  The formation and presence of clathrate hydrates could influence the
composition and stability of planetary ices and comets; they are at the heart
of the development of numerous complex planetary models, all of which include
the necessary condition imposed by their stability curves, some of which
include the cage occupancy or host-guest content and the hydration number, but
fewer take into account the kinetics aspects. We measure the
temperature-dependent-diffusion-controlled formation of the carbon dioxide
clathrate hydrate in the 155-210~K range in order to establish the clathrate
formation kinetics at low temperature. We exposed thin water ice films of a few
microns in thickness deposited in a dedicated infrared transmitting closed cell
to gaseous carbon dioxide maintained at a pressure of a few times the pressure
at which carbon dioxide clathrate hydrate is thermodynamically stable. The time
dependence of the clathrate formation was monitored with the recording of
specific infrared vibrational modes of CO2 with a Fourier Transform InfraRed
(FTIR) spectrometer. These experiments clearly show a two-step clathrate
formation, particularly at low temperature, within a relatively simple
geometric configuration. We satisfactorily applied a model combining surface
clathration followed by a bulk diffusion-relaxation growth process to the
experiments and derived the temperature-dependent-diffusion coefficient for the
bulk spreading of clathrate. The derived apparent activation energy
corresponding to this temperature-dependent-diffusion coefficient in the
considered temperature range is E_a = 24.7 +/- 9.7 kJ/mol. The kinetics
parameters favour a possible carbon dioxide clathrate hydrate nucleation mainly
in planets or satellites.
