Multiple equilibria description of type H1 hysteresis in gas sorption isotherms of mesoporous materials

Abstract

We report argon adsorption/desorption isotherms of MCM-41 and of SBA-15. The shape of all hysteresis loops we have observed corresponds to type H1. The data have been analyzed quantitatively using the multiple equilibria description and applying the notion of metastable thermodynamic equilibrium. It is remarkable and important that for both mesoporous materials the desorption process can be understood according to this description but with a corresponding equilibrium constant. This procedure therefore allows determining the thermodynamic values for the enthalpy and the free enthalpy of cavity desorption and thus to obtain information not available so far. We observed that the MCM-41 adsorption isotherms show first an increase with the characteristic Langmuir shape, followed by the almost instantaneous filling of cavities that ends as soon as all cavities are completely filled. The SBA-15 isotherms show a characteristic Langmuir shape at low relative pressure. The pressure slightly below the inflection point at prel, infl = 0.312 marks the beginning of the growth of a second layer, before an almost instantaneous filling of cavities takes place. It is interesting to observe that the values of the enthalpy and the free enthalpy for cavity filling and cavity desorption differ by about 0.1 kJ/mol for both, MCM-41 and SBA-15. This means that the driving force for developing a hysteresis is small. The hysteresis loop is therefore driven by delicate changes occurring within the cavities, partially or completely filled by the adsorbate. The monolayer coverage and monolayer desorption processes are decoupled from the cavity filling and cavity emptying processes. Knowing thermodynamic parameters for the hysteresis loop ultimately helps to better characterize and understand the experimental observations.