Simple models of adsorption in nanotubes

We present two very simple models of adsorption in cylindrical pores. It is assumed that a layer-by-layer mechanism occurs similarly to that in the BET theory. The major assumption is that in the pores having an adsorption space with cylindrical geometry, the surface area of the upper surface (in comparison with the bottom surface) should be diminished in proportion to the radii of a cylinder. Two cases are considered: the adsorbate–adsorbate interactions are neglected or they are taken into account according to the lattice model developed by Fowler and Guggenheim. It is shown that the data simulated by Ohba and Kaneko for adsorption of nitrogen in the internal space of carbon nanotubes are successfully described by our models. On the basis of the fitted data we show that the relation between the monolayer capacity in cylindrical pores and on flat surfaces is in excellent agreement with the equation developed recently by Salmas and Androutsopoulos. Moreover, our models are verified for two sets of experimental data reported by Kaneko et al. We obtain excellent agreement between the values of the pore diameters calculated by us and suggested by these authors (from HRTEM, the GCMC simulations, and the IDBdB model). It is concluded that proposed simple and fast models can be applied as a first approximation to the estimation of the internal nanotube diameters if they do not exceed ca. 5 nm and are slightly dispersed.