Markov Chain Modeling of Surfactant Critical Micelle Concentration and Surface Composition

A Markov chain (MC) model has been used to model the following binary surfactant mixtures: linear alkylbenzenesulfonate (LAS4)/octaethylene glycol monododecyl ether (C12E8) at 10 and 25 °C, LAS6/acidic sophorolipid (AS), C12Betaine/C12Maltoside, sodium lauryl ether sulfate (SLES2)/C12E8, and rhamnolipid (R1)/LAS6. The critical micellar concentration and the composition of the adsorbed layer, for each system, can be modeled using the same monomer reactivity ratio values, g₁ and g₂. This implies that the interactions between the surfactants in the bulk solution and at the interface are the same, within error. For the LAS4/C12E8 system at 25 °C, the ranges of g₁ and g₂ values which can model both sets of data are within 0.03-0.05 and 1.55-2.10, respectively; g₁ ≪ g₂ implies that C12E8 is significantly more surface active than LAS4. The MC model indicates a negative change in the free energy upon mixing for all of the surfactant systems, consistent with the literature. The interfacial mixing behavior of LAS4/SLES2 is inferred from the results of the MC analysis of the LAS4/C12E8 and SLES2/C12E8 systems, which share a common surfactant partner in C12E8, and the prediction is in line with the published data.