Detailed knowledge of the self-assembly and phase behavior of pH-sensitive surfactants has implications in areas such as targeted drug delivery. Here we present a study of the formation of micelle and bilayer from lauric acids using a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with conformational sampling in explicit solvent and the pH-based replica-exchange protocol. We find that at high pH conditions a spherical micelle is formed, while at low pH conditions a bilayer is formed with a considerable degree of interdigitation. The mid-point of the phase transition is in good agreement with experiment. Preliminary investigation also reveals that the effect of counterions and salt screening shifts the transition mid-point and does not change the structure of the surfactant assembly. Based on these data we suggest that CpHMD simulations may be applied to computational design of surfactant-based nano devices in the future.