Adsorption isotherm data were acquired by frontal analysis (FA) and large sample-size band profiles were recorded for phenol and caffeine. For both compounds, the isotherm data fit well to the Langmuir, Toth, and Bi-Langmuir models of adsorption. The Langmuir model must be dismissed because it does not predict accurately the overloaded band profiles. However, profiles calculated using the unimodal Toth and the bimodal Bi-Langmuir models are indistinguishable. The expectation-maximization procedure was used to calculate directly the affinity energy distribution (AED) from the raw FA data points. For both compounds, the AED converges to a bimodal distribution at high numbers of iterations. This result, which shows the high sensitivity of the EM method, suggest that the Bi-Langmuir model makes better physical sense than the Toth model. This model also permits a detailed investigation of the properties of active sites, a feature often evoked in chromatography but so far rarely the topic of a quantitative investigation.