The Flory-Huggins isotherm

The Flory-Huggins adsorption isotherm is defined by the following equation:


bc = θ
(1 − θ)n
where b is the equilibrium binding constant, c the concentration of the adsorbate in solution, θ the fraction of adsorbent sites occupied by the adsorbate and n a positive exponent. The equation can be linearized as follows:

ln θ
c
 = lnb + n ln(1 − θ)
Unfortunately, some authors have replaced, in the previous equation, the variable c by a constant c0, resulting in an equation in the single variable θ. This mistake has considerably hampered the use of the isotherm!


Figure 1: Our investigation reveals that the Flory-Huggins adsorption isotherm was destroyed beyond recognition by a farcical linearization method. It is not a pretty picture. We are on a mission to resurrect the original isotherm. Let's dig in. (Graphic credit: Aan Chu)

Fitting the Flory-Huggins isotherm

In practice, θ is computed as θ = q / qm where q is the adsorbed quantity and qm its maximal value (adsorption capacity). The experimental curve is therefore defined by q = f(c).

The computer program Flory_Huggins.bas written in FreeBASIC fits the curve by nonlinear regression, using simulated annealing followed by Marquardt's method. The fitted parameters are qm, b and n. No linearization is used.



Reference

K. H. Chu, M. A. Hashim, H. Bashiri, J. Debord, M. Harel, J. C. Bollinger. The Flory-Huggins Isotherm and Water Contaminant Adsorption: Debunking Some Modeling Fallacies. Industrial & Engineering Chemistry Research, 2023, 62, 1121−1131 https://pubs.acs.org/doi/10.1021/acs.iecr.2c03799