10.1021/es202359j.s001 David M. Lorenzetti David M. Lorenzetti Michael D. Sohn Michael D. Sohn Numerical Solution of the Polanyi-DR Isotherm in Linear Driving Force Models American Chemical Society 2016 sorption relations concentration isotherm model complexity method Numerical Solution transport rate microporous materials 2016-02-22 12:53:12 Journal contribution https://acs.figshare.com/articles/journal_contribution/Numerical_Solution_of_the_Polanyi_DR_Isotherm_in_Linear_Driving_Force_Models/2577769 The Polanyi–Dubinin–Radushkevich isotherm has proven useful for modeling the adsorption of volatile organic compounds on microporous materials such as activated carbon. When embedded in a larger dynamic simulatione.g., of whole-building pollutant transportit is important to solve the sorption relations as quickly as possible. This work compares numerical methods for solving the Polanyi-DR model, in cases where transport to the surface is assumed linear in the bulk-to-surface concentration differences. We focus on developing numerically stable algorithms that converge across a wide range of inputs, including zero concentrations, where the isotherm is undefined. We identify several methods, including a modified Newton-Raphson search, that solve the system 3–4 times faster than simple bisection. Finally, we present a rule of thumb for identifying when boundary-layer diffusion limits the transport rate enough to justify reducing the model complexity.