REVIEW 3 major objections 4 minor 29 references
Perfect proton selectivity in ion transport through two-dimensional crystals
T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash
Pith's one-line read Defect-free monolayers of graphene and hexagonal boron nitride let protons through while blocking chloride ions completely, according to membrane-potential measurements that fit the ideal Nernst value.
desk verdict Solid experimental resolution of a real controversy, with a well-targeted caveat: the 'perfect' selectivity claim slightly outruns the defect characterization, but the core result stands. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the Nernst membrane-potential relation connecting the reversal voltage $V_0$ to the two ion transport numbers $t_H$ and $t_{Cl}$: $V_0 = (t_{Cl} - t_H)(k_BT/e)\ln(\Delta C)$. Measuring $V_0$ for known concentration ratios directly gives the fraction of current carried by protons, because any chloride contribution would shift $V_0$ toward zero. The experiments combine this electrochemical probe with nanoballoon gas-leak tests, which can detect even a single angstrom-sized vacancy by watching whether a sealed gas-filled cavity deflates; only membranes that showed no leakage in those tests were used for the ion-transport measurements.
What would settle it
Deliberately etch a single known vacancy into one of these exfoliated membranes using the same ultraviolet treatment used in the nanoballoon controls and re-measure the reversal potential: the fitted $t_H$ should drop measurably below 1 and $V_0$ should move toward zero if defects are what control ion transport. Alternatively, place an isotopically labelled chloride tracer ($^{36}\mathrm{Cl}^-$) in the high-concentration compartment and look for its appearance on the low-concentration side; any detected chloride through a pristine membrane would directly falsify perfect proton selectivity.
Extended reading notes
Core claim
The central discovery is that mechanically exfoliated, essentially defect-free graphene and hBN membranes exhibit perfect Nernst selectivity for protons. When the two sides of the membrane are filled with HCl at different concentrations, the zero-current voltage follows $V_0 = -(2t_H - 1)(k_BT/e)\ln(\Delta C)$ with $t_H \approx 1$; for $\Delta C = 10$ the measured $V_0$ is $-58$ mV at $20^\circ$C, and over $\Delta C = 1$ to 30 the best fit is $t_H = 0.99 \pm 0.02$. Protons therefore account for all ionic current through the membrane while chloride is blocked. The same behavior appears in graphene, with $V_0 = -55 \pm 9$ mV. Because the crystals passed nanoballoon gas-leak tests sensitive to single vacancies, the authors conclude the selectivity is a property of the pristine lattice, not of defects, and that the much larger currents and weak selectivity reported for CVD graphene reflect defect-dominated transport.
Load-bearing premise
The conclusion rests on the assumption that the exact crystals used in the ion-transport measurements were as defect-free as the separately made nanoballoon devices; if any measured membrane contained an unseen vacancy or crack, chloride could pass through it and the perfect selectivity would not reflect the pristine lattice.
Editorial extensions
If this is right
- A pristine monolayer of hBN or graphene can act as a proton-only membrane, excluding every other ion, which is the defining behavior of an ideal proton-exchange membrane.
- The result corroborates the earlier claim that thermal protons pierce defect-free 2D crystals and removes the vacancy-based alternative explanation for those experiments.
- The conductance of exfoliated crystals is nearly three orders of magnitude below that reported for CVD graphene, so CVD membranes are not representative of intrinsic 2D-crystal ion transport.
- In nanoporous 2D separation membranes, the proton permeability of the bulk crystal itself contributes to ion current and must be included when designing for selectivity.
- The ideal Nernst reversal potential doubles as a quality assay: a membrane that gives $V_0 = -58$ mV at a tenfold gradient is behaving as a defect-free proton conductor.
Reading between the lines
- If the pristine lattice truly blocks every ion except protons, then replacing HCl with other acids or salts should change the picture sharply: sulfuric and nitric acids should give the same ideal reversal potential, while salts without a proton gradient should produce no current.
- The fact that chloride, with its small hydrated diameter, is rejected suggests the selectivity works on bare protons rather than hydrated-ion size, so the same membranes should also block larger alkali and halide ions in electrochemical applications.
- A practical extension the authors leave implicit: a large-area, defect-free hBN or graphene layer could serve as a proton-selective barrier that prevents anion crossover in fuel cells or electrolysers, if the required crystal quality can be scaled.
- Reversal-potential measurements could become a quantitative in-situ probe for atomic-scale damage in 2D membranes, sensitive enough to complement nanoballoon gas tests.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports ion-transport measurements through mechanically exfoliated monolayer graphene and hexagonal boron nitride (hBN) membranes separating hydrochloric acid solutions of different concentrations. The authors measure areal conductivities at various HCl concentrations, and for concentration ratios ΔC from 1 to 30 they record the zero-current (reversal) potential V0. For ΔC = 10 they find V0 ≈ −58 mV independent of the absolute concentrations, which matches the Nernst prediction for a membrane with proton transport number tH = 1. A fit to the data gives tH = 0.99 ± 0.02 for hBN, and graphene yields −55 ± 9 mV. Porous-glass control experiments give tH = 0.81 ± 0.04, in agreement with bulk HCl transport numbers. The paper concludes that exfoliated, defect-free 2D crystals exhibit 'perfect' Nernst selectivity, with protons accounting for all ionic current and chloride ions blocked, corroborating earlier claims of intrinsic proton permeation through such crystals.
Significance. If the strong claim holds, this is an important result: it would establish that mechanically exfoliated monolayer graphene and hBN can act as nearly ideal proton-selective membranes, with direct implications for theories of proton permeation through 2D crystals and for separation technologies. The experimental approach is clean: the Nernst prediction for tH = 1 is parameter-free, the porous glass control independently calibrates the setup, bare-aperture devices show that series resistance is negligible, and leakage currents are reported. The comparison with CVD graphene results is also valuable. However, the 'perfect' selectivity claim is stronger than the precision of the transport-number fit, and the inference that the specific measured crystals were defect-free rests on indirect evidence, so the significance as stated is not yet fully established.
major comments (3)
- [Supplementary 'Leak tests using nanoballoons'; Device fabrication and electrical measurements] The claim that the transport membranes are defect-free relies on nanoballoon gas-leak tests that were performed on sibling devices, not on the exact crystals used for the ion-transport measurements. The Supplementary leak-test section describes sealing microcavities with monolayer graphene only, yet the main text states that hBN and graphene membranes were tested; the monolayer hBN devices that yield the quantitative tH = 0.99 result are not individually leak-tested. In addition, the transport devices underwent SU-8 washer transfer and a 150 °C bake after exfoliation, a process not included in the nanoballoon protocol and one that could introduce damage. Because a small chloride-conducting defect would still allow a reversal potential close to −58 mV, the conclusion that pristine, defect-free crystals block chloride ions is not established for the specific measured membranes.
- [Fig. 2b and Eq. (1)] The wording 'perfect Nernst selectivity' and 'no detectable flow of counterions' exceeds the measurement precision. The best fit tH = 0.99 ± 0.02 gives tCl ≤ 0.02 within uncertainty, and the experiment does not directly detect chloride flux; it only determines the reversal potential. The claim should be softened to 'near-perfect selectivity' or 'selectivity consistent with tH = 1 within experimental accuracy' in the title, abstract, and conclusion.
- [Fig. 2b, Nernst equation] The Nernst potential is evaluated using concentration ratios ΔC rather than ion activities. For HCl concentrations up to 3 M, the mean ionic activity coefficient varies substantially with concentration, so the relation V0 = −(kBT/e)ln(ΔC) is an approximation. Please state whether activity corrections were applied, and if not, discuss how the extracted transport number and the presented comparison V0 ≈ −58 mV for 0.3 M | 3 M are affected.
minor comments (4)
- [Abstract and introduction] The abstract says defect-free monolayers were 'previously shown' to be proton-permeable, while the main text describes the membranes as having 'few if any atomic-scale defects'; please make the defect-characterization language consistent.
- [Supplementary Figure 4] The Supplementary figure title reads 'Supplementary Figure 4I Leak tests using nanoballoons'; the 'I' appears to be a typo for the vertical bar separator.
- [Fig. 2b] Please report the number of independent devices and measurements underlying each data point in Fig. 2b, and indicate whether the error bars represent device-to-device or measurement-to-measurement scatter.
- [Supplementary 'Membrane potential measurements'] The subtraction of the Ag/AgCl redox potential is described qualitatively; please provide the numerical value used for Vredox and the measured Vcell values for a representative device.
Circularity Check
No significant circularity: reversal potentials are compared against an external Nernst relation, and the fitted proton transport number is an outcome, not an input.
full rationale
The paper's key comparison is Eq. (1), V0 = (tCl – tH)(kBT/e)ln(ΔC), an external textbook Nernst relation. For ΔC=10, the predicted V0 for tH=1 is -(kBT/e)ln10 ≈ -58 mV, and the measured I-V curves intersect the x-axis at V0 ≈ -58 mV. Fitting Eq. (1) to the data yields tH = 0.99 ± 0.02; this fitted transport number is the reported result, not a parameter recycled into the prediction. The porous-glass control gives tH = 0.81 ± 0.04, in agreement with literature values for bulk HCl, independently validating the measurement setup. The defect-free status of the membranes is inferred from external nanoballoon techniques (refs 15–17) and sibling-device tests; while this is an evidence extrapolation and a possible correctness limitation, it is not a circular reduction. Refs 1 and 2 are prior work with overlapping authors, but they are used only for context and for comparing relative conductivities; the central selectivity claim rests on the measured membrane potentials and the external Nernst equation. No equation in the derivation is equivalent to its input by construction, and no fitted parameter is renamed as a prediction.
Assumptions & free parameters
free parameters (1)
- proton transport number tH =
0.99 ± 0.02
assumptions (4)
- domain assumption Nernst equation relating membrane potential to transport numbers (Eq. 1)
- domain assumption Ionic current through the membrane is the only significant current path
- domain assumption Similarity of defect density between nanoballoon-tested and transport membranes
- domain assumption Ideal solution behavior: activities replaced by concentrations
Cite this review
Pith. "Pith review of Perfect proton selectivity in ion transport through two-dimensional crystals." pith.science (2026). https://pith.science/paper/4OJNKVSL
@misc{pith2026190807852,
author = {Pith},
title = {Pith review of: Perfect proton selectivity in ion transport through two-dimensional crystals},
year = {2026},
howpublished = {\url{https://pith.science/paper/4OJNKVSL}},
note = {Machine review of arXiv:1908.07852}
}
read the original abstract
Defect-free monolayers of graphene and hexagonal boron nitride were previously shown to be surprisingly permeable to thermal protons, despite being completely impenetrable to all gases. It remains untested whether small ions can permeate through the two-dimensional crystals. Here we show that mechanically exfoliated graphene and hexagonal boron nitride exhibit perfect Nernst selectivity such that only protons can permeate through, with no detectable flow of counterions. In the experiments, we used suspended monolayers that had few if any atomic-scale defects, as shown by gas permeation tests, and placed them to separate reservoirs filled with hydrochloric acid solutions. Protons accounted for all the electrical current and chloride ions were blocked. This result corroborates the previous conclusion that thermal protons can pierce defect-free two-dimensional crystals. Besides importance for theoretical developments, our results are also of interest for research on various separation technologies based on two-dimensional materials.
Reference graph
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Reviewed August 14, 2026 · model on record in the stance chip above.
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