Carbon dioxide clathrate hydrate formation at low temperature. Diffusion-limited kinetics growth as monitored by FTIR E. Dartois1, F. Langlet2, 1 Institut des Sciences Moléculaires d’Orsay, CNRS, Université Paris-Saclay, Bât 520, Rue André Rivière, 91405 Orsay, France e-mail: [email protected] 2 Institut d’Astrophysique Spatiale (IAS), UMR8617, CNRS, Université Paris-Saclay, Bât. 121, 91405 Orsay, France keywords: Infrared: planetary systems; Planets and satellites: composition; Comets: general; Methods: laboratory: solid state; Solid state: volatile; Molecular processes To appear in Astronomy & Astrophysics Abstract tion in climate change if natural fields are destabilised (Riboulot et al. 2018). Carbon dioxide clathrate hydrate is of interest for The formation and presence of clathrate hydrates could influ- fundamental research on Earth, or for its potential use in green- ence the composition and stability of planetary ices and comets; house gas sequestration (Duc et al. 2007; House et al. 2006). they are at the heart of the development of numerous complex planetary models, all of which include the necessary condition In a planetary or astrophysical context, clathrate hydrates imposed by their stability curves, some of which include the are considered because they can retain volatile molecules at cage occupancy or host-guest content and the hydration number, pressures higher than the pure compound that would otherwise but fewer take into account the kinetics aspects. We measure sublimate under most astrophysical conditions, and/or influence the temperature-dependent-diffusion-controlled formation of the the geophysics of large bodies (e.g. Fortes & Choukroun 2010; carbon dioxide clathrate hydrate in the 155-210 K range in or- Choukroun et al. 2010; Bollengier et al. 2013). The existence der to establish the clathrate formation kinetics at low temper- of clathrate hydrates in Solar System bodies has been explored ature. We exposed thin water ice films of a few microns in in many models, principally on the basis of the stability curves thickness deposited in a dedicated infrared transmitting closed for these inclusion compounds. During the evolution of the so- cell to gaseous carbon dioxide maintained at a pressure of a few lar nebula, the existence of clathrate hydrate, or rather its sta- times the pressure at which carbon dioxide clathrate hydrate is bility, depends on pressure and temperature. These thermody- thermodynamically stable. The time dependence of the clathrate namic properties represent a necessary but not sufficient condi- formation was monitored with the recording of specific infrared tion. In many bodies, in particular small bodies such as comets, or low-temperature objects orbiting at large distances, such as vibrational modes of CO2 with a Fourier Transform InfraRed (FTIR) spectrometer. These experiments clearly show a two- trans-Neptunian objects, including Kuiper Belt objects, the ki- step clathrate formation, particularly at low temperature, within netics for their formation becomes a primary driving factor to a relatively simple geometric configuration. We satisfactorily take into account in the modelling. applied a model combining surface clathration followed by a Carbon dioxide is a significant constituent of large to smaller bulk diffusion-relaxation growth process to the experiments and icy bodies of the Solar System. The kinetics of carbon diox- derived the temperature-dependent-diffusion coefficient for the ide clathrate hydrate formation (Schmitt 1986; Schmitt et al. bulk spreading of clathrate. The derived apparent activation en- 2003; Circone et al. 2003; Genov et al. 2003) is a key in- ergy corresponding to this temperature-dependent-diffusion co- gredient in any discussion about clathrate formation. Kinetics experiments have been performed on clathrates using, for exam- efficient in the considered temperature range is Ea =24.7 ± 9.7 kJ/mol. The kinetics parameters favour a possible carbon diox- ple, neutron diffraction experiments monitoring the ice structural ide clathrate hydrate nucleation mainly in planets or satellites. change towards clathrate formation (Falenty et al. 2013; Hen- ning et al. 2000), or more classical, Pressure, Volume, Temper- ature (PVT) experiments (Falenty et al. 2013) in the 272-185K 1. Introduction range. These experiments are mostly based on the polydisperse distribution of ice spheres, with peak size distributions generally Clathrate hydrates are inclusion compounds that trap molecules in the 20-200 microns range. The interpretation of these data arXiv:2107.01377v1 [physics.chem-ph] 3 Jul 2021 in a crystalline water ice network. For the two main structures, is performed using a modified so-called Johnson-Mehl-Avrami- these clathrate hydrates form water-based cages of different sizes Kolmogorov (JMAK) phenomenological model and knowledge and of two types, a larger one (forming a hexagonal truncated of the size distribution of ice particles. The duration of the neu- trapezohedron or hexadecahedron) and a smaller one (forming tron diffraction experiments is often limited to typically tens of a pentagonal dodecahedron), leading to the simplest clathrate hours because of the availability of diffraction beam lines shifts, structures I and II, respectively. On Earth, the main interest in which can limit the temperature range explored. Indeed, as the clathrate hydrates is focused on methane clathrate hydrate, either diffusion coefficient generally follows an Arrhenius equation, it as a potential hydrocarbon resource (e.g. Jin et al. 2020; Boswell evolves exponentially with temperature and going to lower tem- et al. 2020) or for for the problems caused by its ability to block peratures becomes a difficult issue, requiring long-duration ex- pipelines in the petrol industry (e.g. Fink 2015) or its participa- periments. In this article, we develop an alternative experimental + 2 + LC 1 3 2 3 1.5 SC LC SC 165K 118d evac. 3 1.0 100d 2 118d evac. 30d 0.5 Optical depth Optical depth 1 100d 30d 1d 1d 0.0 0 Model Model 165K 4000 3000 2000 1000 3750 3700 3650 3600 Wavenumber (cm-1) Wavenumber (cm-1) Fig. 1. Infrared spectra of the clathrate kinetics experiment performed at 165K. Spectra extracted after 1, 30, and 100 days of exposure of the ice −1 film to CO2 gas at 60 mbar are shown in the 4500-600 cm range in the left panel. The upper trace is the spectrum recorded just after evacuation of the gas at the end of the experiment after 118 days. A close-up on the gas and clathrate hydrate signatures in the ν1 +ν3 and 2ν2 +ν3 combination modes is shown in the right panel. Under each spectrum is shown the baseline-corrected spectrum of the contribution by the CO2 in the clathrate cages after subtraction of the gas phase contribution to the spectrum. The CO2 signatures in the small (SC) and large (LC) cages of the clathrate hydrate are labelled in the upper trace. The lower trace is a model of the CO2 gas phase at 165K. See text for details. approach based on the direct measurement, in transmittance, of CO2 was purchased from Air liquide. The initial purity is the infrared signature of the caged molecules within a controlled N25 (99.999%). The experimental setup consists in a gold- thin ice film structure. This approach allows us to extend the coated copper cell, thermally coupled to a liquid N2-transfer measurements to lower temperatures (down to 155K) at which cold finger placed in a high-vacuum, evacuated cryostat (P < the kinetics are measured. The article is organised as follows: in 10−7mbar). Infrared transmitting zinc selenide windows of 4 mm the following section, we describe the kinetics experiments per- in thickness facing each other with some space in between, are formed and the two-step diffusion and nucleation model adjusted sealed with indium gaskets, and allow the spectrometer beam to the data. We then discuss the results, derive the kinetics and to record clathrate hydrate spectra in transmittance. A soldered apparent activation energy of the low-temperature carbon diox- stainless steel injection tube brazed to the lower part of the cell ide clathration, and discuss their astrophysical implications. allows the entry or evacuation of gas. A description of such a cell can be found in Dartois et al. (2010) for example. The cell was modified to limit the distance between the two ZnSe windows to a space of the order of 200 µm, which is sufficiently small to al- 2. Experiments low us to monitor the clathration of CO2 while the ice film is ex- posed to the gas. To prepare the ice film, water vapour is injected into the evacuated cell pre-cooled to 240K, and condenses on the Table 1. Summary of experiments ZnSe windows. The cell is then lowered to the temperature of study. The guest gas is then injected, with a pressure excess a a TPexp Peq Duration Thickness few times the clathrate stability pressure, and below the CO2 ice (K) (mbar) (mbar) h/(days) (µm) condensation pressure. The pressures used are given in Table 1, 155 20 9.32 430(18) 2.6±0.4 as well as the expected equilibrium pressure for the clathrate 165 60 23.5 2820(118) 3.6±0.5 stability. The thickness of the produced ice film varied from a 170 120 37.3 1260(53) 0.7±0.1 fraction of a micron to several microns, and 13 mm in diame- 177.5 200 71.7 1778(74) 5.0±0.7 ter. The thickness is monitored by Fourier Transform InfraRed 185 400 128.6 1595(66) 5.0±0.7 (FTIR) spectroscopy, over the central 7 mm of the IR windows 190 700 186.5 1196(50) 6.5±1.0 of the cell. Spectra were recorded regularly as a function of time, 200 1200 365.0 379(16) 5.1±0.7 with a spectral resolution set between 0.16 and 0.32 cm−1, with 205 1600 498.0 1080(45) 20±3 a liquid nitrogen (LN2) Mercury Cadmium Telluride (MCT) de- 207.5 1700 588.4 254(11) 4.9±0.7 tector.