I'm not a specialist in this field but the study of adsorption/desorption reminds me temperature programmed desorption (TPD) and polarization modulation reflection absorption infrared spectroscopy (PR-RAIRS)
For equilibrium adsorption and kinetic uptake measurements gravimetric analyzers are also routinely used. For dynamic adsorption/desorption studies a fixed bed adsorber with pressure/temperature swing facility may be used.
I definitely suggest you to use TGA under CO2 (adsorption)/N2 (desorption) atmosphere. It is quite straightforward to measure sorption capacity as a function of temperature or time (sorption kinetic).