Unambiguous characterization of in-plane dielectric response in nanoconfined liquids: water as a case study

Jon Zubeltzu

arxiv: 2604.00700 · v3 · submitted 2026-04-01 · ❄️ cond-mat.soft · cond-mat.mes-hall

Unambiguous characterization of in-plane dielectric response in nanoconfined liquids: water as a case study

Jon Zubeltzu This is my paper

Pith reviewed 2026-05-13 22:13 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mes-hall

keywords nanoconfined waterin-plane dielectric response2D polarizabilitymolecular dynamicsfluctuation-dissipation theorycapacitor methoddielectric properties

0 comments

The pith

The in-plane dielectric response of nanoconfined water is unambiguously characterized by a 2D polarizability independent of water width.

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

The paper proposes the in-plane 2D polarizability as a clear measure of how water responds to electric fields parallel to the plane when squeezed into thin layers. Conventional dielectric constants vary with the arbitrary thickness assigned to the water slab, making comparisons unreliable. Two separate calculation routes from molecular dynamics simulations, one from fluctuation theory and one from capacitor-induced dipoles, produce matching values that stay constant across different width choices. This matters for any situation where water sits between surfaces, such as in membranes or devices, because it supplies a stable number that experiments and simulations can both use.

Core claim

We propose the in-plane 2D polarizability, α_parallel, as an unambiguous characterization of the in-plane dielectric response under 2D confinement, in analogy to what has been recently done for the perpendicular response. Using classical molecular dynamics simulations, we compute α_parallel via two independent and consistent methods: based on fluctuation-dissipation theory, and from the induced dipole moment when water is placed in a capacitor. Our results provide the framework to quantify the in-plane dielectric response of polar liquids across simulations and experiments.

What carries the argument

The in-plane 2D polarizability α_parallel, which quantifies the dielectric response to fields parallel to the confinement plane without depending on any chosen water slab thickness.

If this is right

Polar liquids under 2D confinement now have a width-independent metric for their in-plane dielectric response.
Results obtained in different simulations or experiments can be compared on the same footing.
The same logic already applied to the perpendicular response now extends symmetrically to the in-plane direction.
The approach supplies a practical route to report dielectric data for any nanoconfined polar liquid.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The measure could be tested on electrolytes or other solvents inside nanopores to check whether it remains useful beyond pure water.
Experimental groups might begin reporting 2D polarizabilities rather than conventional constants to avoid width ambiguities.
Models of ion transport or capacitance in confined geometries could incorporate α_parallel directly to improve predictions.

Load-bearing premise

The two calculation methods produce the same α_parallel value and this value stays unchanged when the water width definition is varied in every confinement regime.

What would settle it

A molecular dynamics run in which the fluctuation-dissipation and capacitor methods return different α_parallel numbers, or in which α_parallel shifts when the water width is redefined, would show the characterization is not unambiguous.

Figures

Figures reproduced from arXiv: 2604.00700 by Jon Zubeltzu.

**Figure 2.** Figure 2: shows the resulting values. We find that convergence is already achieved for L∥ = 37.5 ˚A, yielding an estimate of α PBCy,fluc ∥ ∼ 620 ˚A ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Capacitor-based estimates of the in-plane 2D polarizability, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Induced charge on the gold atom rows of the pos [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Perpendicular 2D polarizability, [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

The in-plane dielectric constant of nanoconfined water has attracted growing interest over the last years. Nevertheless, this magnitude is not well-defined at the nanoscale due to its dependence on the arbitrary choice of water width. We propose the in-plane 2D polarizability, $\alpha_{\parallel}$, as an unambiguous characterization of the in-plane dielectric response under 2D confinement, in analogy to what has been recently done for the perpendicular response. Using classical molecular dynamics simulations, we compute $\alpha_{\parallel}$ via two independent and consistent methods: based on fluctuation--dissipation theory, and from the induced dipole moment when water is placed in a capacitor. Our results provide the framework to quantify the in-plane dielectric response of polar liquids across simulations and experiments.

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 defines a width-independent in-plane 2D polarizability α_parallel for nanoconfined water via two consistent methods, but the independence from slab choice is asserted rather than fully demonstrated across regimes.

read the letter

The main point is that Zubeltzu proposes α_parallel as a 2D polarizability that sidesteps the arbitrary water-slab width problem in the usual in-plane dielectric constant. He computes it from polarization fluctuations and from the induced dipole in a capacitor setup, and the two routes agree. That agreement is the concrete evidence offered for the claim that this quantity gives an unambiguous characterization under 2D confinement, extending the perpendicular analog that appeared recently. The approach is straightforward and the protocols are spelled out enough to be usable in other simulations of polar liquids. The central advantage is practical: it should let people report numbers that can be compared directly between different groups and with experiment without first arguing over where the water layer ends. The soft spot is exactly the one the stress-test flags. The abstract states that α_parallel is independent of the chosen width, yet it does not show recomputations for alternate density cutoffs or integration limits, especially in the strongly confined cases where the density profile is most inhomogeneous. If those checks are missing or weak in the full manuscript, the unambiguity claim rests on the two-method consistency alone rather than on direct proof of width invariance. No circular fitting or hidden parameters appear. The work is for people who already run molecular dynamics of confined water or similar liquids and need a cleaner way to quote in-plane response. A reader in that niche will find the framework immediately applicable. It is worth sending to peer review so the width-independence tests can be examined in detail and, if needed, strengthened.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that the in-plane dielectric constant of nanoconfined water is ill-defined because it depends on the arbitrary choice of water slab width. It proposes the in-plane 2D polarizability α_parallel as an unambiguous alternative characterization of the in-plane dielectric response under 2D confinement, in direct analogy to recent treatments of the perpendicular response. Using classical molecular dynamics, α_parallel is computed via two independent routes—fluctuation-dissipation theory applied to polarization fluctuations and the induced dipole moment when the confined water is placed inside a capacitor—and the two routes are reported to give consistent numerical values, thereby supplying a practical framework for quantifying in-plane dielectric response across simulations and experiments.

Significance. If the width-independence of α_parallel is rigorously established, the work supplies a useful, physically grounded quantity that removes an arbitrary parameter from the description of confined polar liquids. The explicit use of two independent computational routes is a methodological strength that enhances credibility. The framework could be adopted in nanofluidics, electrochemistry, and membrane studies where in-plane dielectric properties matter.

major comments (2)

[Abstract] Abstract: the central claim that α_parallel is unambiguous rests on its independence from the arbitrary water width. The abstract asserts consistency between the fluctuation-dissipation and capacitor routes but supplies no data on recomputation of α_parallel for alternate slab boundaries (different density cutoffs or integration limits) in the strongly confined regime where the density profile is highly inhomogeneous. Without such tests the claimed advantage over the conventional dielectric constant is not demonstrated.
[Results] Results section (presumed): the manuscript must show explicit numerical checks that α_parallel remains constant when the slab width is varied by ±0.5 Å or by changing the density threshold used to define the water region. If these checks are absent or limited to a single width, the load-bearing assertion of unambiguity fails.

minor comments (2)

[Abstract] Notation: ensure that the symbol α_parallel and its units are defined identically in the abstract, main text, and any equations; the 2D polarizability should be clearly distinguished from the conventional 3D polarizability.
[Methods] The abstract mentions 'classical molecular dynamics simulations' but does not specify the water model or force field; this detail should appear in the first paragraph of the Methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We agree that explicit demonstration of the width-independence of α_parallel is central to our claim and will strengthen the presentation by adding the requested checks.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that α_parallel is unambiguous rests on its independence from the arbitrary water width. The abstract asserts consistency between the fluctuation-dissipation and capacitor routes but supplies no data on recomputation of α_parallel for alternate slab boundaries (different density cutoffs or integration limits) in the strongly confined regime where the density profile is highly inhomogeneous. Without such tests the claimed advantage over the conventional dielectric constant is not demonstrated.

Authors: We acknowledge that the abstract does not explicitly reference robustness tests against slab-boundary choice. The main text already shows consistency between the two computational routes for our chosen definition, but to directly address the referee's concern we will revise the abstract to state that α_parallel is independent of the water-slab definition and will add a short sentence pointing to the new numerical checks (detailed below) that confirm this independence even in the strongly confined regime. revision: yes
Referee: [Results] Results section (presumed): the manuscript must show explicit numerical checks that α_parallel remains constant when the slab width is varied by ±0.5 Å or by changing the density threshold used to define the water region. If these checks are absent or limited to a single width, the load-bearing assertion of unambiguity fails.

Authors: The referee correctly identifies that explicit variation tests are required to substantiate the unambiguity claim. In the original manuscript the results focus on the agreement between fluctuation-dissipation and capacitor methods at a single standard slab definition. We will add the requested checks in the revised Results section: α_parallel will be recomputed for slab widths shifted by ±0.5 Å and for several density-cutoff thresholds that alter the integration limits. These additional data will be presented in a new figure or table and will show that α_parallel remains constant within statistical uncertainty, thereby confirming the advantage over the conventional dielectric constant. revision: yes

Circularity Check

0 steps flagged

No circularity: α_parallel derived from independent observables without reduction to inputs

full rationale

The paper defines the in-plane 2D polarizability α_parallel directly from two independent physical routes—fluctuation-dissipation applied to polarization fluctuations integrated over a slab and the induced dipole moment under an external capacitor field—both computed from molecular dynamics trajectories. These quantities are obtained from raw simulation data (positions, dipoles) rather than fitted to any target output or prior result. No equation equates α_parallel to itself by construction, no parameter is fitted on a subset and then relabeled as a prediction, and the analogy to perpendicular response is merely motivational without invoking a self-citation as a uniqueness theorem. The claim of width-independence is presented as an empirical outcome to be checked, not a definitional necessity, leaving the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on classical MD being sufficient to capture dielectric response and on the two computational routes being equivalent by construction; no free parameters are introduced in the abstract.

axioms (1)

domain assumption Classical molecular dynamics with standard water models accurately reproduces the dielectric response of confined water
Invoked implicitly by using MD to compute both fluctuation and induced-dipole routes.

invented entities (1)

in-plane 2D polarizability α_parallel no independent evidence
purpose: Width-independent characterization of in-plane dielectric response
New derived quantity introduced to replace the conventional dielectric constant under 2D confinement.

pith-pipeline@v0.9.0 · 5425 in / 1277 out tokens · 33893 ms · 2026-05-13T22:13:52.732826+00:00 · methodology

discussion (0)

Reference graph

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As a result, the capacitor-based estimate of the in-plane 2D polarizability,α cap ∥ , is ex- pected to be influenced by these edges and to depend on the plate separationl p

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Figure 5 illustrates the sensitivity ofε ∥ to the chosen widthw, usingα ∥ = 620 ˚A as obtained in this work

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[1] [1]

PBC y We analyze the convergence of the in-plane 2D polar- izability with respect to the lateral dimensions of the simulation supercell,L ∥, and the simulation length, as obtained from dipole-moment fluctuations via Eq. (4). Figure 2 shows the resulting values. We find that con- vergence is already achieved forL ∥ = 37.5 ˚A, yielding an estimate ofα PBCy,...

work page

[2] [2]

As a result, the capacitor-based estimate of the in-plane 2D polarizability,α cap ∥ , is ex- pected to be influenced by these edges and to depend on the plate separationl p

Capacitor In contrast to the PBC y calculations, the water film in the capacitor set-up is finite alongy, so boundary regions are expected to contribute differently from the central, bulk-like part. As a result, the capacitor-based estimate of the in-plane 2D polarizability,α cap ∥ , is ex- pected to be influenced by these edges and to depend on the plate...

work page

[3] [3]

Figure 5 illustrates the sensitivity ofε ∥ to the chosen widthw, usingα ∥ = 620 ˚A as obtained in this work

Sensitivity ofε ∥ to width We now analyze how the choice of an effective film thickness affects the in-plane dielectric constant. Figure 5 illustrates the sensitivity ofε ∥ to the chosen widthw, usingα ∥ = 620 ˚A as obtained in this work. Dashed ver- tical lines indicate three choices ofwthat have been em- ployed in the literature [19]: (i) the separation...

work page 2005

[4] [4]

Severo Ochoa

We also acknowledge the SGIker/IZO-SGIker facilities of the University of the Basque Country (UPV/EHU), supported by MICINN, GV/EJ, ERDF and ESF, as well as the DIPC Supercomputing Center, for generous allocations of computational resources and technical support. DIPC was supported by the “Severo Ochoa” Programme for Centres of Excellence in R&D (MINECO, ...

work page 1956

[5] [5]

N. R. Aluru, F. Aydin, M. Z. Bazant, D. Blankschtein, A. H. Brozena, J. P. de Souza, M. Elimelech, S. Faucher, J. T. Fourkas, V. B. Koman,et al., Fluids and electrolytes under confinement in single-digit nanopores, Chemical reviews123, 2737 (2023)

work page 2023

[6] [6]

Ballenegger and J.-P

V. Ballenegger and J.-P. Hansen, Dielectric permittivity profiles of confined polar fluids, The Journal of chemical physics122, 10.1063/1.1845431 (2005)

work page doi:10.1063/1.1845431 2005

[7] [7]

Marti, G

J. Marti, G. Nagy, E. Guardia, and M. Gordillo, Molec- ular dynamics simulation of liquid water confined inside graphite channels: dielectric and dynamical properties, The Journal of Physical Chemistry B110, 23987 (2006)

work page 2006

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Zhang, F

C. Zhang, F. Gygi, and G. Galli, Strongly anisotropic di- electric relaxation of water at the nanoscale, The Journal of Physical Chemistry Letters4, 2477 (2013)

work page 2013

[9] [9]

Zubeltzu, F

J. Zubeltzu, F. Corsetti, M. Fernandez-Serra, and E. Ar- tacho, Continuous melting through a hexatic phase in confined bilayer water, Physical Review E93, 062137 (2016)

work page 2016

[10] [10]

Schlaich, E

A. Schlaich, E. W. Knapp, and R. R. Netz, Water dielec- tric effects in planar confinement, Physical review letters 117, 048001 (2016)

work page 2016

[11] [11]

De Luca, S

S. De Luca, S. K. Kannam, B. Todd, F. Frascoli, J. S. Hansen, and P. J. Daivis, Effects of confinement on the dielectric response of water extends up to mesoscale di- mensions, Langmuir32, 4765 (2016)

work page 2016

[12] [12]

Fumagalli, A

L. Fumagalli, A. Esfandiar, R. Fabregas, S. Hu, P. Ares, A. Janardanan, Q. Yang, B. Radha, T. Taniguchi, K. Watanabe,et al., Anomalously low dielectric constant of confined water, Science360, 1339 (2018)

work page 2018

[13] [13]

Dufils, C

T. Dufils, C. Schran, J. Chen, A. Geim, L. Fumagalli, and A. Michaelides, Origin of dielectric polarization sup- pression in confined water from first principles, Chemical Science15, 516 (2024)

work page 2024

[14] [14]

Papadopoulou, J

E. Papadopoulou, J. Zavadlav, R. Podgornik, M. Praprotnik, and P. Koumoutsakos, Tuning the dielectric response of water in nanoconfinement through surface wettability, ACS nano15, 20311 (2021)

work page 2021

[15] [15]

Ahmadabadi, A

I. Ahmadabadi, A. Esfandiar, A. Hassanali, and M. R. Ejtehadi, Structural and dynamical fingerprints of the anomalous dielectric properties of water under confine- ment, Physical Review Materials5, 024008 (2021)

work page 2021

[16] [16]

Olivieri, J

J.-F. Olivieri, J. T. Hynes, and D. Laage, Confined wa- ter’s dielectric constant reduction is due to the surround- ing low dielectric media and not to interfacial molecular ordering, The Journal of Physical Chemistry Letters12, 4319 (2021)

work page 2021

[17] [17]

Monet, F

G. Monet, F. Bresme, A. Kornyshev, and H. Berthoumieux, Nonlocal dielectric response of water in nanoconfinement, Physical Review Letters126, 216001 (2021)

work page 2021

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Mondal and B

S. Mondal and B. Bagchi, Anomalous dielectric response of nanoconfined water, The Journal of Chemical Physics 154, 10.1063/5.0032879 (2021)

work page doi:10.1063/5.0032879 2021

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