Desorptive diffusion coefficients

The nature of the cations present in a zeolite can have a marked effect upon the rate of intracrystalline counterdiffusion, as shown by studies with several selected aromatic hydrocarbons in a series of ion-exchanged forms of the type Y zeolite. For 1-methylnaphthalene diffusing from type Y into bulk cumene, the desorptive diffusion coefficients vary by 2 orders of magnitude over different ion-exchanged forms in the order ... 

With regard to the liqiiid-phase mass-transfer coefficient, Whitney and Vivian found that the effect of temperature upon coiild be explained entirely by variations in the liquid-phase viscosity and diffusion coefficient with temperature. Similarly, the oxygen-desorption data of Sherwood and Holloway [Trans. Am. Jnst. Chem. Eng., 36, 39 (1940)] show that the influence of temperature upon Hl can be explained by the effects of temperature upon the liquid-phase viscosity and diffusion coefficients. 

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

Fig.3.1.9 (a) The adsorption-desorption isotherm (circles, right axis) and the self-diffusion coefficients D (triangles, left axis) for cyclohexane in porous silicon with 3.6-nm pore diameter as a function of the relative vapor pressure z = P/PS1 where Ps is the saturated vapor pressure, (b) The self-diffusion coefficients D for acetone (squares) and cyclohexane (triangles) as a function of the concentration 0 of molecules in pores measured on the adsorption (open symbols) and the desorption (filled symbols) branches. 

Equation 17.59 has been confirmed experimentally, suggesting that molecules move over a surface by hopping to adjacent adsorption sites. It may be assumed that this process involves a lower energy of activation than that required for complete desorption. The molecule will continue to hop until it finds a vacant adsorption site, thus explaining the increase of surface diffusion coefficient with coverage. 

For this estimate, values for the surface diffusion coefficient (D) and the surface exchange coefficient (i) in eq 2 were obtained by linearizing Mitterdorfer s rate expressions for surface transport and adsorption/desorption (ref 84) and re-expressing in terms of the driving forces in eq 2. 

The purpose of most experimental studies of diffusion is to obtain accurate diffusion coefficients as a function of temperature, pressure, and composition of the phase. For this purpose, the best approach is to design the experiments so that the diffusion problem has a simple anal3hical solution. After the experiments, the experimental results are compared with (or fit by) the anal3hical solution to obtain the diffusivity. The method of choice depends on the problems. The often used methods include diffusion-couple method, thin-source method, desorption or sorption method, and crystal dissolution method. 

The following effective diffusion coefficients D may be defined on the basis of standard sorption and permeation experiments 149 151 (when absorption or desorption conditions need to be specified, superscripts a or d respectively are again used) ... 

Since the fraction of empty sites in a zeolite channel determines the correlation factor (Section 5.2.2), as is well known from single-file diffusion in the pores of a membrane, the strong dependence of the diffusion coefficients on concentration can be understood. This is why a simple Nernst-Planck type coupling of the diffusive fluxes (see, for example, [H, Schmalzried (1981)]) is also not adequate. Therefore, we should not expect that sorption and desorption are symmetric processes having identical kinetics. Surveys on zeolite kinetics can be found in [A. Dyer (1988) J. Karger, D.M. Ruthven (1992)]. 

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