Characterizing the Importance of Desorption Activation Energies on Delivery Rates of Volatiles to the Lunar Cold Traps

Introduction

It is now generally accepted that water and other volatiles exist on the Moon [1, 2], though their distribution and abundance are still poorly-constrained. Much work has been put into understanding how lunar volatiles are transported from their delivery sites to the polar cold traps where they have been detected. These models can generally be divided into two regimes: collisional transport through a transient post-impact atmosphere [3] and ballistic transport through a non-collisional surface-bounded exosphere [e.g. 4, 5, 6]. Transient atmospheres allow for rapid but episodic delivery of volatiles to cold traps, while ballistic transport permits a much slower but potentially continuous delivery.

Given the exponential dependence of the residence time on temperature, there has been significant focus on characterizing the Moon’s thermal environment, particularly at scales below the resolution of existing orbital datasets [e.g. 3, 7]. However, comparatively little attention has been dedicated to another key parameter: the desorption activation energy. The activation energy (E_a) is as significant to a molecule’s time adsorbed to the surface as the temperature is, with larger values leading to longer residence times:

Most ballistic transport models use a single value for the activation energy. This is a problematic assumption for several reasons. Temperature-programmed desorption (TPD) measurements of water desorption from Apollo samples have indicated that a single surface can have a broad range of activation energies [8, 9]. Additionally, the lunar surface does not have a uniform composition, with the most significant compositional dichotomy occurring between the maria and the highlands [10]. There is no reason to assume that these different surfaces would have the same (or even similar) activation energies. This allows for the potential of a positional dependence on the ability of water and other species to desorb from the surface, which may challenge the idea that ballistic transport results in a more-or-less uniform delivery to all cold traps.

Furthermore, the specific value (or range of values) of the activation energy is not well-understood, particularly for non-water volatiles. The applicability of a frequently-cited value of 0.415 eV for water is questionable, as this value was derived for water molecules sublimating from a water-ice substrate [11]. Except for limited areas within the polar cold traps, this is unlikely to be representative of real-world conditions. Even a small (~10%) increase in the activation energy has the potential to measurably affect transport behaviour, particularly when small-scale surface roughness is considered due to the greater dependence of residence time on temperature for larger activation energies [3].

Our goal is to highlight the importance of developing a more comprehensive understanding of activation energies for lunar volatiles, whether through experimental work (e.g. TPD) or models (e.g. molecular dynamics).

Methods

We use a standard ballistic transport model adapted from the one presented in Kloos et al. [6]. Molecules desorb from the surface in a random direction with a speed chosen from the Maxwell-Boltzmann distribution for the residence site’s surface temperature. For simplicity, we do not include the effects of small-scale roughness. Molecules hop across the surface until they land in a cold trap or are photolyzed. The activation energy is modeled both as a single value and as a distribution of values, following the form laid out by Schöghofer [12].

Results

An overview of the relationship between surface temperature, desorption activation energy, and surface residence time is presented in Figure 1. As the activation energy increases, so does the temperature at which the residence time is a significant fraction of a lunar day. This effect is more pronounced at lower temperatures, suggesting that transport near the lunar poles may be particularly affected by the choice of activation energy, particularly given the seasonally-shadowed regions that create complex and time-variable areas of sustained low temperatures [6].

We plan to present results examining a wide range of parameter space, including uniform and non-uniform surface compositions and the relative importance of single-value activation energies versus a broad distribution of energies.

Figure 1. The interrelated effects of desorption activation energy and surface temperature on the surface residence time for water molecules. The horizontal dotted line in each panel represents a residence time of half a lunar day. The vertical dotted line in the left panel indicates the typical maximum temperature of the Moon’s permanently-shadowed regions.

References

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