Adsorption-Diffusion of Water in Activated Lunar Soil

ADSORPTION-DIFFUSION OF WATER IN ACTIVATED LUNAR SOIL. Norbert Sch¨ orghofer1,1Planetary Science Institute, Honolulu, HI & Tucson, AZ, USA ([email protected]) Introduction: The Moon has water in the form of cold-trapped ice deposits in permanently shadowed regions [1, 2] and possibly adsorbed water in sunlit regions [e.g., 3, 4]. Water diffusion in the lunar soil differs from standard diffusion in porous media for several reasons. First, the time of migration is dominated by surface residence times not by the time of flight. Second, lunar grains are covered by amorphous rims, metamict layers whose crystalline structure has been lost due to solar-wind irradiation damage or impactgenerated vapors [5]. Space weathering (electromagnetic and particles) leads to the formation of highly reactive surface atoms [6, 7] and a range of desorption energies is present within a single grain surface. Third, the microporosity and specific surface are extremely high. The goal of this work is to develop a quantitative adsorption-diffusion model that takes these extreme physical conditions into account. Adsorption of water: Laboratory measurements on crushed lunar samples [8], micronized JSC-1A [9, 10], and fresh Apollo samples [11, 12] reveal a wide range of desorption energies. A small fraction of the surfaces of lunar grains has remarkably high desorption (binding) energies. Figure 1 shows a theoretical fit to laboratory measurements, which illustrates the wide range of desorption energies. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 1 2 3 4 5 Energy (eV) n Ep Eu Eice Figure 1: Distribution of desorption energies in an idealized model (blue line). Fits to laboratory measurements suggest Eice = 0.53 eV, Ep≈0.65 eV, and an exponential decay width of about 0.22 eV [13]. One end-member model for adsorption is to assume water molecules migrate to the sites with the highest binding energies. In this case, the highest desorption energies are filled first (blue shaded area). Figure 2 shows a parametrization of molecular residence times for H2O as a function of temperature and adsorbate coverage. Note that at lunar temperatures adsorption residence times exceed time-of-flight between grains. For more than one monolayer coverage, the desorption rate can be calculated from BET theory. An approximation to the BET isotherm was developed 400 300 200 150 100 75 Temperature (K) 10 -20 10 -15 10 -10 10 -5 10 0 10 5 10 10 Residence Time (years) lunation ballistic flight intergrain time-of-flight ice BET monolayer (15563) TPD 0.65 eV, =1013 /s TPD 0.78 eV, =1016 /s TPD 1.5 eV, =1016 /s 10 -10 10 -5 10 0 10 5 10 10 10 15 Residence Time (seconds) Figure 2: Residence times of H2O as a function of inverse temperature for ice, a monolayer of adsorbed water according to the BET isotherm, and several energies from Temperature-Programmed-Desorption (TPD) measurements for lunar samples. Figure form Ref. [13]. that continuously connects to the submonolayer desorption rates and and approaches the BET behavior for many layers [13]. The activation energy for surface diffusion is typically 5–20% of the desorption energy [14]. However, for complex surfaces this fraction can be significantly higher [15]. If grain surface diffusion is efficient, impinging water molecules will migrate and end up in the strong binding sites. Without grain surface diffusion, molecules have to impinge multiple times before encountering a strong binding site. Two end-member models for adsorption are developed, one assuming grain surface diffusion is very efficient and the other assuming adsorbed water molecules do not migrate on the grain surface at all. For the first end-member model, the flux of desorbed molecules can be calculated analytically and the result resembles that of the Freundlich isotherm [13]. The other end-member model requires to keep track of the adsorbate density for each energy. Diffusion model: Vapor diffusion models for lunar soil have been used by a number of authors [e.g., 16–21]. Here, the extreme heterogeneity of the surfaces is incorporated into the governing equations. Continuum-formulations for diffusion through activated lunar soil (i.e., grain surfaces have a range of desorption energies) are developed for both end-member model. For the first-end member (H2O molecules quickly migrate to the sites with the highest desorption energies), the evolution of the adsorbate density, θ(number of water molecules per grain surface area), is found to 0 2 4 6 8 10 0 0.02 0.04 0.06 0.08 0.1 #adsorbedH2Olayers Depth,z(m) 130K 130K±40K 100 120 140 160 0 0.02 0.04 0.06 0.08 0.1 Temperature(K) Figure 3: Depth profiles of H2O adsorbate concentration between the surface and ice at 10 cm depth as calculated with the new adsorption-diffusion model. The mean surface temperature is 130 K. follow Y∂θ ∂t =ϕλ2 2 ∂2S ∂z2(1) where Yis a roughness factor, ttime, ϕporosity, λan inter-grain distance, S(θ, T )is the desorption rate, and zdepth below the surface. A more general formulation considers the adsorbate density for each energy, Θ(E). The integral over Θis θ. The following governing equation was derived: Y∂Θ ∂t =−Ξ + S+ϕλ2 2 ∂2S ∂z2n(2) Θ(E)is the adsorbate density for each adsorption energy, Ξ(E, Θ, T )the desorption rate for adsorption energy E(the integral over Ξis S), and n(E)is the distribution of desorption energies (Fig. 1). Adsorption profile above buried ice: One of many applications of these models is to predict the adsorbate concentration profile above buried ice. Consider water ice buried 10 cm below the surface. Grains desorb water molecules, but at the same time receive and adsorb water molecules desorbed from their neighbors. On the surface, no adsorbed water is present and at the ice table the desorption rate approaches the sublimation rate (grains are coated by many monolayers). When the temperature is constant with time, the system evolves toward an equilibrium concentration profile. Figure 3 shows the adsorbate concentration profile obtained with this model. Within the first grain layer, the concentration jumps to more than one monolayer. This huge concentration gradient is caused by the contrast between residence times for subversus multi-layer coverage. The dynamic adsorption-diffusion model can be used to calculate adsorption profile even under the influence of a diurnal temperature cycle. As shown in Figure 3, a temperature amplitude flattens the adsorbate profile, but the concentration still increases rapidly within the top layer. Hence, with or without a temperature amplitude, adsorbate concentrations become large already at a fraction of the burial depth. This expectation may be helpful for exploratory drilling operations in the lunar polar regions. Buried ice should manifest itself by high adsorbate concentrations long before the ice table is reached. At a typical specific surface area of 500 m2/kg for lunar soil, one monolayer corresponds to 150 ppm of water by weight, so multi-layer abundances could reach permil level. Additional applications of the model include: (i) diurnal variations of adsorbed water concentrations, (ii) vapor pumping and subsurface cold-trapping, and (iii) vapor emission and isotopic fractionation during drilling operations. Acknowledgments: This material is based upon work supported by NASA through the Solar Systems Workings Program. References [1] W. C. Feldman, et al. Science 281: 1496–1500, 1998. [2] A. Colaprete, et al. Science 330: 463–468, 2010. [3] R. N. Clark. Science 326: 562–564, 2009. [4] A. R. Hendrix, et al. GRL 46: 2417–2424, 2019. [5] L. P. Keller and D. S. McKay. Geochim. Cosmochim. 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