  Observations by ISO and Spitzer towards young stellar objects (YSOs) showed
that CO$_2$ segregates in the icy mantles covering dust grains. Thermal
processing of ice mixture was proposed as responsible for the segregation.
Although several laboratory studied thermally induced segregation, a satisfying
quantification is still missing. We propose that the diffusion of CO$_2$ along
pores inside water ice is the key to quantify segregation. We combined
Temperature Programmed Desorption (TPD) and Reflection Absorption InfraRed
Spectroscopy (RAIRS) to study how CO$_2$ molecules interact on a non-porous
amorphous solid water (np-ASW) surface. We found that CO$_2$ diffuses
significantly on a np-ASW surface above 65~K and clusters are formed at well
below one monolayer. A simple rate equation simulation finds that the diffusion
energy barrier of CO$_2$ on np-ASW is 2150$\pm$50 K, assuming a diffusion
pre-exponential factor of 10$^{12}$ s$^{-1}$. This energy should also apply to
the diffusion of CO$_2$ on wall of pores. The binding energy of CO$_2$ from
CO$_2$ clusters and CO$_2$ from H$_2$O ice have been found to be $2415\pm20$
and $2250\pm20$~K, respectively, assuming the same prefactor for desorption.
CO$_2$-CO$_2$ interaction is stronger than CO$_2$-H$_2$O interaction, in
agreement with the experimental finding that CO$_2$ does not wet np-ASW
surface. For comparison, we carried out similar experiments with CO on np-ASW,
and found that the CO-CO interaction is always weaker than CO-H$_2$O. As a
result, CO wets np-ASW surface. This study should be of help to uncover the
thermal history of CO$_2$ on the icy mantles of dust grains.
