Dielectric properties of CO2 clathrate hydrates for the exploration of the jovian icy moons
Authors: Ercilla Herrero Oscar , Sanchez-Benitez Javier , Muñoz-Iglesias Victoria , Prieto-Ballesteros Olga 
Published: September 2022

&lt;p&gt;&lt;strong&gt;Introduction&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;CO&lt;sub&gt;2&lt;/sub&gt; clathrate is one of the possible compounds in the crust of ice moons. The analysis of the data provided by the NASA Galileo mission revealed that the Jovian moons have both, the chemical and the physical conditions required for clathrate hydrates to be formed from the surface to deeper layers (Prieto-Ballesteros &lt;em&gt;et al.&lt;/em&gt; 2005, Hand &lt;em&gt;et al.&lt;/em&gt; 2006, Izquierdo-Ruiz &lt;em&gt;et al.&lt;/em&gt; 2020).&lt;/p&gt;&lt;p&gt;The study of the dielectric properties of water-related minerals is key to understand the results of future missions to Jupiter and its satellites. The JUICE (ESA) and Europa Clipper (NASA) missions will try to determine the internal subsurface structure of these Jovian icy moons with the radar instruments onboard: RIME and REASON respectively. These instruments will operate both at a frequency of 9 MHz, with capacity to penetrate from 1 to 30 km depth. REASON has an extra antenna of 60 MHz to explore shallow depths (that is, 300 m to 4.5 km).&lt;/p&gt;&lt;p&gt;There are many works about the physical properties of clathrate hydrates (for instance: Sloan &lt;em&gt;et al&lt;/em&gt;, 2007), but just a few of them are focused on their electrical properties in planetary conditions. Davidson (1973) and Davidson &amp; Ripmeester (1978) determined the high frequency permittivity (&amp;#949;&lt;sub&gt;&amp;#42649;&lt;/sub&gt;) of several clathrates, finding a value of 2.85 at 233 K for clathrates of simple guest molecules such as argon and nitrogen. This value increases over 7.7 for other guest molecules and structures such as ethylene oxide and acetone. So far, only Stern &lt;em&gt;et al.&lt;/em&gt; (2021) investigated CO&lt;sub&gt;2&lt;/sub&gt;- and CH&lt;sub&gt;4&lt;/sub&gt;- clathrate hydrates to determine their electrical conductivity, but not their permittivity.&lt;/p&gt;&lt;p&gt;In this work we present novel results for CO&lt;sub&gt;2&lt;/sub&gt; clathrate including a combined electrical conductivity and permittivity study.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Methodology&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;We use a stainless-steel high pressure chamber with an internal volume of 60 ml for the formation of clathrate hydrates. In this cell we mixed distillated water with CO&lt;sub&gt;2&lt;/sub&gt; gas at 30 bar of pressure.&lt;/p&gt;&lt;p&gt;The conditions of temperature and pressure are recorded at fixed time intervals by sensors inserted into the cell during all the testing period. For the electrical measurements we used a Teflon cell inside the pressure chamber with two polished stainless steel electrodes. Data were taken in isothermal conditions, stabilizing the sample during 10 minutes at each temperature step, when the conductance (G) and parallel capacitance (Cp) were measured, in the frequency range from 20 Hz to 10&lt;sup&gt;6&lt;/sup&gt; Hz in several steps using an LCR precision meter (IM3536-01 Hioki).&lt;/p&gt;&lt;p&gt;The electrical measurements were taken at different temperatures inside the boundaries of the CO&lt;sub&gt;2 &lt;/sub&gt;clathrate equilibrium curves, where several phases such as water, CO&lt;sub&gt;2&lt;/sub&gt; dissolved, CO&lt;sub&gt;2&lt;/sub&gt; gas, water ice, and/or CO&lt;sub&gt;2&lt;/sub&gt; clathrate, can co-exist, following the phase diagram H&lt;sub&gt;2&lt;/sub&gt;O-CO&lt;sub&gt;2&lt;/sub&gt;. We have performed &lt;em&gt;in situ&lt;/em&gt; Raman spectroscopy through the sapphire window of the chamber, in order to determine the specific phases stabilized at each temperature step before collecting the electrical data measurement..&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Results&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;We measured the electrical conductivity and real permittivity values for samples of 1) CO&lt;strong&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/strong&gt; clathrate and, 2) water with CO&lt;sub&gt;2&lt;/sub&gt;. The results allowed us to discriminate the presence of the CO&lt;sub&gt;2&lt;/sub&gt; clathrate phase respecting to other phases that could also be formed during the experiments.&lt;/p&gt;&lt;p&gt;When CO&lt;sub&gt;2&lt;/sub&gt; clathrate is formed, the electrical characterization shows the conductivity and the real part of the permittivity constant with frequencies higher than 100 kHz, with smooth variation with the temperature. At 255 K the real permittivity (&amp;#949;&lt;sub&gt;&amp;#42649;&lt;/sub&gt;) was 2.5, and the conductivity (&amp;#963;) was 1.5&amp;#183;10&lt;sup&gt;-6&lt;/sup&gt; S/cm. Both obtained values are in good agreement with Stern &lt;em&gt;et al.&lt;/em&gt; (2021).&lt;/p&gt;&lt;p&gt;The conductivity and real permittivity of the two phases sample H&lt;sub&gt;2&lt;/sub&gt;O+CO&lt;sub&gt;2&lt;/sub&gt; with no clathrate formation showed a steeper dependence with frequency and temperature in comparison with the CO&lt;sub&gt;2&lt;/sub&gt; clathrate. At 265 K, &amp;#949;&lt;sub&gt;&amp;#42649;&lt;/sub&gt; was 1.5, and &amp;#963; was 1.04&amp;#183;10&lt;sup&gt;-6&lt;/sup&gt; S/cm.&lt;/p&gt;&lt;p&gt;The attenuation of the signal was calculated from the experimental values of conductivity and real permittivity according to the next equation (Petinelli &lt;em&gt;et al.&lt;/em&gt;, 2015) at 10 kHz.&lt;/p&gt;&lt;p&gt;&amp;#120572; &amp;#8773; &amp;#120590;/(2&amp;#119888;&amp;#120576;&lt;sub&gt;0&lt;/sub&gt;( &amp;#8730;&amp;#120576;&amp;#180;))&lt;/p&gt;&lt;p&gt;The attenuation showed clear differences between CO&lt;sub&gt;2&lt;/sub&gt; clathrate, icy water with dissolved CO&lt;sub&gt;2&lt;/sub&gt;, and ice water itself, with attenuation obtained values of 10.99, 1.35 and 0.34 dB/km at 265 K, respectively.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Conclusions&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;The different phases of the H&lt;sub&gt;2&lt;/sub&gt;O-CO&lt;sub&gt;2&lt;/sub&gt; system have appreciable differences in their electrical properties, which means that differences in the physical state could be identifiable by radar measurements. The possible relation with surface morphological features could eventually help to understand the geological activity of the moons, such as the mechanism of jets formation proposed for Europa (Shibley &amp; Laughlin, 2021) or&amp;#160; the formation of the double ridge structures (Culberg &lt;em&gt;et al.&lt;/em&gt;, 2022).&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Acknowledgments&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;This work was supported by the ESA contract 4000126441/19/ES/CM, and the MINECO Projects PID2019-107442RBC32, and PRE2020-093227.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Prieto-Ballesteros, O. &lt;em&gt;et al.&lt;/em&gt; 2005 Icarus, 177, 491-505.// Hand, K. &lt;em&gt;et al.&lt;/em&gt; 2006, Astrobiology Vol 6, 3. 463-482. // Izquierdo-Ruiz, F. &lt;em&gt;et al.&lt;/em&gt; 2020 ACS Earth and Space Chemistry 2020 4 (11), 2121-2128 // Sloan Jr, E.D. &lt;em&gt;et al.&lt;/em&gt; 2007. Clathrate Hydrates of Natural Gases (3rd ed.). CRC Press // Davidson, D.W. 1973 The Physical Chemistry of Water Vol2 115-234. // Davidson D.W. &amp; Ripmeester J.A. 1978. Journal of Glaciology, 21, 33-49. // Stern L. A. &lt;em&gt;et al.&lt;/em&gt; 2021, Geophysical Research Letters, 48 // Petinelli &lt;em&gt;et al.&lt;/em&gt; 2015. Reviews of Geophysics 53, 593-641 // Shibley, N.C. &amp; Laughlin, G. 2021. The Planetary Science Journal, 2:221 // Culberg &lt;em&gt;et al.&lt;/em&gt; 2022. Nat Commun&amp;#160;13,&amp;#160;2007&lt;/p&gt;