Deviations from Arrhenius dynamics in high temperature liquids, a possible collapse, and a viscosity bound

TL;DR

This study investigates how real liquids deviate from simple Arrhenius behavior in viscosity at high temperatures, revealing more complex dynamics and proposing a generalized scaling approach that better captures their temperature dependence.

Contribution

The paper provides experimental evidence of deviations from Arrhenius dynamics in liquids and introduces a generalized scaling method to describe viscosity over a wide temperature range.

Findings

Viscosity increases more rapidly than Arrhenius predictions as temperature drops.

A lower bound scale for viscosity related to $nh$ (density times Planck's constant) is identified.

A scaling of temperature partially collapses viscosity data across different liquids.

Abstract

Liquids realize a highly complex state of matter in which strong competing kinetic and interaction effects come to life. As such, liquids are more challenging to understand than either gases or solids generally. In weakly interacting gases, the kinetic effects dominate. By contrast, low temperature solids typically feature far smaller fluctuations about their ground state. Notwithstanding their complexity, with the exception of quantum fluids and supercooled liquids, various aspects of common liquid dynamics such as their dynamic viscosity are often assumed to be given by rather simple, Arrhenius-type, activated forms with nearly constant (i.e., temperature independent) energy barriers. In this work, we analyze experimentally measured viscosities of numerous liquids far above their equilibrium melting temperature to see how well this assumption fares. We find, for the investigated liquids, marked deviations from simple activated dynamics. Even far above their equilibrium melting temperatures, as the temperature drops, the viscosity of these liquids increases more strongly than predicted by activated dynamics dominated by a single uniform energy barrier. For metallic fluids, the scale of the prefactors of the best Arrhenius fits for the viscosity is typically consistent with that given by the product $nh$ with $n$ the number density and $h$ Planck's constant. In various fluids that we examined, $nh$ constitutes a lower bound scale on the viscosity. We find that a scaling of the temperature axis (complementing that of the viscosity) leads to a partial collapse of the temperature dependent viscosities of different fluids; such a scaling allows for a functional dependence of the viscosity on temperature that includes yet is far more general than activated Arrhenius form alone. We speculate on relations between non-Arrhenius dynamics and thermodynamic observables.