Fluctuations of local electric field and dipole moments in water between metal walls

TL;DR

This study combines analytic theory and molecular dynamics simulations to analyze the fluctuations of local electric fields and dipole moments in water confined between metal walls, revealing Gaussian distributions and dynamic behaviors influenced by hydrogen bonding.

Contribution

It derives the Kirkwood-Fröhlich formula considering volume effects and characterizes the distribution and dynamics of local electric fields and dipoles in water near metal surfaces.

Findings

Gaussian distribution of local electric field magnitude with a large mean value

Parallel alignment of dipole moments with local electric fields due to hydrogen bonding

Distinct timescales for dipole reorientation and librational motions

Abstract

We examine the thermal fluctuations of the local electric field $E_k^{\rm loc}$ and the dipole moment $\mu_k$ in liquid water at $T=298$ K between metal walls in electric field applied in the perpendicular direction. We use analytic theory and molecular dynamics simulation. In this situation, there is a global electrostatic coupling between the surface charges on the walls and the polarization in the bulk. Then, the correlation function of the polarization density $p_z(r)$ along the applied field contains a homogeneous part inversely proportional to the cell volume $V$. Accounting for the long-range dipolar interaction, we derive the Kirkwood-Fr$\ddot{\rm{o}}$hlich formula for the polarization fluctuations when the specimen volume $v$ is much smaller than $V$. However, for not small $v/V$, the homogeneous part comes into play in dielectric relations. We also calculate the distribution of $E_k^{\rm loc}$ in applied field. As a unique feature of water, its magnitude $|E_k^{\rm loc}|$ obeys a Gaussian distribution with a large mean value $E_0 \cong 17~$V$/$nm, which arises mainly from the surrounding hydrogen-bonded molecules. Since $|\mu_k|E_0\sim 30 k_{\rm B}T$, $\mu_k$ becomes mostly parallel to $E_k^{\rm loc}$. As a result, the orientation distributions of these two vectors nearly coincide, assuming the classical exponential form. In dynamics, the component of $\mu_k(t)$ parallel to $E_k^{\rm loc}(t)$ changes on the timescale of the hydrogen bonds $\sim 5$ ps, while its smaller perpendicular component undergoes librational motions on timescales of 0.01 ps.