When Liquid Rays Become Gas Rays: Can Evaporation Ever Be Non-Maxwellian?

Gilbert M Nathanson

doi:10.1007/978-3-030-63963-1_27

Abstract

AbstractA rare mistake by Otto Stern led to a confusion between density and flux in his first measurement of a Maxwellian speed distribution. This error reveals the key role of speed itself in Stern’s development of “the method of molecular rays”. What if the gas-phase speed distributions are not Maxwellian to begin with? The molecular beam technique so beautifully advanced by Stern can also be used to explore the speed distribution of gases evaporating from liquid microjets, a tool developed by Manfred Faubel. We employ liquid water and alkane microjets containing dissolved helium atoms to monitor the speed of evaporating He atoms into vacuum. While most dissolved gases evaporate in Maxwellian speed distributions, the He evaporation flux is super-Maxwellian, with energies up to 70% higher than the flux-weighted average energy of 2 RTliq. The explanation of this high-energy evaporation involves two beautiful concepts in physical chemistry: detailed balancing between He atom evaporation and condensation (starting with gas-surface collisions) and the potential of mean force on the He atom (starting with He atoms just below the surface). We hope that these measurements continue to fulfill Stern’s dream of the “directness and simplicity of the molecular ray method.”

Highlights

Otto Stern’s first publication, in 1920, described an ingenious Coriolis measurement of the root-mean-square speed of a Maxwellian distribution of silver atoms emitted from a hot oven (“gas rays”) [1]
One rule of thumb emerges from these investigations: the more insoluble the gas, the steeper the Potential of Mean Force (PMF), the greater the force on the evaporating gas atoms, and the more likely that the He atom will emerge in a non-Maxwellian distribution
Its behavior is opposite to expectations: instead of evaporating in a slower, subMaxwellian distribution, as predicted by argon desorbing from tungsten mentioned above, the He atoms evaporate in a distinctly faster, super-Maxwellian distribution! The extent of non-Maxwellian behavior can be gauged by the average translational energy of the exiting He atoms: 1.14 · (2RT liq) for dodecane at 295 K, 1.37 · (2RT liq) for pure supercooled water at 252 K, and 1.70 · (2RT liq) for 7 M LiBr/H2O at 255 K, which are 14, 37, and 70% higher than expected [42, 43]

Summary

Introduction

Otto Stern’s first publication, in 1920, described an ingenious Coriolis measurement of the root-mean-square (rms) speed of a Maxwellian distribution of silver atoms emitted from a hot oven (“gas rays”) [1]. The Maxwellian properties of number-density and flux distributions are thoroughly summarized by David and Comsa, a review article I highly recommend [4]. Make an “O” with your thumb and forefinger: the speed distribution of molecules passing through the “O” is instead the flux (speed-weighted) distribution, J (c, θ ) ∼ c3e−mc2/2RT cosθ ngas, where θ is the polar angle. In this case, J(c, θ )sinθ dθ dφ dc is the number of molecules passing through a unit area per second per unit speed and solid angle interval.

Condensation and Evaporation as Reverse Processes

Rules of Thumb for Gas-Surface Energy Transfer and Trapping

Implications of Detailed Balance

Maxwellian Evaporation and a Two-Step Model for Solvation

Non-Maxwellian Evaporation Discovered!

A View from the Interior

Findings

Future Non-Maxwellian Adventures