Expansion or Contraction of Slit Pores Due to Gas Uptake

Adsorption inside a slit pore of flexible width w is explored, with a focus on how w varies as a function of the external pressure P of a gas in equilibrium with the adsorbate within the pore. The analysis is first carried out in general, using a minimization of the thermodynamic grand potential energy of the system. This leads to an equation predicting both the gas uptake N as a function of chemical potential mu and the expansion (or contraction) of the pore in response to the adsorbate's pressure. The resulting equilibrium behavior depends on the elastic parameters of the host material. Explicit results are derived for three adsorption systems: a low density fluid, Ar (a classical fluid at finite temperature T) in a graphite pore and (4)He within a Au pore at T=0. The resulting behaviors include some situations where the pore expands and others for which it contracts. The difference arises from the sign of the thermodynamic response of the fluid as a function of slit width.