A nonlinear frequency response method for estimation of single solute and competitive adsorption isotherms

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Understanding adsorption isotherms is essential for optimizing chromatographic processes, yet even simple isotherms for single solute adsorption must be determined experimentally. Choosing the appropriate experimental method can be challenging, and while competitive isotherms can sometimes be derived theoretically, these models often fail to accurately describe equilibrium behavior at higher concentrations due to non-ideal conditions. Frequency response (FR) techniques, traditionally used in mechanical and electrical engineering, have potential applications in chemical engineering as well. Historically, the FR method has focused on analyzing adsorption kinetics and material characterization at small excitation amplitudes to maintain linearity. However, employing nonlinear FR analysis can yield valuable insights into kinetic and equilibrium parameters. This work introduces a nonlinear FR method for determining adsorption isotherms by examining the nonlinear FR of a chromatographic column subjected to sinusoidal concentration changes, utilizing higher order FR functions (FRFs). This method estimates both single solute and competitive isotherms by analyzing concentration changes over time in the frequency domain. Simulations were conducted to explore practical applications before experimental validation. The method was tested against classical techniques for selected case studies, revealing that single solute isotherms showed bet