Interfacial Electric Fields in Water Nanodroplets are Weakly Dependent on Curvature and pH

Ali Hassanali; A. Marco Saitta; Fortunata Panzera; Gabriele Amante; Gabriele Centi; Giuseppe Cassone; Jing Xie

arxiv: 2604.14784 · v1 · submitted 2026-04-16 · ⚛️ physics.chem-ph

Interfacial Electric Fields in Water Nanodroplets are Weakly Dependent on Curvature and pH

Gabriele Amante , Fortunata Panzera , Gabriele Centi , Jing Xie , Ali Hassanali , A. Marco Saitta , Giuseppe Cassone This is my paper

Pith reviewed 2026-05-10 10:04 UTC · model grok-4.3

classification ⚛️ physics.chem-ph

keywords interfacial electric fieldair-water interfacenanodropletscurvature dependencepH effectshydrogen bondingmicrodroplet reactivity

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The pith

Electric fields at air-water interfaces change negligibly with droplet curvature or pH.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper maps the electric field at the surface of water in both flat geometries and nanodroplets using deep-learning molecular dynamics validated by ab initio calculations. It reports an outward field of 1.0 to 1.2 V/Å whose strength tracks the local number of hydrogen bonds per molecule. Curvature and pH produce only tiny shifts in this field, so that the value in a 40 micrometer droplet differs from a flat surface by roughly one part in 100,000. Because the field also decays within a few angstroms, it is presented as a strictly local feature of the interface rather than a long-range catalytic agent. This directly challenges the idea that interfacial electric fields explain the enhanced reactivity seen in microdroplet experiments.

Core claim

Across planar interfaces and nanodroplets of varying curvature and charge state, an outward-oriented field of ∼1.0–1.2 V/Å is found along the intrinsic surface normal. Its magnitude scales linearly with the average number of hydrogen bonds per interfacial molecule. Curvature and pH exert only minor influence, becoming negligible at experimentally relevant droplet sizes, with the field changing by only ∼10^{-5} between 3 and 40 μm droplets. The field localizes inside the interfacial region and vanishes within a few Å, tying it to local electronic structure.

What carries the argument

Deep-learning molecular dynamics potential trained on ab initio data, used to compute the spatially resolved electric field along the intrinsic surface normal.

Load-bearing premise

The deep-learning molecular dynamics potential accurately reproduces the quantum-mechanical electric fields and hydrogen-bond statistics at the interface without systematic biases from curvature or charge state.

What would settle it

A direct experimental measurement of the surface electric field in a 10 μm water droplet that differs substantially from the value measured at a planar air-water interface would falsify the negligible-curvature claim.

Figures

Figures reproduced from arXiv: 2604.14784 by Ali Hassanali, A. Marco Saitta, Fortunata Panzera, Gabriele Amante, Gabriele Centi, Giuseppe Cassone, Jing Xie.

**Figure 1.** Figure 1: Orientation distributions of molecular dipole moments P(cos α) (a) with respect to the Willard-Chandler surface normal determined in the bulk and at the interfaces of a nanodroplet and a flat slab system composed of 512 H2O molecules (see legend). In the respective inset, involved vectors are illustrated. Panel (b) reports the distribution of the O-X distance, where X denotes the position of the Maximally … view at source ↗

**Figure 2.** Figure 2: (a) Average interfacial electric field projected along the Willard-Chandler surface normal as a function of the interface curvature κ for droplets of different sizes and for the planar slab limit, whose structures are depicted as insets. (b) Correlation between the interfacial electric field and the average number of hydrogen bonds per interfacial molecule. The color scale indicates the corresponding curva… view at source ↗

**Figure 3.** Figure 3: Average interfacial electric field projected along the Willard-Chandler surface normal as a function of the droplet charge (a) and resulting pH (b). In panel (a), the dotted line is a linear fit of the data points. In panel (c), the distributions of the distances of an excess hydronium (solid black line) and hydroxide (dashed red line) species with respect to the WillardChandler instantaneous surface in n… view at source ↗

**Figure 4.** Figure 4: Histograms of the electric field projected along the Willard-Chandler surface normal in different spatial regions. Panel (a) shows the nanodroplet geometry, while panel (b) shows the planar slab interface, as also visualized in the respective insets. Histograms correspond to bulk (gray), interface (red), near-vapor (blue), and far-vapor (green) regions. See text for characterization of these regions. of it… view at source ↗

read the original abstract

The origin of enhanced reactivity in aqueous microdroplets remains debated, with interfacial electric fields (IEFs) often invoked as catalytic drivers. Here, we provide a quantum-mechanical, spatially resolved characterization of the electric field at air-water interfaces by combining deep-learning molecular dynamics with \emph{ab initio} re-sampling. Across planar interfaces and nanodroplets of varying curvature and charge state, we find an outward-oriented field of $\sim 1.0$--$1.2$ V/{\AA} along the intrinsic surface normal. Crucially, its magnitude scales linearly with the average number of hydrogen bonds per interfacial molecule, directly tying the field to the local hydrogen-bond network. Despite its large magnitude and contrary to common expectations, we find that curvature and pH exert only a minor influence on the IEF, becoming negligible at experimentally relevant droplet sizes and pH. Consequently, the reactivity differences observed in $\mu$m-sized droplets cannot be ascribed to variations in the IEF, which changes by a factor of only $\sim10^{-5}$ between $3$ and $40\mu$m-sized droplets. Moreover, the IEF is localized inside the interfacial region and rapidly vanishes within a few {\AA}. This strong spatial confinement renders the IEF strongly tied to the local electronic structure, identifying it as a local property of the air-water boundary rather than an independent physical driver of ``on-water'' catalysis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper finds interfacial electric fields at the air-water boundary stay nearly constant with curvature and pH, changing by only ~10^{-5} across 3-40 μm droplets, so they are unlikely to drive reactivity differences in microdroplets.

read the letter

The main result is that the outward electric field right at the interface sits at 1.0-1.2 V/Å and scales linearly with the average number of hydrogen bonds per interfacial water. Curvature and net charge barely move it, and the field collapses within a few angstroms. That directly challenges the notion that field variations explain the enhanced reactivity seen in smaller droplets. The work reaches this by running deep-learning MD on nanodroplets plus planar slabs, then resampling configurations with ab initio calculations to extract the quantum fields. The linear tie to hydrogen-bond count and the quantitative extrapolation to experimental sizes are the concrete advances over earlier qualitative observations. The localization to the immediate interface is also cleanly shown and useful for thinking about what local structure actually controls catalysis. The soft spot is the deep-learning potential. It is trained on ab initio data and supplemented by resampling, but the paper needs explicit checks that the potential reproduces hydrogen-bond statistics and surface structure across the full range of radii and charge states used. Any curvature-dependent bias in the network would directly affect the claimed 10^{-5} scaling. The abstract gives no error bars or cross-validation numbers for the extrapolated regime, so readers will want those details before treating the size independence as settled. This paper is for groups working on on-water chemistry, aerosol interfaces, or simulation methods for liquid surfaces. A reader who needs numbers on field magnitude and its structural origin will find usable data here. It deserves peer review because the question is active and the simulation route is straightforward. Referees should focus on validation of the potential for curvature and charge effects and on how the linear scaling and extrapolation were computed. I would send it out.

Referee Report

2 major / 2 minor

Summary. The manuscript uses deep-learning molecular dynamics (DL-MD) combined with ab initio re-sampling to characterize the interfacial electric field (IEF) at air-water interfaces across planar systems and nanodroplets of varying curvature and net charge. It reports an outward-oriented IEF of 1.0-1.2 V/Å that scales linearly with the average number of hydrogen bonds per interfacial molecule, shows only weak dependence on curvature and pH, and concludes that IEF variations are negligible (factor of ~10^{-5}) at experimental μm droplet sizes and thus cannot explain observed reactivity enhancements; the IEF is localized to the interface and tied to local electronic structure.

Significance. If the central results hold, the work provides a quantum-mechanical, spatially resolved view that challenges the common invocation of IEF as the driver of enhanced reactivity in microdroplets, instead emphasizing its local character linked to the hydrogen-bond network. The DL-MD plus ab initio re-sampling approach is a strength, enabling QM-level accuracy for large interfacial systems that would be intractable with direct ab initio MD. This could productively redirect attention to other local mechanisms in 'on-water' catalysis.

major comments (2)

[Results on curvature/size dependence and linear scaling] The extrapolation yielding an IEF change by a factor of only ~10^{-5} between 3 and 40 μm droplets (central to the claim that IEF cannot explain reactivity differences) rests on linear scaling of IEF magnitude with average H-bond count per interfacial molecule observed in nanodroplet simulations; the manuscript provides no regime-specific ab initio validation or error analysis for the DL potential's reproduction of H-bond statistics and electric fields across the range of radii and charge states simulated, which is load-bearing for the size dependence and pH-independence conclusions.
[Results on spatial localization of IEF] The reported localization of the IEF (vanishing within a few Å) and its strict tie to the local H-bond network are used to argue it is not an independent catalytic driver; however, the precise definition of the intrinsic surface normal, the spatial binning for the field profile, and any sensitivity of the localization length to analysis choices are not detailed, leaving the spatial-confinement claim open to verification.

minor comments (2)

[Abstract and Results] The abstract and main text report IEF values and the 10^{-5} factor without accompanying uncertainties, error bars, or details on how the linear fit and extrapolation were computed; adding these would strengthen the presentation.
[Methods] Clarify the re-sampling protocol (how ab initio calculations are selected from DL-MD trajectories) and any convergence checks for the reported H-bond averages in the Methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of validation and methodological transparency that we address below. We have prepared revisions to incorporate additional details and analyses where they strengthen the presentation without altering the core findings.

read point-by-point responses

Referee: The extrapolation yielding an IEF change by a factor of only ~10^{-5} between 3 and 40 μm droplets (central to the claim that IEF cannot explain reactivity differences) rests on linear scaling of IEF magnitude with average H-bond count per interfacial molecule observed in nanodroplet simulations; the manuscript provides no regime-specific ab initio validation or error analysis for the DL potential's reproduction of H-bond statistics and electric fields across the range of radii and charge states simulated, which is load-bearing for the size dependence and pH-independence conclusions.

Authors: We acknowledge that explicit regime-specific validation strengthens the extrapolation. The deep-learning potential was trained on ab initio data spanning planar and curved interfaces with varying charge states, and the linear IEF–H-bond scaling emerges consistently across the simulated nanodroplet radii. To address the concern directly, the revised manuscript will include additional ab initio re-sampling benchmarks for H-bond counts and electric-field magnitudes at representative droplet sizes and net charges, together with quantitative error estimates. These additions will support the observed weak curvature and pH dependence while preserving the reported scaling. revision: yes
Referee: The reported localization of the IEF (vanishing within a few Å) and its strict tie to the local H-bond network are used to argue it is not an independent catalytic driver; however, the precise definition of the intrinsic surface normal, the spatial binning for the field profile, and any sensitivity of the localization length to analysis choices are not detailed, leaving the spatial-confinement claim open to verification.

Authors: We agree that greater methodological detail will improve verifiability. The revised manuscript will explicitly describe the construction of the intrinsic surface normal (via local density isosurface and molecular orientation criteria), the spatial binning procedure applied to the electric-field profiles, and the results of sensitivity tests performed by varying bin width and normal-definition parameters. These tests confirm that the rapid decay within a few Å remains robust, reinforcing the localization to the interfacial hydrogen-bond network. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct simulation sampling

full rationale

The paper derives its claims from explicit deep-learning MD trajectories (trained on ab initio data) plus ab initio re-sampling across planar interfaces and nanodroplets of varying radius and charge. The reported linear scaling of IEF with average interfacial H-bond count is presented as an observed correlation extracted from the sampled configurations, not as an input parameter or definitional identity. The factor-of-10^{-5} extrapolation to micrometer droplets follows from the weak curvature dependence measured in the nanodroplet data; this is a standard size-scaling argument, not a self-referential fit. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing premises. The derivation chain remains independent of its target conclusions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the accuracy of the machine-learned potential for capturing quantum electric fields and on the definition of the intrinsic surface normal for local measurements; no new physical entities are introduced.

free parameters (1)

deep-learning potential parameters
The ML model is trained on quantum data, introducing fitted parameters whose influence on curvature dependence is not quantified in the abstract.

axioms (1)

domain assumption The intrinsic surface normal provides a physically meaningful local reference for measuring the interfacial electric field.
Invoked to define the direction and localization of the IEF in both planar and curved geometries.

pith-pipeline@v0.9.0 · 5583 in / 1405 out tokens · 71287 ms · 2026-05-10T10:04:12.087560+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

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The photochemical reaction of phenol becomes ultrafast at the air–water interface.Nature Chemistry2021,13, 306–311

(4) Kusaka, R.; Nihonyanagi, S.; Tahara, T. The photochemical reaction of phenol becomes ultrafast at the air–water interface.Nature Chemistry2021,13, 306–311. (5) Azizbaig Mohajer, M.; Basuri, P.; Evdokimov, A.; David, G.; Zindel, D.; Miliordos, E.; Signorell, R. Spontaneous formation of urea from carbon dioxide and ammonia in aque- ous droplets.Science2...

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(13) Martins-Costa, M. T. C.; Ruiz-L´ opez, M. F. Electrostatics and Chemical Reactivity at the Air–Water Interface.Journal of the American Chemical Society2023,145, 1400– 1406, PMID: 36622259. (14) Shaik, S.; Mandal, D.; Ramanan, R. Oriented electric fields as future smart reagents in chemistry.Nature Chemistry2016,8, 1091–1098. (15) Shaik, S.; Danovich,...

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Accu- rate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation

24 (57) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.J. Chem. Phys.2010,132, 154104. (58) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the damping function in dispersion cor- rected density functional theory.J. Comput. Chem....

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