Kinetics of Adsorption: The S-Shaped z-t Plot

• Main Author: C. Aharoni
• Format: Article
• Language: English
• Published: Hindawi - SAGE Publishing 1984-03-01
• Series: Adsorption Science & Technology
• Online Access: https://doi.org/10.1177/026361748400100101

One characteristic property of the kinetics of adsorption is the fact that the plot of the reciprocal of the rate against the time is S-shaped. The initial part of this plot is convex and can be fitted by a power equation (i.e. with the amount adsorbed being proportional to a fractional power of the time), the final part is concave and can be fitted by a Langmuir-type equation (i.e. with the rate decreasing linearly with the amount adsorbed) and the intermediate region around the inflection point can be fitted by the Elovich equation (i.e. with the amount adsorbed increasing logarithmically with the time). In many cases the above regions are preceded by a region at which the rate is constant. The equation dθ/dt = A(1 – θ)/θ where θ is the fractional coverage, t is the time and a is a constant, is consistent with these kinetics. It corresponds to kinetics in which the activation energy increases logarithmically with the coverage. It can be derived on the basis of a statistical-rate theory or on the basis of a precursor-state theory. The diffusion equation q / q ∞ = 1 - ∑ n = 0 n = ∞ a n exp ( - b n tD / r 2 ) where q and q x are the quantities adsorbed at time t and t = ∞, a n and b n are parameters determined by the integers n, D is the diffusion coefficient and r the length path, is also consistent with the above kinetics. Both equations have also been extended to heterogenous surfaces. Isotherms with constant initial rate are associated with non-activated adsorption and measurements at low pressures. The constant initial rate corresponds to a state at which the kinetics are determined by the rate of arrival of the gas molecules to the surface.