Enhanced electro-osmosis in propylene carbonate salt solutions

Single pores of well-defined geometries and chemistries are often employed as model systems to probe the electrochemical properties of solid–liquid interfaces and how these properties can tune ionic and molecular transport.^1–3 In nanoscale pores, excess surface charges can induce ionic selectivity such that negatively (positively) charged pores will transport mostly positive (negative) ions.^4–8 Surface charges in conjunction with the asymmetric geometry of the nanopores have led to ion current rectification and the preparation of ionic diodes.^9–12 In meso- and micro-pores, surface charges are responsible for electrokinetic phenomena such as electro-osmosis.^1,13 Single pores are often probed by measuring current–voltage curves in symmetric and asymmetric salt solutions. The signal of the ion current is sensitive to the presence and polarity of the surface charges and has been used to understand the electrochemical properties of biological channels¹⁴ and model pores.^5,7,9,15

Single pores have also been widely applied in pore analytics to detect and identify molecules, particles, and cells.^16–22 In resistive-pulse sensing, the transmembrane electric potential (or pressure difference) causes the passage of individual objects through a pore that is detected as a transient change in the transmembrane current, called a pulse or event.²³ The amplitude, duration, and local ion current characteristics of each pulse afford information about the physical and chemical properties of the analyte.^20,24,25 However, in situations where the analyte is known, e.g., when a particle is of known size and shape, the recorded current pulses can be used to inform us on the geometry of the pore used in the experiments. The shape of the ion current pulses reveals, e.g., the conical shape of a pore^26,27 or the existence of local inhomogeneities in the pore opening.^28,29

In this paper, we illustrate how probing electro-osmotic transport through the recording of current–voltage curves and the electro-osmotic passage of particles in polymer pores can provide information on the polarity and magnitude of the effective surface charge/electric potential in aqueous and organic media. Experiments were performed with single polyethylene terephthalate (PET) pores prepared by the track-etching technique.³⁰ The etched pores were placed in contact with aqueous and propylene carbonate LiClO₄ solutions. First, we show current–voltage curves recorded in the presence of a salt concentration gradient. One side of the pore was in contact with 20 mM LiClO₄, and the other side was in contact with 200 mM LiClO₄. As described in our previous report,³¹ a pore with excess surface charges placed in a salt concentration gradient will induce electro-osmotic flow: For one voltage polarity, the pore will be filled with the more concentrated solution, and for the opposite polarity, the pore will be filled with the less concentrated solution. Such a pore exhibits conductance that is dependent on the polarity of the applied voltage and the surface charges and ultimately rectifies the ion current. Similar to our earlier findings,³² the PET pores reported here were shown to switch their effective surface charge from negative in the aqueous LiClO₄ concentration gradient to positive in the propylene carbonate salt concentration gradient. To further quantify the negative surface charge/potential in water, and the positive surface charge/potential in propylene carbonate solutions, we also utilized the resistive-pulse technique. Using largely uncharged polystyrene particles as a probe, we measured their electro-osmotic velocity in a single PET pore in the two solvents as a function of applied voltage.¹ These measurements allowed us to determine the polarity of the surface charge of the pore walls and estimate the zeta potential of the polymer wall/solution (solid–liquid) interface. Our results revealed that in propylene carbonate solutions the electro-osmotic transport was not only reversed but also significantly enhanced compared to the recordings in water. We concluded that the positive zeta potential of the pore walls observed in the 200 mM LiClO₄ propylene carbonate solution has a significantly higher magnitude than the negative zeta potential in aqueous LiClO₄.

The origin of the positive surface charge of the PET pores in propylene carbonate solutions of LiClO₄ can be explained by the adsorption of Li⁺ ions and the ordered structure of the solvent molecules at the interface.^32–34 The comparative studies of the zeta potential of the PET pore walls in water and propylene carbonate can potentially provide insight into the atomistic picture of interfaces in organic solvents. For example, the measured zeta potential of the PET pore walls in propylene carbonate allowed us to estimate the density of adsorbed lithium ions. Although this paper depicts experiments performed in LiClO₄ solutions in propylene carbonate and with polymer films, the methods developed to probe the surface properties of the pores using electro-osmotic transport are expected to be applicable to any material/solvent interface.

Lithium perchlorate (LiClO₄), poly(allylamine hydrochloride) (average M_W ≈ 17 500) (PAH), TWEEN 20, and propylene carbonate were purchased from Sigma-Aldrich (St. Louis, MO, USA). Potassium chloride (KCl), sodium hydroxide (NaOH), TWEEN 80, and molecular sieves 3A, 4 to 8 mesh, were purchased from Fischer Scientific (Hampton, NH, USA). Doubly deionized (Milli-Q) water was purified to a resistivity of 18.2 MΩ using a Milli-Q IQ 7000 water purification system (MilliporeSigma, Burlington, MA, USA). Unfunctionalized 400 nm polystyrene particles were purchased from Bangs Laboratory Inc. (Fishers, Indiana, USA). Size specifications for the particles were reported by the manufacturer. All chemicals were used as received and not purified any further.

Polyethylene terephthalate (PET) membranes with single pores were fabricated using the track-etch method described previously.³⁰ Briefly, 3 cm diameter and 12 µm thick films of PET (Hostaphan RH12 Hoechst) were irradiated using a single, heavy, energetic (11.4 MeV/µ) Au ion at the UNILAC [Universal Linear Accelerator (GSI Helmholtz Center for Heavy Ion Research, Darmstadt, Germany)].³⁵ This irradiation process caused the formation of a single damage track through each film. The passage of only one heavy ion was assured by placing a metal mask with a 100 µm aperture in front of the films and by adjusting the ion beam so that on average, only one heavy ion passed through the mask aperture. Once the heavy ion was detected by a detector placed on the opposite side of the film, the heavy ion beam was shut down. Next, the films were UV irradiated for 1 h on each side using a 115 V, UVGL-25 Compact UV Lamp from UVP, LLC (Upland, California, USA) at 365 nm before being subjected to wet chemical etching in 2M NaOH heated to a temperature of 60 °C.³² The average pore diameter increases linearly with etching time. Once etched, the pore was left overnight in Milli-Q water before being sized. Pores etched along the latent track in this manner are known to have a well-approximated cylindrical shape. However, the semi-crystalline structure of PET leads to inhomogeneities of the local pore diameter with an amplitude of up to ∼20% of the local value.^28,36 Pores used in the experiments had opening diameters between 660 nm and 1.2 µm.

Due to a large surface area of the PET films used, sizing the pores using imaging (scanning electron microscopy) would be extremely difficult to execute experimentally. Therefore, to measure the opening diameter of the pores, we used a well-established, non-destructive technique based on electrochemical characterization. To this end, each pore was subjected to current–voltage measurements in unbuffered 1M KCl prior to use.^28,37,38 The measurements were performed with a Keithley 6487 picoammeter/voltage source (Keithley Instruments, Solon, Ohio, USA) and software written in-house in MATLAB (MathWorks, Natick, Massachusetts, USA). The voltage was changed from −1 V to +1 V with 100 mV steps. Using a two-electrode configuration, Ag/AgCl electrodes (in-house chlorinated Ag wire) were used as both the working and reference electrodes. These electrodes were placed in opposing chambers of a custom-built conductivity cell with a single PET pore mounted between the chambers. The measured pore conductance from the current–voltage curve was used to calculate the pore diameter, assuming that it has an ideal cylindrical shape.^31,32

Current–voltage curves were recorded with the Keithley 6487 picoammeter/voltage source and software written in-house in MATLAB. One side of the pore was in contact with the 20 mM solution of LiClO₄ in water (or propylene carbonate), while the other side was in contact with the 200 mM solution of LiClO₄ in water (or propylene carbonate). The working electrode was placed into the chamber of the conductivity cell containing the solution of higher conductivity (200 mM LiClO₄), and the reference electrode was placed into the chamber containing the solution of lower conductivity (20 mM LiClO₄). A linear potential sweep (−2 to 2 V at 200 mV/s) was applied to the working electrode for three forward and reverse scans. The subsequent average and standard deviation of the three scans were formed into current voltage curves and used to verify the effective surface charge of the PET pore.

Preceding the PAH modification of the PET pore, 0.625 g of PAH was dissolved in 5 ml, pH 6 Milli-Q water. After sizing, the PET pore was submerged into this solution, left overnight before being rinsed with Milli-Q water, and used for experimentation. Current–voltage curves as described previously were obtained to verify modification success.³² Positively charged PAH adsorbs on PET pores because the pore walls contain a high density of negatively charged carboxyl groups. The adsorption of PAH renders the pores positively charged.

Amperometric detection of particle translocation through the PET pores (resistive-pulse sensing) was performed with an Axon Instruments Axopatch 200B integrated patch clamp and a 1322A Digidata acquisition system (Molecular Devices, LLC, San Jose, CA, USA). All resistive-pulse measurements were hardware low-pass Bessel filtered at 1 kHz (80 db/Decade), sampled at a frequency of 20 kHz, and digitized at 10 kHz. 100 mM KCl and LiClO₄ solutions containing 0.001% v/v TWEEN 20 for aqueous and 200 mM LiClO₄, and 0.05% v/v TWEEN 80 for organic (propylene carbonate) solutions were used throughout experimentation. The concentration of the uncharged 400 nm polystyrene particles in the one chamber of the conductivity cell was ∼10⁹ particles/ml. In these measurements, the concentration of salt was the same in both chambers of the cell. Once assembled, the entire apparatus was placed inside a Faraday cage (Warner Instruments, Hamden, CT, USA) on top of a vibration cancellation table (TMC, Peabody, MA, USA) in order to minimize the ambient background, electrical noise. The ion current in time series measurements was analyzed using Clampfit 10.4 (Molecular Devices, LLC, San Jose, CA, USA).

Dynamic light scattering (DLS) measurements were performed on a Zetasizer Nano-ZS (Malvern Panalytical Ltd., Worcester, United Kingdom). Three mL aliquots of organic, 200 mM LiClO₄ propylene carbonate solutions containing 0.05% v/v TWEEN 80 and the unfunctionalized 400 nm polystyrene particles were analyzed in quartz cuvettes (World Precision Instruments, Sarasota, FL, USA) at 25 °C. The polydispersity index (PDI) was calculated using the Dispersion Technology Software (DTS) Zetasizer software version 7.14.

The properties of the solid–liquid interface in aqueous and propylene carbonate solutions of LiClO₄ were probed using a model system, which utilizes a single cylindrically shaped pore prepared in 12 µm thick films of PET. The pore diameter was measured using an electrochemical method of relating the pore conductance to its geometry, as described in Sec. II.^28,38 In aqueous solutions, PET pores have well-defined and known surface characteristics. As-prepared, track-etched PET pores have surface carboxyl groups at a density of ∼1/nm² with pKa ≈ 3.5.³⁹ For some experiments, the pore walls and membrane surfaces were rendered positively charged by the electrostatic adsorption of a polyelectrolyte, poly(allylamine hydrochloride) (PAH), as described previously.^12,32 The amine-terminated functionalities of PAH have a pKa of 9.5, which causes them to adsorb to the PET surface carboxyls.¹² Therefore, in water at a neutral pH, we expect an as-prepared PET pore to have an effective negative surface charge and after PAH modification to have an effective positive surface charge. Recordings in water with negatively and positively charged PET pores were used as a guideline that facilitated the interpretation of the recordings in propylene carbonate solutions.

Figure 1 shows the current–voltage curves of a single 660 nm PET pore placed in contact with 20 mM and 200 mM concentration gradients of LiClO₄. The measurements were performed with LiClO₄ due to the salt being soluble in a variety of different solvents. When a pore with negative or positive surface charges is placed in contact with two solutions of differing concentrations and, thus, differing conductivities, the recorded current–voltage curves show rectification, i.e., the currents for voltages of one polarity are greater than the currents for voltages of the opposite polarity. The rectification stems from electro-osmosis that depending on the voltage polarity fills the pore with a solution of higher or lower conductivity.^1,31,32 Pores with negative surface charges and pores with positive surface charges on the walls are expected to exhibit distinct current–voltage curves that are symmetric with respect to the origin of the coordinate system (Fig. 1).

For an unmodified pore in contact with aqueous solutions, when the working electrode is placed into the solution of higher conductivity (200 mM LiClO₄) and the ground electrode into the solution of lower conductivity (20 mM LiClO₄), the cationic (Li⁺) current will electro-osmotically fill the pore with the 200 mM LiClO₄ solution at positive potentials and with the 20 mM solution at negative potentials [Fig. 1(a)]. The measured ion current is directly proportional to the solution conductivity and the number of charge carriers in the pore.⁴⁰ Therefore, a pore as prepared in aqueous solutions will exhibit an ion current rectification wherein currents at positive voltages are greater than currents at negative voltages [Fig. 1(a) and the blue recording in Fig. 1(c)]. Conversely, after PAH modification, the anionic (ClO₄^-) current electro-osmotically fills the pore with the solution of higher conductivity at negative potentials and the solution of lower conductivity at positive potentials. Therefore, a pore with an effective positive surface charge exhibits larger currents at negative voltages than at positive voltages [Fig. 1(b) and the red recording in Fig. 1(c)]. The experiments performed in Fig. 1(c) exemplify how the polarity of the effective surface charge of a PET pore can indeed be inferred from the direction of rectification observed in the current–voltage curves and recorded with the salt concentration gradient. The measurements also provided evidence for the successful modification of the PET pore with the positively charged polyelectrolyte, PAH.

The same unmodified pore as shown in Fig. 1(c) was also tested using the 20 and 200 mM concentration gradients of LiClO₄ in propylene carbonate. The I–V curve of an as-prepared pore in the propylene carbonate solutions of LiClO₄ [Fig. 1(d)] has the same direction of rectification as the I–V curve of the positively charged pore probed using the aqueous salt concentration gradient [red curve in Fig. 1(c)]. The recordings suggest that the same pore that was negatively charged in water became effectively positively charged in the organic solvent. These findings are in agreement with our previous results showing the effective positive surface charge of PET³² and polycarbonate pores in propylene carbonate salt solutions.³³ 

The method of probing the surface charge polarity via ion current rectification and salt concentration gradients is applicable to pores of any size and shape. However, it does not provide any quantitative information on the surface charge density or magnitude of the surface potential. To compare the electrochemical properties of the PET–liquid interface in water and propylene carbonate, we performed resistive-pulse experiments where individual polystyrene particles were electrokinetically transported through a single PET pore.

Resistive-pulse measurements were initially performed in water to characterize and verify that the direction of electro-osmotic translocation agreed with the effective surface charge of PET pores. Experiments were performed with as-prepared single PET pores characterized with negative surface charges and pores subjected to PAH modification [Figs. 2(a) and 2(b)]. We began experimenting with aqueous KCl solutions since the resistive-pulse measurements in this electrolyte are best understood.^{16–18,20,21} In our first experiment, we used unfunctionalized, i.e., mostly uncharged, 400 nm polystyrene beads suspended in 100 mM KCl and 0.001% v/v TWEEN 20. The concentration of the particles was ∼10⁹ particles/ml. The particles are largely uncharged as elucidated from their low, few mV magnitude of zeta potential.⁴¹ The particles’ suspension was placed on one side of the conductivity cell with the ground electrode. The other side of the pore was in contact with the same salt solution without particles [Figs. 2(a) and 2(b)].

Figure 2(c) shows ion current signals in time recorded with a pore as prepared that had an effective opening diameter of 1 µm. Recordings with another pore that had prior been modified with PAH are shown in Fig. 2(d). Both pores were tested at ±500 mV. Distinct ion current pulses were observed for the negatively charged pore only at negative transmembrane potentials and for the positively charged pore at positive voltages. The particles only translocated through the pores for the voltage polarities that electro-osmotically brought the solution with particles into the pores [Figs. 2(a) and 2(b)]. The direction of electro-osmotic translocation agrees with the effective surface charge of the pores’ walls, by which a pore with an effective negative (positive) surface charge exhibits particle translocation in the direction determined by cations (anions). The absence of measurable ion current pulses in the opposite (electrophoretic) direction further validates the notion that the polystyrene particles used throughout experimentation were largely uncharged. Figures 2 (e) and 2(f) show examples of zoomed-in ion current pulses recorded for the two examined pores using the 400 nm particles. The presence of current undulations within each pulse is in agreement with earlier reports showing the pores exhibit an undulating diameter along the axis.^25,28 The repeatable signature of the current pulses also allows us to confirm that the pulses correspond to particles’ complete translocations and not approaches to the pore opening without successful passages.

The relative amplitude of ion current pulses, ΔI/I_p, is known to be a function of particle, d, and pore, D, diameters,^17,23

where R_p and R_e (I_p and I_e) indicate the electrical resistance (ion current) of the system with and without a particle in the pore, respectively, and L is the pore length. The expression 0.8D accounts for the access resistance of the pore.^42,43 The proportionality coefficient, $SdD$⁠, is the so-called shape factor and has the following form:²³ 

Figures 2(g) and 2(h) show the analysis of the relative current decrease (the events) associated with the passage of the 400 nm particles through the negatively charged single pores. The magnitude of the experimentally observed current change, ΔI/I_p, correlates very well with the magnitude predicted by Eq. (1) at all the examined voltages, suggesting that the particles do translocate individually and do not undergo aggregation. The histograms of ΔI/I_p recorded at different voltages are shown in Fig. S1.

Resistive-pulse experiments were also performed in an aqueous solution of LiClO₄, the salt used in the propylene carbonate based experiments. Figures 3(a)–3(d) show examples of pulses obtained in 100 mM LiClO₄ and compare them with recordings in 100 mM KCl for the same pore. The passage of particles only occurred at negative voltages in KCl and LiClO₄. This confirms that the pore was negatively charged in the presence of K⁺ and Li⁺ ions. At negative voltages, our electrode configuration sources cations from the side of the pore that contains the particle suspension, enabling particle passage. The amplitude of the ion current pulses in both salts correlated well with one another. Example ion current pulses shown in Figs. 3(c) and 3(d) indicate that the passage velocities of the particles in KCl and LiClO₄ are similar, further suggesting that the PET/liquid interface in these two salts is comparable. The event duration time is analyzed in detail below.

Resistive-pulse measurements were also performed in a 200 mM LiClO₄ solution in propylene carbonate to further probe how the organic solvent affects the effective surface charge of the PET pores and to substantiate the results obtained in Fig. 1. With a similar experimental setup as used with the aqueous solutions (Figs. 2 and 3), 400 nm polystyrene particles were suspended in a 200 mM LiClO₄ propylene carbonate solution with 0.05% v/v TWEEN 80. We used 200 mM (LiClO₄) as the concentration of the background electrolyte due to the significantly reduced conductivity of propylene carbonate based salt solutions. The increased salt concentration (compared to 100 mM KCl in water) allowed us to increase the signal of the ion current and the current change due to particle translocation.

To probe the effective surface charge of an as-prepared PET pore in the propylene carbonate LiClO₄ solution, the suspension containing the uncharged 400 nm polystyrene particles was once again placed into the chamber of the conductivity cell containing the ground electrode [Fig. 4(a)]. This allowed the effective surface charge of the PET pore to be elucidated from the directionality of electro-osmotic translocation of the particles. Figure 4(b) shows ion current recordings observed at positive and negative voltages, ±1 V. The measurements revealed that the particles translocated through the pore only at positive voltages. This suggests that the effective surface charge of the PET pore became positive since positive voltages can bring the particles into the pore only if the direction of electro-osmotic flow is determined by negative ions, much like the recordings in Fig. 2(d). The results shown in Fig. 4 also indicate a larger variability of the pulse amplitude compared to the recordings in water. Additional zoomed-in sections of the ion current pulses are shown in Fig. S2. The 1 µm pore used in these experiments is the same pore as in Figs. 2(c), 2(e), and 2(g). The similar shapes of the ion current pulses in aqueous [Fig. 2(e)] and propylene carbonate [Fig. 4(c)] based solutions suggest that the particles successfully translocated in both media.

Recordings of the ion current in propylene carbonate were subjected to a similar analysis as performed in Figs. 2(g) and 2(h). Figure 4(d) shows that the average amplitude of the ion current pulses at three magnitudes of applied voltage is still consistent with the predicted ΔI/I_p. However, the histograms of the experimentally measured amplitude of the events [Fig. 4(e) at 1 V and Fig. S3] reveal the presence of ΔI/I_p values that are even twice the theoretical prediction. These large values of ΔI/I_p suggest that the particles might have undergone aggregation when in the propylene carbonate based solution. Figure S4 shows similar recordings and analysis as in Fig. 4 for another independently prepared pore with an opening diameter of 780 nm.

The hypothesis of the particles aggregating in solution is also supported by the observation that their translocations would typically be recorded within the first ∼20 min of introducing the particles into the solution. Moreover, DLS experiments performed with suspensions of these particles in 200 mM LiClO₄ propylene carbonate did not yield any tangible results concerning the particles’ size due to the large polydispersity index (≥∼0.3) that increased with the measurement time.

Finally, we confirmed that the exposure of the PET pores to propylene carbonate based solutions did not change the effective pore opening. Figure S5 shows current–voltage curves of an 860 nm pore in 1M KCl before and after exposing it to a 200 mM LiClO₄ propylene carbonate solution with 0.05% v/v TWEEN 80. Both current–voltage curves are nearly identical to one another. This suggests that the pore did not undergo swelling or any other changes that would alter its effective opening. We would also like to note that the average ΔI/I_p recorded in propylene carbonate agrees well with the theoretically predicted value, providing evidence that the particles did not undergo swelling in the organic solution either.

The voltage polarity at which the particles translocate through the pore informs us about the polarity of the effective surface charges of the pore walls. In a negatively (positively) charged pore, the particles are transported in the direction of electro-osmotic flow as determined by the cations (anions) in the solution. To quantify the magnitude of the surface potential, we analyzed in detail the duration of the ion current pulses, which is a measure of the particles’ translocation velocity. From the Einstein–Smoluchowski equation, the velocity of each resistive-pulse event can be related to the zeta (ζ) potential of the pore walls through the following relation:¹ 

where ν_EOF is the electro-osmotic velocity of the particles, ε₀ is the permittivity of free space (8.85 × 10⁻¹² F/m), ε_r is the dielectric constant, ζ_Pore is the zeta potential of the pore wall, E is the electric field strength, and η is the solution viscosity. Equation (3) assumes that the particles are uncharged. Note that ζ_Pore is the potential at the shear plane. The value of ζ_Pore is expected to be less than the electric potential at the surface.¹³ Acknowledging that $νEOF=Lt$⁠, where t is the resistive-pulse event duration time, and knowing that $E=VL$⁠, one obtains

Rearranging Eq. (4) allows one to plot the duration of resistive-pulses as a function of inverse applied voltage,²⁴ 

Figure 5(a) shows the event duration time measured in 100 mM aqueous LiClO₄ using the same pore as shown in Fig. 3. The magnitude of ζ_Pore for the PET pore walls in the aqueous solution was calculated to be −4 ± 1 mV. This value agrees with earlier reports on the decreased zeta potential in concentrated salt solutions.^1,44 Recordings in 100 mM KCl for the same pore are shown in Fig. S6. The measured ζ_Pore for this salt solution was also ∼−4 mV.

Figure 5(b) shows the dataset of the event duration time plotted as a function of the inverse voltage in propylene carbonate. The first striking difference between the results in water and propylene carbonate is the independence of the event duration time on voltage in the organic solvent. Note that the uncertainty of determination of the passage time is ∼2 ms. Since the event duration time on average is only ∼5 ms, the ∼2 ms uncertainty of each measurement prevents us from verifying whether there is a relationship between the passage time and voltage. The measurement of the event duration could not be improved by increasing the bandwidth of our recordings^45,46 because this would lead to a significant decrease in the signal-to-noise ratio and in turn make detecting the events (∼100 pA in magnitude, Fig. S2) more difficult. Equally unexpected is the event duration time, which is ∼ten times shorter than in water for the same voltage, even though the viscosity of propylene carbonate is ∼three times higher than the viscosity of water.⁴⁷ The electro-osmotic velocity of the particles in 200 mM LiClO₄ in propylene carbonate reached 10⁻³ m/s. To confirm these findings, similar recordings were performed with another independently prepared pore whose opening diameter is 780 nm (Fig. S4). Ion current pulses with duration times less than 10 ms were again observed using a 200 mM LiClO₄ propylene carbonate solution and 400 nm polystyrene particles, further validating the enhancement of the electro-osmotic velocity.

The voltage independence of the event duration time prevents us from directly calculating the zeta potential of the PET pore walls in propylene carbonate using Eq. (5). However, if we assumed that the increase in the electro-osmotic velocity in propylene carbonate was due to the increase in the magnitude of ζ_Pore, the estimated zeta potential would be ∼120 mV once the solvent viscosity was accounted for. Therefore, the magnitude of the positive ζ_Pore in propylene carbonate is ∼30 times larger than the negative ζ_Pore in water. The lack of clear dependence of ζ_Pore in propylene carbonate on voltage, at least in the voltage range that we probed, also points to a significantly enhanced zeta potential in this solvent.

The zeta potential allows us to estimate the electrokinetic surface charge density (σ_el) that can be considered as an effective charge density at the shear plane with ζ_Pore.¹³ We can use here the Graham equation, which relates the surface potential, ζ_Pore, in this case, to σ_el,^48,49

where c₀ is the bulk salt concentration, k_B is the Boltzmann constant, T is the temperature, and N_A is the Avogadro number.

Using Eq. (6), σ_el was determined to be equal to ∼−3 mC/m² in 100 mM aqueous LiClO₄, and ∼+0.3 C/m² in 200 mM LiClO₄ in propylene carbonate. To further understand the estimated value of σ_el, we need to consider the origin of the surface potential and charge in these two solvent systems. A PET pore in contact with an aqueous solution will be negatively charged due to the presence of the dissociated, surface carboxyl groups. The density of carboxyl groups is known to be ∼1/nm². However, the shear plane is located in the solution beyond the outer Helmholtz layer.¹³ Consequently, due to charge screening, ζ_Pore in high ionic strength solutions is significantly lower than the potential right at the surface. Propylene carbonate is a polar, aprotic solvent. Therefore, it is not expected to participate in any Brønsted–Lowry acid–base reactions with the surface carboxyl groups of the PET surface and change its surface potential. The positive surface charge in propylene carbonate was postulated to have originated from the adsorption of Li⁺ ions and possible ordering of solvent molecules at the interface.^32,33 Since the location and density of the adsorbed Li⁺ ions are not limited by the specific chemical groups on the polymer surface, it is possible that the surface charge from the adsorbed Li⁺ ions is screened differently than predicted by the classical Poisson–Boltzmann equations. The estimated σ_el of 0.3 C/m² corresponds to ∼2 Li⁺ ions per nm². Admittedly, we do not have yet an explanation for the large magnitude of zeta potential and electrokinetic charge density in propylene carbonate. However, we anticipate that future modeling will be able to unravel the atomistic structure of this and other organic solid–liquid interfaces.

This paper shows how probing electro-osmotic transport through model single pores can provide information on the electrochemical properties of the solid–liquid interface. Current–voltage curves recorded in the presence of a salt concentration gradient give information on the direction of electro-osmotic flow and consequently on the polarity of surface charges.^31,32 The electro-osmotic passage of uncharged particles through model pores informs us not only on the polarity of surface charges but also the magnitude of the zeta potential of the pore walls. We showed that PET pores studied here were negatively charged in aqueous solutions of LiClO₄ but acquired a positive charge when placed in contact with LiClO₄ solutions in propylene carbonate. The magnitude of the pore walls’ positive zeta potential in propylene carbonate was demonstrated to be significantly higher than the magnitude of the negative zeta potential in water. The values of zeta potential were in turn used to estimate the electrokinetic charge density, i.e., the density of charges on the shear plane. As it was postulated in earlier reports, the positive charge of the polymer pores in LiClO₄ solutions in propylene carbonate stemmed from adsorbed lithium ions.^32,33 Our measurements estimated the density of adsorbed Li⁺ ions to be ∼2/nm². We hope this work will become an inspiration for further experimental and theoretical research aimed at elucidating the molecular arrangement of ions and the solvent at interfaces in non-aqueous media. We believe that the description of solid–liquid interfaces with organic solvents will require a multi-scale approach. Molecular dynamics simulations will need to include the arrangement not only of solvent molecules⁵⁰ but also of ions from the solution as well as an external electric field to connect the molecular structure of the interface to the experimentally measured electrochemical signals.

See the supplementary material for additional experimental data of particle transport through the single nanopore in aqueous and propylene carbonate media.

W.S.R. designed the experiments, recorded all the data, performed data analysis, and wrote the manuscript. Z.S. co-designed the experiments, analyzed the recordings, and wrote the manuscript.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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 at the University of California, Irvine, under Award No. DE-SC0019112. We are grateful to all principal investigators of the DOE Center for discussions and insightful input. Additionally, we thank Dr. Dmitry Fishman and the Laser Spectroscopy Labs at UC Irvine for help.