Adsorption energy distributions: Theory and applications in liquid chromatography

• Theoretical foundations of Adsorption Energy Distribution (AED) are reviewed • Explanation of how to visualize and interpret the AED plot has been provided • Effects of kernel function choice on AED plot and calculations are analyzed • Impact of concentration, iteration number, and grid points on AED plot is assessed • AED analysis reveals system heterogeneity and aids in adsorption model selection In liquid chromatography (LC), adsorption heterogeneity arises from the distribution of adsorption sites on stationary phases with varying interaction energies, affecting retention and separation performance. This heterogeneity can cause peak tailing, reduced resolution, and unpredictable retention times in analytical chromatography, as well as broad, asymmetric elution profiles in preparative systems. Adsorption heterogeneity depends on the combined effects of the stationary phase, the mobile phase composition, the analyte properties, and the chromatographic conditions. Traditional adsorption isotherms often fail to fully describe these complex interactions because they assume uniform adsorption energies. The Adsorption Energy Distribution (AED) framework offers a powerful alternative by modelling adsorption as a sum of independent homogeneous sites, each with a specific energy, offering a realistic representation of heterogeneous adsorption. This review introduces the theoretical foundations of AED, including its mathematical formulation and computational approaches, and discusses its application in interpreting retention mechanisms in LC. AED analysis is illustrated through its use in both chiral and achiral separations, as well as its ability to explain peak tailing and surface heterogeneity. Practical considerations, such as the range of concentration data in the adsorption isotherm, the selection of a suitable kernel function, and the number of iterations and grid points in AED analysis, are discussed. Special emphasis is given on how to visualize and interpret the AED. This review aims to provide chromatographers with a comprehensive understanding of AED, emphasizing its practical value in characterizing the chromatographic system and elucidating retention mechanisms in liquid chromatography.