Are there any isotherms or explanations for the decreasing equilibrium uptake after reaching the maximum value?
The following functional behavior may represent the adsorption kinetics as you have described above:
dy/dt = e/to Ymax(1-t/to) exp(-t/to) which after integration results,
y=e*Ymax(t/to) exp(-t/to) + Yf ; which is maximum at t/to =1, and to relaxation time of the adsorption reaction, Yf is stationary state adsorption density.
Ymax is maximum value.
This is often the case when the adsorbed amount is given as the excess value (Nex, as opposed to the absolute value, Nabs). Conceptually, the excess amount is the 'extra' gas adsorbed due to the presence of your adsorbent. The two quantities can be related if you know the total pore volume of your adsorbent:
Nabs = Nex + (Vp . rho)
Where Vp is the pore volume and rho is the bulk density of the gas at a certain external pressure.
Now for why this leads to a decrease in the isotherm... Once the maximum capacity of the adsorbent is reached, the total number of adsorbed molecules (Nabs) becomes constant. The external pressure, however, is still being increased, which means that the bulk density of the gas is still increasing and, following the above equation, Nex must decrease for Nabs to remain constant. For a much more detailed look at the thermodynamics, you might try Myers and Monson's 2002 Langmuir article (the open source version of which is linked below). I should also credit my PhD supervisor, Dr. Tina Deuren for explaining this concept to me many moons ago!
Hope this helps,
Matt
http://www.seas.upenn.edu/~amyers/langrev.pdf
The article commented above is purely thermodynamic in nature nothing to do with the kinetics aspect of the problem. That means one has to solve this problem using the methods developed in the field of chemical kinetics based on the experimental observations (i.e., phenomenological connections). The final should be presented in terms of integro-differential equation format. GOOD LUCK
