Lags in Desorption of Lunar Volatiles

Abstract

Monte Carlo simulations of gas motion inside a granular medium are presented in order to understand the interaction of lunar gases with regolith and improve models for surface-boundary exospheres, a common type of planetary atmosphere. Results demonstrate that current models underestimate the lifetime of weakly bonded adsorbates (e.g., argon) on the surface by not considering the effect of Knudsen diffusion, and suggest that thermal desorption of adsorbates should be modeled as a second-or-higher-order process with respect to adsorbate coverage. An additional discrepancy between present models and outgassing from a realistic porous boundary is found for surface-adsorbate systems containing a distribution of activation energies (e.g., water). In that case, the mobility of adsorbates between desorption events (i.e., surface diffusion), not considered in global models of the exosphere, controls their surface residence time via transitions between sites of low and high binding energy. Without mobility the equatorial surface retains more water over a lunar day because sites of low binding energy are not repopulated by motion along the grain surface when depleted. The effects of Knudsen and surface diffusion apply to other volatile species and help us partly understand why measurements of lunar exosphere constituents appear to indicate stronger bonding of gas with the lunar surface than measured in some laboratory experiments. © 2021. The Author(s). Published by the American Astronomical Society.

Full text

Lags in Desorption of Lunar Volatiles
M. Sarantos
1
and S. Tsavachidis
2
1
Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA; menelaos.sarantos-1@nasa.gov
2
Houston, TX, USA
Received 2021 April 14; revised 2021 August 18; accepted 2021 August 20; published 2021 September 28
Abstract
Monte Carlo simulations of gas motion inside a granular medium are presented in order to understand the
interaction of lunar gases with regolith and improve models for surface-boundary exospheres, a common type of
planetary atmosphere. Results demonstrate that current models underestimate the lifetime of weakly bonded
adsorbates (e.g., argon)on the surface by not considering the effect of Knudsen diffusion, and suggest that thermal
desorption of adsorbates should be modeled as a second-or-higher-order process with respect to adsorbate
coverage. An additional discrepancy between present models and outgassing from a realistic porous boundary is
found for surface-adsorbate systems containing a distribution of activation energies (e.g., water). In that case, the
mobility of adsorbates between desorption events (i.e., surface diffusion), not considered in global models of the
exosphere, controls their surface residence time via transitions between sites of low and high binding energy.
Without mobility the equatorial surface retains more water over a lunar day because sites of low binding energy are
not repopulated by motion along the grain surface when depleted. The effects of Knudsen and surface diffusion
apply to other volatile species and help us partly understand why measurements of lunar exosphere constituents
appear to indicate stronger bonding of gas with the lunar surface than measured in some laboratory experiments.
Unified Astronomy Thesaurus concepts: The Moon (1692);Exosphere (499);Lunar surface (974);Surface
processes (2116);Land-atmosphere interactions (900)
1. Introduction
Because the exosphere of the Moon is a macroscopic
manifestation of interactions between gas atoms and the surface
(e.g., Stern 1999), exospheric measurements can be used to
extract information about the gas-surface bond. With some
exceptions (H
2
,He,Ne), gas particles accumulate, or adsorb, on
the cold surface at lunar night and desorb from the warmer
dayside soils, with the local time of the density peak constraining
the temperature dependence of the desorption rate and the
strength of the bond. Exosphere models are tasked with
retrieving the strength of gas-surface interaction from such
measurements by repeatedly simulating adsorption and deso-
rption events until loss of these atoms and molecules by
photoionization or dissociation. They tend to overestimate the
desorption rate because they do not account for the porosity of
the powdery surface, and must compensate by using a higher
effective activation energy for desorption than measured in
laboratories to fit exospheric measurements (e.g., Grava et al.
2015; Hodges 2016). This has been interpreted as indicating that
experiments conducted in laboratories do not represent the
pristine conditions found on the Moon. While this conclusion
may be fair, we demonstrate that an improved treatment of the
porous surface in exosphere models reduces these discrepancies.
Furthermore, we show that accurate knowledge of the distribu-
tion of adsorption energies from experiments is a necessary but
not sufficient condition for high-fidelity exosphere models.
Additional uncertainty is introduced by the role of surface
diffusion, whose effect on desorption has been ignored by
previous exosphere models.
We used two exemplary species, argon and water, to illustrate
the range of outgassing delays caused by diffusion. Argon bonds
very weakly with the surface (e.g., Grava et al. 2015;Kegerreis
et al. 2017, and references therein), while the interaction between
water and the lunar surface is stronger (Poston et al. 2015;Jones
et al. 2020a). Argon gas is a product of radioactive decay of
40
K
in the lunar soil and has repeatedly been measured in the lunar
exosphere, both during the Apollo days and more recently by the
Lunar Atmosphere and Dust Environment Explorer (LADEE;
Benna et al. 2015; Hodges & Mahaffy 2016). To interpret the
existing data Kegerreis et al. (2017)implemented a simple
model to account for diffusion of argon adsorbates. They
assumed that some argon atoms penetrate randomly into the
ground at night, only to reemerge during the daytime with a
uniform distribution in delay times when the regolith warms.
The argon density peak at sunrise, and the day to night ratio near
sunrise, could be simulated if the trapping fraction of a few parts
per thousand atoms was assumed on every bounce. They
concluded that diffusion provides an alternative to assuming
very high activation energies for desorption (Hodges 2016;
Hodges & Mahaffy 2016). A sophisticated model of a granular
surface is used here to quantify how Ar moves between the
subsurface and vacuum.
Desorption of adsorbed water has been presumed to be the
cause of slope changes in reflectance spectra measured over a
lunar day by the Lunar Reconnaissance Orbiter (LRO; Hendrix
et al. 2019). Water gas may be generated by recombinative
desorption of solar wind-implanted hydroxyl (Jones et al. 2018),
and by meteoroid impacts, as shown by the detection of water-
group products in the lunar exosphere during meteor showers
(Benna et al. 2019). The gas form, water or hydroxyl, was not
determined from these LADEE measurements. If water, the
LADEE measurements imply that the water does not accumulate
on the nightside and it lacks signatures of repeated adsorption–
desorption cycles, perhaps because of dissociative adsorption to
The Astrophysical Journal Letters, 919:L14 (7pp), 2021 October 1 https://doi.org/10.3847/2041-8213/ac205b
© 2021. The Author(s). Published by the American Astronomical Society.
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further
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1

the regolith (Gun’ko et al. 1998). Whether or not water is
continuously present in the lunar exosphere, in this study we use
water as an example of an adsorbate that interacts with the lunar
surface with a wide distribution of binding energies (Jones et al.
2020a). On such heterogeneous surfaces the residence time of
different molecules on the surface will differ considerably. By
analogy to volume diffusion controlling the timescale of
hydrogen release from grain rims when they contain a
distribution of crystal defects (e.g., Farrell et al. 2017),surface
diffusion has been hypothesized to slow thermal desorption of
adsorbates from heterogeneous planetary surfaces (Killen et al.
2018). This effect has not been considered in exosphere models
and is quantified for the first time in this study.
2. Model Formulation and Kinetic Parameters
A detailed description of the processes taking place on an
isolated astrophysical grain is provided by He & Vidali (2014).
Additionally, when a grain is enveloped in a grain pile, some
desorption events lead to readsorption and some lead to diffusion
deeper into the powder. And, finally, surface diffusion, i.e., the
thermal migration of adsorbates between adjacent sites, or local
minima of the adsorption potential on a grain, enables particles
to find grain contact points and slowly travel onto other grains
(e.g., Sarantos & Tsavachidis 2020).
Three random sphere-packings were computer-generated
(Kloss et al. 2012)to simulate the disordered structure of lunar
regolith. Each packing had width of 1 ×1mm
2
, depth of
∼5–7 mm, and consisted of 30,000 spherical grains. The grain
size distribution for each packing was based on three Apollo
and Luna samples that were representative of size distributions
for mature (72141), submature (24109), and immature (67481)
lunar soils.
3
The samples were truncated at one standard
deviation, with a most likely particle diameter of ∼29 μm, a
mean particle size of 44 μm, a maximum grain size of 374 μm,
and a void fraction of 0.5 for the sample of intermediate
maturity. Although piles of spherical grains provide better
representation of the granularity of lunar regolith for gas
calculations than the current state-of-the-art models, most lunar
regolith particles are not spheres, and future work should
include more appropriate particle geometries.
An obstructed random walk of 20,000 randomly distributed
test particles was initiated in these packings to simulate gas
transport. The spaces between grains in these simulations
provided realistic diffusion paths. Similar approaches have
previously been used to study gas transport in porous media
under atmospheric pressures (e.g., Zalc et al. 2003; Hlushkou
et al. 2013), but under lunar conditions the test particles collide
only with grains or escape to vacuum. Particles were either
deposited all at one time for isothermal simulations (Figure 1),
or with a time profile for temperature-programmed desorption
(TPD)simulations (Figures 2–3). Particles in the continuous
dosing scenario (TPD runs)were uniformly distributed in time
from sunset to sunrise to simulate adsorption during the long
lunar night. For time-dependent runs the temperature was
changed for every time step in order to simulate the heating rate
experienced by patches of the lunar surface. Continuous linear
heating or cooling from a lunar thermal model (Hurley et al.
2015)was used, but with a more gradual temperature ramp-up
near the terminator due to realistic shadowing (Williams et al.
2017). No lateral or vertical temperature gradients were
assumed, and their additional effects on the lifetime of
adsorbates (e.g., Davidsson & Hosseini 2021)should be
assessed in future work. Particles were removed when they
escaped the medium, and particles remaining in the grain pile
were permitted to undergo diffusion. Desorption events were
recorded. We thus calculated a realistic initial condition for the
distribution of adsorbates with depth as the surface element
arrives at the dawn terminator.
On every time step we separate the adsorption, desorption,
and surface diffusion events. At the beginning of the step we
insert new particles (for the time-dependent dosing simulations)
and we test for each particle whether desorption is to take
place. If desorbed, we mark with ray tracing whether the
particle hits another grain, including perhaps many successive
collisions with other grains until it comes to a stop (Knudsen
diffusion), and if it escapes to vacuum it is removed from the
simulation. If no desorption occurs, we check the probability
for surface diffusion, and for those particles that will undergo
hopping events we update the binding energy and location.
When the sites have different adsorption energies, we randomly
select the binding energy after each sticking event or surface
diffusion hop by importance sampling of the binding energy
distribution. This means that there is no correlation between
activation energies of successive jumps. The distance traveled
along the spherical grain from an adsorbateʼs current position
within a time step of 1–4 s is simulated probabilistically as
described in Sarantos & Tsavachidis (2020)(see also Hołyst
et al. 1999).
Sticking is one of the parameters enhancing the retentiveness of
soil. Higher sticking probability per collision of a desorbed atom
with intervening grains leads to readsorption onto adjacent grains,
prolonging the time to escape from the granular bed. The
adsorption probability during single collisions with grains is
described by a sticking coefficient, S, while the probability of
reflection is 1-S. Values of S for gases on lunar regolith have not
been reported, so we used values for simple metal oxides. The
sticking probability of Ar on MgO decreases exponentially with
gas incident energy, E, for gas speeds >250 m s
−1
(Dohnalek et al.
2002). Using their empirical relation S(E)=exp
−a(E-E0)
,where
a=0.202 mol kJ
−1
and E
0
=2.08 kJ mol
−1
, and integrating over
aMaxwell–Boltzmann distribution for thermally accommodated
gas, we find population-averaged sticking probabilities of S≈1at
T=50 K, S≈0.76 at T=200 K, and S≈0.55 at T=400 K. The
high sticking probabilities used in our simulation are consistent
with the efficient energy accommodation of lunar argon as
indicated by LADEE measurements of the scale height (Hodges &
Mahaffy 2016). The sticking probability of water on CaO single
crystals is constant at temperatures 120–300 K and near 0.85–0.9
(Seifert et al. 2021). Similarly, a temperature-independent sticking
coefficient near unity has been measured for low-coverage water
on MgO single crystals at temperatures 100–250 K (Stirniman
et al. 1996). In the results presented here we assumed S=0.85 for
single collisions of water with the lunar surface at all temperatures.
The adsorption time of a test particle between desorption events
is calculated as −ln(1−ξ)/R
des
,whereR
des
is the desorption rate
and ξa random number that is uniformly distributed between zero
and one. This numerical scheme generates exponentially dis-
tributed waiting times for desorption with mean residence time
τ=1/R
des
. The desorption rate increases with grain temperature,
T,R
des
=v
0
×exp(−E
des
/KT). Desorption parameters for Ar were
adopted from the work of Grava et al. (2015), who simulated the
decay of argon density from sunset to sunrise using Apollo data.
3
https://www-curator.jsc.nasa.gov/lunar/lsc/index.cfm
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The surface interaction was empiricallydescribedbyanunusually
low pre-exponential factor v
0
=2×10
9
s
−1
and E
des
=0.281 eV,
values adopted here, although other values of v
0
and E
des
will give
similar results (Kegerreis et al. 2017). The kinetic parameters
describing the interaction of water with lunar grains were obtained
by Jones et al. (2020a). A pre-exponential factor of v
0
=10
13
s
−1
and a wide distribution of binding energies between 0.6 and
1.9 eV, with the most likely value 0.63 eV, were derived from
TPD experiments on Apollo Highlands sample 14163, and were
adopted in these simulations.
The surface diffusion of adsorbates is simulated as a random
walk between neighboring sites of potential energy with a jump
rate, R
hop
=v
0
×exp(−E
diff
/KT). The barrier to surface diffu-
sion, E
diff
, is uncertain and is usually expressed as E
diff
=αE
des
,
where α<1 is a surface corrugation ratio. For complex surfaces
and weakly adsorbed species α∼0.7–0.8 (e.g., Perets et al.
2007). Values around 0.5–0.6 are reported for gases adsorbing
on glass (Gilliland et al. 1974). Theoretical estimates of Ar tracer
diffusion on oxides, carried out by Riccardo & Steele (1996),
suggested α≈0.45, the value assumed for the argon simulations
here. As to water, its mobility on complex oxide surfaces is
uncertain. On the one hand, high mobility of adsorbed molecules
along the surface is expected from the finding that their entropies
near desorption are 2/3 of their gas phase entropies, implying
that only motion perpendicular to the grain surface is restricted
(Campbell & Sellers 2012;Weaver2013). Theoretical calcula-
tions on some model oxide surfaces confirm this expectation for
water. For instance, the motion of an isolated water molecule
adsorbed on MgO was estimated by McCarthy et al. (1996),
indicating that adsorbed water molecules are very mobile on this
surface (α≈0.25). On the other hand, water molecules on many
oxides are partially dissociated, and the dissociation products are
shown to be immobile (e.g., Matthiesen et al. 2009). Yet for
dissociation to occur, some mobility of water molecules is
necessary to even reach the active sites (Schaub et al. 2001).For
these reasons, a wide range of values (α=0.25–1)for water
surface diffusion have been assumed in our work. When there is
a distribution of sites this ratio, α, was assumed to be constant at
all sites regardless of the depth of the adsorption well.
The model of gas–solid interaction adopted here is suitable to
extended regions of the Moon. Adsorbate–adsorbate repulsive or
attractive interactions can be neglected if the average separation
between adsorbates is large. Hendrix et al. (2019)inferred that less
than 0.01 of a water monolayer (1ML∼10
15
cm
−2
)exists on the
lunar surface. The adsorbate abundance, C
ads
,influx balance with
the argon gas density, n
g
, can be estimated as C
ads
=n
g
×v
g
×t
res
.
To support a gas density n
g
=2×10
4
cm
−3
(Benna et al. 2015)
for a thermally accommodated gas of mean speed v
g
with the
Grava et al. (2015)parameters for the surface residence time, tres,
the surface coverage of adsorbed argon must be C
ads
∼
10
12
–10
13
cm
−2
, i.e., 1 in every 100–1000 sites near sunrise are
occupied. In many gas-surface systems abundances higher than a
tenth of a monolayer must be inferred before coverage-dependent
kinetic parameters must be considered (e.g., Zhdanov 1991).
Furthermore, gas atoms and molecules are deposited not only on
the top 1 or 2 grains of the porous regolith, but up to 10 grains into
the subsurface (Figure 1(a); see also Kulchitsky et al. 2018).Thus,
the grains are essentially bare over large portions of the lunar
surface, and the noninteracting test particle approach is valid.
3. Results and Discussion
3.1. Adsorbed Argon
The left panel of Figure 1shows how the argon reservoir
evolves with time during an isothermal simulation at T=115 K.
Because of the gaps between grains and because some atoms do
not stick the first time they meet a grain, deposited particles
(black line, t=0)can reach significant depths compared to the
mean grain size. About 10% of all argon test particles are
initially deposited at a depth exceeding 200 μm. With diffusion
between grain voids this fraction rises to ∼15% within one day
as desorption events occur. This population represents a “fat tail”
of slowly desorbing particles that, as we will show next, do not
follow exponentially distributed waiting times for desorption
from the grain pile.
Figure 1. Isothermal desorption of argon at T=115 K. (a)Argon diffuses into the grain pile as shown by the changing distribution of atoms with depth as a function
of time. (b)Due to this motion the gas removal rate from a powder is slower than an exponential decay, and is better approximated by a second-order process.
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The Astrophysical Journal Letters, 919:L14 (7pp), 2021 October 1 Sarantos & Tsavachidis

The right panel of Figure 1shows the cumulative probability
of argon desorption (desorbed fraction)with time. The black
line shows the outgassing from our simulation of the porous
medium. A first-order model (µ
d
Ndt N
), where Nis the
number of test particles remaining in the packing, was used to
simulate the outgassing from a single grain (blue line).
Defining lag as the time it takes to remove 63.2% of the
adsorbate reservoir, the porous soil takes 6 to 7 times longer to
reach full effect than the exponential decay with the same
microphysical parameters. A reduction of the rate by a factor of
4 when a grain is enveloped in a pile of grains somewhat
extends the applicability of the exponential decay to longer
timescales (red line). The sum of two exponential decays,
one fast and one slow, did not improve the fitting. Thus,
thermal desorption is not an exponential decay: because of
diffusion, the release is decelerating. A second-order model
(µ
d
Ndt N
2)better estimates the average residence time of
adsorbates, although it fails for the last ∼30% of particles at
depth (yellow line), while a third-order model (magenta line)
predicts too slow a depletion of the surface reservoir. In
conclusion, a kinetic model with order between two to three
with respect to coverage should be adopted to model thermal
desorption from a powder.
Figure 2shows the desorption of sequestered argon as the
porous surface approaches and crosses sunrise. Time-dependent
simulations were performed at two different latitudes, equatorial
(left)and 45°north (right). In black is the outgassing from the grain
pile under the temperature heating profile shown in gray. Also
shown are the TPD curves from a smooth surface (exponential
decay with Eb =0.281 eV, blue), and a model with reduced rate as
established in the isothermal simulation (red), which both show the
asymmetric peak shape typical of first-order TPD curves. The first-
order model with a reduced rate correctly predicts the timing of the
peak at sunrise, but overestimates its amplitude (the slow ramp-up
in outgassing from the powder). Additionally, a porous surface
outgasses for up to 10 hr longer than a smooth surface. Not only
is the symmetric TPD curve from the grain pile qualitatively
consistent with second-order desorption (magenta line), but also we
confirmed quantitatively with an Arrhenius plot of ln(R/N
n
)versus
1/T(De Jong & Niemantsverdriet 1990),wherenis the order of
desorption, that second or even higher desorption order is justified.
The effect of increasing the sticking coefficient is an increase in the
order of desorption.
What is the mechanism causing slow desorption? In order to
appreciably diffuse inward during the long lunar night via the
slower surface diffusion mechanism, an argon atom would
require a low activation barrier for surface diffusion. However,
in time-dependent simulations that better approximate the
expected depth distribution of adsorbates at sunrise, we found
only small differences in the outgassing profile when α0.25.
This finding suggests that the initial distribution of particles
with depth, followed by Knudsen diffusion, were the main
cause of the delay in desorption. The increase of Knudsen
diffusion into porous media at the onset of desorption has been
demonstrated experimentally (Ballinger et al. 1989). Outward
diffusion of an adsorbate through MgO powders with nano-
sized interparticle voids showed both a fast and a slow
diffusion channel, suggestive of bonding on two types of sites,
and thermal desorption followed a symmetric TPD curve unlike
afirst-order curve (Kim et al. 2009, their Figure 4). We suggest
that these experimental results are similar to our findings that
desorption from a powder is slower than an exponential decay
of the adsorbate reservoir even for well-defined sites.
While Kegerreis et al. (2017)correctly identified diffusion as a
rate-limiting process, we do not confirm their implementation of
diffusive effects. Our recommendation is a change in the adopted
desorption order. Second-order kinetics, which are usually
associated with recombinative desorption, describe the time
profile of diffusion-controlled gas release from a grain pile even
for monoatomic gases. Furthermore, with this formulation we
retrieve meaningful desorption energies (i.e., the single-grain
attachment of 0.281 eV), whereas if we treated desorption as a
first-order process, we would erroneously infer a distribution of
binding energies for this gas-surface system from the TPD curve
(see Sarantos & Tsavachidis 2020).
Figure 2. Time-dependent simulations of argon, accumulated during the lunar nighttime onto a computer-generated powder, illustrate the slow release of sequestered
argon from porous regolith at sunrise (black). Simulations of exponential decay (blue and red), the current standard used in exosphere models, fail to reproduce the
long tail of the regolith outgassing. A second-order model (magenta)better describes the diffusion-controlled removal of gas near the terminator as the regolith is
heated (right axis).
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3.2. Adsorbed Water
Figure 3illustrates the effects of porosity and diffusion on
the timing of the desorption of deposited water. For these
simulations we used the activation energy of water release from
a Highlands sample 14163 (Jones et al. 2020a). For the surface
diffusion barrier we assumed α=0.25–0.99. To highlight the
porosity effects we also used the equations in Barrie (2008)to
illustrate the expected TPD curve from a flat surface with this
binding energy distribution under the assumptions of first-order
desorption and no surface diffusion. The latter are the typical
assumptions in exosphere models.
The simulated TPD spectrum, recorded as the total number
of desorption events every 1000 s, is shown in Figure 3(a). For
rapid surface diffusion values (α0.5), shown in blue, we get
a TPD curve similar to argon. In this limit shallow sites are
immediately upon desorption replenished by diffusion from the
active sites, accelerating desorption. For the same distribution
of desorption energies but intermediate values of surface
diffusion (α=0.7), shown in black, the desorption shifts to
higher temperature and exhibits a tail of long-lived adsorbates.
Our result confirms the analysis by Xia et al. (2007), who
predicted that the desorption rate in a TPD experiment from
surfaces with a broad energy distribution should peak at lower
temperatures when surface diffusion is considered. A case with
equal diffusion and desorption barriers is shown in red, and the
case for first-order desorption from a flat surface with no
diffusion is shown in green (Barrie 2008). Contrasting these
four cases, it can be concluded that high migration barriers
(α>0.5)and readsorption reduce the outgassing rates.
The cumulative desorbed fraction (Figure 3(b)) shows a
sigmoid curve characteristic of deadtime, while the powder
retains different amounts of water depending on the surface
diffusion assumption. With no surface diffusion (red curve), the
surface begins to outgas at lower temperature but overall
retains more molecules over a full thermal cycle. Up to 9% of
the deposited water test particles were retained for an entire
lunar day at equatorial latitudes when no surface diffusion and
the rate reduction due to porosity were simulated, compared to
2% retention from a single grain and/or smooth surface
(green).(This high retention efficiency reflects the fraction of
sites with initial binding energies >1.5 eV in the Jones et al.
2020a data, readsorption because of the high sticking
coefficient, and Knudsen diffusion deeper into the grain pile.)
For diffusion barriers lower than the desorption barrier (blue
and black lines), there is an additional deadtime of ∼3×10
4
s
(∼10 hr, or ∼6°in local time)before desorption commences as
shallow sites populate active sites via surface diffusion at early
morning temperatures. Although this migration delays the
onset of desorption, mobile atoms, which would be trapped
throughout a lunar cycle if immobile, can at higher tempera-
tures migrate to shallow sites and desorb repeatedly, like an
avalanche, overcoming loss to readsorption. Hence, over a
lunar day the surface is less retentive at equatorial and
midlatitudes for this gas-substrate system when the surface
diffusion barrier is much lower than the desorption barrier. On
the other hand, for latitudes experiencing maximum dayside
temperatures less than 190 K the initial deadtime from surface
diffusion results in a surface being more retentive for this
distribution of binding energies. We note that the desorption
curves are approximately independent of the assumed grain
size distributions (right panel of Figure 3), although their
asymptotic content may differ.
Our conclusions on the role of surface diffusion apply
regardless of the assumed distribution of binding energies
provided that there is a tail of chemisorption sites. This
statement was confirmed by repeating these simulations using
the energy distributions of Jones et al. (2020a)from the mare
sample 10084, which produced similar sigmoid curves (not
shown here). Furthermore, the absence of high-temperature
desorption when high adsorbate mobility is assumed is similar
to that observed by Jones et al. (2020a)from the Mare sample,
Figure 3. Porosity and surface diffusion complicate the desorption of adsorbed molecular water from regolith simulants. All cases adopted the same distribution of
desorption energies, E
des
, but varied the barrier for surface diffusion, E
diff
. Solid lines show desorption from the submature soil, whereas the dotted and dashed lines
show the effect of decreasing and increasing maturity through the particle size distribution.
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The Astrophysical Journal Letters, 919:L14 (7pp), 2021 October 1 Sarantos & Tsavachidis

suggesting that differences in surface diffusion be considered
as one of the processes that contribute to the differences
between Mare and Highlands soils (Poston et al. 2015; Jones
et al. 2020a).
4. Conclusions
We find two sources of gas lag corresponding to two forms
of diffusion. When all sites are equivalent, the desorption lag is
due to Knudsen diffusion followed by readsorption. The time
dependence of the adsorbate reservoir beyond the half-life, and
hence the exosphere longevity, is not correctly described by an
exponential decay because thermal desorption and Knudsen
diffusion form a negative feedback loop inside a powder
(Figures 1–2). To describe the removal of gas and derive
meaningful activation energies for desorption without explicitly
treating the multiple types of diffusion covered here, expressing
the gas release as a second-order reaction with respect to
surface concentration is a reasonable approximation in global
exosphere models.
We suggest that the thermal desorption flux be modeled as
F
out
(t)≈0.25 ×R
des
×σ×C
ads
(t)
2
, where F
out
is the instanta-
neous outgassing flux corresponding to an adsorbate coverage
C
ads
,R
des
is the single-grain desorption rate, and σ=10
−15
cm
2
is the cross section of an adsorption site. The factor 0.25
denotes the reduction of the yield from flat surfaces due to
readsorption (Figures 1–2). This parametric change will
describe how volatile adsorbates dissipate after sudden changes
(e.g., crossing the terminator, following a natural or manmade
impact, or following the descent of a lunar lander).
Surface diffusion, another diffusion mechanism ignored in
exosphere models, has measurable macroscopic effects. For
strongly bound gases, such as alkalis at the Moon, surface
diffusion assists adsorbates to escape microscopic shadows,
enabling more adsorbates to be degassed by photons but limiting
the photodesorption rates (Sarantos & Tsavachidis 2020).For
volatiles the effect of surface diffusion is more pronounced when
a wide distribution of binding energies is assumed. Thermal
hopping of adsorbates between physisorption (shallow)and
chemisorption (active)sites, i.e., diffusion in the energy dimen-
sion, affects the desorption rate in a complicated way, suppressing
desorption at lower temperatures (He & Vidali 2014),but
enhancing desorption over a lunar day depending on the
maximum dayside temperature of the soil. With this redistribution
mechanism, desorption at sunrise is slower and occurs at later
local times for species like water (Figure 3). More generally, when
surface diffusion has a lower barrier than desorption, the
occupancy of desorption energies is not evolved correctly with
time in exosphere models, and the modeling error (e.g., local time
of the peak density)grows as a wider distribution of binding
strengths is assumed. Kinetic parameters for adsorbate mobility
and desorption are equally needed from experiments.
The demonstrated effects of Knudsen and surface diffusion
apply to obtaining upper limits for all lunar volatile gases.
Volatiles such as CO, methane, and CO
2
, which adsorb weakly
with the nightside soil, will experience slower outgassing and
peak at later local times. Given binding energies and surface
mobility, the modeled output is less sensitive to remaining
parameters (sticking coefficient, grain size distribution).Onlythe
timeline and magnitude of the gas delays change with the
strength of the gas-surface bond, not the general trends described
here (higher-than-first-order desorption from granular medium,
nonlinear effect of mobility on outgassing from heterogeneous
surfaces). For instance, the second-or-higher-order desorption
effect under diffusive conditions also appears in the simulation of
alkali gas removal from loosely packed beds at Mercuryʼssurface
temperatures (Figure 3 of Sarantos & Tsavachidis 2020).
Although the strength of that bond, 1.85 eV, is much stronger
than the argon-surface bond, 0.28 eV, the granular medium
produces the same slow desorption. For these reasons, the effects
presented here do not merely describe specificgas-surface
systems, but can be generalized to all exosphere-surface
interactions involving thermal desorption.
This research was supported by the NASA Solar System
Workings program and the Solar System Exploration and
Research Virtual Institute (SSERVI)through LEADER. The
granular beds for these simulations were produced with
LIGGGHTS-Public v3.6.0. The Jones et al. (2020a)data were
retrieved from Jones et al. (2020b). Output of simulations
depicted in Figures 1–3is available at Zenodo (doi: 10.5281/
zenodo.5231999).
ORCID iDs
M. Sarantos https://orcid.org/0000-0003-0728-2971
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