The adsorption of the anionic surfactants, lithium, sodium and cesium dodecylsulfates, and sodium decylsulfonate, on the positively charged C-plane (0001) of sapphire (alumina) has been measured using neutron reflection. For each of the four surfactants there is a strong maximum in the adsorption at about the critical micelle concentration. The maximum becomes more marked from lithium to cesium. The measurements were reproduced over a range of different physical conditions and could not be accounted for in terms of impurities. The maximum is explained quantitatively by using the combination of a mass action model to calculate the mean activity of the surfactant, and a cooperative model of the adsorption (Frumkin), in which saturation of the layer is not attained until well above the critical micelle concentration. (C) 2016 Elsevier Inc. All rights reserved.