Surface diffusion, that is, diffusion of adsorbed molecules or atoms on surfaces, has long been investigated (Kapoor et al., 1989). Diffusion of sorbate in zeolite, called zeolitic diffusion, has attracted a special interest recently because of the increasing importance of zeolite in separation and catalysis. One of the most intriguing aspects of both surface diffusion and zeolitic diffusion is the strong dependence of diffusivity (Fickian diffusivity) on sorbate concentration. However, seemingly different concentration dependences have been observed for surface diffusion and zeolitic diffusion, and these dependences have been interpreted by different and unrelated theories (Yang, 1987).Surface diffusivity increases with sorbate concentration. The H 1 0 theory (Higashi, Itoh and Oishi, 1963) stipulates that D / D , = 1/(1 -0), where D is diffusivity, O is fractional surface coverage, and Do is zero surface coverage. The H I 0 theory has been modified by Yang et al. (1973) to account for secondlayer adsorption, and hence a slower rise of diffusivity with 8 . To date, all observed concentration dependences of surface diffusivity follow the increasing trend ( D increases with 0), although the opposite is possible if the sorbate-sorbate bond is stronger than the sorbate-surface bond, according to the model of Yang et al. (1973). The concentration dependence of zeolitic diffusion seems to be more complex and erratic; all possible types of dependence have been observed (Yang, 1987). In most of the published results, an increasing dependence similar to the HIO-type is seen. A popular interpretation of this dependence is based on Darken's theory (1948). However, lingering questions remain regarding the assumptions made in the derivation of the Darken-type theory (Yang, 1987) and, more important, on the origin of the concentration dependence of diffusivity.In this note, we propose aunified model based on the random walk/hopping mechanism. This model is capable of interpreting both increasing and decreasing concentration dependences for both surface diffusion and zeolitic diffusion, and it sheds light on the origin of the concentration dependence for both kinds of diffusion.

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The breakthrough curves in fixed-bed, multicomponent adsorption are characterized by the widely known phenomenon of roll-up or roll-over of the weakly adsorbed (or lighter) components (Hsieh et al., 1977). The typical breakthrough behavior for a two-adsorbate system is shown in Figure 1. Roll-up refers to the hump on the breakthrough curve for the weaker adsorbate (N, in this study) where the concentration exceeds that in the feed. The hump corresponds to a plateau zone predicted by the equilibrium theory, i.e., no mass transfer limitations. For an Nadsorbate mixture, there are N -1 roll-up plateau zones. The above discussion pertains to isothermal conditions; for nonisothermal conditions more roll-up zones can occur (Rhee et al., 1972;Basmadjian and Wright, 1981;Liapis and Crosser, 1982). The vast literature on the subject of adsorber dynamics has recently been reviewed (Ruthven, 1984;Yang, 1987).Discussions in the literature on the roll-up phenomenon have been limited to that caused by differences in adsorption affinity, i.e., the displacement of a weaker adsorbate by a stronger one that arrives later. This is because the majority of the commercial processes are based on equilibrium separation. As more molecular-sieving sorbents have been developed, commercial processes have emerged that are based on kinetic separation, i.e., separation due to different pore diffusivities (Yang, 1987). The most significant process is the production of nitrogen from air using molecular sieve carbon (MSC). Understanding of the kinetic separation is, however, very primitive. In this note, we report the salient features of the breakthrough behavior, which are considerably different from those encountered in the conventional equilibrium adsorption processes. Pore-Diffusion Model, Thermodynamic and Diffusivity DataThe isothermal adsorption of multicomponent gas mixtures in a fixed bed of MSC is considered. The breakthrough behavior is governed by two interactive effects among the sorbates: competition in the mass transfer process (due to different diffusivities), and thermodynamic, competitive adsorption (due to different Correspondence concerning this paper should bc addressed to R. T. Yang. adsorption affinities). Generally the heavier gas component has a higher adsorption affinity and a lower diffusivity. The mixtures selected for this study are representative of this situation and may be regarded as model systems.The MSC pellets (Takeda Chemical Co., Japan, type 5A, lot number HGY 3 18) consist of agglomerated microcrystals. The micropore opening and macropore radius are 5A and ,2.0 pm, respectively (Chihara et al., 1978). The adsorber behavior can be predicted adequately by a bidisperse pore-diffusion model developed in this laboratory (Doong, 1986;Doong and Yang, 1987). This model is used directly.Binary mixtures of NZ-C2H6 and CH4-C2H6, at 5 vol. % each, carried by the inert He, are considered. The micropore diffusivities of N,, CH,, and C2H6 in the same type MSC have been reported, covering the temperature range 250-1,000 K (...

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