Ionic fluctuations in finite volumes: fractional noise and hyperuniformity

TL;DR

This paper investigates ionic fluctuations in finite volumes, revealing fractional noise with a 1/f^{3/2} spectrum and persistent hyperuniformity, providing a new analytical framework applicable to various systems with pairwise interactions.

Contribution

It introduces an analytical framework for ionic fluctuations in finite volumes, capturing fractional noise and hyperuniformity, applicable beyond ionic solutions.

Findings

Noise spectrum decays as 1/f^{3/2}

Charge fluctuations exhibit hyperuniformity over time

Correlations scale with observation volume area and perimeter

Abstract

Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite observation volumes. However, kinetic properties have received less attention, especially not in ionic solutions, where electrostatic interactions play a decisive role. Here, we probe ionic fluctuations in finite volumes with Brownian dynamics and build an analytical framework that reproduces our simulation results and is broadly applicable to other systems with pairwise interactions. Particle number and charge correlations exhibit a rich phenomenology with time, characterized by a diversity of timescales. The noise spectrum of both quantities decays as $1/f^{3/2}$, where $f$ is the frequency. This signature of fractional noise shows the universality of $1/f^{3/2}$ scalings when observing diffusing particles in finite domains. The hyperuniform behaviour of charge fluctuations, namely that correlations scale with the area of the observation volume, is preserved in time. Correlations even become proportional to the box perimeter at sufficiently long times. Our results pave the way to understand fluctuations in more complex systems, from nanopores to single-particle electrochemistry.