Multicomponent surface diffusion of adsorbed species: a description based on the generalized Maxwell—Stefan equations

Abstract

Surface diffusion of n sorbed species is described using the generalized Maxwell-Stefan (GMS) formulation of irreversible thermodynamics. The approach treats the vacant sites (V) as the ( n + 1)th component in the diffusing mixture. The diffusion coefficients defined in the GMS treatment are basically of two kinds: (i) the coefficient Đ; iV , signifying the facility for diffusive exchange between species i and the vacant sites; and (ii) the coefficients Đ; ij , describing the facility for counter-exchange between the sorbed species i and j. The GMS counter-sorption diffusivity is, in turn, relatable to the coefficients Đ; iV and Đ; jV ; the latter are estimated from single-sorbent diffusivity data. The direct influence of the fractional surface analyzed. For diffusion of a single sorbed species the Fick surface diffusivity D 1 V is related to the GMS diffusivity Đ; 1 V by D 1 V = Đ; 1 V /(1 − θ 1) a known result; the GMS coefficient Đ; 1 V is commonly referred to as the “intrinsic” or “corrected” diffusivity while the Fick coefficient D 1 V is usually termed the “apparent” diffusivity. The expression for the tracer diffusivity: ▪ derived from the GSM formulation is a convenient new result; its utility in interpretation of tracer diffusion data is demonstrated using the experiments of Pope (1967, Trans. Faraday Soc. 63, 734–742). Surface diffusion of multicomponent ( n⩾2) sorbed species is described by a matrix of Fick diffusivities [D] ≡ [B] −1 [Γ]. The elements of [B] are explicitly related to the GMS coefficients Đ; iV and Đ; if , while the matrix of thermodynamic factors [Γ], derivable from the adsorption isotherm, portrays the direct influence of the surface occupancies θ i on surface transport. The results of the prediction of [D] fo binary sorption are in broad agreement with the Monte Carlo simulations of Palekar and Rajadhyaksha (1986, Chem. Engng Sci. 41, 463–468). For constant value of the Fick matrix [D], analytical solutions for transient uptake of multicomponent mixtures are obtained as n-dimensonal matrix analogs of the corresponding solution for single-component sorpton. The application of the suggested solution technique is demonstrated by simulation of the transient uptake of n-heptane and benzene on NaX zeolite. The model is capable of reproducing the maximum in the n-heptane kinetic sorption curve, as experimentally observed by Kärger and Bülow (1975, Chem. Engng Sci. 30, 893–896). Analysis of binary counter-sorption using the GMS approach helps to explain the experimental observation that adsorption and desorption rates may be significantly different; the rationale is to be found in the dependence of the GMS counter-sorption diffusivity on surface composition. It is concluded that the GMS formulation provides the most convenient practical formulation on multicomponent surface diffusion.