A model is proposed for the description of diffusion-controlled
adsorption kinetics on fractal surfaces. This
model is based on a constitutive equation between the mass flux and the
concentration gradient of the adsorbing
species expressed in terms of a Riemann−Liouville (fractional)
operator of noninteger order ν. The order ν
depends on the fractal dimension d
f of the
adsorbent surface, ν = df −
d
T, d
T being its
topological dimension.
The model is compared with Monte Carlo simulations and with the
approach proposed by Seri-Levy and
Avnir and displays a good level of agreement with Monte Carlo data over
all time scales.
The relationships between geometric roughness and energetic heterogeneity are discussed by considering a thermodynamically consistent model of adsorption isotherms (Keller model) which encompasses fractal scaling and the dependence of the adsorption energies on the coverage. Experimental results validate this model and indicate that it can be used not only to interpolate experimental data but also to predict adsorption equilibria of multicomponent rnixtures. The peculiar non-Henry behaviour of the Keller model at low pressure is discussed by considering a simple model of preferential adsorption on a rough energy landscape and including the effect of surface diffusion.
We propose a general method to generate correlated energy landscapes for model heterogeneous surfaces. It is based on the representation of an energy landscape as a superposition of exponentially correlated Gaussian processes. This method is the extension of a previous work of Giona and Adrover to reconstruct binary lattice models of porous structures to a random energy field with values between 0 and ∞. The application to dual bond-site models is also developed.
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