Several studies report the existence of a local minimum of the surface tension near the critical micelle concentration (CMC) of surfactant solutions. The interpretation of this phenomenon is not unambiguous. While some authors conceive this observation as a normal feature, others consider it to be a clear indication of the presence of an impurity which is more surface active than the surfactant itself. We present a phenomenological description of the behavior of surfactant molecules near the CMC which indicates that a local maximum of the chemical potential can indeed be explained for a pure surfactant solution. This theoretical treatment is applied to the results of an experimental study of the non-ionic surfactant POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) dissolved in the polar solvent HPN (3-hydroxypropionitrile) which does not only provide surface tension data but also provides the chemical potential of POPC as a function of the concentration as well. The theory not only provides an explanation for the local maximum of the chemical potential and, thus, for the local minimum of the surface tension, but also gives in addition an estimate of the micelle size.