A model for surface diffusion of ethane and propane in activated carbon

In this paper we present a model for surface diffusion in heterogeneous activated carbon. A structural model for activated carbon was first assumed, upon which a model for the surface diffusion mechanism was proposed. This model allows for the penetration of molecules into graphitic layer units, diffusion through it and evaporation out of it. Upon leaving the graphitic units, molecules then rejoin with other molecules diffusing through the porous medium via the larger void space parallel to the graphitic layers. They in turn then diffuse through the amorphous region of the activated carbon. The sequence of these steps repeats itself in a periodic pattern. The model gives rise to an 'apparent' surface diffusivity which is an explicit function of temperature and concentration of the adsorbed species. The activation energy of this 'apparent' surface diffusivity was found to take values between the activation energy for diffusion through the graphitic units and the heat of adsorption. Under proper conditions, it can be equal to the heat of adsorption. In terms of the concentration dependence, this model shows a very strong dependence of the surface diffusivity on the adsorbed concentration; for example, when the Langmuir isotherm prevails, the dependence of D(s) on fractional loading takes the following form: D(s) = D(s)(0)/(1-θ) which exhibits a much stronger dependence on the concentration than the traditional Darken relation, D(s) = D(s)(0)/(1-θ). Experimental data of surface diffusion of ethane and propane on activated carbon obtained in our laboratory exhibit this strong dependence on the adsorbed concentration.In this paper we present a model for surface diffusion in heterogeneous activated carbon. A structural model for activated carbon was first assumed, upon which a model for the surface diffusion mechanism was proposed. This model allows for the penetration of molecules into graphitic layer units, diffusion through it and evaporation out of it. Upon leaving the graphitic units, molecules then rejoin with other molecules diffusing through the porous medium via the larger void space parallel to the graphitic layers. They in turn then diffuse through the amorphous region of the activated carbon. The sequence of these steps repeats itself in a periodic pattern. The model gives rise to an 'apparent' surface diffusivity which is an explicit function of temperature and concentration of the adsorbed species. The activation energy of this 'apparent' surface diffusivity was found to take values between the activation energy for diffusion through the graphitic units and the heat of adsorption. Under proper conditions, it can be equal to the heat of adsorption. In terms of the concentration dependence, this model shows a very strong dependence of the surface diffusivity on the adsorbed concentration; for example, when the Langmuir isotherm prevails, the dependence of D on fractional loading takes the following form: D = D(0)/(1 - θ) which exhibits a much stronger dependence on the concentration than the traditional Darken relation, D = D(0)/(1 - θ). Experimental data of surface diffusion of ethane and propane on activated carbon obtained in our laboratory exhibit this strong dependence on the adsorbed concentration