Electrical noise in electrolytes: a theoretical perspective

Abstract

Seemingly unrelated experiments such as electrolyte transport through nanotubes, nano-scale electrochemistry, NMR relaxometry and Surface Force Balance measurements, all probe electrical fluctuations: of the electric current, the charge and polarization,...

Ionic fluctuations in finite volumes: fractional noise and hyperuniformity

“…Here, we have chosen minimal interactions between ions; in particular, we have neglected hydrodynamic interactions 72 to isolate the effect of electrostatic interactions. In a companion paper, 73 we found that the same BD simulations, in a ∼1 M aqueous electrolyte solution, compared with molecular dynamics simulations, capture well the main features of the dynamic structure factor of charges. However, deviations are observed for intermediate wavenumbers, which can be partially improved by improving the description of static correlations.…”

“…where k = jkj and k D = 1/l D . Eqn (6) for the static charge structure factor S static rr (k) corresponds to the classical result of Debye-Hückel, 73,84 which is expected since linearized sDFT yields the lowest order coupling between diffusion and electrostatics, i.e. dynamics close to equilibrium.…”

“…Beyond relaxation dynamics, other ionic-specific kinetic properties may be extracted from dynamical fluctuations in finite volumes. For example, conductivity 35 and the dielectric permittivity and susceptibility 73 also derive from integrals of structure factors, and can be addressed within the same theoretical framework as proposed here. Since even a quantity as simple as the number density has non-trivial fluctuations, with fractional noise signature, it is clear that more complex variables might exhibit rich behaviour in finite volumes.…”

“…While this is somewhat expected at low enough salt concentrations C 0 , steric effects should modify number uctuations at high concentrations. Steric effects result in oscillations of the static structure factor, 84,88 that are only weakly captured by BD 73 and not at this stage with sDFT in eqn (6). Steric effects can, however, be captured by improving the expression of the static structure factor analytically [88][89][90] or by tting numerically obtained structure factors 73 and will be the object of future work.…”

“…More generally, the dynamic structure factor expression in eqn (6) holds for various elds, as long as they derive from Markovian (no memory) and Gaussian processes (forces are conservative and derive from an energy that is quadratic in the eld). 73,76,85 The present formalism can thus easily be extended to study different pairwise interactions, such as steric interactions. Still, it should be modied to account e.g.…”