(346d) The Myers Isotherm: A Highly Flexible Equation to Regress Adsorption Data over Large Temperature and Pressure Ranges.

An important contribution from Alan Myers (2003) is the introduction of the Langmuir-virial isotherm, which combines the two isotherms to provide an expression that can be used also to derive easily integral thermodynamic functions. We would like to propose the renaming of this isotherm to the Myers isotherm.

By combining the Langmuir and virial expressions one obtains a new isotherm that overcomes some severe limitations of the original models. The Myers isotherm has incredible flexibility and can describe very accurately any shape that has a finite saturation capacity, thus overcoming many limitations of the Langmuir isotherm. Furthermore, by imposing explicitly a finite saturation capacity, it overcomes one of the main limitations of the virial isotherm, providing a constraint that reduces in part the occurrence of physically incorrect extrapolations.

In this contribution we present a robust approach to determine the parameters of the Myers isotherm. It transforms the regression into an algorithm that combines a line search on the saturation capacity with the direct calculation of the remaining parameters using the method of polynomials orthogonal to summation developed by Taqvi and Levan (1997) for the virial isotherm. As with any virial approximation, one can generate multiple fits increasing the order of the polynomial therefore an integral part of the algorithm is the method to decide the order of the virial expansion. Here we adopt the statistical measure based on the Bayesian Inference Criterion (Raftery, 1995) to determine where to stop the virial expansion. This provides a balance between goodness of fit and the number of parameters in the model, avoiding overfitting. The method is applied to several datasets from the literature over large temperature ranges and for both low and high pressure systems.

Myers A.L. Equation of State for Adsorption of Gases and Their Mixtures in Porous Materials. Adsorption 9, 9–16 (2003). https://doi.org/10.1023/A:1023807128914

Taqvi S.M. and Levan M.D. A Simple Way To Describe Nonisothermal Adsorption Equilibrium Data Using Polynomials Orthogonal to Summation. Ind. Eng. Chem. Res. 36, 419–423 (1997). https://doi.org/10.1021/ie960366d

Raftery A.E. Bayesian Model Selection in Social Research. Sociological Methodology 25, 111–163 (1995). https://doi.org/10.2307/271063