1 M aqueous KCl were also performed after all measurements with organic solvents had been completed. Nearly identical current−voltage curves measured for an as-prepared pore and after all experiments in organic solvents provide evidence that the material did not undergo significant swelling, and the pore diameter was stable in all solutions (Figure S1). Conductivity of all solutions was measured using a Fisher Scientific accumet Basic AB30 Conductivity Meter. Note that because of the etching process, the membrane thickness decreased from 12 to 11 μm. Modification of Pore Walls with Positively Charged Polyelectrolytes. Walls of a pore shown in Figure 1 were rendered positively charged using poly(allylamine hydrochloride) (PAH) (MW ≈ 17 500, Sigma-Aldrich).54 The process entailed incubation of the pore in a 2.5 mM solution of PAH in deionized water for 30 min. Measurements of Ion Current. Single pore membranes were placed between two chambers of a home-made conductivity cell. Current−voltage curves were recorded using Keithley 6487 picoammeter/voltage source (Keithley Instruments, Cleveland, OH) and two pellet Ag/AgCl electrodes. The voltage was changed between −1 and +1 V with 0.1 V steps, between −2 and +2 V with 0.2 V steps or between −5 and +5 V with 0.5 V steps.

silica surface potential from negative to positive but only in solvents with a dielectric constant lower than 25.41 In this manuscript, we explore properties of a polymer carboxylated surface whose effective charge can be modulated as well as inverted from negative to positive in LiClO4 solutions in organic solvents with dielectric constant that is higher or lower than 25. The method we apply enables probing surface charge properties not only as a function of the solvent and salt concentration but also as a function of voltage, thus providing a direct link between surface charge properties and electrokinetic phenomena. Experiments in LiClO4 solutions in propylene carbonate, acetone, and alcohol/water mixtures are presented; the salt concentration is changed between 1 and 700 mM. The properties of the polymer/liquid interface are probed using cylindrically shaped single mesopores of known pore diameter prepared in a 12 μm thick polyethylene terephthalate (PET) film. The pores were fabricated by the track-etching technique, which in PET exposes carboxyl groups at the density of ∼1 per nm2.42 As it was demonstrated in our previous study,43 such polymer pores in contact with LiClO4 solutions in propylene carbonate could unexpectedly acquire effective positive charge. It was hypothesized that the positive charge stemmed from two effects: (i) ordering of the solvent molecules at the surface this process could be facilitated by the high dipole moment of the solvent,43−47 and/or (ii) adsorption of lithium ions to the surface.48,49 This previous work was performed using conically shaped nanopores, which exhibit ICR that is dependent on the salt concentration even if the surface charge is constant.11,13,50 Because Li+ adsorption was predicted to increase with the increase of the salt concentration, earlier experiments did not allow us to probe relative importance of two effects, solvent organization and lithium ions adsorption. Here, we propose an experimental setup, which determines not only the presence of finite surface charge but also its dependence on salt concentration and voltage. The experiments are supported by numerical modeling performed with coupled Poisson− Nernst−Planck (PNP) and Navier−Stokes (NS) equations. The modeling revealed that the effective charge of pore walls can have complex profiles along the pore axis, dependent on the type of solvent, salt concentration, gradient as well as voltage polarity.

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RESULTS AND DISCUSSION In order to probe surface charge properties of single PET mesopores, we used an approach developed in our previous study to induce electro-osmotically driven rectification.53 6124


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Figure 2. (a) Current−voltage curves through a single PET pore placed in contact with an aqueous solution of 100 mM LiClO4 on one side and 100 mM LiClO4 solution in water/ethanol mixtures on the other side. (b) Rectification degree calculated as a ratio of currents at +1 and −1 V together with the ratio of conductivities: conductivity of the aqueous solution and of water/ethanol mixtures. The pore had a diameter of 700 nm.

As the next step, we examined the surface charge properties of the same 700 nm diameter mesopore in the presence of alcohols. Figure 2 shows recordings of current−voltage curves in symmetric salt concentration conditions, 100 mM LiClO4, but one side was in contact with an aqueous solution while the solution on the other side of the membrane contained 10 or 60% of ethanol. The ethanol-containing solutions were characterized by a lower conductivity than the corresponding aqueous solution. Consequently, in our electrode configuration, we expected the pore to be filled with the water/ ethanol solution for negative voltages so that negative currents would be lower than positive currents. Data in Figure 2 show that the predictions were correct and suggested that even if the surface charge density of the pore walls was diminished by the presence of alcohol, as suggested by earlier work,37 it was sufficient to induce electro osmotic filling of the pore. We also calculated rectification degrees, as the ratio of currents at both voltage polarities, +1 and −1 V, and found they were equal to the ratios of solution conductivities, supporting the claim that the pore was filled with respective solutions on both sides of the membrane. Additional experiments were performed with LiClO4 dissolved in water/methanol mixtures, which yielded similar results to these shown in Figure 2 (see Figure S2). As the next step, we performed ion current measurements in LiClO4 solutions in propylene carbonate and acetone. Propylene carbonate is an aprotic solvent that is expected not to support deprotonation of the surface carboxyl groups. Our recent study of ion current through nanopores suggested, however, that the solvent could induce positive charge of surfaces, which are negatively charged in aqueous environment.43 The switch of surface charge polarity from negative in water to positive in propylene carbonate was agnostic to the pore material and occurred in pores prepared in PET, polycarbonate, and even glass pipettes.43,55 Previous experiments were performed with conically shaped nanopores, which in symmetric electrolyte conditions rectify ion current such that the I−V curve asymmetry informs on the polarity of surface charges. With the ground electrode placed at the narrow side of the cone-shaped pores, a negatively charged nanopore in aqueous solutions rectified the current such that negative currents were higher than positive currents. The same nanopore in propylene carbonate solutions of LiClO4 exhibited an inverted I−V curve, suggesting the surface charge of the nanopore was switched to positive. The effective positive

Briefly, when a cylindrically shaped mesopore with surface charges is placed between two media that differ in conductivity, it rectifies current, and the current−voltage curve can be predicted quantitatively based on the conductance of both solutions. In the previous experiments, the gradient of ionic conductivity in aqueous solutions was achieved by preparing (i) two solutions of the same ionic strength but different viscosity and (ii) two solutions with different salt concentrations and the same viscosity. Because of the presence of negative surface charges on the pore wall, depending on the voltage polarity, the pore was filled either with a solution of higher conductivity or a solution with lower conductivity. Polarity-dependent ionic conductivity led to ICR with a degree equal to the ratio of conductivities of the two solutions present on both the sides of the membrane. In this study, a single 700 nm in the diameter pore was first placed in contact with aqueous solutions of 100 and 10 mM LiClO4. The conductivity of the two solutions differed by a factor of ∼7, thus in accordance with previous results, the current for positive voltages was 7 times higher than the current for negative voltages. The rectification direction is indeed in agreement with the negative surface charge of the pore walls. With the ground electrode placed in the solution with lower concentration, positive voltages sourced cations from the higher conductivity solution, which electro osmotically filled the pore.7 Note, that because of mesoscale opening of the pore, the surface conductance contributed to the measured current in a negligible manner. In order to confirm the dominant role of electro osmosis in inducing the ICR, we modified the pore walls so that the charge was switched from negative to positive. We used an approach reported before, which involved incubation of the pore with a solution of a positively charged polyelectrolyte, PAH that electrostatically adsorbed to negatively charged walls.54 After modification, the pore was exposed to the same 100 mM/10 mM LiClO4 salt gradient. As expected, the observed current−voltage curves before and after PAH attachment were symmetric with respect to the origin of the coordinate system, suggesting the surface charge of the pore walls indeed switched polarity (Figure 1b). The measurements in Figure 1 provided guidelines for interpretation of our experimental results: a pore with effective negative (positive) surface charges features positive (negative) currents that are higher than the currents for the opposite voltage polarity. 6125


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Figure 3. (a) Scheme of the experimental setup. The ground electrode was placed in the solution with lower salt concentration. (b−d) Experimental data for a 700 nm in the diameter PET pore placed in contact with gradients of LiClO4 concentration in propylene carbonate. Current−voltage curves together with rectification degrees and ratios of ionic conductivities. (d) Analysis of I−V curves shown in (c) with the LiClO4 concentration of 10 mM kept constant on the side of the membrane with the ground electrode; salt concentration on the opposite side of the membrane was changed between 10 and 500 mM. Rectification was calculated as the ratio of currents at −1 and +1 V.

Figure 4. (a−c) Current−voltage curves for a single PET pore in LiClO4 concentrations gradients in propylene carbonate together with conductivity ratios and rectification degrees calculated based on currents measured at ±1 V. Note that panels (a,c) show behavior of the same pore in two different voltage ranges. (d) Current−voltage curves recorded when a pore was in contact with LiClO4 gradients in acetone. The ground electrode was placed in the solution with lower salt concentration. All recordings were performed with a 700 nm diameter pore.

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Figure 5. Schematic representation of the modeling system where a 700 nm in diameter and 11 μm in length pore connects two large reservoirs (not to scale). The relationship between the salt concentration and the surface charge density σw on the pore walls satisfies the conditions of case I (black line) and case II (green dashed-dotted line) described in Table 1.

3). Note that the diffusion current at 0 V in Figure 3b has nearly the same magnitude (∼−0.6 nA) for the 10-fold and the 100-fold LiClO4 concentration gradients, which also points to the modulation of surface charge by salt concentration. In order to understand the dependence of charge density of the pore wall on lithium-ion concentration, we formulated the following testable hypothesis. We assumed the charge density would increase with the increase of LiClO4 concentration until a threshold concentration, above which the effective charge density was not expected to change. In order to provide evidence for this claim, another set of experiments was performed with 700 mM LiClO4 held constant on one side and changing the concentration on the other side of the membrane between 10 and 500 mM (Figure 4). In this case, all recorded I−V curves were also rectifying and suggested existence of a net positive charge on the walls. Moreover, we found the rectification degrees were in good agreement with the conductivity ratios, suggesting that the surface charge density indeed saturated at ∼100 mM LiClO4. Surface charge properties of a PET mesopore were also probed in LiClO4 solutions in acetone. Similar to observations in propylene carbonate, the walls of PET pores became effectively positively charged when the lithium ion concentration in acetone exceeded a value of 10 mM. Interestingly, for the gradient 10 mM/1 mM LiClO4, the pore was rectified as if the pore wall was negatively charged, pointing to the crucial role of Li+ ions in the formation of the positive surface charge. The measurements of ion current in propylene carbonate have been modeled using coupled PNP and NS equations solved by the commercial finite-element software COMSOL Multiphysics 5.2a on a high-performance computer. Figure 5 illustrates the simulated system where a cylindrical pore, 700 nm in diameter and 11 μm in length, is connected to two large identical reservoirs.56 The left (right) reservoir is filled with the LiClO4 solution of high (low) bulk concentration, Chigh (Clow). An external voltage is applied in a way that mimics our experimental setup so that the right reservoir with lower salt

charge in the propylene carbonate solutions was hypothesized to stem from a partial ordering of the solvent molecules characterized with a high dipole moment and adsorption of lithium ions.43−48 The previous measurements did not, however, allow us to evaluate the role of lithium ions in the formation of positive charge. This is because, even though an increase of lithium concentration in the bulk was expected to increase the pore wall effective positive charge via adsorption and to enhance I−V asymmetry, diminished screening length at higher ionic strengths7 dominated the system behavior and ultimately led to linear current−voltage curves. In this manuscript, we probed the presence and polarity of surface charges using a cylindrically shaped mesopore placed in contact with a salt concentration gradient. If lithium ions are necessary for the positive surface charge to form, we expected to observe different directions of ICR in low and high LiClO4 concentrations. In order to probe the role of salt for the pore surface charge properties, two sets of experiments were performed. In the first set of measurements, two gradients of 10 mM/1 mM and 100 mM/1 mM LiClO4 were used. In the second set, one side of the membrane was in contact with 10 mM LiClO4, and the concentration of the opposite side was gradually increased to reach 500 mM (Figure 3). In the 10 mM/1 mM gradient, the I−V curve was linear suggesting that the surface charge of the pore walls was modified in the presence of the propylene carbonate-based solutions of LiClO4. A linear I−V curve could be obtained if the surface was overall neutral, stemming from the aprotic character of propylene carbonate. However, for the 100 mM/1 mM gradient as well as all gradients which involved 10 mM on one side of the membrane, rectifying I−V curves were observed; the direction of ICR suggested that the effective charge of the walls was positive. Comparison of rectification degrees with ratio of ionic conductivities showed lack of agreement between these two parameters, suggesting that the effective charge density of the pore walls could depend on the salt concentration and perhaps even on voltage polarity (Figure 6127


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As shown in Figure 6, the simulated current−voltage curves agree well with the experimental observations. For the concentration gradient of 100 mM/10 mM, the simulated ionic current at negative voltage bias is larger than that at positive voltage bias for both the cases of charge density, case I and case II. For the gradient 10 mM/1 mM LiClO4, the current−voltage curve predicted based on charge density described by case I is linear (as seen experimentally in propylene carbonate, Figure 3b), and rectifying for case II (as observed in acetone, Figure 4d). Note that the rectification seen in case II for 10 mM/1 mM is in the direction indicative of an overall negative charge at low Li+ concentrations. A case of a different concentration gradient, 100 mM/1 mM, is shown in Figure S3 of the Supporting Information. The modeling confirmed that effective charge density of the pore walls depends on solvent and salt concentration. To further investigate the mechanism of ion transport through pores in contact with salt concentration gradient, the axial variation of the surface charge density for various experimental conditions is plotted in Figure 7 (case I) and S4 (case II). Because of the imposed salt gradient, the concentration of Li+ is expected to depend on the position along the pore axis.64 For the case of Chigh/Clow = 100 mM/10 mM, the pore surface is positively charged for both +1 and −1 V (Figures 7a and S4a), however, with polarity-dependent magnitude of charge density. Higher currents are observed for negative voltage polarity, which assures higher charge density and for which the majority carriers, perchlorite ions, are moving down the concentration gradient. Note that for −1 V at Chigh/Clow = 100 mM/10 mM, the charge density is nearly position-independent because the concentration of Li+ in the pore is at the level at which the charge density reaches its maximum value, see below. At +1 V, however, the imposed concentration gradient caused pore entrance in contact with 100 mM to be positively charged, while the opposite pore opening was neutral. The concept of salt concentration-dependent charge density can be further demonstrated by examining the ionic concentration profile inside the pore, as shown in Figures 8 and S5. For both cases I and II, the pore is filled with a higher ionic concentration at −1 V under the gradient of 100 mM/10 mM. This polarity-dependent ion concentration leads to the observed current rectification (Figure 6a). On the other hand, for the salt gradient Chigh/Clow = 10 mM/1 mM and case II, the

concentration is grounded. The viscosity and relative permittivity of the fluid are assumed as 2.5 cP and 65, respectively, as reported before for propylene carbonate.57,58 The diffusivities of lithium and perchlorate ions in the diluted propylene carbonate solution can be estimated as 2.5 × 10−10 m2/s.59,60 Other detailed boundary conditions can be found in previous studies.61,62 In order to describe the experimental observations, the coupled PNP−NS equations were solved assuming that the charge density on the PET wall, σw, was Li+concentrationdependent via the adsorption process. The adsorption of Li+ on the pore wall would change both the magnitude and sign of the surface charge density of the pore wall, which can be described as a sigmoid function of the Li+ concentration,63 yielding ij yz b zz σw [mC/m 2] = a + jjj −d ×[Li+]s z (1) k1 + c e { + where [Li ]s is the molar concentration of lithium ions on the pore surface, which depends on the bulk concentration, salt gradient, and voltage. Coefficients a, b, c, and d are functioncontrolling parameters for determining the charge density. Table 1 shows the parameters for case I that describes the

Table 1. Surface Charge Density σw Assumed at Various Concentrations of Lithium Ions Based on the Sigmoid Function Case I (Black Curve in Figure 5):

yz 80 ji zz σw [mC/m 2] = − 0.2 + jjjj z −0.12 ×[Li+]s z { k 1 + 1325 e Li+ concentration (mM) 100 10 σw (mC/m2) 79 0 Case II (Green Curve in Figure 5):

1 −0.13

yz ij 90 zz σw [mC/m 2] = − 10 + jjjj z −0.1 ×[Li+]s z { k 1 + 21.7 e

Li+ concentration (mM) σw (mC/m2)

100 80

10 0

1 −5.6

recordings in propylene carbonate and case II for ion current data in acetone solutions of LiClO4. Modeling was performed with salt concentration gradients as used in the experiments.

Figure 6. Numerically predicted current−voltage curves of a single mesopore placed in contact with a LiClO4 concentration gradient. The model considers dependence of surface charge density on the pore wall on Li+ concentration, as described in Table 1. Simulated current−voltage curves of an 11 μm long cylindrical pore with the pore diameter of 700 nm for various LiClO4 concentration gradients. (a) Chigh = 100 mM and Clow = 10 mM; (b) Chigh = 10 mM and Clow = 1 mM. Black and green curves were obtained using charge density calculated and denoted as case I and case II, respectively, Table 1. 6128


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Figure 7. Axial variation of surface charge density of the pore wall σw at three levels of applied voltage for case I of surface charge density (Table 1). (a) Chigh = 100 mM and Clow = 10 mM; (b) Chigh = 10 mM and Clow = 1 mM.

Figure 8. Profiles of total ionic concentration in a pore for three magnitudes of applied voltage for surface charge density described as case I, Table 1 (Figure 6). Left column: Chigh = 100 mM and Clow = 10 mM; right column: Chigh = 10 mM and Clow = 1 mM.

concentration and voltage. A polymer carboxylated surface was shown to switch the polarity of surface charge from negative in aqueous media to positive in LiClO4 solutions in propylene carbonate and acetone. As the salt concentration increased to ∼100 mM, the positive charge density saturated, as captured by the adsorption-based model. This study contributes to our understanding of the effective surface charge in nonaqueous media and will inspire future studies to unravel the atomistic details of the solid/liquid interface. The numerical modeling we developed can be used in cases when the charge density of the pore walls is not a constant value but rather depends on the experimental conditions including presence of adsorbing species in the solution and electric field. Future experiments will be performed in a range of salts with different sizes of cations and anions as well as solvents with different dielectric constants. We expect these additional experiments will help elucidate the mechanism of lithium-ion adsorption and the structure of the electrical double layer in nonaqueous media.

pore is expected to be cation-selective because of its negative surface charge (Figures 4d and S4b). When a voltage of +1 V (−1 V) is applied, lithium ions are driven toward the side of low concentration, moving in the same (opposite) direction as that of the concentration gradient. Consequently, the recorded current at +1 V is larger than that at −1 V (see squares of Figure 4d and green curve of Figure 6b). For case I, however, the surface charge density is close to zero (Figure 7b), as confirmed by nearly identical distribution of ionic concentrations for positive and negative voltage bias (Figure 8); no rectification was observed for this case experimentally or in modeling. Figures 7 and S4 also show surface charge of a pore in contact with the concentration gradient at 0 V. As expected for a cylindrical pore, if no bias is applied, the surface charge density changes in a linear fashion along the pore axis. It is the external voltage in combination with the concentration gradient and concentration-dependent cation adsorption, which leads to tunable charge density and rectification.

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ASSOCIATED CONTENT

S Supporting Information *

CONCLUSIONS The manuscript presents a method to probe effective charge of surfaces via electro osmosis-induced rectification in pores that are in contact with a salt concentration gradient. This experimental approach allows one to map the dependence of surface charge properties on the type of solvent, on salt

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.9b04969. Additional experimental recordings and details of numerical modeling (PDF) 6129


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 949-824-8290. ORCID

Chih-Yuan Lin: 0000-0002-2425-5548 Zuzanna S. Siwy: 0000-0003-2626-7873 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany for providing irradiated membranes. This work was supported as part of the Center for Enhanced Nanofluidic Transport, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DESC0019112.

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