In-plane dielectric constant and conductivity of confined water

In-plane dielectric constant and conductivity of confined water

Article Date: 15 October 2025
Article URL: https://www.nature.com/articles/s41586-025-09558-y
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Summary

This Nature paper reports direct, local measurements of the in-plane (parallel) dielectric constant (ε//) and electrical conductivity (σ//) of water confined in atomically flat nanochannels made from hexagonal boron nitride (hBN) and graphite. Using scanning dielectric microscopy (SDM) with an AFM tip over an extended frequency range (0.1 kHz–1.1 GHz) and careful 3D numerical modelling, the team separated effects of dielectric polarisation and conduction to extract ε// and σ// as functions of channel height h (≈1–60 nm).

Key experimental findings:
– For channels thicker than ~4 nm, in-plane permittivity is close to bulk (ε// ≈ 74 ± 17).
– For quasi-2D water (h ≈ 1–2 nm) ε// jumps dramatically to ~1,000 (±350), i.e. ferroelectric-like behaviour, while the out-of-plane permittivity ε⊥ remains suppressed (≈2).
– In-plane conductivity σ// increases with confinement, following ≈1/h at moderate confinement and peaking around σ// ≈ 3 S m−1 at h ≈ 1.5 nm (4–5 molecular layers), then falling for the very thinnest channels.

The authors interpret these results as two regimes: (1) moderate confinement where water consists of bulk-like interior plus interfacial layers (enhanced σ near surfaces and anisotropic dielectric response), and (2) atomically strong confinement where layered (quasi-2D) water acquires collective dipolar reorientations (large ε//) and superionic-like protonic conduction (very high σ//). The work is supported by extensive calibration, 3D finite-element simulations and simple circuit/analytical models that relate characteristic spectral frequencies to ε// and σ//.