Is the Frumkin (Fowler–Guggenheim) adsorption isotherm a two- or three-parameter equation?

Abstract

The Frumkin or Fowler–Guggenheim isotherm, which has three fitting parameters, is often converted to a linear form with two fitting parameters to facilitate parameter estimation by linear regression. This conversion is made possible by way of replacing the unknown capacity parameter of the Frumkin isotherm with a surrogate value. The capacity parameters of certain simple isotherms (e.g., Dubinin–Radushkevich) are often used as surrogates. However, such surrogates have never been evaluated for validity or accuracy. In this paper, the three-parameter Frumkin isotherm was fit to previously published isotherm data to identify all three unknown parameters, including the capacity parameter. In the cases examined, the fitted capacity values were found to differ rather significantly from the surrogate capacity values used in the two-parameter Frumkin isotherm. The dubious practice of transforming the three-parameter Frumkin isotherm into the two-parameter Frumkin isotherm for linear estimation of parameters should be discarded in favor of estimating all three parameters by nonlinear regression.