Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations

Ionic fluctuations in finite volumes: fractional noise and hyperuniformity

“…The collapse of timescales on a single master curve spanning all intermediate combinations of s Debye and s Diff is strikingly similar to the result of a recent study, including some of the authors of the response to an oscillating electric eld of an electrolyte conned between two plates separated by a distance L. 32 There, the critical timescale dening a conducting or insulating behaviour, typically the time to "charge" the plates by transporting the ions, is either close to s Debye or s Diff = L 2 /D according to the separation of length scales l D /L, and spans all intermediate regimes. Remarkably, here in an equilibrium and bulk context, this behaviour remains, showing the universality of such response in electrolytes.…”

“…As mentioned in the introduction, the interplay between s Debye and s Diff can produce a variety of timescales that could all explain part of the behaviour. 32,[63][64][65] To understand the relaxation behaviour more systematically, we explore in Fig. 5 the relaxation of C Q (t)e t/sDebye .…”

“…However, there is a broad intermediate region where T Q spans a combination of both timescalesresonating with other studies which also nd numerous timescales to characterize the charge of electrodes. 32,[63][64][65] The global timescale T Q accounts remarkably for the relaxation of charge correlations. Fig.…”

“…Yet, Green-Kubo integralsthe kinetic counterpart of Kirkwood-Buff integralsgive access to various dynamic properties. Integration of uctuating uxes over an entire domain enables to probe conductivity, permeance, friction on surfaces, and more, [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] including far from equilibrium. [42][43][44][45] The relevance of Green-Kubo integrals over sub-volumes has only recently been raised, particularly to coarse-grain molecular dynamics near interfaces.…”

“…De facto, various mixed timescales, as a combination l D n L obs 2−n /D with n a real number, will also play a role, as was seen in the charging dynamics of two parallel plates separated by a distance L playing the role of L obs here. 32,[63][64][65] Which timescale dominates uctuations in nite volumes? Here, we use a combination of Brownian dynamics simulations and analytical calculations to rationalize ionic uctuations in nite volumes (Section 1).…”