The FHH Multilayer Expression: Effects of Particle Size

Abstract

Frenkel-Halsey-Hill (FHH) plots are presented using the adsorption data from eleven silicas with surface areas between 40 and 1200 m 2 g −1 . These materials consist of regular nonporous primary particles which have been approximated as monomodal size distributions of spheres. Two models (semi-infinite slab and spherical particle) were used to make the FHH plots. The results from these plots indicate that the FHH coefficient and exponent vary with particle size. A model is proposed for a particle having a featureless Lennard-Jones surface which predicts (a) that the actual variation is in the coefficient alone, which depends upon coverage as well as particle size, but (b) on a ‘spherical particle’ FHH plot, this variation will manifest itself as a particle size dependence of both coefficient and exponent. However, the model predicts that the exponent should decrease with particle size; experimental results show it to increase. The model also predicts that ‘flat surface’ FHH plots should be less linear than the ‘spherical particle’ plots, and should deviate downwards at high coverage, when in fact the ‘flat surface’ plots are more linear. Predictions obtained by recalculating the model in the absence of the surface energy term are in much better agreement with the experimental results, indicating that the surface energy correction is possibly excessive, e.g. if the particles were actually polyhedral instead of spherical.