Chemistry-driven autonomous nanopore membranes

Domain: chemistry
Published: 2026-02-18
Editorial outcome: major_revision

Abstract
Fabrication of pores at the atomic scale remains a significant challenge in modern nanotechnology, hindering the study of ion transport and molecular dynamics in confined spaces. Here, we introduce a chemically controllable break-membrane approach that enables the repeated formation and closure of nanoscale pores in SiNx membranes through manipulating the in-pore electrochemical reaction conditions by transmembrane voltage. Ionic current measurements reveal distinct conductance features that are consistent with ion dehydration and transport through highly confined channels approaching sub-nanometer dimensions. The scalable nature of this platform, which allows multiple pores to be actuated simultaneously, offers a powerful tool for probing ion transport and fluid dynamics in extreme confinement. Beyond advancing fundamental understanding of ion transport and fluid dynamics, this chemically driven membrane system holds promise for applications in single-molecule sensing, neuromorphic computing, and nanoreactor design.

Introduction
Evolution of life has created ion channels for the maintenance of non-equilibrium physicochemical environments within cells to support biological functions in physiological matrices1,2. The channels exist in transmembrane proteins featuring ångström-sized constrictions of atomically precise geometries dictated by their ingenious molecular structures3–6. Their unique architecture enables permselective transport by admitting only the ions of sufficiently small size to traverse the minuscule conduits. Another key function is gating, where conformational changes in protein structure open or close the channels in response to external stimuli, generating action potentials via the selective ion flux crucial for intercellular communication and perception7–9.

Inspired by nature, advances in nanotechnology have driven growing interest in mimicking the distinct capability of biological ion channels with solid-state nanopores10–12. Self-organized nanoporous structures in synthetic membranes are found to serve as a nanofluidic system with permselectivity13, filtering specific types of ions for desalination and osmotic power generation14,15. Meanwhile, electron and ion beam milling allow the fabrication of single-digit nanochannels in dielectric membranes16,17, enabling studies of ion transport at the individual pore level18,19. Ångström-scale slits are another promising platform20 comprising a two-dimensional channel of sub-nanometer heights in stacked 2D materials with rich transport properties involving ion pairing21 and quantum friction22. These emerging nanostructures have proven useful for investigating the transport phenomena in confined spaces at a scale relevant to the biological ion channels. However, probing ion flow in such infinitesimal conduits remains challenging due to the difficulty of creating such confined spaces with reproducible precision, limiting the number of channels available for systematic study23,24. In contrast, we herein introduce a chemically driven break-membrane strategy that exploits voltage-controlled precipitation and dissolution of metal phosphates inside a lithographically defined nanopore to autonomously create, seal, and recreate sub-nanometer conduits. This voltage-facilitated in-pore chemistry enables repeated pore formation with high stability over hundreds of cycles and reveals rich ion-transport phenomena, including spontaneous ionic spiking reminiscent of biological channels, tunable pore sizes governed by solution composition and pH, and selective transport of chaotropic or kosmotropic ion through pores approaching the scale of dehydrated species. By providing a scalable route to generate and study thousands of ångström-scale pores within a single solid-state nanopore, this framework establishes a new experimental platform to probe ion dynamics at the limits of confinement for developing chemically active membranes relevant to single-molecule sensing, adaptive iontronics, and nanoscale reactors.

Results
The method uses a nanoscale hole of diameter dpore in a silicon nitride membrane (thickness is 30 nm, otherwise stated) as a nanoreactor25–28. The in-pore reaction is induced by the ion flux under the transmembrane voltage Vb with the trans and cis compartments filled with 2 M MnCl2 and phosphate-buffered saline (PBS), respectively (Fig. 1a, see also Supplementary Table 1). As Mn2+ cations electromigrate into the pore under negative voltage, they react with the phosphoric acid anions in PBS to undergo nucleation and growth of manganese phosphates. Eventually, the precipitated layer completely seals the nanopore, strongly suppressing the ionic current Iion during the negative Vb scans (Fig. 1b–d). Turning the voltage to positive, on the other hand, the precipitate is dissolved by the acidic MnCl2 solution of pH 4.2, reverting the nanopore to a fully opened state. The resulting diode-like behavior features a high Iion rectification ratio rrec = I+1 / I−1 of over 30,000, where I+1 and I−1 are the ionic current at Vb = +1 V and −1 V, respectively29. The sequence of chemical reactions is stable over 756 voltage scanning for >10 hours, suggesting the robust nature of the voltage-controlled precipitation/dissolution processes inside the nanopore (Fig. 1e, see also Supplementary Fig. 1)29,30.

The precipitated layer activates repetitive formation of small pores. This can be found as conductive Iion spikes stochastically fired under constant negative transmembrane voltage (Fig. 2a, see also Supplementary Figs. 2 and 3), the feature of which resembles the spontaneous activity of ionic channels31. They are characterized as pulse signals of amplitude Ip and width td (Fig. 2b, c). The underlying mechanism involves the interplay of in-pore chemistry and voltage-driven ion transport (Fig. 2d). Precipitation reaction under negative Vb fills the nanopore with a phosphate manganese film. Once complete sealing occurs, meanwhile, the applied voltage becomes ineffective in causing the precipitation since it generates no ion flux. Meanwhile, the dissolution reaction at the acidic MnCl2 solution side proceeds to gradually narrow the nanopore layer. As a result, a small pore is pierced at a certain moment, causing the rapid rise in Iion (b). Simultaneously, the focused electric field starts to feed the reactant ions into the pore for the precipitation, leading to the closure of the pore (c). These three stages of chemical reactions occur autonomously to repeatedly form and close small pores, which is observed as the firing of Iion spikes. The rate of pore piercing fp is presented by the time interval Δt between two consecutive Iion spikes. Fitting the Δt distribution with a Gaussian peak given as Δt = A exp [−4ln2 (x − xc)2 / w2] (1) where A and w are the peak area and width at half maximum, respectively, the characteristic fp = Δt−1 is estimated to be ~10 Hz from the peak position xc for the case in the MnCl2/PBS system under Vb = −1.1 V (Supplementary Figs. 5 and 6). While similar features were observed in voltage-driven motions of nanoprecipitates at the tip of a nanopipette25–28,30, they were unable to seal the channel completely, leading to random oscillations in the base level current. In contrast, the nanopore reactor in the thin SiNx membrane provides finer control over in-pore chemical reaction conditions, enabling the repeated formation of small pores through the autonomous nanoelectrochemistry29.

This breathing mode of the precipitated nanopore membrane is tunable by the ionic reactants on the cis side (Fig. 3a). In the presence of MgCl2 (2 M), for instance, the in-pore reaction equilibrium shifts toward dissolution, preventing the precipitate layer from sealing the nanopore. Conversely, non-dissolvable aluminum phosphates are formed with AlCl3 (2 M). For these salts, the breathing mode is absent, resulting in either a partially occluded or permanently sealed nanopore. Meanwhile, the reaction kinetics in CaCl2 (2 M) promotes spontaneous membrane piercing, demonstrating conductive Iion spikes. While the overall feature is similar to that observed in MnCl2, the pulses are found as relatively large in CaCl2 as evident in the Ip versus td scatterplots displaying clusters of data above 10 nA with CaCl2 (Fig. 3b, c). The result is similar in an equimolar mixture of MnCl2 (1 M) and CaCl2 (1 M), suggesting the coexistence of manganese and calcium phosphate precipitation reactions within the nanopore (Fig. 3d).

Compared to the stochastic nature of pore piercing in MnCl2, the spontaneous activity in CaCl2 demonstrates a distinct pattern (Fig. 3e). Being sealed by calcium phosphate under negative transmembrane voltage, the ionic current remains silent for ~0.2 s (Fig. 3f). This is followed by small conductive pulses, resembling those observed in MnCl2, which persist for ~1.5 s. Subsequently, larger pulses begin to appear, culminating in a single giant spike. After that, the Iion state returns to the silent mode. The cycle of events repeats periodically to fire giant ionic spikes roughly every 4 s (Supplementary Fig. 7). This burst mode can be ascribed to the slow reaction rate of the calcium phosphate precipitation (Fig. 3g). Initially, calcium phosphate blocks the pore, preventing ion flux through the membrane. Since it inhibits the ion transport for further precipitation, the precipitate layer undergoes isotropic corrosion, leading to gradual thinning to stochastic small pore piercing. What is different from the case of MnCl2/PBS system is that the precipitation dynamics cannot compensate for the rapid dissolution to repair the phosphate layer under corrosion. As a result, small nanopores tend to merge into larger ones. Ultimately, the phosphate membrane partially or fully ruptures, either spontaneously or under the influence of electroosmotic flow32, producing a giant Iion spike. This resets the reaction system by resealing the SiNx nanopore through phosphate precipitation.

Since the pores formed by the cyclic in-pore chemical reactions are anticipated to be at the ultimate scale, ion transport therein likely exhibits intriguing size effects intrinsic to the confined space. Molecular dynamics simulations predict the notable influence of hydrated water molecules around ions on their mobility when passing through sub-nanometer-scale fluidic channels33,34. This factor is particularly critical for understanding and controlling the ion blockade behavior of biomolecules in the presence of ionic reagents belonging to the so-called Hofmeister series35–37. In this context, we examined the ion transport characteristics using F− and I− as chaotrope and kosmotrope, respectively, which are expected to form more ordered and disordered hydration shells compared to Cl−38. These halide anions are added on the trans side as KF (1 M) and KI (1 M) in PBS (Fig. 4a) to keep the solution reactions to allow the spontaneous pore piercing. In both cases, the SiNx nanopores are sealed with the precipitates at Vb = −0.5 V in the presence of 2 M MnCl2 on the cis side.

The addition of the chaotropic and kosmotropic agents induces distinct changes in the spontaneous activity of the phosphate membranes. For example, KF facilitated the firing of the ionic spikes, enhancing fp by a factor of 6 (Fig. 4b), while also increasing their amplitude (Fig. 4c). Here, F− is a kosmotrope bearing ordered water molecules to form a thicker hydration shell39,40. The fact that F− enabled larger conductance indicates a minor role of the energy barrier in disrupting the hydration structure under the focused electric field. Given its smaller ionic radius, instead, the result suggests the higher mobility of F− in the infinitesimal pores compared to Cl−. In contrast, KI induces negative pulses (Fig. 4d–f). The comparatively large ion radius of I− restricts its passage through the small channels24,39. As their presence at the entrance impedes the transmembrane ion flux, the focused electric field accumulates other anions and cations at the pore. Upon the closure of the channel by the precipitation reaction, the stored ionic charges relax to cause transient changes in the ionic current. These contrasting features of the chaotropic and kosmotropic ions coexist in a mixture of KI (0.5 M) and KF (0.5 M) in PBS, manifesting the tunability of the ionic flow in the infinitesimal channels by the ion radii (Fig. 4g).

The transmembrane voltage dependence of the conductive pulses provides further insight into the ion transport characteristics. The ionic current traces are silent under small negative Vb, suggesting an insufficient electric field to squeeze the hydrated ions into the pierced channels before they are closed via the precipitation reaction. As the negative voltage increases, meanwhile, ionic current spikes become observable, resembling the ionic Coulomb blockade characteristics of MoS2 sub-nanometer-pores41,42. Noticeably, the threshold voltage for observing the conductive pulses is smaller for MnCl2 than CaCl2 (Fig. 5a, b, see also Supplementary Figs. 8–10). Since both solutions have the same concentration of Cl− on the trans side, the difference manifests in the distinct roles of Mn2+ and Ca2+. According to the Coulomb blockade theory, ions of the same valence should experience energy barriers of similar heights41,42. The difference in the threshold voltage is, thus, ascribed to the hydration energy. According to the Hofmeister series, however, Mn2+ is more kosmotropic than Ca2+43, indicating the interplay of factors beyond the Coulomb blockade and hydration effects in the pore piercing to ion translocation processes.

Determining the size of the pores is crucial. In the MnCl2/PBS system, nevertheless, the Ip distributions exhibit no evidence of well-defined channel structures formed by the membrane piercing mechanism (Fig. 5c, see also Supplementary Fig. 11), which is attributed to an energy barrier arising from Coulombic interactions and steric effects of hydration shells42. While ions are able to transit the pierced pores under the energy barrier at Vb > 0.1 V, their height likely depends on the arbitrary size of the pores42, resulting in the featureless Ip distributions observed. Similar pulse height distributions are found in the CaCl2/PBS system, except for giant spikes (~40 nA) associated with membrane rupture in the burst mode (Supplementary Figs. 12 and 13). Maxwell–Hall theory44 describes the ionic conductance (Gpore) of a cylindrical pore with diameter dpore and depth Lpore as Gpore = (Rpore + Racc)−1, where Racc = ρ/dpore is the access resistance45,46 and Rpore = 4ρLpore / πdpore2 is the resistance inside the pore, with ρ denoting the solution resistivity. This model accurately predicts pore conductance when counterion conduction47 and fluid dynamics48 have negligible effects on in-pore ion flux, as is the case during membrane rupture under high salinity. From the 40 nA heights of the giant spikes and ρ of 8.3 S/m (Supplementary Fig. 14), therefore, Rpore is estimated to be 12.5 MΩ, which suggests the opening of nanopores with diameters around 10 nm with the CaCl2/PBS configuration.

Unlike manganese and chloride ions, F− was found to electromigrate through the ångström-scale pores without significant steric impedance. This is evident from the log10 Ip distributions with a pronounced peak shifting monotonically to higher current levels with Vb (Fig. 5d, see also Supplementary Figs. 15 and 16). Plotting the peak positions, assessed by Gaussian fitting to the histograms, the characteristic ionic current states are revealed to scale linearly with the transmembrane voltage (Fig. 5e with a fitting curve Ip = I0 + rVb, where I0 and r are the intercept and the slope, respectively), which signifies the F− transport through a channel of a well-defined structure with negligible contributions from the Coulomb blockade- and hydration-derived energy barriers42. The differential conductance obtained from this is 3.9 nS. Neglecting the effect of pore length, verified by the measurements using SiNx nanopore membranes of different thickness (Supplementary Fig. 17), the diameter of the pores is calculated from Racc to be 0.39 nm (Fig. 5e inset)24 with ρ = 0.1 Ωm for 1 M KF in the sub-nanometer-pores with the fast ion mobility of dehydrated fluoride ions49. The pores are, thus, larger than the fluoride ions (0.3 nm diameter) but smaller than the hydrated forms (0.7 nm diameter)39, suggesting the dehydration-mediated F− transport (Table 1)50. Additionally, a 0.28 V offset at zero current is observed, which is consistent with the suppressed transport of hydrated ions at low voltages due to the significant effects of Coulombic and steric interactions42. It is important to emphasize, however, that this pore size estimate is indirect and based solely on ionic current measurements. Additional factors, such as counterion conduction47, permselectivity51, electroosmotic flow52, and ion–ion correlations53, may also contribute to the observed conductance and have not been fully accounted for in this model. While the results are consistent with the formation of sub-nanometer pores, direct structural observation54 and refined theoretical modelings55 are essential to validate the inferred dimensions and to fully capture the ion transport physics within such confined environments.

The incorporation of KF also increased the ionic spiking rate. Pores form via dissolution-induced thinning of the metal phosphate layer and subsequently reclose through precipitation, driven by electric-field-mediated translocation of Mn2+ and phosphate ions. During this cycle, pores remain undetectable in ionic current measurements until they expand sufficiently to accommodate the relatively large Cl− ions when F− is absent. Many pores, therefore, remain invisible, sealed by precipitation before becoming detectable. The introduction of smaller F− anions enables ionic conduction through these nascent pores, revealing their existence and enhancing the observed spiking frequency.

The reaction dynamics are explored by inspecting the conductive pulse waveforms. Aligning the ionic signals with respect to the onsets and tails, defined as the moments when the ionic current rises above or returns to the base level, we obtain ensemble-averaged Iion profiles revealing how the ångström pores are formed and closed (Fig. 5f, g). They exhibit smooth changes in the ionic current, suggestive of the non-discrete nature of the reaction-driven pore opening/closure kinetics. Both the onset and tail phases can be fitted with the exponential function Iion ∼ exp(±rt), where the coefficient r characterizes the speed of the pore evolution (Supplementary Figs. 18 and 19). The observed decrease in r with increasing Vb suggests that higher electric fields slow down the dissolution and precipitation reactions (Fig. 5h), ascribed to the role of the associated stronger flows of non-reactant chloride ions in suppressing the reaction.

The autonomous spiking behavior of the nanopore membrane is highly tunable via chemical control. For example, reducing the MnCl2 concentration on the cis side from 2 M progressively suppresses spiking activity, yielding featureless ionic current traces (Supplementary Fig. 20). This inactivation arises from a concomitant pH increase from 4.2 to ~7, which inhibits the dissolution of manganese phosphate nanoprecipitates once formed, mirroring the behavior observed in the AlCl3/PBS system. When the pH was adjusted back to 4.2, lowering the MnCl2 concentration to 0.1 M resulted in larger ionic spikes, indicative of pore opening driven by a reduced precipitation rate under limited Mn2+ supply (Supplementary Figs. 21–23). Further dilution of MnCl2 eventually caused rupture of the phosphate layer through dissolution, marking the transition from self-oscillatory to fully open states.

Reaction kinetics can also be modulated through the concentration of anionic reactants. Substituting PBS with Hank’s balanced salt solution (HBSS) eliminates the strong ionic rectification in the Iion–Vb curves, as HBSS lacks phosphate even in the presence of 2 M MnCl2 in cis. Meanwhile, introducing phosphate sources, H3PO4 (Supplementary Figs. 24 and 25), K2HPO4 (Supplementary Figs. 26 and 27), or Na2HPO4 (Supplementary Figs. 28 and 29), into trans restores manganese phosphate nucleation within the nanopore, producing pronounced current suppression at negative Vb. The required concentration threshold depends strongly on the phosphate species: Na2HPO4 induces precipitation at levels as low as 10−5 M, whereas H3PO4 requires >0.1 M due to its low pH (1.5), accelerating dissolution.

For Na2HPO4 in trans, ionic spiking emerges at concentrations above 5 × 10−3 M (Supplementary Figs. 30 and 31). Below this threshold, insufficient phosphate flux fails to maintain a complete precipitate seal against the relatively fast cis-side dissolution. Conversely, at higher concentrations, the spiking frequency decreases and pulses become weaker and narrower (Supplementary Figs. 32–36), reflecting more rapid pore closure by an enhanced phosphate ion flux that prevents pores from growing to larger sizes.

Beyond reactant concentration, pH adjustment offers a way for reproducible, size-controlled pore formation. In MnCl2/PBS systems, lowering the trans-side pH below 7.4 with HCl steadily increases spike amplitudes (Fig. 6a–g, Supplementary Figs. 37–44). Simultaneously, the distribution of pulse heights narrows, indicating reduced pore-to-pore size variability (Fig. 6h). Using the Maxwell–Hall model under the condition Rpore >> Racc (Supplementary Fig. 14), the mean pore diameter is estimated to be tunable from ~2 nm to ~7 nm solely through pH control, demonstrating sub-nanometer precision in autonomous pore size regulation. Similar behavior was observed with pH adjustment on the cis side, although excessively acidic conditions led to membrane instability, limiting its utility for controlled operation (Supplementary Figs. 45 and 46).

The automated membrane piercing for repeated nanopore formation is scalable to multipore systems. A single SiNx nanopore of dpore = 100 nm can serve as a template for precipitating metal phosphates under transmembrane voltage (Fig. 7a), enabling the chemically driven autonomous actuation to open and close minuscule pores. Expanding the number of 100-nm-sized pores Npore in two-dimensional arrays in the membrane results in a linear increase in the ionic conductance (Supplementary Fig. 47). Scanning Vb to examine the repetitive in-pore reactions with the MnCl2/PBS configuration, we observe strong ionic rectification at negative voltages (Supplementary Fig. 48). The absence of discrete features in the Iion–Vb curves, suggestive of sequential nanopore closure via phosphate precipitation, confirms the synchronized activity of the multiple SiNx pores in response to the transmembrane voltage. Consistently, the spiking frequency at −0.5 V increases linearly with Npore (Fig. 7b, c, see also Supplementary Fig. 49). Here, Fig. 7c is fitted with a linear function fp = γ Npore with the slope γ. Notably, this level of control is unattainable by merely enlarging dpore in a single SiNx nanopore (Supplementary Figs. 50–52), manifesting the chemical kinetics distinction in the pores of different sizes.

The high efficiency of Iion spiking allowed the observation of Cl− transport signature through the nanopores. Whereas the log10 Ip distribution is featureless for 13,204 Iion spikes detected with a single 100-nm-sized nanopore, a pronounced peak appears ~1.8 nA, well described by the Gaussian function log10 Ip = A exp [−4ln2 (x − xc)2 / w2] (2) with the peak position (xc), area (A), and width at half maximum (w), for 88,651 signals obtained with the quadrupore (Npore = 4) (Fig. 7d, e, see also Supplementary Fig. 53). The peak becomes even more pronounced with 163,241 signals from the hexadecapores (Npore = 16). This amount of current can be compared to the F− conductance giving 0.8 nA at Vb = −0.5 V. The higher conductance seen for Cl− is attributable to its 1.7-fold larger mobility than F−56. Only 0.009% and 0.02% of the total current are carried by the Cl− spikes for Npore = 4 and 16, respectively, manifesting the potential of the high-f systems for resolving dehydration-mediated ion transport. Overall results are consistent in validating the chemically controllable break-membrane approach for systematic evaluations of the ion transport in ångström-scale small pores.

Methods
Fabrication of solid-state nanopores
A 4-inch silicon wafer is coated with 30-nm-thick SiNx layers from both sides by low-pressure chemical vapor deposition. It is then diced into 25 mm × 25 mm square chips. Photoresist AZ5206-E (MicroChemicals co.) is spin-coated on a chip, followed by patterning of a microelectrode pattern by photolithography. After development, a 20 nm-thick Au with a 5 nm Ti adhesion layer is deposited by radio-frequency magnetron sputtering (Samco co.). The chip is immersed in N,N-dimethylformamide overnight and ultrasonicated to lift off the residual resist. Subsequently, the SiNx layer on the opposite side of the microelectrodes is partially removed by reactive ion etching (Samco co.) via a metal mask. After that, the exposed Si is wet-etched in KOH aq. (Wako co.) on a hot plate, creating a SiNx membrane at the bottom of the deep trench formed. On the membrane, ZEP520 resist is spin-coated. A circle of diameter dpore is delineated by electron beam lithography (Elionix co.). The residual resist after the development is used as a mask to sculpt a nanopore by the reactive ion etching. The chip is immersed in N,N-dimethylformamide overnight again to remove the resist layer. Finally, it is rinsed with ethanol and acetone.

Fabrication of nanoheater-embedded nanopores
A nanopore of dpore = 50 nm is formed in a SiNx membrane by the fabrication processes described above. Using a part of the microelectrodes as markers, a nanoscale coil pattern is delineated in the resist layer (ZEP520) coated on the membrane by the electron beam lithography. After development, 50 nm-thick Pt is deposited by sputtering. Lifting off the resist in N,N-dimethylformamide, the chip is rinsed with ethanol and acetone. Finally, 20-nm-thick SiO2 is grown on the membrane, which serves as a protection layer for the nanoheater. As the SiO2 is deposited on the nanopore wall, it causes the pore diameter to shrink to approximately 40 nm. We note that this nanoheater-embedded nanopore is used only for examining the in-pore chemistry at elevated temperature. All other measurements use the pristine nanopores in 30 nm-thick SiNx membranes.

Nanopore sealing
Polymer blocks are adhered to both sides of a nanopore chip for the ionic current measurements. They are made of polydimethylsiloxane (PDMS) formed on a SU-8 mold. Specifically, SU-8 resist is spin-coated on a 4-inch Si wafer. An I-shaped pattern is created by photolithography, which is used as a mold to cure PDMS. This is performed by pouring Sylgard 184 (Dow co.) on the mold, degassing in a vacuum, and heating in an oven at 90 °C for 6 hours. After curing PDMS, a 15 mm × 15 mm × 5 mm block is cut out with a surgical knife. Because of the SU-8 pattern, the block has an I-shaped trench serving as a fluidic channel for pouring electrolyte solution into nanopores. In the block, three holes are punched using a tool for biopsy. The surface of the PDMS block and the nanopore chip is activated by oxygen plasma (Femto co.). Subsequently, the two surfaces are put together for the bonding. The series of processes was carried out to attach another PDMS block to the other side of the nanopore.

Ionic current measurements
Electrolyte solution is poured into one of the three holes in a PDMS block attached to a nanopore chip using a pipette. Subsequently, another solution is added through the holes in the polymer block on the other side. After that, two Ag/AgCl rods are inserted into the holes in the two PDMS. Transmembrane voltage Vb is applied through one of the Ag/AgCl, and the resulting ionic current is recorded through the other Ag/AgCl. A picoammeter-source unit Keithley 6487 (Keithley co.) is used for the Iion–Vb characteristics measurements, which is GPIB-controlled under a program coded in Visual Basic. On the other hand, time course changes in the ionic current are recorded at 1 MHz sampling rate using a nanopore reader equipped with a fast current amplifier of 100 MHz bandwidth (Elements co.). After each measurement, HCl is added to the nanopore to completely dissolve the residual precipitates on the membrane surface for the condition initialization. After that, the PDMS channels are filled with ultrapure water (Millipore co.). The water is then replaced with an electrolyte solution for another ionic current measurement.

Ionic current spike extraction
The ionic current spikes fired upon the precipitate membrane piercing are extracted as follows. The open pore current is offset to zero by linear fits to the partial 0.5 s ionic current traces and subtracting the fitted components from the raw data. The offset traces are smoothed by the second-order Savitzky-Golay function for noise reduction, coded in Python. To extract the ionic current spikes, the local maxima points are searched above a threshold level of 300 pA. Subsequently, 2.5 ms of data before and after the current maxima are saved in a separate file, collecting the datasets of the ionic current spikes. For the ensemble averaging of the spike signals, the points where the current decreases to below zero amperes from the current maxima are identified, followed by data saving with the time at the zero-crossing point set to zero. The spikes extracted in this way are ensemble-averaged to examine the spike onsets and tails. All these pulse extraction processes are performed automatically under a program coded in Visual Basic.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This work introduces a novel approach using chemically controllable break membranes to generate and investigate ångström pores, overcoming traditional limitations in reproducibility and precision. The repeated formation and closure of pores in SiNx membranes occurs via in-pore chemical reactions, enabling the study of ion transport at ångström scales. The dynamic behavior of ion flux through these infinitesimal channels reveals distinct dehydration-mediated ionic conductance signatures for F⁻ and Cl⁻ ions. However, it is not suggested to publish in NC due to the novelty. There are some issues that need to be resolved.\n• In the article, there is no explanation for the meaning of counts in figures 1 c-d. Please clarify them in the article.\n• In the article, the diameter of the ultra-small pores is calculated from Racc to be 3.9 Å (Figure 5c inset). It should be displayed in the figure 5e inset. In the MnCl2/PBS system, however, the Iₚ distributions exhibit no evidence of well-defined channel structures formed by the membrane piercing mechanism (Figure 5c; see also Supplementary Figure 8). This should be in Figure 5a. In Figure 5, there is no indication for figure d. Therefore, the markings in figure 5 should be revised in the content as well.\n• In the experimental section, finally, 20 m-thick SiO2 is grown on the membrane, serving as a protective layer for the nanoheater. 20 m should be incorrect.\n• In the experimental section, as the SiO2 is deposited on the nanopore wall, it causes the pore diameter to shrink to approximately 40 nm. However, in the results section, the method uses a nanoscale hole of diameter dpore in a silicon nitride membrane (with a thickness of 30 nm unless otherwise stated) as a nanoreactor. Which is correct?\n• In the article, the produced pore size is just calculated. Is there any experimental data to identify the ångström size?\n• In the sentence - The giant spikes are, therefore, likely correspond to the opening of 178 nanopores with diameters around 10 nm -, is 10 nm from the calculation or experimental data? Could you please clarify it?\n• In the article, there is no data to demonstrate the repeated formation and closure of pores generated in SiNx membranes.\n• Can these pores with ångström size be controlled precisely and produced repeatedly?", "reviewer_2": "This work presents a novel approach for dynamically creating and closing ångström-scale pores in silicon nitride membranes to achieve reversible pore gating through applying transmembrane voltage to regulate in-pore chemical processes (such as manganese/calcium phosphate precipitation and dissolution). The authors systematically investigated ion transport mechanisms by analyzing current signatures of various anions (F⁻ and Cl⁻) through these ultrafine channels, revealing distinct dehydration-mediated conduction behaviors. The experimental results are interesting, and the article, with its complete dataset and comprehensive analysis of ion transport mechanisms, provides fundamental insights into ion transport and potential nanofluid applications. Therefore, I recommend its publication after the following revisions：\nQuestions:\n1. Through the analysis of ion current spike parameters, this article provides a novel perspective on analyzing nanofluidic transport within pores. However, the characterization method is not enough, it is beneficial to add several SEM images to illustrate the nanopore structure in real.\n2. Line 84-86, “The rate of pore piercing fp is presented by the time interval Δt between two consecutive Iion spikes, which is about 10 Hz for the case in the MnCl2/PBS system under Vb = -1.1 V.” The authors mentioned that pore piercing frequency in the MnCl2/PBS system. Does the spiking frequency depend on concentration in the MnCl2/PBS system or other factors?\n3. In Figure 4, the·author examines ion transport·characteristics by introducing halide anions into the PBS solution. When F- is added as a kosmotrope, the amplitude and frequency of the current spikes increase. Compared to·Cl-, F- can electromigrate through the ultra-fine pores without·significant steric impedance, providing a reasonable explanation for the increase in peak current amplitude (lp). However, the dynamic precipitation/dissolution processes within the nanopore remain primarily driven by Mn²⁺ and phosphate ions, even in the PBS/KF system. Given that both the electrolyte buffer pH and phosphoric acid concentration were held nearly constant, the sixfold increase in pulsed current frequency induced by non-reacting F⁻ ions remains unexplained. This phenomenon requires a more detailed mechanistic explanation.\n4. In the MnCl2/PBS system, the acidity (pH 4.2) of the cis-side MnCl₂ solution drives precipitate dissolution. While applied electric fields slow this dissolution at higher strengths, pH remains a critical factor for precipitation-dissolution equilibrium in nanopore research. Therefore, modulating the pH of MnCl₂ could alter dissolution kinetics. Would this approach provide an alternative method to regulate the amplitude and frequency of ion current spikes in ultrasmall pores via pH modulation?\n5. Figure 5 appears to be missing the panel label '(d)' in the current version. The authors should carefully proofread all figures to ensure consistent labeling throughout the manuscript.\n6. Line 181-189, there are inconsistencies between descriptions and figures. The authors should check this part carefully to ensure a correct description of Figure 5.\n7. In Line 204, the voltage symbol Vβ should be unified to Vb throughout for consistency.\n8. Please systematically verify and standardize the correspondence and description between the figure and its captions in Figure S8 and Figure 6, respectively.", "reviewer_3": "This manuscript describes an approach for fabricating and controlling ultra-small pores at the Ångström scale by using chemically controllable break membranes in SiNx substrates. By applying simple voltage control to drive in-pore chemical reactions, the authors aim to demonstrate repeated pore formation and closure, which is intended to enable the study of ion transport and molecular dynamics in confined spaces. However, I have several major and minor concerns that should be addressed.\nMajor Issues\n1. Chemical Reaction Process\nThe authors propose a chemistry-driven method for fabricating Ångström pores, but the manuscript provides less discussion of the chemical reaction process (e.g., reactant concentration). How do the reaction parameters influence the pore formation mechanism?\n2. Pore Reaction Stability\nIn Figure 1e, why does the rectification ratio gradually drop below 30,000 after 400 curves? The authors should clarify the possible reasons for this decline.\n3. Ion Transport Design\nThe selection of these two ions (F- and I-) for the transport study is intended to address which application requirements or scientific problems? The authors should provide additional details on the experimental testing procedure for the ion transport property studies.\n4. Scaling Up to Array\nHow should the kinetic differences be understood between enlarging individual SiNx pore sizes and producing SiNx pore arrays as two approaches for increasing the overall membrane area?\n5. Sub-Nanometer Pore Density\nThe authors claim: “By generating and measuring thousands of sub-nanometer pores from a large pore using simple voltage control, this approach overcomes longstanding challenges in fabricating ultra-fine channels with reproducible precision.” Is it necessary to quantify pore density more rigorously? How was the pore density mentioned in this statement determined?\n6. Data Analysis\nIs it scientifically appropriate to conduct a linear fit using only three data points (array results)? The authors should add the number of data points or adjust the data processing method accordingly.\nMinor Issues\n8. What explains the difference in peak heights in Figure 3e and Figure 3f?\n9. Would adding the 0.4 V data point in Figure 5h affect the overall trend?\n10. In Figure 5, the label for panel (d) is missing.\n11. Please confirm whether the voltage legends in Figures 5f and 5g are accurate.\n12. Why is there an inconsistency between the pore diameter mentioned in the text (100 nm) and the legend (20 nm) in Figure 6?"}, "author_response": "Chemistry-driven autonomous ångström pore membranes\nMakusu Tsutsui, Wei-Lun Hsu, Denis Garoli, Ali Douaki, Yuki Komoto, Hirofumi Daiguji, and\nTomoji Kawai\nWe are grateful to the referees for their careful evaluation of our manuscript and for\nproviding insightful and constructive comments, which have been invaluable in improving\nthe quality of the work. We have carefully addressed all comments and implemented the\nfollowing revisions as we wrote in the point-by-point reply to each comment.\nReviewer #1\nReviewers Comments:\nThis work introduces a novel approach using chemically controllable break membranes to\ngenerate and investigate ångström pores, overcoming traditional limitations in reproducibility\nand precision. The repeated formation and closure of pores in SiNx membranes occurs via\nin-pore chemical reactions, enabling the study of ion transport at ångström scales. The\ndynamic behavior of ion flux through these infinitesimal channels reveals distinct\ndehydration-mediated ionic conductance signatures for F⁻ and Cl⁻ ions. However, it is not\nsuggested to publish in NC due to the novelty. There are some issues that need to be\nresolved.\n(Reply)\nWe greatly appreciate the referee for reviewing our work. We have studied your\ncomments carefully to improve the manuscript. In this revised version, we newly\ninvestigated the effects of ionic reactant concentration and solution pH on the activity of the\nautonomous nanopore membranes (Supplementary Figures 19-40), which is found useful\nfor controlling the pore size at a sub-nanometer resolution (newly prepared Figure 6). We\nalso verified whether the pores were actually opened/closed by examining the\nmeasurements on a pristine SiN membrane without any nanopores (Supplementary Figure\nx\n2). We have also found that the method can be used for discriminating small molecules by\nthe conductive pulse analysis, which strongly indicates that the pores are actually opened\nand their size is small enough to resolve the ion blockade characteristics of the\nsub-nanometer-sized molecules (please see the uploaded Figure R1 (Review only\nmaterial)). Overall, our results establish that the autonomous membrane approach allows\nrepetitive formation of small pores with controllable sizes. This capability holds strong\npotential for applications ranging from small-molecule analysis to nanopore sequencing.\nWe believe these findings are both novel and impactful, warranting publication in Nature\nCommunications.\nMain text (p9 line 218 – p10 line 246)\n(Added)\nThe autonomous spiking behavior of the nanopore membrane is highly tunable\nvia chemical control. For example, reducing the MnCl concentration on the cis side\n2\nfrom 2 M progressively suppresses spiking activity, yielding featureless ionic current\ntraces (Supplementary Figure 19). This inactivation arises from a concomitant pH\nincrease from 4.2 to ∼7, which inhibits the dissolution of manganese phosphate\nnanoprecipitates once formed, mirroring the behavior observed in the AlCl /PBS\n3\nsystem.\nReaction kinetics can also be modulated through the concentration of anionic\nreactants. Substituting PBS with Hank’s balanced salt solution (HBSS) eliminates the\nstrong ionic rectification in the I - V curves, as HBSS lacks phosphate even in the\nion b\npresence of 2 M MnCl in cis. Meanwhile, introducing phosphate sources, H₃PO₄\n2\n(Supplementary Figs. 20, 21), K₂HPO₄ (Supplementary Figs. 22, 23), or Na₂HPO₄\n(Supplementary Figs. 24, 25), into trans restores manganese phosphate nucleation\nwithin the nanopore, producing pronounced current suppression at negative V .\nb\nThe required concentration threshold depends strongly on the phosphate species:\nNa₂HPO₄ induces precipitation at levels as low as 10-5 M, whereas H₃PO₄ requires >\n0.1 M due to its low pH (1.5) accelerating dissolution.\nFor Na₂HPO₄ in trans, ionic spiking emerges at concentrations above 5 × 10⁻³\nM (Supplementary Figs. 26, 27). Below this threshold, insufficient phosphate flux\nfails to maintain a complete precipitate seal against the relatively fast cis-side\ndissolution. Conversely, at higher concentrations, the spiking frequency decreases\nand pulses become weaker and narrower (Supplementary Figs. 28–32), reflecting\nmore rapid pore closure by an enhanced phosphate ion flux that prevents pores from\ngrowing to larger sizes.\nBeyond reactant concentration, pH adjustment offers a way for reproducible,\nsize-controlled pore formation. In MnCl /PBS systems, lowering the trans-side pH\n2\nbelow 7.4 with HCl steadily increases spike amplitudes (Fig. 6a–g, Supplementary\nFigs. 33–40). Simultaneously, the distribution of pulse heights narrows, indicating\nreduced pore-to-pore size variability (Fig. 6h). Using the Maxwell–Hall model under\nthe condition R >> R (Supplementary Fig. 13), the mean pore diameter is\nacc pore\nestimated to be tunable from ∼2 nm to ∼7 nm solely through pH control,\ndemonstrating sub-nanometer precision in autonomous pore size regulation.\n(Added)\nFigure 6. Pore size modulation by pH control. a, An illustrative description of a chemistry-driven\nautonomous membrane interfacing 2 M MnCl2 and acidic PBS with HCl. b, Ionic current traces recorded for\nthe MnCl2/(PCB + HCl) systems with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V.\npH at trans is 6.7 (red) and 3.2 (blue). c-e, Ip versus td scatter plots for the cases of pH 6.7 (c), 5.2 (d), and 3.2\n(e). f, Log10Ip distributions at pH 6.7 (red), 5.2 (green), and 3.2 (blue) at the trans. g, Average Ip estimated by\nthe Gaussian fits. Axis at the right denotes the pore diameter dpore estimated from the pulse heights based on\nMaxwell-Hall’s model. h, Variations in the pulse heights represented as the full-widths at half-maxima of the\nGaussian peaks fitted in (f).\n(Added)\nSupplementary Figure 19. Ionic current traces under different MnCl2 concentrations. a-e, Ionic\ncurrent traces recorded in MnCl2/PBS systems with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The MnCl2 concentration is varied as: 2 M (pH 4.2), 1 M (pH 5.0), 0.5 M (pH 5.4), 0.2 M\n(pH 5.9), and 0.1 M (pH 6.0). As the lower concentration raises the solution pH, it tends to suppress the\ndissolution of the manganese phosphate layer formed in the nanopore, inactivating the membrane to fire no\nionic spikes.\n(Added)\nSupplementary Figure 20. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of H3PO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, H3PO4 is added to HBSS in the trans at the following concentrations: 1.5 x 10-6 M (a), 1.5 x 10-5\nM (b), 1.5 x 10-4 M (c), 1.5 x 10-3 M (d), 1.5 x 10-2 M (e), 1.5 x 10-1 M (f), 1.5 M (g), 3.0 M (h), 4.5 M (i), 6.0 M\n(j), and 7.5 M (k). Ionic current suppression at negative Vb starts to be observable at high H3PO4\nconcentrations above 4.5 M. The large amount of H3PO4 above 1.5 M also led to enhanced ionic\nconductance at the positive voltage.\n(Added)\nSupplementary Figure 21. Onset H3PO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the H3PO4 concentration cphos in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 20. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cphos = 4.5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 22. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of K2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, K2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6 M\n(b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high K2HPO4 concentrations\nabove 0.1 M. The range of K2HPO4 concentration examined is relatively low compared to 1.37 M NaCl in\nthe HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 23. Onset K2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the K2HPO4 concentration cpot in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 22. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cpot = 0.1 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 24. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of Na2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, Na2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6\nM (b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high Na2HPO4\nconcentrations above 0.1 M. The range of Na2HPO4 concentration examined is relatively low compared to\n1.37 M NaCl in the HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 25. Onset Na2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the Na2HPO4 concentration csod in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 24. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at csod = 10-5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 26. Ionic current traces under different Na2HPO4 concentrations. a-h, Ionic\ncurrent traces recorded in MnCl2/HBSS system with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The concentration of Na2HPO4 in the trans is varied as: 0.002 M (a), 0.005 M (b), 0.010\nM (c), 0.020 M (d), 0.050 M (e), 0.100 M (f), 0.200 M (g), and 0.500 M (h). Insets in (g-h) show magnified\nviews by ten times in the ionic current.\n(Added)\nSupplementary Figure 27. Spike signal profiles with Na2HPO4 in a MnCl2/HBSS system. a-g, Ionic\ncurrent spike height (Ip) versus width (td) scatter plots obtained for the ionic current spikes detected with a\n100 nm nanopore membrane interfacing 2 M MnCl2 and HBSS under the applied voltage of -0.5 V. In\naddition, Na2HPO4 is added to the HBSS at concentrations of 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050\nM (d), 0.100 M (e), 0.200 N (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 28. Ionic spike height distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10Ip histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 29. Ionic spike width distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10td histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\nGreen curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 30. Ionic spike width dependence on the Na2HPO4 concentration. Average td\ndeduced by the Gaussian fits to the log10td histograms in Supplementary Figure 29.\nSupplementary Figure 31\n(Added)\nSupplementary Figure 31. Inter-spike time distributions in MnCl2/ (HBSS + Na2HPO4) systems. a-g,\n-0.5 V. The concentration of Na2HPO4 in the trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d),\n0.100 M (e), 0.200 M (f), and 0.500 M (g). Red curves are Gaussian fits to the distributions.\nSupplementary Figure 32\n(Added)\nSupplementary Figure 32. Spiking frequency in MnCl2/ (HBSS + Na2HPO4) systems. The spiking\nfrequency fp = Δtave -1 at different Na2HPO4 concentration (csod) calculated from Δtave deduced by the\nGaussian fitting to the data in Supplementary Figure 31.\n(Added)\nSupplementary Figure 33. Ionic current traces in MnCl2/ (PBS + HCl) systems. a-g, Iion – t curves\nrecorded with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side\nis changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 34. Ionic current traces in MnCl2/ (PBS + HCl) systems with highly acidic\nconditions at the trans side. a-e, Iion – t curves recorded with a 100 nm nanopore in a 30 nm thick SiNx\nmembrane under Vb = -0.5 V. pH at the trans side is changed by adding HCl to 2.4 (a), 2.0 (b), 1.9 (c), 1.8\n(d), 1.1 (e), and 0.9 (f).\n(Added)\nSupplementary Figure 35. Ionic spike profiles under different pH at trans in MnCl2/PBS systems.\na-g, Ip – td scatter plots of ionic current spikes detected for MnCl2/ (PBS + HCl) systems with a 100 nm\nnanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side is changed by adding\nHCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 36. Ionic spike heights in MnCl2/ (PBS + HCl) systems. a-g, Log10Ip\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 37. Ionic spike widths in MnCl2/ (PBS + HCl) systems. a-g, Log10td\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 38. pH dependence of spike widths in MnCl2/ (PBS + HCl) systems. Average\ntd obtained by the Gaussian fitting in Supplementary Figure 39 showing no notable dependence on the pH\nat the trans side.\nSupplementary Figure 39\n(Added)\nSupplementary Figure 39. Inter-spike interval time in MnCl2/ (PBS + HCl) systems. a-g, Log10Δt\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n23\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\nSupplementary Figure 40\n(Added)\nSupplementary Figure 40. Spiking frequency in MnCl2/ (PBS + HCl) systems. The frequency fp of\nionic current spike detections estimated as fp = Δtave -1, where Δtave is the average Δt deduced by the\nGaussian fitting to the histograms in Supplementary Figure 37. No notable relationship is found between\nfp and the pH at the trans side.\nSupplementary Figure 2\n(Added)\nSupplementary Figure 2. Ionic current characteristics of a 30 nm-thick SiNx membrane without\nnanopores. a, Schematic illustration depicting a pristine SiNx membrane. b, Ionic current versus\ntransmembrane voltage characteristics in phosphate buffered saline (1.37 M NaCl). Red and blue plots\nare data obtained under positive and negative Vb scans. The transient current behaviors indicate\ncharging/discharging at the membrane capacitance. Green plots are the average of the data acquired at\ndifferent voltage scanning directions. c, Ionic current characteristics with cis and trans filled with 2 M\nVb cannot induce any ion flux across the closed membrane. d, Partial ionic current trace under Vb = -1.0 V\nwith the solution configuration in (c). The curve is featureless showing no pulse-like signal.\n• In the article, there is no explanation for the meaning of counts in figures 1 c-d. Please\nclarify them in the article.\n(Reply)\nThank you for the comment. Figure 1c–d presents two-dimensional histograms of 756\nI -V curves obtained under repetitive scanning of the transmembrane voltage from -1.5 V\nion b\nto 1.5 V. The color scale indicates the number of data points within each bin (0.02 V in\nvoltage and 20 nA in current).\nWe have revised the figure caption as follows to clarify this point.\nFigure 1c-d caption\n(Revised) c-d, Stability of the in-pore reactions. I\nion\n– V\nb\ncurves are highly\nreproducible over 756 cycles of voltage scans from -1.5 V to 1.5 V in about 10 hours\n(c-d). The curves are presented in a form of two-dimensional histogram, where the\ncolor coding denotes the counts of data points in each bin of size 20 nA and 0.02 V.\ne, Rectification ratio r at V = ±1 V in each of the 756 I – V curves.\nrec b ion b\n• In the article, the diameter of the ultra-small pores is calculated from Racc to be 3.9 Å\n(Figure 5c inset). It should be displayed in the figure 5e inset. In the MnCl2/PBS system,\nhowever, the Iₚ distributions exhibit no evidence of well-defined channel structures formed\nby the membrane piercing mechanism (Figure 5c; see also Supplementary Figure 8). This\nshould be in Figure 5a. In Figure 5, there is no indication for figure d. Therefore, the\nmarkings in figure 5 should be revised in the content as well.\n(Reply)\nThank you very much for pointing out the typos regarding Figure 5. We have corrected\nthe citations of Figs. 5a through 5e in the main text. We have also added the missing label\n“d” for Fig. 5d as shown below.\n(Revised)\n• In the experimental section, finally, 20 m-thick SiO2 is grown on the membrane, serving as\na protective layer for the nanoheater. 20 m should be incorrect.\n(Reply)\nWe appreciate for letting us know the typo. We have corrected “20 m” to “20 nm”.\n• In the experimental section, as the SiO2 is deposited on the nanopore wall, it causes the\npore diameter to shrink to approximately 40 nm. However, in the results section, the method\nuses a nanoscale hole of diameter dpore in a silicon nitride membrane (with a thickness of\n30 nm unless otherwise stated) as a nanoreactor. Which is correct?\n26\n(Reply)\nThank you for pointing out the misleading description. The SiO deposition on the\n2\nnanopore wall was performed for fabricating the nanoheater-embedded nanopores (please\nsee Supplementary Figures 4). The dielectric coating was necessary to suppress current\nleakage through the Pt nanoheater upon its use (as we described in detail in our recent work\nin ACS Nano 19, 28900 (2025)) for observing the in-pore chemistry activity in the\nlocally-heated SiN nanopore (Supplementary Figures 5). Meanwhile, the other pores are\nx\nformed in 30 nm-thick SiN membranes without any SiO deposition, as described in\nx 2\n“Fabrication of solid-state nanopores” of the Materials and Methods section.\nTo avoid misunderstanding, we have added a note that the nanoheater-embedded\nnanopores are used only for examining the autonomous membrane activity in a\nlocally-heated nanopore.\nMaterials and Methods (p13 line 313 – p14 line 315)\n(Added) We note that this nanoheater-embedded nanopore is used only for\nexamining the in-pore chemistry at elevated temperature. All other measurements\nuse the pristine nanopores in 30 nm-thick SiN membranes.\nx\n• In the article, the produced pore size is just calculated. Is there any experimental data to\nidentify the ångström size?\n(Reply)\nThank you for the comment. While we do not yet have direct experimental\nmeasurements that resolve the ångström-scale dimensions of the pores formed by the\nin-pore chemistry approach, this is due to the current lack of techniques with sufficient\nspatiotemporal resolution to visualize such atomic-scale conduits in action. For instance,\nalthough liquid-phase transmission electron microscopy can image nanostructures in liquids\n(Nat. Chem. 3, 624 (2019)), it cannot capture the millisecond-scale stochastic opening and\nclosing of these ultra-small pores at the required spatial resolution.\nThat said, our results strongly suggest that the pores operate at the sub-nanometer\nscale. This inference comes from measurements performed with nucleotide monomers\nadded to PBS in the trans chamber (please see the uploaded Figure R1 (Review only\nmaterial)). In these experiments, we adjusted the solution conditions to produce slightly\nlarger pores than those obtained under 2 M MnCl₂/10×PBS. Upon increasing the\nnucleotide concentration, the signal height distributions exhibited well-defined peaks, with\nthe peak positions shifting depending on the nucleotide species. This behavior is naturally\n27\nexplained if the pore dimensions are comparable to the molecular size of the nucleotide\nmonomers.\nMoreover, the data indicate that the pore length is short enough to achieve single-base\nresolution, supporting the assumption of R >> R . We are preparing a separate\nacc pore\nmanuscript presenting these findings, together with additional results for other molecules, to\nhighlight the potential of autonomous nanopore membranes for single-molecule sensing.\n• In the sentence - The giant spikes are, therefore, likely correspond to the opening of 178\nnanopores with diameters around 10 nm -, is 10 nm from the calculation or experimental\ndata? Could you please clarify it?\n(Reply)\nThank you very much for your comment. As there is currently no method to directly\ncapture the instantaneous, stochastic formation of nanopores at random positions in liquid,\nwe estimated the size of the relatively large pores formed in the CaCl₂/PBS system by\nback-calculating d using the Maxwell–Hall equation. This calculation is based on the\npore\nionic current signal height and assumes R >> R , a condition validated by our\nacc pore\nsingle-nucleotide measurements.\nWe have added sentences to clarify this calculation procedure in the manuscript.\nMain text (p8 line 178 – 181)\n(Added) From the 40 nA heights of the giant spikes and ρ of 8.3 S/m (Supplementary\nFigure 13), therefore, R is estimated to be 12.5 MΩ, which suggests the opening\npore\nof nanopores with diameters around 10 nm with the CaCl /PBS configuration.\n2\n• In the article, there is no data to demonstrate the repeated formation and closure of pores\ngenerated in SiNx membranes.\n(Reply)\nWe appreciate the comment. Although direct visualization of pore formation and closure\nis not currently possible, due to the lack of techniques capable of capturing such events in\nreal time and space, the ionic current characteristics provide strong evidence for the\nenvisaged chemistry-driven activity of the autonomous membranes.\nFirst, in our previous work, scanning electron microscopy confirmed the presence of a\nthin nanoprecipitate layer within a SiNₓ nanopore (Figure R2). In some cases, this layer\n28\nwas inadvertently fractured and then reformed under a negative transmembrane voltage,\nproducing a rapid rise and drop in the ionic current (Figure R3). This behavior\ndemonstrates the full opening and subsequent closure of a large pore driven by in-pore\nchemical reactions under constant voltage. Similar signatures were observed in the\nCaCl /PBS system, where the ionic current reached >40 nA (Figure 3a) or even exceeded\n2\nthe 280 nA detection limit, consistent with repetitive large-pore formation and closure.\nBy analogy, the small ionic current spikes in the MnCl /PBS system suggest the\n2\ntransient piercing of ultra-small pores through the nanoprecipitate layer. The fact that spike\namplitudes increased under more dilute salt solutions and acidic pH at the trans side (Figure\n6 and Supplementary Figures 19–40) supports the interpretation that larger pores form\nwhen manganese phosphate dissolution is enhanced. Furthermore, the observation that\nspike heights vary according to the nucleotide type (Figure R1) indicates pore diameters\ncomparable to the sub-nanometer size of these molecules.\nTo rule out alternative explanations, we measured a pristine 30 nm-thick SiNₓ membrane\nwith no nanopores. Under MnCl₂/PBS at –0.5 V, the ionic current was completely silent\n(Supplementary Figure 2), eliminating the possibility that the spikes arise from\nelectrode–electrolyte electrochemical reactions without ion transport across the membrane.\nCollectively, these results consistently support the conclusion that the spiking features\noriginate from repetitive formation and closure of pores via in-pore precipitation/dissolution\nreactions of metal phosphates.\nFigure R2\n(Review only)\nFigure R2. False-colored scanning electron micrograph of a 300 nm nanopore after forming aluminum phosphate via the\ntransmembrane voltage of -0.5 V in the AlCl3/PBS. The contrast in the nanopore became observable only at a low\nelectron beam energy, suggesting that it is a highly thin layer (data taken from our previous paper published on Nat.\nCommun. 16, 1089 (2025)).\n(Review only)\nFigure R3. Am example of Iion-Vb curves showing temporal rupture of the manganese phosphate nanoprecipitate layer\nunder negative transmembrane voltage (data taken from our previous paper published on Nat. Commun. 16, 1089\n(2025)).\nSupplementary Figure 2\n(Added)\nSupplementary Figure 2. Ionic current characteristics of a 30 nm-thick SiNx membrane without\nnanopores. a, Schematic illustration depicting a pristine SiNx membrane. b, Ionic current versus\ntransmembrane voltage characteristics in phosphate buffered saline (1.37 M NaCl). Red and blue plots\nare data obtained under positive and negative Vb scans. The transient current behaviors indicate\ncharging/discharging at the membrane capacitance. Green plots are the average of the data acquired at\ndifferent voltage scanning directions. c, Ionic current characteristics with cis and trans filled with 2 M\nVb cannot induce any ion flux across the closed membrane. d, Partial ionic current trace under Vb = -1.0 V\nwith the solution configuration in (c). The curve is featureless showing no pulse-like signal.\n• Can these pores with ångström size be controlled precisely and produced repeatedly?\n(Reply)\nThank you for the comment. To improve reproducibility and gain control over pore size,\nwe systematically explored chemical parameters that tune the in-pore reactions. Among\nthe factors tested, including cationic and anionic reactant concentrations (Supplementary\nFigures 19–40), the pH at the trans side proved particularly effective for regulating\nautonomous membrane activity.\nSpecifically, lowering the pH of PBS at the trans from 6.7 to 3.2 using HCl increased the\npore diameter from ~2 nm to ~7 nm (Figure 6g), achieving subnanometer-scale control.\nThis adjustment also narrowed the spike height distribution, enabling repeated pore\nformation with enhanced reproducibility (Figure 6h). Leveraging this insight, we created\nslightly larger pores for nucleotide detection experiments (Figure R1).\nThese results demonstrate that both the precision and reproducibility of ångström-scale\npore formation can be finely tuned by controlling in-pore chemistry through various\nparameters.\nMain text (p9 line 218 – p10 line 246)\n(Added)\nThe autonomous spiking behavior of the nanopore membrane is highly tunable\nvia chemical control. For example, reducing the MnCl concentration on the cis side\n2\nfrom 2 M progressively suppresses spiking activity, yielding featureless ionic current\ntraces (Supplementary Figure 19). This inactivation arises from a concomitant pH\nincrease from 4.2 to ∼7, which inhibits the dissolution of manganese phosphate\nnanoprecipitates once formed, mirroring the behavior observed in the AlCl /PBS\n3\nsystem.\nReaction kinetics can also be modulated through the concentration of anionic\nreactants. Substituting PBS with Hank’s balanced salt solution (HBSS) eliminates the\nstrong ionic rectification in the I - V curves, as HBSS lacks phosphate even in the\nion b\npresence of 2 M MnCl in cis. Meanwhile, introducing phosphate sources, H₃PO₄\n2\n(Supplementary Figs. 20, 21), K₂HPO₄ (Supplementary Figs. 22, 23), or Na₂HPO₄\n(Supplementary Figs. 24, 25), into trans restores manganese phosphate nucleation\nwithin the nanopore, producing pronounced current suppression at negative V .\nb\nNa₂HPO₄ induces precipitation at levels as low as 10-5 M, whereas H₃PO₄ requires >\n0.1 M due to its low pH (1.5) accelerating dissolution.\nFor Na₂HPO₄ in trans, ionic spiking emerges at concentrations above 5 × 10⁻³\nM (Supplementary Figs. 26, 27). Below this threshold, insufficient phosphate flux\nfails to maintain a complete precipitate seal against the relatively fast cis-side\ndissolution. Conversely, at higher concentrations, the spiking frequency decreases\nand pulses become weaker and narrower (Supplementary Figs. 28–32), reflecting\nmore rapid pore closure by an enhanced phosphate ion flux that prevents pores from\ngrowing to larger sizes.\nBeyond reactant concentration, pH adjustment offers a way for reproducible,\nsize-controlled pore formation. In MnCl /PBS systems, lowering the trans-side pH\n2\nbelow 7.4 with HCl steadily increases spike amplitudes (Fig. 6a–g, Supplementary\nFigs. 33–40). Simultaneously, the distribution of pulse heights narrows, indicating\nreduced pore-to-pore size variability (Fig. 6h). Using the Maxwell–Hall model under\nthe condition R >> R (Supplementary Fig. 13), the mean pore diameter is\nacc pore\nestimated to be tunable from ∼2 nm to ∼7 nm solely through pH control,\ndemonstrating sub-nanometer precision in autonomous pore size regulation.\n(Added)\nFigure 6. Pore size modulation by pH control. a, An illustrative description of a chemistry-driven\nautonomous membrane interfacing 2 M MnCl2 and acidic PBS with HCl. b, Ionic current traces recorded for\nthe MnCl2/(PCB + HCl) systems with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V.\npH at trans is 6.7 (red) and 3.2 (blue). c-e, Ip versus td scatter plots for the cases of pH 6.7 (c), 5.2 (d), and 3.2\n(e). f, Log10Ip distributions at pH 6.7 (red), 5.2 (green), and 3.2 (blue) at the trans. g, Average Ip estimated by\nthe Gaussian fits. Axis at the right denotes the pore diameter dpore estimated from the pulse heights based on\nMaxwell-Hall’s model. h, Variations in the pulse heights represented as the full-widths at half-maxima of the\nGaussian peaks fitted in (f).\nReviewer #2\nThis work presents a novel approach for dynamically creating and closing ångström-scale\npores in silicon nitride membranes to achieve reversible pore gating through applying\ntransmembrane voltage to regulate in-pore chemical processes (such as\nmanganese/calcium phosphate precipitation and dissolution). The authors systematically\ninvestigated ion transport mechanisms by analyzing current signatures of various anions (F⁻\nand Cl⁻) through these ultrafine channels, revealing distinct dehydration-mediated\nconduction behaviors. The experimental results are interesting, and the article, with its\ncomplete dataset and comprehensive analysis of ion transport mechanisms, provides\nfundamental insights into ion transport and potential nanofluid applications. Therefore, I\nrecommend its publication after the following revisions：\n(Reply)\nWe appreciate your positive remarks on our work and have revised the manuscript\naccordingly, as detailed in the point-by-point reply below.\nQuestions:\n1. Through the analysis of ion current spike parameters, this article provides a novel\nperspective on analyzing nanofluidic transport within pores. However, the characterization\nmethod is not enough, it is beneficial to add several SEM images to illustrate the nanopore\nstructure in real.\n(Reply)\nThank you very much for the comment. We have updated the schematic models with\nnewly acquired SEM images of pristine SiN single- and multipores, as well as a\nx\nnanoheater-embedded nanopore, in both the main text and Supplementary Information, as\nshown below.\n(SEM images added to Figure 7b)\nFigure 7. Scalability of spiking characteristics. a, A sketch describing multipore in a SiNx membrane with cis and\ntrans filled with 2 M MnCl2 and PBS, respectively. b, Ionic current traces under Vb = -0.5 V for 100 nm-sized multipore\nmembranes with the number of pores Npore = 1 (red), 4 (green), 16 (orange), and 36 (blue). False-colored scanning\nelectron micrographs, with white bars denoting 1 μm, show the arrangement of nanopores. c, fp plotted against Npore.\nGray line is a linear fit crossing zero fp at Npore = 0. d, Ip versus td scatter plots for the multipores of Npore = 1 (red) and 36\n(blue). e, Logarithmic Ip histograms for the multipores of Npore = 1 (red), 4 (green), and 36 (blue). Pink curves are\nGaussian fit to the peak profiles. Dashed line points at Ip of the ionic spikes detected with KF in trans at Vb = -0.5 V.\nSupplementary Figure 4\n(SEM images added to Supplementary Figure 4b)\nSupplementary Figure 4. Structure of nanoheater-embedded nanopore. a, Schematic model of the\nnanoheater-embedded nanopore consisting of a Pt coil and a nanopore formed in a 30 nm-thick SiNx\nmembrane by electron beam lithography, radio-frequency magnetron sputtering, and reactive ion etching\nprocesses.S1 A 20 nm-thick SiO2 is also deposited on the entire structure from the top by chemical vapor\ndeposition for protection of the Pt coil under use (only partially depicted in the illustration). The heater\n35\nvoltage VH is applied to the Pt coil for local Joule heating. b, False-colored scanning electron micrograph\nof the nanoheater-embedded nanopore with a 40 nm diameter nanopore at the center.\nSupplementary Figure 43\n(SEM images added)\nSupplementary Figure 43. Iion – Vb characteristics of multipores interfacing 2M MnCl2 and PBS.\na-b, Iion – Vb curves under positive (red) and negative (blue) Vb scans for multipores consisting of 16 (a) and\n36 (b) 100 nm-sized nanopores in 30 nm-thick SiNx membranes. c-d, Magnified views near 0V. No\nnotable changes in Iion suggestive of sequential opening/closure of the multipores are present, such as\nstepwise rise and depression of the current. False-colored scanning electron micrographs, with white\nbars denoting 1 μm, show the arrangement of nanopores.\n(SEM images added)\nSupplementary Figure 45. Ionic current spike height distributions in cases of different pore sizes.\na-e, Ip histograms prepared from the ionic current spikes detected under Vb = -0.5 V in pores of diameter\ndpore = 20 nm (a), 60 nm (b), 100 nm (c), 300 nm (d), and 600 nm (e) in a 30 nm-thick SiNx membrane with\ncis and trans filled with 2 M MnCl2 and PBS, respectively. False-colored scanning electron micrographs\ndisplay the size and shape of the nanopores.\nSupplementary Figure 46\n(SEM images added)\nSupplementary Figure 46. Ionic current spike waveforms in cases of different pore sizes. a-e, Ip\n37\nversus td scatter plots prepared from the ionic current spikes detected under Vb = -0.5 V in pores of\ndiameter dpore = 20 nm (a), 60 nm (b), 100 nm (c), 300 nm (d), and 600 nm (e) in a 30 nm-thick SiNx\nmembrane with cis and trans filled with 2 M MnCl2 and PBS, respectively. False-colored scanning\nelectron micrographs display the size and shape of the nanopores.\nSupplementary Figure 47\n(SEM images added)\nSupplementary Figure 47. Ionic current spike waveforms in case of SiNx multipores. a-d, Ip versus\nVb scatter plots obtained under Vb = -0.5 V for arrays of 1 x 1 (a), 2 x 2 (b), 4 x 4 (c), and 6 x 6 (d) multipores\nof 100 nm diameter in a 30 nm-thick SiNx membrane separating 2 M MnCl2 and PBS at the cis and trans.\nFalse-colored scanning electron micrographs, with white bars denoting 1 μm, show the arrangement of\nnanopores.\n2. Line 84-86, “The rate of pore piercing fp is presented by the time interval Δt between\ntwo consecutive Iion spikes, which is about 10 Hz for the case in the MnCl2/PBS system\nunder Vb = -1.1 V.” The authors mentioned that pore piercing frequency in the MnCl2/PBS\nsystem. Does the spiking frequency depend on concentration in the MnCl2/PBS system or\nother factors?\n(Reply)\nWe appreciate the referee’s insightful comment regarding the tunability of autonomous\n38\nnanopore membrane activity through chemical parameters. In response, we have\nsystematically investigated how the spiking characteristics vary with both cationic and\nanionic reactant concentrations.\nAs for Mn2+, we reduced the MnCl concentration at the cis side from 2 M to 0.1 M by\n2\ndilution with ultrapure water. As shown in Supplementary Figure 19, decreasing the\nconcentration to 1 M resulted in weaker spikes at lower frequency, while more dilute\nsolutions produced featureless traces. This trend is linked to the associated pH rise (from\n4.2 at 2 M to 5.0 at 1 M), which slows the dissolution of manganese phosphate in the SiN\nx\nnanopore, thereby reducing pore opening frequency and size. At lower concentrations, pH\nbecomes even higher, allowing the nanoprecipitate layer to be kept intact, and thus firing no\nionic current spikes. As such, MnCl concentration modulates both spike amplitude and\n2\nfiring frequency via pH-dependent dissolution kinetics.\nTo investigate the roles of the anionic reactants, we replaced PBS with Hank’s balanced\nsalt solution (HBSS), which contains 1.37 M NaCl but no phosphate (pH ~7), in order to\nexamine phosphate concentration effects without altering NaCl content. Under HBSS\nalone, no ionic current suppression was observed (Supplementary Figure 20), confirming\nthe absence of precipitation. We then added varying amounts of H PO , K HPO , or\n3 4 2 4\nNa HPO (Supplementary Figures 20–25), keeping NaCl constant at 1.37 M. All three\n2 4\nphosphates induced ionic current suppression above characteristic onset concentrations,\nwith Na HPO being the most effective, triggering precipitation at concentrations as low as\n2 4\n10-5 M (Supplementary Figure 25), likely due to pH effects that favor precipitation over\ndissolution.\nSpiking behavior emerged above these critical concentrations. For Na HPO , the\n2 4\nnanopore is sealed completely above 0.002 M, while lower concentrations produced current\nfluctuations indicative of insufficient precipitation speed. Above 0.005 M, stable spiking\nwas observed, with spike amplitude decreasing and width narrowing as concentration\nincreased (Supplementary Figures 27–30), consistent with faster pore closure by enhanced\nprecipitation under the stronger flux of phosphate ions. The spike firing rate also declined\nmarkedly, from ~100 spikes/s at 0.005 M to a few spikes/s at 0.5 M (Supplementary Figures\n31–32), suggesting that more pores were closing before becoming detectable.\nThese results demonstrate that cationic and anionic reactants influence pore formation\nvia distinct mechanisms, Mn2+ concentration mainly through pH-dependent dissolution,\nand phosphate concentration through precipitation kinetics, enabling tunable control over pore\nsize, amplitude, and firing frequency.\nThese new data have been added to the Supplementary Information as Supplementary\nFigures 19–32.\n(Added)\nThe autonomous spiking behavior of the nanopore membrane is highly tunable\nvia chemical control. For example, reducing the MnCl concentration on the cis side\n2\nfrom 2 M progressively suppresses spiking activity, yielding featureless ionic current\ntraces (Supplementary Figure 19). This inactivation arises from a concomitant pH\nincrease from 4.2 to ∼7, which inhibits the dissolution of manganese phosphate\nnanoprecipitates once formed, mirroring the behavior observed in the AlCl /PBS\n3\nsystem.\nReaction kinetics can also be modulated through the concentration of anionic\nreactants. Substituting PBS with Hank’s balanced salt solution (HBSS) eliminates the\nstrong ionic rectification in the I - V curves, as HBSS lacks phosphate even in the\nion b\npresence of 2 M MnCl in cis. Meanwhile, introducing phosphate sources, H₃PO₄\n2\n(Supplementary Figs. 20, 21), K₂HPO₄ (Supplementary Figs. 22, 23), or Na₂HPO₄\n(Supplementary Figs. 24, 25), into trans restores manganese phosphate nucleation\nwithin the nanopore, producing pronounced current suppression at negative V .\nb\nThe required concentration threshold depends strongly on the phosphate species:\nNa₂HPO₄ induces precipitation at levels as low as 10-5 M, whereas H₃PO₄ requires >\n0.1 M due to its low pH (1.5) accelerating dissolution.\nFor Na₂HPO₄ in trans, ionic spiking emerges at concentrations above 5 × 10⁻³\nM (Supplementary Figs. 26, 27). Below this threshold, insufficient phosphate flux\nfails to maintain a complete precipitate seal against the relatively fast cis-side\ndissolution. Conversely, at higher concentrations, the spiking frequency decreases\nand pulses become weaker and narrower (Supplementary Figs. 28–32), reflecting\nmore rapid pore closure by an enhanced phosphate ion flux that prevents pores from\ngrowing to larger sizes.\n(Added)\nSupplementary Figure 19. Ionic current traces under different MnCl2 concentrations. a-e, Ionic\ncurrent traces recorded in MnCl2/PBS systems with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The MnCl2 concentration is varied as: 2 M (pH 4.2), 1 M (pH 5.0), 0.5 M (pH 5.4), 0.2 M\n(pH 5.9), and 0.1 M (pH 6.0). As the lower concentration raises the solution pH, it tends to suppress the\ndissolution of the manganese phosphate layer formed in the nanopore, inactivating the membrane to fire no\nionic spikes.\n(Added)\nSupplementary Figure 20. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of H3PO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, H3PO4 is added to HBSS in the trans at the following concentrations: 1.5 x 10-6 M (a), 1.5 x 10-5\nM (b), 1.5 x 10-4 M (c), 1.5 x 10-3 M (d), 1.5 x 10-2 M (e), 1.5 x 10-1 M (f), 1.5 M (g), 3.0 M (h), 4.5 M (i), 6.0 M\n(j), and 7.5 M (k). Ionic current suppression at negative Vb starts to be observable at high H3PO4\nconcentrations above 4.5 M. The large amount of H3PO4 above 1.5 M also led to enhanced ionic\nconductance at the positive voltage.\n(Added)\nSupplementary Figure 21. Onset H3PO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the H3PO4 concentration cphos in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 20. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cphos = 4.5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 22. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of K2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, K2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6 M\n(b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high K2HPO4 concentrations\nabove 0.1 M. The range of K2HPO4 concentration examined is relatively low compared to 1.37 M NaCl in\nthe HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 23. Onset K2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the K2HPO4 concentration cpot in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 22. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cpot = 0.1 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 24. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of Na2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, Na2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6\nM (b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high Na2HPO4\nconcentrations above 0.1 M. The range of Na2HPO4 concentration examined is relatively low compared to\n1.37 M NaCl in the HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 25. Onset Na2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the Na2HPO4 concentration csod in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 24. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at csod = 10-5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 26. Ionic current traces under different Na2HPO4 concentrations. a-h, Ionic\ncurrent traces recorded in MnCl2/HBSS system with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The concentration of Na2HPO4 in the trans is varied as: 0.002 M (a), 0.005 M (b), 0.010\nM (c), 0.020 M (d), 0.050 M (e), 0.100 M (f), 0.200 M (g), and 0.500 M (h). Insets in (g-h) show magnified\nviews by ten times in the ionic current.\n(Added)\nSupplementary Figure 27. Spike signal profiles with Na2HPO4 in a MnCl2/HBSS system. a-g, Ionic\ncurrent spike height (Ip) versus width (td) scatter plots obtained for the ionic current spikes detected with a\n100 nm nanopore membrane interfacing 2 M MnCl2 and HBSS under the applied voltage of -0.5 V. In\naddition, Na2HPO4 is added to the HBSS at concentrations of 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050\nM (d), 0.100 M (e), 0.200 N (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 28. Ionic spike height distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10Ip histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 29. Ionic spike width distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10td histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\nGreen curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 30. Ionic spike width dependence on the Na2HPO4 concentration. Average td\ndeduced by the Gaussian fits to the log10td histograms in Supplementary Figure 29.\n(Added)\nSupplementary Figure 31. Inter-spike time distributions in MnCl2/ (HBSS + Na2HPO4) systems. a-g,\nLog10Δt histograms obtained from the ionic current traces recorded using a 100 nm nanopore under Vb =\n-0.5 V. The concentration of Na2HPO4 in the trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d),\n0.100 M (e), 0.200 M (f), and 0.500 M (g). Red curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 32. Spiking frequency in MnCl2/ (HBSS + Na2HPO4) systems. The spiking\nfrequency fp = Δtave -1 at different Na2HPO4 concentration (csod) calculated from Δtave deduced by the\nGaussian fitting to the data in Supplementary Figure 31.\n3. In Figure 4, the·author examines ion transport·characteristics by introducing halide anions\ninto the PBS solution. When F-is added as a kosmotrope, the amplitude and frequency of\nthe current spikes increase. Compared to·Cl-, F- can electromigrate through the ultra-fine\npores without·significant steric impedance, providing a reasonable explanation for the\nincrease in peak current amplitude (lp). However, the dynamic precipitation/dissolution\nprocesses within the nanopore remain primarily driven by Mn²⁺ and phosphate ions, even in\nthe PBS/KF system. Given that both the electrolyte buffer pH and phosphoric acid\nconcentration were held nearly constant, the sixfold increase in pulsed current frequency\ninduced by non-reacting F⁻ ions remains unexplained. This phenomenon requires a more\ndetailed mechanistic explanation.\n(Reply)\nThank you for the incisive comment. As depicted by the reviewer, a pore forms through\ndissolution-induced thinning of the metal phosphate layer and subsequently recloses via\nprecipitation, driven by the electric-field-mediated translocation of Mn²⁺ and phosphate ions.\nDuring this process, ultra-small pores remain undetectable in ionic current measurements\n54\nuntil they enlarge sufficiently to permit passage of relatively bulky Cl⁻ ions. Many pores are\ntherefore effectively “invisible,” as precipitation seals them before they reach this detectable\nsize. Introducing smaller F⁻ anions enables ionic conduction through these nascent pores,\nrevealing their presence and markedly increasing the observed spiking frequency.\nWe have added the above explanation in the main text as follows.\nMain text (p8 line 199 – p9 line 206)\n(Revised) The addition of KF also increased the ionic spiking rate. Pores form via\ndissolution-induced thinning of the metal phosphate layer and subsequently reclose\nthrough precipitation, driven by electric-field-mediated translocation of Mn²⁺ and\nphosphate ions. During this cycle, ultra-small pores remain undetectable in ionic\ncurrent measurements until they expand sufficiently to accommodate the relatively\nlarge Cl⁻ ions when F- is absent. Many pores therefore remain invisible, sealed by\nprecipitation before becoming detectable. The introduction of smaller F⁻ anions\nenables ionic conduction through these nascent pores, revealing their existence and\nenhancing the observed spiking frequency.\n4. In the MnCl2/PBS system, the acidity (pH 4.2) of the cis-side MnCl₂ solution drives\nprecipitate dissolution. While applied electric fields slow this dissolution at higher strengths,\npH remains a critical factor for precipitation-dissolution equilibrium in nanopore research.\nTherefore, modulating the pH of MnCl₂ could alter dissolution kinetics. Would this approach\nprovide an alternative method to regulate the amplitude and frequency of ion current spikes\nin ultrasmall pores via pH modulation?\n(Reply)\nThank you for the constructive comment. As shown in the results of diluted MnCl\n2\nsolution (Supplementary Figure S19), higher pH tends to stabilize the manganese\nphosphate layer to deteriorate the activity of the autonomous nanopore membrane. As\npointed out by the reviewer, pH is thus an effective factor for tuning the in-pore chemical\nreaction kinetics.\nTo see how pH modulation varies the spiking behavior in more detail, we extended the\nmeasurements for acidic pH at the trans by adding HCl to PBS. When adding excessive\namount of HCl, the precipitate layer became highly unstable, causing large ionic current\nfluctuations (Supplementary Figure 34). At moderate pH, on the other hand, stable spiking\nfeatures were observed demonstrating slightly enlarged ionic spikes at lower pH\n(Supplementary Figure 33). Estimation of the pore size from the spike amplitudes using\n55\nthe Maxwell-Hall model suggested the controllability of its diameter in a range from 2 m to 7\nnm with pH of 6.7 to 3.2 (Figure 6f-g; Supplementary Figures 35 and 36). Simultaneously,\nthe spike height distributions also become narrower (Figure 6h), indicating less variations in\nthe pore size formed under the lower pH at the trans. This is due to the associated\nelimination of small pulses with a relatively large variation (Figure 6c-e and Supplementary\nFigure 35). It physically means that the ultra-small pores tend to coalesce into a large pore,\nsimilar to the case observed in the CaCl /PBS system. As this lowers the number of visible\n2\npores per time, the spiking frequency showed no notable dependence on the pH condition\n(Supplementary Figures 39 and 40).\nWe have added this result, representing the pore size controllability at a sub-nanometer\nprecision, in the manuscript as Figure 6 and Supplementary Figures 33-40.\nMain text (p10 line 239 – 246)\n(Added)\nBeyond reactant concentration, pH adjustment offers a way for reproducible,\nsize-controlled pore formation. In MnCl /PBS systems, lowering the trans-side pH\n2\nbelow 7.4 with HCl steadily increases spike amplitudes (Fig. 6a–g, Supplementary\nFigs. 33–40). Simultaneously, the distribution of pulse heights narrows, indicating\nreduced pore-to-pore size variability (Fig. 6h). Using the Maxwell–Hall model under\nthe condition R >> R (Supplementary Fig. 13), the mean pore diameter is\nacc pore\nestimated to be tunable from ∼2 nm to ∼7 nm solely through pH control,\ndemonstrating sub-nanometer precision in autonomous pore size regulation.\n(Added)\nSupplementary Figure 33. Ionic current traces in MnCl2/ (PBS + HCl) systems. a-g, Iion – t curves\nrecorded with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side\nis changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 34. Ionic current traces in MnCl2/ (PBS + HCl) systems with highly acidic\nconditions at the trans side. a-e, Iion – t curves recorded with a 100 nm nanopore in a 30 nm thick SiNx\nmembrane under Vb = -0.5 V. pH at the trans side is changed by adding HCl to 2.4 (a), 2.0 (b), 1.9 (c), 1.8\n(d), 1.1 (e), and 0.9 (f).\n(Added)\nSupplementary Figure 35. Ionic spike profiles under different pH at trans in MnCl2/PBS systems.\na-g, Ip – td scatter plots of ionic current spikes detected for MnCl2/ (PBS + HCl) systems with a 100 nm\nnanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side is changed by adding\nHCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 36. Ionic spike heights in MnCl2/ (PBS + HCl) systems. a-g, Log10Ip\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 37. Ionic spike widths in MnCl2/ (PBS + HCl) systems. a-g, Log10td\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 38. pH dependence of spike widths in MnCl2/ (PBS + HCl) systems. Average\ntd obtained by the Gaussian fitting in Supplementary Figure 39 showing no notable dependence on the pH\nat the trans side.\nSupplementary Figure 39\n(Added)\nSupplementary Figure 39. Inter-spike interval time in MnCl2/ (PBS + HCl) systems. a-g, Log10Δt\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n62\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\nSupplementary Figure 40\n(Added)\nSupplementary Figure 40. Spiking frequency in MnCl2/ (PBS + HCl) systems. The frequency fp of\nionic current spike detections estimated as fp = Δtave -1, where Δtave is the average Δt deduced by the\nGaussian fitting to the histograms in Supplementary Figure 37. No notable relationship is found between\nfp and the pH at the trans side.\n5. Figure 5 appears to be missing the panel label '(d)' in the current version. The authors\nshould carefully proofread all figures to ensure consistent labeling throughout the\nmanuscript.\n(Reply)\nWe appreciate the reviewer for letting us know the missing label in Figure 5. We have\nadded the label as shown below. We checked all the other figures as well.\n(Label d added)\n6. Line 181-189, there are inconsistencies between descriptions and figures. The authors\nshould check this part carefully to ensure a correct description of Figure 5.\n(Reply)\nThank you very much for pointing out the inconsistent citations of Figure 5. We have\ncorrected the citations in the main text.\n7. In Line 204, the voltage symbol Vβ should be unified to Vb throughout for consistency.\n(Reply)\nThank you for letting us know the typo. We have fixed it to V .\nb\n64\n8. Please systematically verify and standardize the correspondence and description\nbetween the figure and its captions in Figure S8 and Figure 6, respectively.\n(Reply)\nThank you for carefully reading our manuscript. We have corrected the caption in\nSupplementary Figure 8 (now 10 in this revised manuscript). For Figure 6 (now Figure 7)\nin the manuscript, we have corrected “d = 20 nm” to “d = 100 nm”. We also replaced\npore pore\nthe schematic models of the multipores with scanning electron micrographs\nSupplementary Figure 10 caption\n(Revised)\nSupplementary Figure 10. Ionic current spike waveforms in a MnCl /PBS\n2\nconfiguration. a-i, Scatter plots of the spike height I with respect to the width t for\np d\nthe signals larger than 300 pA detected by a 100 nm-sized nanopore in a 30 nm-thick\nSiN membrane under various V with cis and trans filled with 2 M MnCl and PBS,\nx b 2\nrespectively.\nFigure 7\n(Revised)\ncis and trans filled with 2 M MnCl2 and PBS, respectively. b, Ionic current traces under Vb = -0.5 V for 100\nnm-sized multipore membranes with the number of pores Npore = 1 (red), 4 (green), 16 (orange), and 36 (blue).\nFalse-colored scanning electron micrographs, with white bars denoting 1 μm, show the arrangement of\nnanopores. c, fp plotted against Npore. Gray line is a linear fit crossing zero fp at Npore = 0. d, Ip versus td\nscatter plots for the multipores of Npore = 1 (red) and 36 (blue). e, Logarithmic Ip histograms for the multipores\nof Npore = 1 (red), 4 (green), and 36 (blue). Pink curves are Gaussian fit to the peak profiles. Dashed line\npoints at Ip of the ionic spikes detected with KF in trans at Vb = -0.5 V.\nReviewer #3\nThis manuscript describes an approach for fabricating and controlling ultra-small pores at\nthe Ångström scale by using chemically controllable break membranes in SiNx substrates.\nBy applying simple voltage control to drive in-pore chemical reactions, the authors aim to\ndemonstrate repeated pore formation and closure, which is intended to enable the study of\nion transport and molecular dynamics in confined spaces. However, I have several major\nand minor concerns that should be addressed.\nMajor Issues\n1. Chemical Reaction Process\nThe authors propose a chemistry-driven method for fabricating Ångström pores, but the\nmanuscript provides less discussion of the chemical reaction process (e.g., reactant\nconcentration). How do the reaction parameters influence the pore formation mechanism?\n(Reply)\nWe thank the referee for highlighting the tunability of autonomous nanopore membrane\nactivity via chemical control. In response, we investigated how spiking characteristics vary\nwith ionic reactant concentration and solution pH.\nThe Mn2+ concentration at the cis side was reduced by diluting MnCl from 2 M to 0.1 M\n2\nwith ultrapure water. As shown in Supplementary Fig. 19, reducing the concentration to 1\nM yielded smaller, less frequent spikes, while further dilution produced featureless current\ntraces. This behavior correlates with the pH increase from 4.2 (2 M) to 5.0 (1 M), which\nreduces the dissolution efficiency of manganese phosphate in the SiN nanopore. The\nx\nweakened dissolution allows the precipitation reaction to dominate, closing pores more\nreadily and producing smaller spikes. At still higher pH, dissolution is too slow to disrupt the\nmanganese phosphate layer, eliminating spiking entirely. Thus, MnCl concentration\n2\ninfluences both spike amplitude and firing rate via pH-dependent dissolution–precipitation\nbalance.\nTo isolate phosphate effects without altering NaCl concentration, phosphate-buffered\nsaline (PBS) at the trans side was replaced with Hank’s balanced salt solution (HBSS),\nwhich contains 1.37 M NaCl at pH ~7 but no phosphate. In HBSS, no precipitation occurs\n(Supplementary Fig. 20). We then varied phosphate concentration by adding H PO ,\n3 4\nK HPO , or Na HPO (Supplementary Figs. 20–25). Increasing H PO induced strong\n2 4 2 4 3 4\n67\nrectification at negative voltage, indicating nanopore sealing by manganese phosphate;\nsimilar trends occurred with K₂HPO₄ and Na HPO , but with different critical concentrations.\n2 4\nNotably, Na HPO triggered precipitation at only 10-5 M, far below the thresholds for the\n2 4\nother salts, likely due to pH effects: the acidity of H PO (pH 1.5 at 0.15 M) promotes\n3 4\ndissolution, hindering sealing.\nAbove critical phosphate concentrations, ionic spikes appeared. For Na HPO ,\n2 4\nnanopore is sealed completely above 0.002 M, while 0.005 M or higher yielded stable spiking.\nIncreasing Na HPO concentration reduced spike amplitude and width (Supplementary Figs.\n2 4\n27–30), consistent with faster pore closure from enhanced phosphate flux under negative\nvoltage. The firing rate decreased from ~100 spikes/s at 0.005 M to a few spikes/s at 0.5 M\n(Supplementary Figs. 31–32), likely because more pores closed too rapidly to be detected at\nconcentrations favoring larger pore formation and higher rates.\nConsistent with MnCl dilution results, higher pH stabilized the manganese phosphate\n2\nlayer and suppressed activity. To further probe pH effects, we acidified PBS at the trans\nside by adding HCl. Excess HCl destabilized the precipitate, causing large current\nfluctuations (Supplementary Fig. 34), whereas moderate acidification produced stable\nspikes with slightly increased amplitude (Supplementary Fig. 33). Using the Maxwell–Hall\nmodel, we estimated pore diameters tunable from 2 nm to 7 nm across pH 6.7–3.2 (Fig.\n6f–g; Supplementary Figs. 35–36). Lower pH also narrowed spike height distributions (Fig.\n6h), reflecting fewer small, variable pulses, as ultra-small pores tended to merge into larger\nones. This reduced the number of visible pores, leaving spiking frequency largely\npH-independent (Supplementary Figs. 39–40).\nOverall findings manifest the important roles of the reactant concentrations and solution\npH for tuning the activity of the autonomous nanopore membranes.\nMain text (p9 line 218 – p10 line 246)\n(Added)\nThe autonomous spiking behavior of the nanopore membrane is highly tunable\nvia chemical control. For example, reducing the MnCl concentration on the cis side\n2\nfrom 2 M progressively suppresses spiking activity, yielding featureless ionic current\ntraces (Supplementary Figure 19). This inactivation arises from a concomitant pH\nincrease from 4.2 to ∼7, which inhibits the dissolution of manganese phosphate\nnanoprecipitates once formed, mirroring the behavior observed in the AlCl /PBS\n3\nsystem.\nReaction kinetics can also be modulated through the concentration of anionic\nreactants. Substituting PBS with Hank’s balanced salt solution (HBSS) eliminates\n68\nthe strong ionic rectification in the I - V curves, as HBSS lacks phosphate even in\nion b\nthe presence of 2 M MnCl in cis. Meanwhile, introducing phosphate sources,\nNa₂HPO₄ (Supplementary Figs. 24, 25), into trans restores manganese phosphate\nnucleation within the nanopore, producing pronounced current suppression at\nnegative V . The required concentration threshold depends strongly on the\nb\nphosphate species: Na₂HPO₄ induces precipitation at levels as low as 10-5 M,\nwhereas H₃PO₄ requires > 0.1 M due to its low pH (1.5) accelerating dissolution.\nFor Na₂HPO₄ in trans, ionic spiking emerges at concentrations above 5 × 10⁻³\nM (Supplementary Figs. 26, 27). Below this threshold, insufficient phosphate flux\nfails to maintain a complete precipitate seal against the relatively fast cis-side\ndissolution. Conversely, at higher concentrations, the spiking frequency decreases\nand pulses become weaker and narrower (Supplementary Figs. 28–32), reflecting\nmore rapid pore closure by an enhanced phosphate ion flux that prevents pores from\ngrowing to larger sizes.\nBeyond reactant concentration, pH adjustment offers a way for reproducible,\nsize-controlled pore formation. In MnCl /PBS systems, lowering the trans-side pH\n2\nbelow 7.4 with HCl steadily increases spike amplitudes (Fig. 6a–g, Supplementary\nFigs. 33–40). Simultaneously, the distribution of pulse heights narrows, indicating\nreduced pore-to-pore size variability (Fig. 6h). Using the Maxwell–Hall model under\nthe condition R >> R (Supplementary Fig. 13), the mean pore diameter is\nacc pore\nestimated to be tunable from ∼2 nm to ∼7 nm solely through pH control,\ndemonstrating sub-nanometer precision in autonomous pore size regulation.\n(Added)\nFigure 6. Pore size modulation by pH control. a, An illustrative description of a chemistry-driven\nautonomous membrane interfacing 2 M MnCl2 and acidic PBS with HCl. b, Ionic current traces recorded for\nthe MnCl2/(PCB + HCl) systems with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V.\npH at trans is 6.7 (red) and 3.2 (blue). c-e, Ip versus td scatter plots for the cases of pH 6.7 (c), 5.2 (d), and 3.2\n(e). f, Log10Ip distributions at pH 6.7 (red), 5.2 (green), and 3.2 (blue) at the trans. g, Average Ip estimated by\nthe Gaussian fits. Axis at the right denotes the pore diameter dpore estimated from the pulse heights based on\nMaxwell-Hall’s model. h, Variations in the pulse heights represented as the full-widths at half-maxima of the\nGaussian peaks fitted in (f).\n(Added)\nSupplementary Figure 19. Ionic current traces under different MnCl2 concentrations. a-e, Ionic\ncurrent traces recorded in MnCl2/PBS systems with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The MnCl2 concentration is varied as: 2 M (pH 4.2), 1 M (pH 5.0), 0.5 M (pH 5.4), 0.2 M\n(pH 5.9), and 0.1 M (pH 6.0). As the lower concentration raises the solution pH, it tends to suppress the\ndissolution of the manganese phosphate layer formed in the nanopore, inactivating the membrane to fire no\nionic spikes.\n(Added)\nSupplementary Figure 20. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of H3PO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, H3PO4 is added to HBSS in the trans at the following concentrations: 1.5 x 10-6 M (a), 1.5 x 10-5\nM (b), 1.5 x 10-4 M (c), 1.5 x 10-3 M (d), 1.5 x 10-2 M (e), 1.5 x 10-1 M (f), 1.5 M (g), 3.0 M (h), 4.5 M (i), 6.0 M\n(j), and 7.5 M (k). Ionic current suppression at negative Vb starts to be observable at high H3PO4\nconcentrations above 4.5 M. The large amount of H3PO4 above 1.5 M also led to enhanced ionic\nconductance at the positive voltage.\n(Added)\nSupplementary Figure 21. Onset H3PO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the H3PO4 concentration cphos in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 20. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cphos = 4.5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 22. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of K2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, K2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6 M\n(b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high K2HPO4 concentrations\nabove 0.1 M. The range of K2HPO4 concentration examined is relatively low compared to 1.37 M NaCl in\nthe HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 23. Onset K2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the K2HPO4 concentration cpot in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 22. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cpot = 0.1 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 24. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of Na2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, Na2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6\nM (b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high Na2HPO4\nconcentrations above 0.1 M. The range of Na2HPO4 concentration examined is relatively low compared to\n1.37 M NaCl in the HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 25. Onset Na2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the Na2HPO4 concentration csod in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 24. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at csod = 10-5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 26. Ionic current traces under different Na2HPO4 concentrations. a-h, Ionic\ncurrent traces recorded in MnCl2/HBSS system with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The concentration of Na2HPO4 in the trans is varied as: 0.002 M (a), 0.005 M (b), 0.010\nM (c), 0.020 M (d), 0.050 M (e), 0.100 M (f), 0.200 M (g), and 0.500 M (h). Insets in (g-h) show magnified\nviews by ten times in the ionic current.\n(Added)\nSupplementary Figure 27. Spike signal profiles with Na2HPO4 in a MnCl2/HBSS system. a-g, Ionic\ncurrent spike height (Ip) versus width (td) scatter plots obtained for the ionic current spikes detected with a\n100 nm nanopore membrane interfacing 2 M MnCl2 and HBSS under the applied voltage of -0.5 V. In\naddition, Na2HPO4 is added to the HBSS at concentrations of 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050\nM (d), 0.100 M (e), 0.200 N (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 28. Ionic spike height distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10Ip histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 29. Ionic spike width distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10td histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\nGreen curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 30. Ionic spike width dependence on the Na2HPO4 concentration. Average td\ndeduced by the Gaussian fits to the log10td histograms in Supplementary Figure 29.\nSupplementary Figure 31\n(Added)\nSupplementary Figure 31. Inter-spike time distributions in MnCl2/ (HBSS + Na2HPO4) systems. a-g,\n-0.5 V. The concentration of Na2HPO4 in the trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d),\n0.100 M (e), 0.200 M (f), and 0.500 M (g). Red curves are Gaussian fits to the distributions.\nSupplementary Figure 32\n(Added)\nSupplementary Figure 32. Spiking frequency in MnCl2/ (HBSS + Na2HPO4) systems. The spiking\nfrequency fp = Δtave -1 at different Na2HPO4 concentration (csod) calculated from Δtave deduced by the\nGaussian fitting to the data in Supplementary Figure 31.\n(Added)\nSupplementary Figure 33. Ionic current traces in MnCl2/ (PBS + HCl) systems. a-g, Iion – t curves\nrecorded with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side\nis changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 34. Ionic current traces in MnCl2/ (PBS + HCl) systems with highly acidic\nconditions at the trans side. a-e, Iion – t curves recorded with a 100 nm nanopore in a 30 nm thick SiNx\nmembrane under Vb = -0.5 V. pH at the trans side is changed by adding HCl to 2.4 (a), 2.0 (b), 1.9 (c), 1.8\n(d), 1.1 (e), and 0.9 (f).\n(Added)\nSupplementary Figure 35. Ionic spike profiles under different pH at trans in MnCl2/PBS systems.\na-g, Ip – td scatter plots of ionic current spikes detected for MnCl2/ (PBS + HCl) systems with a 100 nm\nnanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side is changed by adding\nHCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 36. Ionic spike heights in MnCl2/ (PBS + HCl) systems. a-g, Log10Ip\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 37. Ionic spike widths in MnCl2/ (PBS + HCl) systems. a-g, Log10td\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 38. pH dependence of spike widths in MnCl2/ (PBS + HCl) systems. Average\ntd obtained by the Gaussian fitting in Supplementary Figure 39 showing no notable dependence on the pH\nat the trans side.\nSupplementary Figure 39\n(Added)\nSupplementary Figure 39. Inter-spike interval time in MnCl2/ (PBS + HCl) systems. a-g, Log10Δt\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n89\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\nSupplementary Figure 40\n(Added)\nSupplementary Figure 40. Spiking frequency in MnCl2/ (PBS + HCl) systems. The frequency fp of\nionic current spike detections estimated as fp = Δtave -1, where Δtave is the average Δt deduced by the\nGaussian fitting to the histograms in Supplementary Figure 37. No notable relationship is found between\nfp and the pH at the trans side.\n2. Pore Reaction Stability\nIn Figure 1e, why does the rectification ratio gradually drop below 30,000 after 400 curves?\nThe authors should clarify the possible reasons for this decline.\n(Reply)\nThank you for the comment. Indeed, the rectification ratio tends to slowly increase in\nthe first 20,000 seconds from around 30,000 to 40,000, while it returns to around 30,000\nduring another 16,000 seconds of measurements. While the exact mechanism remains\nunclear, one possible factor is a slow change in ion concentration due to liquid evaporation\nover the 10-hour measurement period.\nWe have added a sentence noting this point in the caption of Figure 1e as follows.\nFigure 1 caption\n(Added)\ne, Rectification ratio r at V = ±1 V in each of the 756 I – V curves. The\nrec b ion b\nvariation in r is attributable to a change in the ion concentration due to water\nrec\nevaporation during the 10 hours of measurement.\n90\n3. Ion Transport Design\nThe selection of these two ions (F- and I-) for the transport study is intended to address\nwhich application requirements or scientific problems? The authors should provide\nadditional details on the experimental testing procedure for the ion transport property\nstudies.\n(Reply)\nThank you for the comment. The distinct roles of chaotropic and kosmotropic ions,\ncommonly referred to as the Hofmeister effect, are indeed relevant across a wide range of\ndisciplines, from supramolecular chemistry to nanomedicine (Small 18, 2200921 (2022)).\nThis effect arises from ion-specific interactions with water molecules and biomolecular\nsurfaces, which alter hydration structure, interfacial tension, and molecular stability.\nIn the context of nanopore sensing, the Hofmeister effect provides a powerful means of\nmodulating both ion blockade characteristics and the translocation dynamics of\nbiomolecules such as DNA and proteins. Chaotropic ions (e.g., SCN-, I-) tend to disrupt the\nhydration shell and weaken hydrogen bonding networks, thereby reducing the effective size\nand hydration energy barrier of translocating species. This can increase the ionic\nconductance through narrow pores and influence the magnitude and duration of blockade\nevents. Conversely, kosmotropic ions (e.g., SO 2-, F-) strengthen hydration shells and\n4\nstabilize biomolecular conformations, which can slow translocation, increase blockade\namplitude, and enhance resolution for size- or conformation-based discrimination (J. Am.\nChem. Soc. 146, 3171 (2024)).\nThese ion-specific effects can be strategically exploited to tune nanopore performance\nfor different analytical objectives, for example, optimizing event rates, signal-to-noise ratio,\nor selectivity for particular biomolecular targets, without altering the nanopore’s physical\ngeometry.\nThis point has been described in the main text as follows.\nMain text (p5 line 125 – p6 line 127)\n(Revised)\nThis factor is particularly critical for understanding and controlling the ion blockade\nbehavior of biomolecules in the presence of ionic reagents belonging to the so-called\nHofmeister series.36-38\n4. Scaling Up to Array\nHow should the kinetic differences be understood between enlarging individual SiNx pore\n91\nsizes and producing SiNx pore arrays as two approaches for increasing the overall\nmembrane area?\n(Reply)\nThank you for the comment. In our previous work (Nat. Commun. 16, 1089 (2025)), we\nobserved that sealing a micrometer-scale pore with a precipitation layer (Supple,mentary\nFigure 13; see also Figure R4 for a case of CaCl /PBS configuration) is difficult, likely\n2\nbecause a thin precipitate layer lacks the mechanical strength to remain suspended across\nsuch a large opening. As a result, in micropores, the in-pore chemical reactions tend to\nsustain a relatively thick precipitate layer to ensure structural stability. This structural\ndifference alters the balance between dissolution and precipitation, leading to distinctive\nautonomous membrane activity compared with that in small nanopores. Consequently, this\naccounts for the differences in spiking behavior observed between a large single pore and\nsmall multipores.\nFigure R4\n(Review only)\nFigure R4. I -V characteristics of a 3 μm diameter pore with CaCl /PBS solution\nion b 2\nconfiguration. No I suppression occurs at negative V due presumably to a lack of\nion b\nmechanical strength of a thin metal phosphate layer to cover the micropore.\n92\n5. Sub-Nanometer Pore Density\nThe authors claim: “By generating and measuring thousands of sub-nanometer pores from\na large pore using simple voltage control, this approach overcomes longstanding challenges\nin fabricating ultra-fine channels with reproducible precision.” Is it necessary to quantify\npore density more rigorously? How was the pore density mentioned in this statement\ndetermined?\n(Reply)\nThank you for the comment. Here, we meant to describe the repeated formations and\nmeasurements of many small pores using one SiN nanopore, and not pore density. To\nx\nmake this point clearer, we revised this sentence as follows.\nMain text (p12 line 281 – 285)\n(Previous) By generating and measuring thousands of sub-nanometer pores from a\nlarge pore using simple voltage control, this approach overcomes longstanding\nchallenges in fabricating ultra-fine channels with reproducible precision.\n(Revised) By repeatedly forming and measuring thousands of sub-nanometer pores\nin a large pore via the self-regulated cycles of in-pore metal phosphate precipitation\nand dissolution processes under simple voltage control, this approach overcomes\nlongstanding challenges in fabricating ultra-fine channels with reproducible precision.\n6. Data Analysis\nIs it scientifically appropriate to conduct a linear fit using only three data points (array\nresults)? The authors should add the number of data points or adjust the data processing\nmethod accordingly.\n(Reply)\nThank you for the comment. In the previous manuscript, we fitted five data points: four\ndata for N = 1, 4, 16, and 36 with the origin at f = 0 for N = 0. In this revised version,\npore p p\nwe performed additional measurements for the 3 x 3 and 5 x 5 arrays of multipore.\nTherefore, the number of data points for the linear fit now becomes 7.\n(Added)\n(Added)\nSupplementary Figure 43. Spiking frequency by the in-pore chemistry in\nSiN multipore. Histograms of the interval Δt between two consecutively\nx\ndetected ionic current spikes in a SiN multipore composed of 1 (red), 4 (green), 9\nx\n(orange), 16 (blue), 25 (skyblue), and 36 (purple) nanopores of 100 nm diameter\nin a 30 nm-thick membrane. Gray curves are Gaussian fitting.\nMinor Issues\n8. What explains the difference in peak heights in Figure 3e and Figure 3f?\n(Reply)\nThank you for the comment. Figure 3f presents a magnified view of the trace shown in\nrange is limited to 12 nA to clearly display the small pulses that occur immediately before the\nburst peak. As a result, the burst peak, whose actual height exceeds 50 nA, appears\ntruncated at 12 nA in Figure 3f.\nTo avoid confusion, we have added an explanation in the figure caption as follows.\nFigure 3f caption\n(Added)\nf, A close-up view of a giant spike, revealing a specific pattern in the ionic current\nchanges. The I range is limited to a maximum of 12 nA to highlight fine features\nion\nimmediately preceding the spike. Only a portion of the giant spike is shown,\nwhereas its actual amplitude exceeds 50 nA, as depicted in (e). This burst mode of\nI spiking comprises four stages. It begins with a silent state for about 0.2 s,\nion\nfollowed by small spike firing for about 1.5 s. Subsequently, larger spikes are fired.\nSoon after, it caused a giant spike. These processes continue to fire giant spikes\nwith a certain period.\n9. Would adding the 0.4 V data point in Figure 5h affect the overall trend?\n(Reply)\nThank you for the comment. We have added the missing data point at 0.4 V in Figure\n5h.\n(Data point at 0.4 V added)\n10. In Figure 5, the label for panel (d) is missing.\n(Reply)\nThank you for letting us know the missing label d in Figure 5. We have added the label\nas shown below.\n(Label added for panel d)\n11. Please confirm whether the voltage legends in Figures 5f and 5g are accurate.\n(Reply)\nThank you very much for carefully reading the manuscript. We have corrected the\nvoltage to “-0.5 V”.\n(Revised)\n12. Why is there an inconsistency between the pore diameter mentioned in the text (100 nm)\nand the legend (20 nm) in Figure 6?\n(Reply)\nThank you for pointing out our mistake. We have corrected the legend to “100 nm” as\nshown below.\n(Revised)\n1. We have investigated the roles of reactant concentrations on the activity of autonomous\nnanopore membranes.\nSupplementary Figure 19\n(Added)\nSupplementary Figure 19. Ionic current traces under different MnCl2 concentrations. a-e, Ionic\ncurrent traces recorded in MnCl2/PBS systems with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The MnCl2 concentration is varied as: 2 M (pH 4.2), 1 M (pH 5.0), 0.5 M (pH 5.4), 0.2 M\n(pH 5.9), and 0.1 M (pH 6.0). As the lower concentration raises the solution pH, it tends to suppress the\ndissolution of the manganese phosphate layer formed in the nanopore, inactivating the membrane to fire no\nionic spikes.\n(Added)\nSupplementary Figure 20. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of H3PO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, H3PO4 is added to HBSS in the trans at the following concentrations: 1.5 x 10-6 M (a), 1.5 x 10-5\nM (b), 1.5 x 10-4 M (c), 1.5 x 10-3 M (d), 1.5 x 10-2 M (e), 1.5 x 10-1 M (f), 1.5 M (g), 3.0 M (h), 4.5 M (i), 6.0 M\n(j), and 7.5 M (k). Ionic current suppression at negative Vb starts to be observable at high H3PO4\nconcentrations above 4.5 M. The large amount of H3PO4 above 1.5 M also led to enhanced ionic\nconductance at the positive voltage.\n(Added)\nSupplementary Figure 21. Onset H3PO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the H3PO4 concentration cphos in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 20. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cphos = 4.5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 22. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of K2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, K2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6 M\n(b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high K2HPO4 concentrations\nabove 0.1 M. The range of K2HPO4 concentration examined is relatively low compared to 1.37 M NaCl in\nthe HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 23. Onset K2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the K2HPO4 concentration cpot in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 22. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at cpot = 0.1 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 24. Ionic current versus transmembrane voltage characteristics of a 100 nm\nnanopore with different concentrations of Na2HPO4 in trans. a-k, Iion – Vb plots recorded with cis and\ntrans filled with 2 M MnCl2 and Hank’s balanced salt solution (HBSS) containing 1.37 M NaCl, respectively.\nAdditionally, Na2HPO4 is added to HBSS in the trans at the following concentrations: 1 x 10-7 M (a), 1 x 10-6\nM (b), 1 x 10-5 M (c), 1 x 10-4 M (d), 1 x 10-3 M (e), 1 x 10-2 M (f), 0.1 M (g), 0.2 M (h), 0.3 M (i), 0.4 M (j), and\n0.5 M (k). Ionic current suppression at negative Vb starts to be observable at high Na2HPO4\nconcentrations above 0.1 M. The range of Na2HPO4 concentration examined is relatively low compared to\n1.37 M NaCl in the HBSS, giving only a weak effect on the ionic conductance at the positive voltage.\n(Added)\nSupplementary Figure 25. Onset Na2HPO4 concentration for the precipitate sealing of a 100 nm\nnanopore with a MnCl2/HBSS configuration. The nanopore conductance Gpore at positive (red) and\nnegative (blue) Vb regimes plotted as a function of the Na2HPO4 concentration csod in the trans. Gpore is\ndeduced by linear fitting to the Iion – Vb plots in Supplementary Figure 24. Dashed line points at zero\nconductance. Gpore at negative Vb drops rapidly at csod = 10-5 M, suggesting the onset of in-pore\nprecipitation of the manganese phosphates.\n(Added)\nSupplementary Figure 26. Ionic current traces under different Na2HPO4 concentrations. a-h, Ionic\ncurrent traces recorded in MnCl2/HBSS system with 100 nm nanopore in a 30 nm-thick SiNx membrane\nunder Vb of -0.5 V. The concentration of Na2HPO4 in the trans is varied as: 0.002 M (a), 0.005 M (b), 0.010\nM (c), 0.020 M (d), 0.050 M (e), 0.100 M (f), 0.200 M (g), and 0.500 M (h). Insets in (g-h) show magnified\nviews by ten times in the ionic current.\n(Added)\nSupplementary Figure 27. Spike signal profiles with Na2HPO4 in a MnCl2/HBSS system. a-g, Ionic\ncurrent spike height (Ip) versus width (td) scatter plots obtained for the ionic current spikes detected with a\n100 nm nanopore membrane interfacing 2 M MnCl2 and HBSS under the applied voltage of -0.5 V. In\naddition, Na2HPO4 is added to the HBSS at concentrations of 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050\nM (d), 0.100 M (e), 0.200 N (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 28. Ionic spike height distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10Ip histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\n(Added)\nSupplementary Figure 29. Ionic spike width distributions in MnCl2/ (HBSS + Na2HPO4) systems.\na-g, Log10td histograms built for the data in Supplementary Figure 27. The concentration of Na2HPO4 in\nthe trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d), 0.100 M (e), 0.200 M (f), and 0.500 M (g).\nGreen curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 30. Ionic spike width dependence on the Na2HPO4 concentration. Average td\ndeduced by the Gaussian fits to the log10td histograms in Supplementary Figure 29.\nSupplementary Figure 31\n(Added)\nSupplementary Figure 31. Inter-spike time distributions in MnCl2/ (HBSS + Na2HPO4) systems. a-g,\n-0.5 V. The concentration of Na2HPO4 in the trans is 0.005 M (a), 0.010 M (b), 0.020 M (c), 0.050 M (d),\n0.100 M (e), 0.200 M (f), and 0.500 M (g). Red curves are Gaussian fits to the distributions.\nSupplementary Figure 32\n(Added)\nSupplementary Figure 32. Spiking frequency in MnCl2/ (HBSS + Na2HPO4) systems. The spiking\nfrequency fp = Δtave -1 at different Na2HPO4 concentration (csod) calculated from Δtave deduced by the\nGaussian fitting to the data in Supplementary Figure 31.\nMain text (p9 line 218 – p10 line 238)\n(Added)\nThe autonomous spiking behavior of the nanopore membrane is highly tunable\nvia chemical control. For example, reducing the MnCl concentration on the cis side\n2\nfrom 2 M progressively suppresses spiking activity, yielding featureless ionic current\ntraces (Supplementary Figure 19). This inactivation arises from a concomitant pH\nincrease from 4.2 to ∼7, which inhibits the dissolution of manganese phosphate\nnanoprecipitates once formed, mirroring the behavior observed in the AlCl /PBS\n3\nsystem.\nReaction kinetics can also be modulated through the concentration of anionic\nreactants. Substituting PBS with Hank’s balanced salt solution (HBSS) eliminates the\nstrong ionic rectification in the I - V curves, as HBSS lacks phosphate even in the\nion b\npresence of 2 M MnCl in cis. Meanwhile, introducing phosphate sources, H₃PO₄\n2\n(Supplementary Figs. 20, 21), K₂HPO₄ (Supplementary Figs. 22, 23), or Na₂HPO₄\n(Supplementary Figs. 24, 25), into trans restores manganese phosphate nucleation\nwithin the nanopore, producing pronounced current suppression at negative V .\nb\nThe required concentration threshold depends strongly on the phosphate species:\nNa₂HPO₄ induces precipitation at levels as low as 10-5 M, whereas H₃PO₄ requires >\n0.1 M due to its low pH (1.5) accelerating dissolution.\n2. We examined pH control of the autonomous nanopore membrane activity.\nFigure 6\n(Added)\nFigure 6. Pore size modulation by pH control. a, An illustrative description of a chemistry-driven\nautonomous membrane interfacing 2 M MnCl2 and acidic PBS with HCl. b, Ionic current traces recorded for\nthe MnCl2/(PCB + HCl) systems with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V.\npH at trans is 6.7 (red) and 3.2 (blue). c-e, Ip versus td scatter plots for the cases of pH 6.7 (c), 5.2 (d), and 3.2\n(e). f, Log10Ip distributions at pH 6.7 (red), 5.2 (green), and 3.2 (blue) at the trans. g, Average Ip estimated by\nthe Gaussian fits. Axis at the right denotes the pore diameter dpore estimated from the pulse heights based on\nMaxwell-Hall’s model. h, Variations in the pulse heights represented as the full-widths at half-maxima of the\nSupplementary Figure 33\n(Added)\nSupplementary Figure 33. Ionic current traces in MnCl2/ (PBS + HCl) systems. a-g, Iion – t curves\nrecorded with a 100 nm nanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side\nis changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 34. Ionic current traces in MnCl2/ (PBS + HCl) systems with highly acidic\nconditions at the trans side. a-e, Iion – t curves recorded with a 100 nm nanopore in a 30 nm thick SiNx\nmembrane under Vb = -0.5 V. pH at the trans side is changed by adding HCl to 2.4 (a), 2.0 (b), 1.9 (c), 1.8\n(d), 1.1 (e), and 0.9 (f).\n(Added)\nSupplementary Figure 35. Ionic spike profiles under different pH at trans in MnCl2/PBS systems.\na-g, Ip – td scatter plots of ionic current spikes detected for MnCl2/ (PBS + HCl) systems with a 100 nm\nnanopore in a 30 nm thick SiNx membrane under Vb = -0.5 V. pH at the trans side is changed by adding\nHCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e), 3.4 (f), and 3.2 (g).\n(Added)\nSupplementary Figure 36. Ionic spike heights in MnCl2/ (PBS + HCl) systems. a-g, Log10Ip\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 37. Ionic spike widths in MnCl2/ (PBS + HCl) systems. a-g, Log10td\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\n(Added)\nSupplementary Figure 38. pH dependence of spike widths in MnCl2/ (PBS + HCl) systems. Average\ntd obtained by the Gaussian fitting in Supplementary Figure 39 showing no notable dependence on the pH\nat the trans side.\nSupplementary Figure 39\n(Added)\nSupplementary Figure 39. Inter-spike interval time in MnCl2/ (PBS + HCl) systems. a-g, Log10Δt\ndistributions of the ionic current spikes recorded with a 100 nm nanopore in a 30 nm thick SiNx membrane\nunder Vb = -0.5 V. pH at the trans side is changed by adding HCl to 6.7 (a), 5.9 (b), 5.2 (c), 4.4 (d), 3.7 (e),\n120\n3.4 (f), and 3.2 (g). Solid curves are Gaussian fits to the distributions.\nSupplementary Figure 40\n(Added)\nSupplementary Figure 40. Spiking frequency in MnCl2/ (PBS + HCl) systems. The frequency fp of\nionic current spike detections estimated as fp = Δtave -1, where Δtave is the average Δt deduced by the\nGaussian fitting to the histograms in Supplementary Figure 37. No notable relationship is found between\nfp and the pH at the trans side.\nMain text (p10 line 239 - 246)\n(Added)\nBeyond reactant concentration, pH adjustment offers a way for reproducible,\nsize-controlled pore formation. In MnCl /PBS systems, lowering the trans-side pH\n2\nbelow 7.4 with HCl steadily increases spike amplitudes (Fig. 6a–g, Supplementary\nFigs. 33–40). Simultaneously, the distribution of pulse heights narrows, indicating\nreduced pore-to-pore size variability (Fig. 6h). Using the Maxwell–Hall model under\nthe condition R >> R (Supplementary Fig. 13), the mean pore diameter is\nacc pore\nestimated to be tunable from ∼2 nm to ∼7 nm solely through pH control,\ndemonstrating sub-nanometer precision in autonomous pore size regulation.\n3. The autonomous nanopore membrane approach is applied for detecting single\nnucleotides and other small molecules (Figure R1 uploaded as Review Only Material).\n121\n4. We confirmed that no ionic current spikes were observable when using a pristine SiN\nx\nmembrane without any nanopores.\nSupplementary Figure 2\n(Added)\nSupplementary Figure 2. Ionic current characteristics of a 30 nm-thick SiNx membrane without\nnanopores. a, Schematic illustration depicting a pristine SiNx membrane. b, Ionic current versus\ntransmembrane voltage characteristics in phosphate buffered saline (1.37 M NaCl). Red and blue plots\nare data obtained under positive and negative Vb scans. The transient current behaviors indicate\ncharging/discharging at the membrane capacitance. Green plots are the average of the data acquired at\ndifferent voltage scanning directions. c, Ionic current characteristics with cis and trans filled with 2 M\nVb cannot induce any ion flux across the closed membrane. d, Partial ionic current trace under Vb = -1.0 V\nwith the solution configuration in (c). The curve is featureless showing no pulse-like signal.\n5. Scanning electron micrographs of the nanopores were added.\n(SEM images added to Figure 7b)\nFigure 7. Scalability of spiking characteristics. a, A sketch describing multipore in a SiNx membrane with cis and\ntrans filled with 2 M MnCl2 and PBS, respectively. b, Ionic current traces under Vb = -0.5 V for 100 nm-sized multipore\nmembranes with the number of pores Npore = 1 (red), 4 (green), 16 (orange), and 36 (blue). False-colored scanning\nelectron micrographs, with white bars denoting 1 μm, show the arrangement of nanopores. c, fp plotted against Npore.\nGray line is a linear fit crossing zero fp at Npore = 0. d, Ip versus td scatter plots for the multipores of Npore = 1 (red) and 36\n(blue). e, Logarithmic Ip histograms for the multipores of Npore = 1 (red), 4 (green), and 36 (blue). Pink curves are\nGaussian fit to the peak profiles. Dashed line points at Ip of the ionic spikes detected with KF in trans at Vb = -0.5 V.\nSupplementary Figure 4\n(SEM images added to Supplementary Figure 4b)\nSupplementary Figure 4. Structure of nanoheater-embedded nanopore. a, Schematic model of the\nnanoheater-embedded nanopore consisting of a Pt coil and a nanopore formed in a 30 nm-thick SiNx\nmembrane by electron beam lithography, radio-frequency magnetron sputtering, and reactive ion etching\nprocesses.S1 A 20 nm-thick SiO2 is also deposited on the entire structure from the top by chemical vapor\ndeposition for protection of the Pt coil under use (only partially depicted in the illustration). The heater\n124\nvoltage VH is applied to the Pt coil for local Joule heating. b, False-colored scanning electron micrograph\nof the nanoheater-embedded nanopore with a 40 nm diameter nanopore at the center.\nSupplementary Figure 43\n(SEM images added)\nSupplementary Figure 43. Iion – Vb characteristics of multipores interfacing 2M MnCl2 and PBS.\na-b, Iion – Vb curves under positive (red) and negative (blue) Vb scans for multipores consisting of 16 (a) and\n36 (b) 100 nm-sized nanopores in 30 nm-thick SiNx membranes. c-d, Magnified views near 0V. No\nnotable changes in Iion suggestive of sequential opening/closure of the multipores are present, such as\nstepwise rise and depression of the current. False-colored scanning electron micrographs, with white\nbars denoting 1 μm, show the arrangement of nanopores.\n(SEM images added)\nSupplementary Figure 45. Ionic current spike height distributions in cases of different pore sizes.\na-e, Ip histograms prepared from the ionic current spikes detected under Vb = -0.5 V in pores of diameter\ndpore = 20 nm (a), 60 nm (b), 100 nm (c), 300 nm (d), and 600 nm (e) in a 30 nm-thick SiNx membrane with\ncis and trans filled with 2 M MnCl2 and PBS, respectively. False-colored scanning electron micrographs\ndisplay the size and shape of the nanopores.\nSupplementary Figure 46\n(SEM images added)\nSupplementary Figure 46. Ionic current spike waveforms in cases of different pore sizes. a-e, Ip\n126\nversus td scatter plots prepared from the ionic current spikes detected under Vb = -0.5 V in pores of\ndiameter dpore = 20 nm (a), 60 nm (b), 100 nm (c), 300 nm (d), and 600 nm (e) in a 30 nm-thick SiNx\nmembrane with cis and trans filled with 2 M MnCl2 and PBS, respectively. False-colored scanning\nelectron micrographs display the size and shape of the nanopores.\nSupplementary Figure 47\n(SEM images added)\nSupplementary Figure 47. Ionic current spike waveforms in case of SiNx multipores. a-d, Ip versus\nVb scatter plots obtained under Vb = -0.5 V for arrays of 1 x 1 (a), 2 x 2 (b), 4 x 4 (c), and 6 x 6 (d) multipores\nof 100 nm diameter in a 30 nm-thick SiNx membrane separating 2 M MnCl2 and PBS at the cis and trans.\nFalse-colored scanning electron micrographs, with white bars denoting 1 μm, show the arrangement of\nnanopores.\n6. Spiking frequency in 3 x 3 and 5 x 5 multipores was measured.\n(Added)\nSupplementary Figure 43. Spiking frequency by the in-pore chemistry in SiNx multipore.\nHistograms of the interval Δt between two consecutively detected ionic current spikes in a SiNx multipore\ncomposed of 1 (red), 4 (green), 9 (orange), 16 (blue), 25 (skyblue), and 36 (purple) nanopores of 100 nm\ndiameter in a 30 nm-thick membrane. Gray curves are Gaussian fitting.\n7. Sentences were added to explain more clearly how the pore diameter was calculated.\nMain text (p8 line 178 – 181)\n(Added) From the 40 nA heights of the giant spikes and ρ of 8.3 S/m (Supplementary\nFigure 13), therefore, R is estimated to be 12.5 MΩ, which suggests the opening\npore\nof nanopores with diameters around 10 nm with the CaCl /PBS configuration.\n2\n128\n8. Explanation was added for the increased spiking rate by the addition of KF.\nMain text (p8 line 199 – p9 line 206)\n(Revised) The addition of KF also increased the ionic spiking rate. Pores form via\ndissolution-induced thinning of the metal phosphate layer and subsequently reclose\nthrough precipitation, driven by electric-field-mediated translocation of Mn²⁺ and\nphosphate ions. During this cycle, ultra-small pores remain undetectable in ionic\ncurrent measurements until they expand sufficiently to accommodate the relatively\nlarge Cl⁻ ions when F- is absent. Many pores therefore remain invisible, sealed by\nprecipitation before becoming detectable. The introduction of smaller F⁻ anions\nenables ionic conduction through these nascent pores, revealing their existence and\nenhancing the observed spiking frequency.\nMakusu Tsutsui, Wei-Lun Hsu, Denis Garoli, Ali Douaki, Yuki Komoto, Hirofumi Daiguji, and\nTomoji Kawai\nWe sincerely thank the referees for their thorough evaluation of our manuscript and for\nfurther providing insightful and constructive comments, which have been invaluable in\nimproving the quality of our work. We have carefully addressed all points and implemented\nthe corresponding revisions, as detailed in our point-by-point responses in the following.\n1. We have moderated our claims of angstrom-scale pore formation.\nTitle\n(Revised)\nChemistry-driven autonomous nanopore membranes\nAbstract\n(Revised)\nFabrication of ultra-small pores at the atomic scale remains a significant\nchallenge in modern nanotechnology, hindering the study of ion transport and\nmolecular dynamics in confined spaces. Here, we introduce a chemically\ncontrollable break-membrane approach that enables the repeated formation\nand closure of nanoscale pores in SiN membranes through manipulating the\nx\nin-pore electrochemical reaction conditions by transmembrane voltage. Ionic\ncurrent measurements reveal distinct conductance features that are consistent\nwith ion dehydration and transport through highly confined channels\napproaching sub-nanometer dimensions. The scalable nature of this platform,\nwhich allows multiple pores to be actuated simultaneously, offers a powerful\ntool for probing ion transport and fluid dynamics in extreme confinement.\nBeyond advancing fundamental understanding of ion transport and fluid\ndynamics, this chemically driven membrane system holds promise for\napplications in single-molecule sensing, neuromorphic computing, and\nnanoreactor design.\nMain text (p2 line 51 – p3 line 53)\n(Revised)\nIn contrast, we herein report a method for repeated formation of nanoscale pores\nwithin a dielectric membrane, enabling statistical evaluation of ion transport under\nextreme confinement.\nMain text (p8 line 200 – p9 line 207)\n(Added)\nIt is important to emphasize, however, that this pore size estimate is indirect and\nbased solely on ionic current measurements. Additional factors, such as counterion\nconduction,47 permselectivity,51 electroosmotic flow,52 and ion–ion correlations,53 may\n2\nalso contribute to the observed conductance and have not been fully accounted for in\nthis model. While the results are consistent with the formation of sub-nanometer\npores, direct structural observation54 and refined theoretical modellings55 are\nessential to validate the inferred dimensions and to fully capture the ion transport\nphysics within such ultra-confined environments.\nMain text (p12 line 280 – line 282)\n(Revised)\nOverall results are consistent in validating the chemically-controllable break\nmembrane approach for systematic evaluations of the ion transport in ultrasmall\npores.\nMain text (p13 line 325 – line 327)\n(Revised)\nWhile the exact pore dimensions cannot yet be directly verified, the conductance\ndata are consistent with transport through channels approaching the sub-nanometer\nscale.\n2. We have revised the manuscript to make it clear that the transmembrane voltage serves\nas a facilitator for the chemistry-driven pore opening/ closing.\nAbstract\n(Revised)\nHere, we introduce a chemically controllable break-membrane approach that\nenables the repeated formation and closure of nanoscale pores in SiN\nx\nmembranes through manipulating the in-pore electrochemical reaction\nconditions by transmembrane voltage.\nMain text (p3 line 57 – 60)\n(Revised)\nThe in-pore reaction is induced by the ion flux under the transmembrane voltage V\nb\nwith the trans and cis compartments filled with 2 M MnCl and phosphate-buffered\n2\nsaline (PBS), respectively (Figure 1a, see also Supplementary Table 1).\nMain text (p4 line 91 – 93)\n(Revised)\nx\nover in-pore chemical reaction conditions, enabling the repeated formation of small\npores through the autonomous nanoelectrochemistry.29\nMain text (p13 line 304 – line 315)\n(Added)\nThe ability to actuate the repetitive opening and closing of nanopores via in-pore\nchemistry, with transmembrane voltage as a facilitator, manifests the pivotal role of\nsolution composition in governing precipitation–dissolution dynamics of metal\nphosphates under nanoconfinement. Insufficient reactant concentration produces\nonly a partial precipitate, unable to fully seal the SiN nanopore. Conversely, excess\nx\nreactants accelerate precipitation kinetics, closing the channel more effectively and\nyielding smaller pores upon reopening. The solution pH similarly regulates\ndissolution rates: acidic conditions tend to reopen larger pores, while basic conditions\nyield smaller ones. Meanwhile, it is important to note that since the reactant\nconcentration can also shift the solution pH, these effects are mutually coupled, as\nobserved in the MnCl concentration dependence of the I spiking feature. As such,\n2 ion\nboth the frequency of pore piercing and the effective pore size can be tuned by\nmanipulating the degrees of freedom available in solution chemistry.\n3. We have added a discussion on alternative interpretations of the ionic spiking.\nMain text (p12 line 285 – p13 line 303)\n(Added)\nSeveral mechanisms could, in principle, contribute to the ionic current spiking\nbehavior. One possibility is that thin nanoprecipitate layers act as capacitors,\nintermittently charging and discharging under an applied voltage. Such processes,\nhowever, typically yield overshooting non-Faradaic current transients of biphasic\ncharacteristics,57 in contrast to the single, non-overshooting pulses observed here.\nAnother mechanism involves the so-called chemical reaction wave, a transient\nelectrochemical phenomenon in which nucleation and dissolution reactions induce\ntime-dependent morphological changes in a precipitated film on an electrode.58 Yet\nin the present measurement configuration, this pathway is unlikely to generate\nappreciable Faradaic currents unless a new ion-conducting channel is created\n(though it may contribute to the autonomous activity of the nanoprecipitated\nmembranes). Taken together, the most consistent interpretation is that the ionic\ncurrent spikes originate from the spontaneous opening and closing of nanoscale\npores in the precipitate layer, driven by the interplay of voltage-facilitated precipitation\nand dissolution reactions. Further efforts are expected to be devoted to explore how\nthe ultrasmall pores behave under strong salinity gradients and localized electric\nfields. Under such conditions, additional factors including counterion conduction,47\nconcentration polarization,59 permselectivity,51 and electroosmotic flow,52 alongside\nion dehydration,42 are expected to come into play. These effects may further enrich\nthe nonlinear ion transport dynamics and broaden the functional space of\nvoltage-gated chemically active nanopores.\n4. We have evaluated the contribution of water evaporation on the long-term I -V\nion b\ncharacteristics.\nSupplementary Figure 1\n(Added)\nSupplementary Figure 1. Long-term I -V measurements. a-b, Photograph of the setup used for\nion b\nlong-term ionic current measurements. PDMS cells were connected to reservoirs of PBS (1.37 M NaCl)\nand MnCl₂ (2 M) solutions through plastic tubing to suppress water evaporation during extended operation.\nc, Two-dimensional histogram constructed from 4,086 I –V curves recorded over more than two days\nion b\nusing the setup in (a). The white dashed line indicates 1.4 V. d, Ionic current at 1.4 V (I ) extracted from\n1.4\neach curve. d, Time course changes in I . Blue points correspond to data acquired without evaporation\n1.4\nsuppression (Figure 1c, main text), where measurements could only be sustained for <12 h. In contrast,\nthe red points show that the modified setup enabled measurements over much longer durations. The\nreduced conductance arises from the smaller nanopore diameter (70 nm) used in (c). Although\n5\nevaporation suppression stabilized I , small fluctuations persisted, likely reflecting subtle effects of\n1.4\nresidual precipitates on the pore wall during repeated voltage scans.\nFigure 1 caption\n(Added)\nThe variation in r is attributable to a change in the ion concentration due to water\nrec\nevaporation and residual precipitates remained undissolved on the pore wall surface\nduring the 10 hours of measurement.\nReviewer #1\nReviewers Comments:\nAlthough the authors have addressed most of the comments raised, demonstrating the\noutcomes more reasonably is essential and must be addressed before the manuscript can\nbe considered for publication.\n1. Claim of angstrom-scale pores lacks direct evidence. The authors repeatedly refer to\n“angstrom pores” and estimate pore sizes around 3.9 Å based on conductance\nmeasurements and the model. However, no direct structural characterization (e.g., BET,\nTEM, or molecular dynamics validation) is provided to confirm the actual pore size. The\ninference relies heavily on ionic current measurements and assumptions about dehydration,\nwhich may not be sufficient to claim Angstrom-scale dimensions. The observed\nconductance could also be influenced by surface charge, electroosmotic flow, or ion\ncorrelation effects not accounted for in the model. The term “angstrom” should be used\nmore cautiously, and the claims should be tempered unless supported by more direct\nevidence.\n(Reply)\nThank you very much for your valuable comment. We agree with your opinion\nregarding the use of the term 'angstrom' in relation to the pore size estimated from\nconductance measurements. Accordingly, we have moderated our claims of\nangstrom-scale pore formation by revising the title, abstract, and main text, as highlighted in\ngreen.\nTitle\n(Revised)\nChemistry-driven autonomous nanopore membranes\nAbstract\n(Revised)\nFabrication of ultra-small pores at the atomic scale remains a significant\nchallenge in modern nanotechnology, hindering the study of ion transport and\nmolecular dynamics in confined spaces. Here, we introduce a chemically\n7\ncontrollable break-membrane approach that enables the repeated formation\nand closure of nanoscale pores in SiN membranes through manipulating the\nx\nin-pore electrochemical reaction conditions by transmembrane voltage. Ionic\ncurrent measurements reveal distinct conductance features that are consistent\nwith ion dehydration and transport through highly confined channels\napproaching sub-nanometer dimensions. The scalable nature of this platform,\nwhich allows multiple pores to be actuated simultaneously, offers a powerful\ntool for probing ion transport and fluid dynamics in extreme confinement.\nBeyond advancing fundamental understanding of ion transport and fluid\ndynamics, this chemically driven membrane system holds promise for\napplications in single-molecule sensing, neuromorphic computing, and\nnanoreactor design.\nMain text (p2 line 51 – p3 line 53)\n(Revised)\nIn contrast, we herein report a method for repeated formation of nanoscale pores\nwithin a dielectric membrane, enabling statistical evaluation of ion transport under\nextreme confinement.\nMain text (p8 line 200 – p9 line 207)\n(Added)\nIt is important to emphasize, however, that this pore size estimate is indirect and\nbased solely on ionic current measurements. Additional factors, such as counterion\nconduction,47 permselectivity,51 electroosmotic flow,52 and ion–ion correlations,53 may\nalso contribute to the observed conductance and have not been fully accounted for in\nthis model. While the results are consistent with the formation of sub-nanometer\npores, direct structural observation54 and refined theoretical modellings55 are\nessential to validate the inferred dimensions and to fully capture the ion transport\nphysics within such ultra-confined environments.\nMain text (p12 line 280 – line 282)\n(Revised)\nOverall results are consistent in validating the chemically-controllable break\nmembrane approach for systematic evaluations of the ion transport in ultrasmall\npores.\nMain text (p13 line 325 – line 327)\n8\n(Revised)\nWhile the exact pore dimensions cannot yet be directly verified, the conductance\ndata are consistent with transport through channels approaching the sub-nanometer\nscale.\n2. Voltage as a direct control is questionable. While the manuscript emphasizes\nvoltage-controlled pore formation and closure, the underlying mechanism appears to be\npredominantly chemically driven (precipitation/dissolution of metal phosphates), with voltage\nserving mainly to drive ion migration and modulate reaction rates. The role of voltage is not\nas a direct \"control\" but as a facilitator of the chemical reactions. The title, abstract, and\nmain context may overstate the role of voltage. The authors should clarify that voltage is a\nmeans to manipulate the electrochemical conditions that lead to pore dynamics, rather than\na direct actuator of pore size.\n(Reply)\nWe appreciate the comment. We have carefully reviewed the manuscript and revised\nthe descriptions to clarify that the transmembrane voltage does not directly control the pore\nformation/closure processes, but rather serves as a probe to adjust the ionic flow conditions\nfor triggering the in-pore electrochemical reactions, as highlighted in blue\nAbstract\n(Revised)\nHere, we introduce a chemically controllable break-membrane approach that\nenables the repeated formation and closure of nanoscale pores in SiN\nx\nmembranes through manipulating the in-pore electrochemical reaction\nconditions by transmembrane voltage.\nMain text (p3 line 57 – 60)\n(Revised)\nThe in-pore reaction is induced by the ion flux under the transmembrane voltage V\nb\nwith the trans and cis compartments filled with 2 M MnCl and phosphate-buffered\n2\nsaline (PBS), respectively (Figure 1a, see also Supplementary Table 1).\nMain text (p4 line 91 – 93)\n(Revised)\nx\nover in-pore chemical reaction conditions, enabling the repeated formation of small\npores through the autonomous nanoelectrochemistry.29\n3. Limited discussion of alternative interpretations. The observed current spikes could also\nbe explained by transient electrochemical phenomena such as nucleation/dissolution waves,\ncapacitive charging, or ion concentration polarization. The authors should discuss these\nalternative mechanisms and justify why their interpretation (pore formation/closure) is more\nplausible.\n(Reply)\nThank you for the comment. We have added a paragraph discussing alternative\ninterpretations of the observed ionic current spiking behaviors, as shown below.\nMain text (p12 line 285 – p13 line 303)\n(Added)\nSeveral mechanisms could, in principle, contribute to the ionic current spiking\nbehavior. One possibility is that thin nanoprecipitate layers act as capacitors,\nintermittently charging and discharging under an applied voltage. Such processes,\nhowever, typically yield overshooting non-Faradaic current transients of biphasic\ncharacteristics,57 in contrast to the single, non-overshooting pulses observed here.\nAnother mechanism involves the so-called chemical reaction wave, a transient\nelectrochemical phenomenon in which nucleation and dissolution reactions induce\ntime-dependent morphological changes in a precipitated film on an electrode.58 Yet\nin the present measurement configuration, this pathway is unlikely to generate\nappreciable Faradaic currents unless a new ion-conducting channel is created\n(though it may contribute to the autonomous activity of the nanoprecipitated\nmembranes). Taken together, the most consistent interpretation is that the ionic\ncurrent spikes originate from the spontaneous opening and closing of nanoscale\npores in the precipitate layer, driven by the interplay of voltage-facilitated precipitation\nand dissolution reactions. Further efforts are expected to be devoted to explore how\nthe ultrasmall pores behave under strong salinity gradients and localized electric\nfields. Under such conditions, additional factors including counterion conduction,47\nconcentration polarization,59 permselectivity,51 and electroosmotic flow,52 alongside\nion dehydration,42 are expected to come into play. These effects may further enrich\nthe nonlinear ion transport dynamics and broaden the functional space of\nvoltage-gated chemically active nanopores.\n10\n4. pH dependence overshadows voltage dependence. The results in Fig. 6 clearly show that\npH is a more direct and reproducible control knob for pore size than voltage. This\nundermines the narrative of \"voltage-gated\" pores. The authors should reframe the overall\ndiscussion to highlight the chemical nature of the control mechanism, with voltage as a\nsupporting factor.\n(Reply)\nThank you for the comment. We have revised the manuscript to be more accurate on\nthe role of the transmembrane voltage, where we also added a paragraph to emphasize the\nchemistry-driven nature of the pore opening and closing mechanism, as shown below.\nMain text (p13 line 304 – line 315)\n(Added)\nThe ability to actuate the repetitive opening and closing of nanopores via in-pore\nchemistry, with transmembrane voltage as a facilitator, manifests the pivotal role of\nsolution composition in governing precipitation–dissolution dynamics of metal\nphosphates under nanoconfinement. Insufficient reactant concentration produces\nonly a partial precipitate, unable to fully seal the SiN nanopore. Conversely, excess\nx\nreactants accelerate precipitation kinetics, closing the channel more effectively and\nyielding smaller pores upon reopening. The solution pH similarly regulates\ndissolution rates: acidic conditions tend to reopen larger pores, while basic conditions\nyield smaller ones. Meanwhile, it is important to note that since the reactant\nconcentration can also shift the solution pH, these effects are mutually coupled, as\nobserved in the MnCl concentration dependence of the I spiking feature. As such,\n2 ion\nboth the frequency of pore piercing and the effective pore size can be tuned by\nmanipulating the degrees of freedom available in solution chemistry.\nReviewer #3\nThe authors carried out a revision of their manuscript where many comments were\nadequately addressed. However, there are several points which still require clarification as\nset out below：\n1. Chemical Reaction Process: When discussing MnCl2 concentration, the observed\nphenomenon (reduction or disappearance of spikes) is directly attributed to reduced\n“dissolution efficiency” due to pH changes. However, the decrease in MnCl2 concentration\nitself (not just the accompanying pH change) likely directly affects the chemical driving force\n(e.g., reactant concentration, ionic strength) of the precipitation/dissolution reaction at the\npore. The MnCl2 concentration and pH are two co-varying parameters. The experimental\ndesign (diluting MnCl2) simultaneously alters both factors. Conclusions should discuss the\nroles of both the concentration effect and the pH effect.\n(Reply)\nThank you for the comment. We have added a discussion regarding the contributions\nof pH and ionic reactant concentration, as follows.\nMain text (p13 line 304 – line 315)\n(Added)\nThe ability to actuate the repetitive opening and closing of nanopores via in-pore\nchemistry, with transmembrane voltage as a facilitator, manifests the pivotal role of\nsolution composition in governing precipitation–dissolution dynamics of metal\nphosphates under nanoconfinement. Insufficient reactant concentration produces\nonly a partial precipitate, unable to fully seal the SiN nanopore. Conversely, excess\nx\nreactants accelerate precipitation kinetics, closing the channel more effectively and\nyielding smaller pores upon reopening. The solution pH similarly regulates\ndissolution rates: acidic conditions tend to reopen larger pores, while basic conditions\nyield smaller ones. Meanwhile, it is important to note that since the reactant\nconcentration can also shift the solution pH, these effects are mutually coupled, as\nobserved in the MnCl concentration dependence of the I spiking feature. As such,\n2 ion\nboth the frequency of pore piercing and the effective pore size can be tuned by\nmanipulating the degrees of freedom available in solution chemistry.\n12\n2. Pore Reaction Stability: Regarding the issue mentioned: “While the exact mechanism\nremains unclear, one possible factor is a slow change in ion concentration due to liquid\nevaporation over the 10-hour measurement period,” can the impact of water evaporation on\nexperimental results be experimentally verified?\n(Reply)\nThank you for the comment. To examine the effect of water evaporation on long-term\nmeasurements of the ionic current versus transmembrane voltage characteristics, we newly\nconfigured an experimental setup. As shown in Supplementary Figure 1a–c, bottles of 10×\nPBS and 2 M MnCl₂ solutions were prepared, and holes were punched in the lids to insert\nplastic tubes connected to the PDMS cells attached to a nanopore chip. This setup\neffectively suppressed water evaporation and enabled stable ionic current measurements\nfor more than 12 hours. Over the course of more than two days of I –V measurements,\nion b\nthe nanopore conductance remained more stable compared to the case without evaporation\nsuppression (Figure 1c in the main text). Nevertheless, small fluctuations persisted,\nsuggesting a non-negligible role of residual precipitates formed on the nanopore wall during\nrepetitive voltage scans.\nThese results have been added to the Supplementary Information as Supplementary\nFigure 1. We have also revised the caption of Figure 1 in the main text to note the possible\ninfluence of residual precipitates on the observed fluctuations in the ionic current\ncharacteristics.\n(Added)\nSupplementary Figure 1. Long-term I -V measurements. a-b, Photograph of the setup used for\nion b\nlong-term ionic current measurements. PDMS cells were connected to reservoirs of PBS (1.37 M NaCl)\nand MnCl₂ (2 M) solutions through plastic tubing to suppress water evaporation during extended operation.\nc, Two-dimensional histogram constructed from 4,086 I –V curves recorded over more than two days\nion b\nusing the setup in (a). The white dashed line indicates 1.4 V. d, Ionic current at 1.4 V (I ) extracted from\n1.4\neach curve. d, Time course changes in I . Blue points correspond to data acquired without evaporation\n1.4\nsuppression (Figure 1c, main text), where measurements could only be sustained for <12 h. In contrast,\nthe red points show that the modified setup enabled measurements over much longer durations. The\nreduced conductance arises from the smaller nanopore diameter (70 nm) used in (c). Although\n5\nevaporation suppression stabilized I , small fluctuations persisted, likely reflecting subtle effects of\n1.4\nresidual precipitates on the pore wall during repeated voltage scans.\nFigure 1 caption\n(Added)\nThe variation in r is attributable to a change in the ion concentration due to water\nrec\nevaporation and residual precipitates remained undissolved on the pore wall surface\nduring the 10 hours of measurement.\n14"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Although the authors have addressed most of the comments raised, demonstrating the outcomes more reasonably is essential and must be addressed before the manuscript can be considered for publication.\n1. Claim of angstrom-scale pores lacks direct evidence. The authors repeatedly refer to “angstrom pores” and estimate pore sizes around 3.9 Å based on conductance measurements and the model. However, no direct structural characterization (e.g., BET, TEM, or molecular dynamics validation) is provided to confirm the actual pore size. The inference relies heavily on ionic current measurements and assumptions about dehydration, which may not be sufficient to claim Angstrom-scale dimensions. The observed conductance could also be influenced by surface charge, electroosmotic flow, or ion correlation effects not accounted for in the model. The term “angstrom” should be used more cautiously, and the claims should be tempered unless supported by more direct evidence.\n2. Voltage as a direct control is questionable. While the manuscript emphasizes voltage-controlled pore formation and closure, the underlying mechanism appears to be predominantly chemically driven (precipitation/dissolution of metal phosphates), with voltage serving mainly to drive ion migration and modulate reaction rates. The role of voltage is not as a direct \"control\" but as a facilitator of the chemical reactions. The title, abstract, and main context may overstate the role of voltage. The authors should clarify that voltage is a means to manipulate the electrochemical conditions that lead to pore dynamics, rather than a direct actuator of pore size.\n3. Limited discussion of alternative interpretations. The observed current spikes could also be explained by transient electrochemical phenomena such as nucleation/dissolution waves, capacitive charging, or ion concentration polarization. The authors should discuss these alternative mechanisms and justify why their interpretation (pore formation/closure) is more plausible.\n4. pH dependence overshadows voltage dependence. The results in Fig. 6 clearly show that pH is a more direct and reproducible control knob for pore size than voltage. This undermines the narrative of \"voltage-gated\" pores. The authors should reframe the overall discussion to highlight the chemical nature of the control mechanism, with voltage as a supporting factor.", "reviewer_2": "The manuscript is good now. I have no further questions about the revised manuscript.", "reviewer_3": "The authors carried out a revision of their manuscript where many comments were adequately addressed. However, there are several points which still require clarification as set out below：\n1. Chemical Reaction Process: When discussing MnCl2 concentration, the observed phenomenon (reduction or disappearance of spikes) is directly attributed to reduced “dissolution efficiency” due to pH changes. However, the decrease in MnCl2 concentration itself (not just the accompanying pH change) likely directly affects the chemical driving force (e.g., reactant concentration, ionic strength) of the precipitation/dissolution reaction at the pore. The MnCl2 concentration and pH are two co-varying parameters. The experimental design (diluting MnCl2) simultaneously alters both factors. Conclusions should discuss the roles of both the concentration effect and the pH effect.\n2. Pore Reaction Stability: Regarding the issue mentioned: “While the exact mechanism remains unclear, one possible factor is a slow change in ion concentration due to liquid evaporation over the 10-hour measurement period,” can the impact of water evaporation on experimental results be experimentally verified?"}, "author_response": "Chemistry-driven autonomous nanopore membranes\nMakusu Tsutsui, Wei-Lun Hsu, Denis Garoli, Ali Douaki, Yuki Komoto, Hirofumi Daiguji, and\nTomoji Kawai\nWe sincerely thank the referees for their thorough evaluation of our manuscript and for\nfurther providing insightful and constructive comments, which have been invaluable in\nimproving the quality of our work. We have carefully addressed all points and implemented\nthe corresponding revisions, as detailed in our point-by-point responses in the following.\n1. We have moderated our claims of angstrom-scale pore formation.\nTitle\n(Revised)\nChemistry-driven autonomous nanopore membranes\nAbstract\n(Revised)\nFabrication of ultra-small pores at the atomic scale remains a significant\nchallenge in modern nanotechnology, hindering the study of ion transport and\nmolecular dynamics in confined spaces. Here, we introduce a chemically\ncontrollable break-membrane approach that enables the repeated formation\nand closure of nanoscale pores in SiN membranes through manipulating the\nx\nin-pore electrochemical reaction conditions by transmembrane voltage. Ionic\ncurrent measurements reveal distinct conductance features that are consistent\nwith ion dehydration and transport through highly confined channels\napproaching sub-nanometer dimensions. The scalable nature of this platform,\nwhich allows multiple pores to be actuated simultaneously, offers a powerful\ntool for probing ion transport and fluid dynamics in extreme confinement.\nBeyond advancing fundamental understanding of ion transport and fluid\ndynamics, this chemically driven membrane system holds promise for\napplications in single-molecule sensing, neuromorphic computing, and\nnanoreactor design.\nMain text (p2 line 51 – p3 line 53)\n(Revised)\nIn contrast, we herein report a method for repeated formation of nanoscale pores\nwithin a dielectric membrane, enabling statistical evaluation of ion transport under\nextreme confinement.\nMain text (p8 line 200 – p9 line 207)\n(Added)\nIt is important to emphasize, however, that this pore size estimate is indirect and\nbased solely on ionic current measurements. Additional factors, such as counterion\nconduction,47 permselectivity,51 electroosmotic flow,52 and ion–ion correlations,53 may\n2\nalso contribute to the observed conductance and have not been fully accounted for in\nthis model. While the results are consistent with the formation of sub-nanometer\npores, direct structural observation54 and refined theoretical modellings55 are\nessential to validate the inferred dimensions and to fully capture the ion transport\nphysics within such ultra-confined environments.\nMain text (p12 line 280 – line 282)\n(Revised)\nOverall results are consistent in validating the chemically-controllable break\nmembrane approach for systematic evaluations of the ion transport in ultrasmall\npores.\nMain text (p13 line 325 – line 327)\n(Revised)\nWhile the exact pore dimensions cannot yet be directly verified, the conductance\ndata are consistent with transport through channels approaching the sub-nanometer\nscale.\n2. We have revised the manuscript to make it clear that the transmembrane voltage serves\nas a facilitator for the chemistry-driven pore opening/ closing.\nAbstract\n(Revised)\nHere, we introduce a chemically controllable break-membrane approach that\nenables the repeated formation and closure of nanoscale pores in SiN\nx\nmembranes through manipulating the in-pore electrochemical reaction\nconditions by transmembrane voltage.\nMain text (p3 line 57 – 60)\n(Revised)\nThe in-pore reaction is induced by the ion flux under the transmembrane voltage V\nb\nwith the trans and cis compartments filled with 2 M MnCl and phosphate-buffered\n2\nsaline (PBS), respectively (Figure 1a, see also Supplementary Table 1).\nMain text (p4 line 91 – 93)\n(Revised)\nx\nover in-pore chemical reaction conditions, enabling the repeated formation of small\npores through the autonomous nanoelectrochemistry.29\nMain text (p13 line 304 – line 315)\n(Added)\nThe ability to actuate the repetitive opening and closing of nanopores via in-pore\nchemistry, with transmembrane voltage as a facilitator, manifests the pivotal role of\nsolution composition in governing precipitation–dissolution dynamics of metal\nphosphates under nanoconfinement. Insufficient reactant concentration produces\nonly a partial precipitate, unable to fully seal the SiN nanopore. Conversely, excess\nx\nreactants accelerate precipitation kinetics, closing the channel more effectively and\nyielding smaller pores upon reopening. The solution pH similarly regulates\ndissolution rates: acidic conditions tend to reopen larger pores, while basic conditions\nyield smaller ones. Meanwhile, it is important to note that since the reactant\nconcentration can also shift the solution pH, these effects are mutually coupled, as\nobserved in the MnCl concentration dependence of the I spiking feature. As such,\n2 ion\nboth the frequency of pore piercing and the effective pore size can be tuned by\nmanipulating the degrees of freedom available in solution chemistry.\n3. We have added a discussion on alternative interpretations of the ionic spiking.\nMain text (p12 line 285 – p13 line 303)\n(Added)\nSeveral mechanisms could, in principle, contribute to the ionic current spiking\nbehavior. One possibility is that thin nanoprecipitate layers act as capacitors,\nintermittently charging and discharging under an applied voltage. Such processes,\nhowever, typically yield overshooting non-Faradaic current transients of biphasic\ncharacteristics,57 in contrast to the single, non-overshooting pulses observed here.\nAnother mechanism involves the so-called chemical reaction wave, a transient\nelectrochemical phenomenon in which nucleation and dissolution reactions induce\ntime-dependent morphological changes in a precipitated film on an electrode.58 Yet\nin the present measurement configuration, this pathway is unlikely to generate\nappreciable Faradaic currents unless a new ion-conducting channel is created\n(though it may contribute to the autonomous activity of the nanoprecipitated\nmembranes). Taken together, the most consistent interpretation is that the ionic\ncurrent spikes originate from the spontaneous opening and closing of nanoscale\npores in the precipitate layer, driven by the interplay of voltage-facilitated precipitation\nand dissolution reactions. Further efforts are expected to be devoted to explore how\nthe ultrasmall pores behave under strong salinity gradients and localized electric\nfields. Under such conditions, additional factors including counterion conduction,47\nconcentration polarization,59 permselectivity,51 and electroosmotic flow,52 alongside\nion dehydration,42 are expected to come into play. These effects may further enrich\nthe nonlinear ion transport dynamics and broaden the functional space of\nvoltage-gated chemically active nanopores.\n4. We have evaluated the contribution of water evaporation on the long-term I -V\nion b\ncharacteristics.\nSupplementary Figure 1\n(Added)\nSupplementary Figure 1. Long-term I -V measurements. a-b, Photograph of the setup used for\nion b\nlong-term ionic current measurements. PDMS cells were connected to reservoirs of PBS (1.37 M NaCl)\nand MnCl₂ (2 M) solutions through plastic tubing to suppress water evaporation during extended operation.\nc, Two-dimensional histogram constructed from 4,086 I –V curves recorded over more than two days\nion b\nusing the setup in (a). The white dashed line indicates 1.4 V. d, Ionic current at 1.4 V (I ) extracted from\n1.4\neach curve. d, Time course changes in I . Blue points correspond to data acquired without evaporation\n1.4\nsuppression (Figure 1c, main text), where measurements could only be sustained for <12 h. In contrast,\nthe red points show that the modified setup enabled measurements over much longer durations. The\nreduced conductance arises from the smaller nanopore diameter (70 nm) used in (c). Although\n5\nevaporation suppression stabilized I , small fluctuations persisted, likely reflecting subtle effects of\n1.4\nresidual precipitates on the pore wall during repeated voltage scans.\nFigure 1 caption\n(Added)\nThe variation in r is attributable to a change in the ion concentration due to water\nrec\nevaporation and residual precipitates remained undissolved on the pore wall surface\nduring the 10 hours of measurement.\nReviewer #1\nReviewers Comments:\nAlthough the authors have addressed most of the comments raised, demonstrating the\noutcomes more reasonably is essential and must be addressed before the manuscript can\nbe considered for publication.\n1. Claim of angstrom-scale pores lacks direct evidence. The authors repeatedly refer to\n“angstrom pores” and estimate pore sizes around 3.9 Å based on conductance\nmeasurements and the model. However, no direct structural characterization (e.g., BET,\nTEM, or molecular dynamics validation) is provided to confirm the actual pore size. The\ninference relies heavily on ionic current measurements and assumptions about dehydration,\nwhich may not be sufficient to claim Angstrom-scale dimensions. The observed\nconductance could also be influenced by surface charge, electroosmotic flow, or ion\ncorrelation effects not accounted for in the model. The term “angstrom” should be used\nmore cautiously, and the claims should be tempered unless supported by more direct\nevidence.\n(Reply)\nThank you very much for your valuable comment. We agree with your opinion\nregarding the use of the term 'angstrom' in relation to the pore size estimated from\nconductance measurements. Accordingly, we have moderated our claims of\nangstrom-scale pore formation by revising the title, abstract, and main text, as highlighted in\ngreen.\nTitle\n(Revised)\nChemistry-driven autonomous nanopore membranes\nAbstract\n(Revised)\nFabrication of ultra-small pores at the atomic scale remains a significant\nchallenge in modern nanotechnology, hindering the study of ion transport and\nmolecular dynamics in confined spaces. Here, we introduce a chemically\n7\ncontrollable break-membrane approach that enables the repeated formation\nand closure of nanoscale pores in SiN membranes through manipulating the\nx\nin-pore electrochemical reaction conditions by transmembrane voltage. Ionic\ncurrent measurements reveal distinct conductance features that are consistent\nwith ion dehydration and transport through highly confined channels\napproaching sub-nanometer dimensions. The scalable nature of this platform,\nwhich allows multiple pores to be actuated simultaneously, offers a powerful\ntool for probing ion transport and fluid dynamics in extreme confinement.\nBeyond advancing fundamental understanding of ion transport and fluid\ndynamics, this chemically driven membrane system holds promise for\napplications in single-molecule sensing, neuromorphic computing, and\nnanoreactor design.\nMain text (p2 line 51 – p3 line 53)\n(Revised)\nIn contrast, we herein report a method for repeated formation of nanoscale pores\nwithin a dielectric membrane, enabling statistical evaluation of ion transport under\nextreme confinement.\nMain text (p8 line 200 – p9 line 207)\n(Added)\nIt is important to emphasize, however, that this pore size estimate is indirect and\nbased solely on ionic current measurements. Additional factors, such as counterion\nconduction,47 permselectivity,51 electroosmotic flow,52 and ion–ion correlations,53 may\n2\nalso contribute to the observed conductance and have not been fully accounted for in\nthis model. While the results are consistent with the formation of sub-nanometer\npores, direct structural observation54 and refined theoretical modellings55 are\nessential to validate the inferred dimensions and to fully capture the ion transport\nphysics within such ultra-confined environments.\nMain text (p12 line 280 – line 282)\n(Revised)\nOverall results are consistent in validating the chemically-controllable break\nmembrane approach for systematic evaluations of the ion transport in ultrasmall\npores.\nMain text (p13 line 325 – line 327)\n8\n(Revised)\nWhile the exact pore dimensions cannot yet be directly verified, the conductance\ndata are consistent with transport through channels approaching the sub-nanometer\nscale.\n2. Voltage as a direct control is questionable. While the manuscript emphasizes\nvoltage-controlled pore formation and closure, the underlying mechanism appears to be\npredominantly chemically driven (precipitation/dissolution of metal phosphates), with voltage\nserving mainly to drive ion migration and modulate reaction rates. The role of voltage is not\nas a direct \"control\" but as a facilitator of the chemical reactions. The title, abstract, and\nmain context may overstate the role of voltage. The authors should clarify that voltage is a\nmeans to manipulate the electrochemical conditions that lead to pore dynamics, rather than\na direct actuator of pore size.\n(Reply)\nWe appreciate the comment. We have carefully reviewed the manuscript and revised\nthe descriptions to clarify that the transmembrane voltage does not directly control the pore\nformation/closure processes, but rather serves as a probe to adjust the ionic flow conditions\nfor triggering the in-pore electrochemical reactions, as highlighted in blue\nAbstract\n(Revised)\nHere, we introduce a chemically controllable break-membrane approach that\nenables the repeated formation and closure of nanoscale pores in SiN\nx\nmembranes through manipulating the in-pore electrochemical reaction\nconditions by transmembrane voltage.\nMain text (p3 line 57 – 60)\n(Revised)\nThe in-pore reaction is induced by the ion flux under the transmembrane voltage V\nb\nwith the trans and cis compartments filled with 2 M MnCl and phosphate-buffered\n2\nsaline (PBS), respectively (Figure 1a, see also Supplementary Table 1).\nMain text (p4 line 91 – 93)\n(Revised)\nx\nover in-pore chemical reaction conditions, enabling the repeated formation of small\npores through the autonomous nanoelectrochemistry.29\n3. Limited discussion of alternative interpretations. The observed current spikes could also\nbe explained by transient electrochemical phenomena such as nucleation/dissolution waves,\ncapacitive charging, or ion concentration polarization. The authors should discuss these\nalternative mechanisms and justify why their interpretation (pore formation/closure) is more\nplausible.\n(Reply)\nThank you for the comment. We have added a paragraph discussing alternative\ninterpretations of the observed ionic current spiking behaviors, as shown below.\nMain text (p12 line 285 – p13 line 303)\n(Added)\nSeveral mechanisms could, in principle, contribute to the ionic current spiking\nbehavior. One possibility is that thin nanoprecipitate layers act as capacitors,\nintermittently charging and discharging under an applied voltage. Such processes,\nhowever, typically yield overshooting non-Faradaic current transients of biphasic\ncharacteristics,57 in contrast to the single, non-overshooting pulses observed here.\nAnother mechanism involves the so-called chemical reaction wave, a transient\nelectrochemical phenomenon in which nucleation and dissolution reactions induce\ntime-dependent morphological changes in a precipitated film on an electrode.58 Yet\nin the present measurement configuration, this pathway is unlikely to generate\nappreciable Faradaic currents unless a new ion-conducting channel is created\n(though it may contribute to the autonomous activity of the nanoprecipitated\nmembranes). Taken together, the most consistent interpretation is that the ionic\ncurrent spikes originate from the spontaneous opening and closing of nanoscale\npores in the precipitate layer, driven by the interplay of voltage-facilitated precipitation\nand dissolution reactions. Further efforts are expected to be devoted to explore how\nthe ultrasmall pores behave under strong salinity gradients and localized electric\nfields. Under such conditions, additional factors including counterion conduction,47\nconcentration polarization,59 permselectivity,51 and electroosmotic flow,52 alongside\nion dehydration,42 are expected to come into play. These effects may further enrich\nthe nonlinear ion transport dynamics and broaden the functional space of\nvoltage-gated chemically active nanopores.\n10\n4. pH dependence overshadows voltage dependence. The results in Fig. 6 clearly show that\npH is a more direct and reproducible control knob for pore size than voltage. This\nundermines the narrative of \"voltage-gated\" pores. The authors should reframe the overall\ndiscussion to highlight the chemical nature of the control mechanism, with voltage as a\nsupporting factor.\n(Reply)\nThank you for the comment. We have revised the manuscript to be more accurate on\nthe role of the transmembrane voltage, where we also added a paragraph to emphasize the\nchemistry-driven nature of the pore opening and closing mechanism, as shown below.\nMain text (p13 line 304 – line 315)\n(Added)\nThe ability to actuate the repetitive opening and closing of nanopores via in-pore\nchemistry, with transmembrane voltage as a facilitator, manifests the pivotal role of\nsolution composition in governing precipitation–dissolution dynamics of metal\nphosphates under nanoconfinement. Insufficient reactant concentration produces\nonly a partial precipitate, unable to fully seal the SiN nanopore. Conversely, excess\nx\nreactants accelerate precipitation kinetics, closing the channel more effectively and\nyielding smaller pores upon reopening. The solution pH similarly regulates\ndissolution rates: acidic conditions tend to reopen larger pores, while basic conditions\nyield smaller ones. Meanwhile, it is important to note that since the reactant\nconcentration can also shift the solution pH, these effects are mutually coupled, as\nobserved in the MnCl concentration dependence of the I spiking feature. As such,\n2 ion\nboth the frequency of pore piercing and the effective pore size can be tuned by\nmanipulating the degrees of freedom available in solution chemistry.\nReviewer #3\nThe authors carried out a revision of their manuscript where many comments were\nadequately addressed. However, there are several points which still require clarification as\nset out below：\n1. Chemical Reaction Process: When discussing MnCl2 concentration, the observed\nphenomenon (reduction or disappearance of spikes) is directly attributed to reduced\n“dissolution efficiency” due to pH changes. However, the decrease in MnCl2 concentration\nitself (not just the accompanying pH change) likely directly affects the chemical driving force\n(e.g., reactant concentration, ionic strength) of the precipitation/dissolution reaction at the\npore. The MnCl2 concentration and pH are two co-varying parameters. The experimental\ndesign (diluting MnCl2) simultaneously alters both factors. Conclusions should discuss the\nroles of both the concentration effect and the pH effect.\n(Reply)\nThank you for the comment. We have added a discussion regarding the contributions\nof pH and ionic reactant concentration, as follows.\nMain text (p13 line 304 – line 315)\n(Added)\nThe ability to actuate the repetitive opening and closing of nanopores via in-pore\nchemistry, with transmembrane voltage as a facilitator, manifests the pivotal role of\nsolution composition in governing precipitation–dissolution dynamics of metal\nphosphates under nanoconfinement. Insufficient reactant concentration produces\nonly a partial precipitate, unable to fully seal the SiN nanopore. Conversely, excess\nx\nreactants accelerate precipitation kinetics, closing the channel more effectively and\nyielding smaller pores upon reopening. The solution pH similarly regulates\ndissolution rates: acidic conditions tend to reopen larger pores, while basic conditions\nyield smaller ones. Meanwhile, it is important to note that since the reactant\nconcentration can also shift the solution pH, these effects are mutually coupled, as\nobserved in the MnCl concentration dependence of the I spiking feature. As such,\n2 ion\nboth the frequency of pore piercing and the effective pore size can be tuned by\nmanipulating the degrees of freedom available in solution chemistry.\n12\n2. Pore Reaction Stability: Regarding the issue mentioned: “While the exact mechanism\nremains unclear, one possible factor is a slow change in ion concentration due to liquid\nevaporation over the 10-hour measurement period,” can the impact of water evaporation on\nexperimental results be experimentally verified?\n(Reply)\nThank you for the comment. To examine the effect of water evaporation on long-term\nmeasurements of the ionic current versus transmembrane voltage characteristics, we newly\nconfigured an experimental setup. As shown in Supplementary Figure 1a–c, bottles of 10×\nPBS and 2 M MnCl₂ solutions were prepared, and holes were punched in the lids to insert\nplastic tubes connected to the PDMS cells attached to a nanopore chip. This setup\neffectively suppressed water evaporation and enabled stable ionic current measurements\nfor more than 12 hours. Over the course of more than two days of I –V measurements,\nion b\nthe nanopore conductance remained more stable compared to the case without evaporation\nsuppression (Figure 1c in the main text). Nevertheless, small fluctuations persisted,\nsuggesting a non-negligible role of residual precipitates formed on the nanopore wall during\nrepetitive voltage scans.\nThese results have been added to the Supplementary Information as Supplementary\nFigure 1. We have also revised the caption of Figure 1 in the main text to note the possible\ninfluence of residual precipitates on the observed fluctuations in the ionic current\ncharacteristics.\n(Added)\nSupplementary Figure 1. Long-term I -V measurements. a-b, Photograph of the setup used for\nion b\nlong-term ionic current measurements. PDMS cells were connected to reservoirs of PBS (1.37 M NaCl)\nand MnCl₂ (2 M) solutions through plastic tubing to suppress water evaporation during extended operation.\nc, Two-dimensional histogram constructed from 4,086 I –V curves recorded over more than two days\nion b\nusing the setup in (a). The white dashed line indicates 1.4 V. d, Ionic current at 1.4 V (I ) extracted from\n1.4\neach curve. d, Time course changes in I . Blue points correspond to data acquired without evaporation\n1.4\nsuppression (Figure 1c, main text), where measurements could only be sustained for <12 h. In contrast,\nthe red points show that the modified setup enabled measurements over much longer durations. The\nreduced conductance arises from the smaller nanopore diameter (70 nm) used in (c). Although\n5\nevaporation suppression stabilized I , small fluctuations persisted, likely reflecting subtle effects of\n1.4\nresidual precipitates on the pore wall during repeated voltage scans.\nFigure 1 caption\n(Added)\nThe variation in r is attributable to a change in the ion concentration due to water\nrec\nevaporation and residual precipitates remained undissolved on the pore wall surface\nduring the 10 hours of measurement.\n14"}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have addressed my comments well.", "reviewer_3": "Several comments have been adequately addressed. However, key claims remain supported by measurements in which co-varying variables are not disentangled. MnCl2 concentration and pH effects remain confounded, the quantitative linkage of spiking behavior and post-cycle conductance to both variables is incomplete."}, "author_response": "Chemistry-driven autonomous nanopore membranes\nMakusu Tsutsui, Wei-Lun Hsu, Denis Garoli, Ali Douaki, Yuki Komoto, Hirofumi Daiguji, and\nTomoji Kawai\nWe are grateful to both reviewers for their further evaluation of our manuscript. We have\nrevised the manuscript as detailed below.\n1. We have evaluated the MnCl concentration effects on the in-pore chemistry.\n(Added)\nWhen the pH was adjusted back to 4.2, lowering the MnCl concentration to 0.1 M\n2\nresulted in larger ionic spikes, indicative of pore opening driven by a reduced\nprecipitation rate under limited Mn2+ supply (Supplementary Figures 21-23). Further\ndilution of MnCl eventually caused rupture of the phosphate layer through\n2\ndissolution, marking the transition from self-oscillatory to fully open states.\nMain text (p11 line 276 – 278)\n(Added)\nSimilar behavior was observed with pH adjustment on the cis side, although\nexcessively acidic conditions led to membrane instability, limiting its utility for\ncontrolled operation (Supplementary Figures 45 and 46).\n(Added)\nSupplementary Figure 21. Ionic current–voltage characteristics of a 100 nm nanopore at varying\nMnCl2 concentrations in cis. a-g, Ionic current as a function of applied transmembrane voltage,\nrecorded with the trans chamber filled with PBS containing 1.37 M NaCl and the cis chamber containing\nMnCl2 solutions at concentrations of 2 M (a), 1 M (b), 0.5 M (c), 0.2 M (d), 0.1 M (e), 0.01 M (f), and 0.001 M\n(g). The cis-side pH was adjusted to 4.2. Red and blue traces correspond to voltage sweeps performed\nin the negative and positive directions, respectively.\n(Added)\nSupplementary Figure 22. Ionic current traces recorded with a 100 nm nanopore at varying MnCl2\nconcentrations in cis and PBS in trans. a-g, Ionic current as a function of time recorded with the trans\nchamber filled with PBS containing 1.37 M NaCl and the cis chamber containing MnCl2 solutions at\nconcentrations of 2 M (a), 1 M (b), 0.5 M (c), 0.2 M (d), 0.1 M (e), 0.01 M (f), and 0.001 M (g). The ionic\ncurrent in panel g exceeds the detection limit of 280 nA, reflecting rupture of the phosphate layer under\nextremely dilute MnCl2 conditions. All MnCl2 solutions were adjusted to pH 4.2 with HCl.\n(Added)\nSupplementary Figure 23. MnCl2 concentration dependence of ionic current spike heights and\nwidths. a-f, The height (Ip) and width (td) of the ionic current spikes detected for a 100 nm nanopore with\ncis and trans filled with different concentrations of MnCl2 and PBS containing 1.37 M NaCl, respectively.\npH at cis was adjusted to 4.2 with HCl. Concentrations of MnCl2 are 2 M (a), 1 M (b), 0.5 M (c), 0.2 M (d),\n0.1 M (e), and 0.01 M (f).\nSupplementary Figure 45\n(Added)\nSupplementary Figure 45. Instability of phosphate layers under acidic conditions on the cis side. a,\nIonic current–voltage characteristics of a 100 nm nanopore in a 2 M MnCl₂ and PBS system without pH\nadjustment. The pronounced rectification indicates sealing of the pore by a phosphate precipitate under\nnegative bias. b-c, When the cis-side pH was lowered to 3.7 (b) or 1.7 (c), the ionic current exhibited an\nabrupt rise in the negative voltage region, signifying rupture of the phosphate layer due to accelerated\ndissolution. Red and blue traces correspond to current recorded during positive and negative voltage\nsweeps, respectively.\n(Added)\nSupplementary Figure 46. Instability of phosphate layers under acidic conditions in cis. a, Ionic\ncurrent trace recorded from a 100 nm nanopore in a 2 M MnCl2 and PBS system with the cis-side pH\nadjusted to 3.7. The current rapidly increases beyond the detection limit of 280 nA, consistent with rupture\nof the phosphate layer. b, Expanded view of the initial segment of the measurement, revealing transient\nionic spikes that suggest repeated formation and closure of small pores prior to complete layer rupture.\nReviewer #3\nSeveral comments have been adequately addressed. However, key claims remain\nsupported by measurements in which co-varying variables are not disentangled. MnCl2\nconcentration and pH effects remain confounded, the quantitative linkage of spiking\nbehavior and post-cycle conductance to both variables is incomplete.\n(Reply)\nThank you for the comment. We performed additional measurements in which the pH of\nthe diluted MnCl solutions was adjusted to 4.2. Under these conditions, the ionic current\n2\nspiking behavior remained robust, showing no suppression attributable to pH control. The\nmeasurements also revealed larger ionic signals at lower MnCl concentrations, consistent\n2\nwith reduced precipitation rates that permit the formation of larger pores. Further dilution\nresulted in instability of the phosphate layer, which frequently ruptured during the\nmeasurements. These overall features are fully consistent with the trends observed when\nvarying the anion reactants on the trans side.\nWe have added the above results in the main text and Supporting Information as\nfollows.\nMain text (p10 line 249 – 253)\n(Added)\nWhen the pH was adjusted back to 4.2, lowering the MnCl concentration to 0.1 M\n2\nresulted in larger ionic spikes, indicative of pore opening driven by a reduced\nprecipitation rate under limited Mn2+ supply (Supplementary Figures 21-23). Further\ndilution of MnCl eventually caused rupture of the phosphate layer through\n2\ndissolution, marking the transition from self-oscillatory to fully open states.\nMain text (p11 line 276 – 278)\n(Added)\nSimilar behavior was observed with pH adjustment on the cis side, although\nexcessively acidic conditions led to membrane instability, limiting its utility for\ncontrolled operation (Supplementary Figures 45 and 46).\n(Added)\nSupplementary Figure 21. Ionic current–voltage characteristics of a 100 nm nanopore at varying\nMnCl2 concentrations in cis. a-g, Ionic current as a function of applied transmembrane voltage,\nrecorded with the trans chamber filled with PBS containing 1.37 M NaCl and the cis chamber containing\nMnCl2 solutions at concentrations of 2 M (a), 1 M (b), 0.5 M (c), 0.2 M (d), 0.1 M (e), 0.01 M (f), and 0.001 M\n(g). The cis-side pH was adjusted to 4.2. Red and blue traces correspond to voltage sweeps performed\nin the negative and positive directions, respectively.\n(Added)\nSupplementary Figure 22. Ionic current traces recorded with a 100 nm nanopore at varying MnCl2\nconcentrations in cis and PBS in trans. a-g, Ionic current as a function of time recorded with the trans\nchamber filled with PBS containing 1.37 M NaCl and the cis chamber containing MnCl2 solutions at\nconcentrations of 2 M (a), 1 M (b), 0.5 M (c), 0.2 M (d), 0.1 M (e), 0.01 M (f), and 0.001 M (g). The ionic\ncurrent in panel g exceeds the detection limit of 280 nA, reflecting rupture of the phosphate layer under\nextremely dilute MnCl2 conditions. All MnCl2 solutions were adjusted to pH 4.2 with HCl.\n(Added)\nSupplementary Figure 23. MnCl2 concentration dependence of ionic current spike heights and\nwidths. a-f, The height (Ip) and width (td) of the ionic current spikes detected for a 100 nm nanopore with\ncis and trans filled with different concentrations of MnCl2 and PBS containing 1.37 M NaCl, respectively.\npH at cis was adjusted to 4.2 with HCl. Concentrations of MnCl2 are 2 M (a), 1 M (b), 0.5 M (c), 0.2 M (d),\n0.1 M (e), and 0.01 M (f).\nSupplementary Figure 45\n(Added)\nSupplementary Figure 45. Instability of phosphate layers under acidic conditions on the cis side. a,\nIonic current–voltage characteristics of a 100 nm nanopore in a 2 M MnCl₂ and PBS system without pH\nadjustment. The pronounced rectification indicates sealing of the pore by a phosphate precipitate under\nnegative bias. b-c, When the cis-side pH was lowered to 3.7 (b) or 1.7 (c), the ionic current exhibited an\nabrupt rise in the negative voltage region, signifying rupture of the phosphate layer due to accelerated\ndissolution. Red and blue traces correspond to current recorded during positive and negative voltage\nsweeps, respectively.\n(Added)\nSupplementary Figure 46. Instability of phosphate layers under acidic conditions in cis. a, Ionic\ncurrent trace recorded from a 100 nm nanopore in a 2 M MnCl2 and PBS system with the cis-side pH\nadjusted to 3.7. The current rapidly increases beyond the detection limit of 280 nA, consistent with rupture\nof the phosphate layer. b, Expanded view of the initial segment of the measurement, revealing transient\nionic spikes that suggest repeated formation and closure of small pores prior to complete layer rupture.\n11"}]

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