I am currently working on the non-linear adsorption isotherm using SOLVER-add in in Microsoft Excel. May I know what is the basis to estimate/guess the initial value for the isotherm constant?
If you are using the classic Langmuir model [q = qs * b * p / (1 + b * p)], a good initial value will be your maximum adsorbed amount for qs. For the b, divide the slope of the isotherm at the origin (= Henry coefficient) by qs.
The problem is not so complex; if you part from the Langmuir equation: Vads/Vm = KAPA /(1+ KAPA)
applying the inverse of this equation, and rearrange we can obtain the linear transform:
PA/Vads = 1/(vmKA) + PA / Vm,
from the linear form of the Langmuir equation, you can plot PA/Vads vs PA, and finally from the slope and intercept can be determined Vm and KA respectively.
I'm currently working on 3-parameters isotherm model i.e. Sips, Redlich-Peterson, etc. Thus, they cannot be solved using a linear method. In order to solve with non-linear function, I need to guess the initial value. Therefore, I would like to know how to decide on initial value, since different initial value results in difficult outcomes.