Concentration dependence of surface diffusion and zeolitic diffusion

Abstract

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.

Adsorption of pyridine from aqueous solutions by polymeric adsorbents MN 200 and MN 500. Part 2: Kinetics and diffusion analysis

“…In this work, with the effective diffusion coefficient ( ) determined from the homogeneous particle diffusion model and pore diffusion coefficient reported by Ocampo-Perez et al [9], and show the same order of magnitude of effective diffusion coefficients (in Table 2) but much lower than the according pore diffusion coefficients (in Table 3), which indicates a significant effect of surface diffusion on the micropore adsorption kinetics. A trend shows the surface diffusion coefficient increases with temperature from 25 to 55 0 C and this is more prominent for MN 500, supporting the hypothesis that surface diffusion is an activated mass transfer process, where the increase of temperature facilitates molecular hopping between distinct, energetically favourable adsorption sites on the surface [47,75,76]. The surface diffusion coefficient was reported to increase with adsorbent loading, hence is expected to increase with initial adsorbent concentration according to Darken theory [77], although this trend is not well defined in our case, possibly due to the small concentration differences (100 to 200 mg/L).…”

Positron Emission Profiling Study of the Diffusion of 3-Methylpentane in Silicalite-1

“…Apparently, the stretched exponential approximation predicted by Kinetic Monte Carlo simulations [12] seems to be a slightly better fit for the experimental data: first-order decay with the fitted coefficient b ¼ 1=3:239. Even though expression 17 failed to describe the data for 3-methylpentane in silicalite, the fitted value of ¼ 10:02 is in line with the values found by Chen and Yang [18] for the diffusion of thriethylamine in 13X zeolite and for benzene in ZSM-5, that are equal to 10.2 and 2.11 respectively.…”

“…The self-diffusivity at zero coverage depends on the dimension of the lattice only, because there are no interactions between the molecules. (3) From calculations based on transition state theory, a general formula was derived to describe the concentration dependence of surface and zeolitic diffusions [18]:…”

“…Correlation effects were found to be more significant for the molecular diffusion in the poorly connected zeolite matrixes such as silicalite, so that the diffusion coefficient decreased faster with the zeolite loading [12]. A unified model based on the random walk/hopping mechanism has been offered by Chen and Yang [18] capable of describing both decreasing and increasing concentration dependencies.…”

Methane Adsorption Rate and Diffusion Characteristics in Marine Shale Samples from Yangtze Platform, South China

“…This observation is consistent with the reports by Pillalamarry et al [28], while in opposition with the results mentioned above. Based on this, the reduction in methane diffusivity with pressure may be attributed to two reasons: (1) the degree of pore blockage by methane molecule increase with increasing surface coverage (adsorbed volume), making methane molecules difficult to diffuse into adsorption sites through pathways [59]; and (2) as methane diffuses into adsorption sites, the concentration gradient between bulk particles and their surfaces decrease with increasing pressures and adsorbed volume, slowing methane diffusion. It is apparent that there is an evident negative correlation between macropore diffusivity and pressure lower than 3-4 MPa (Figure 9a), while the micropore diffusivity only showed a gentle decreasing trend with pressure (Figure 9b), with the exception of sample YY2-2 and CY1-1.…”