Page 77 - Adsorption Technology & Design, Elsevier (1998)

74 Rates of adsorption of gases and vapours by porous media

Surface diffusion

Surface diffusion of molecules across the interior surface of the adsorbent is
another possible mode of diffusive transport. It occurs in parallel with bulk
and Knudsen diffusion both of which describe diffusion through the gaseous
space contained within pores. Adsorbed species, however, may possess
mobility and move across the surface to other vacant adsorption sites.
Surface diffusion only occurs when molecules are adsorbed and provided the
surface attractive forces are not so strong as to prevent surface mobility.
Surface diffusion is most likely to be significant in porous adsorbents with a
high surface area and narrow pores. The total diffusive flux is then the sum of
the contributions from Knudsen diffusion, bulk diffusion (if there are some
wider pores as well as narrow pores) and surface diffusion. Because surface
diffusion cannot be easily measured directly, the surface diffusive flux has to
be estimated by subtraction of the sum of calculated effective Knudsen and
bulk diffusive fluxes from the total flux measured experimentally in a Wicke
and Kallenbach (1941) cell (see Section 4.3.1). The magnitude of the surface
diffusion coefficient D~ found in this way has been reported to be within the
range 10 -7 to 10 -1~ m 2 s -1. The temperature coefficient for surface diffusion
can be described by an equation analogous to that of the Arrhenius equation
widely used in chemical kinetics. Thus one writes

(4.15)
D~ = Do exp (- Es/RgT)
where Do is the pre-exponential factor for surface diffusion. The value of E~
is generally less than the heat of adsorption. Furthermore, the overall
unidirectional flux J (sum of fluxes for Knudsen and surface diffusion) in the
direction z given by

dc
DK + ppDsK ,-- (4.16)
J- - DK~ + ppDs ---
dz
dz
implies that the net contribution to the flux from surface diffusion depends
on the product DsK (where K is the Henry's law constant given by dq/dc)
and not simply D~. Because K normally decreases with increase of
temperature more rapidly than Ds increases, the extent of surface diffusion
generally declines with increase in temperature. The data of Schneider and
Smith (1968) confirms such decreasing effect of surface diffusion with
increase of temperature. Except at low concentrations (in the concentration
region where Henry's law is obeyed) Ds is found to be strongly dependent on
surface concentration (Gilliland et al. 1974, Sladek et al. 1974) which is
proportional to the amount adsorbed.