1/f spectrum and memory function analysis of solvation dynamics in a room-temperature ionic liquid

TL;DR

This study investigates the solvation dynamics in an ionic liquid using power spectra analysis, revealing 1/f noise behavior and linking it to long memory effects and slow relaxation processes.

Contribution

It introduces a molecular dynamics approach to analyze 1/f noise in ionic liquids and connects spectral features to memory functions and solvation times.

Findings

1/f noise observed over 2-3 decades in ionic liquid

Long memory functions lead to slow solvation dynamics

Contrast with acetonitrile shows faster relaxation and absence of 1/f noise

Abstract

To understand the non-exponential relaxation associated with solvation dynamics in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate, we study power spectra of the fluctuating Franck-Condon energy gap of a diatomic probe solute via molecular dynamics simulations. Results show 1/f dependence in a wide frequency range over 2 to 3 decades, indicating distributed relaxation times. We analyze the memory function and solvation time in the framework of the generalized Langevin equation using a simple model description for the power spectrum. It is found that the crossover frequency toward the white noise plateau is directly related to the time scale for the memory function and thus the solvation time. Specifically, the low crossover frequency observed in the ionic liquid leads to a slowly-decaying tail in its memory function and long solvation time. By contrast, acetonitrile characterized by a high crossover frequency and (near) absence of 1/f behavior in its power spectra shows fast relaxation of the memory function and single-exponential decay of solvation dynamics in the long-time regime.