Markov chain model for the critical micelle concentration of surfactant mixtures

Abstract

An extension of the Markov chain model (MC) for micellization is proposed, which allows the distribution of the surfactants between the monomer solution and the micelles in a mixed surfactant system to be predicted. The dependence of the critical micelle concentration (cmc) on the composition of the solution is investigated. The equilibrium thermodynamic relation between cmc and micelle composition is discussed. The case of ternary mixtures is analyzed, and theoretical triangular diagram is constructed according to MC. Available experimental data for binary and ternary mixtures agree well with the new MC theory. The dependence of MC parameters on the structure of the surfactants is discussed. Comparison of MC with the simple mixture ("regular solution") model is presented. The parameters of the MC theory are related to the interaction parameter β SM of the simple mixture model.

Synergistic effect between amino sulfonate amphoteric surfactant and octylphenol polyoxyethylene ether (10) in aqueous solutions with different acidicities: consideration of different thermodynamic models

“…The interaction parameter ( β 12 ) calculated from Equation (5) is not a unique value but depends on the composition ( X 1 or x 1 ) for all the mixed systems. Similar results have been reported by other investigators . This is probably a consequence of the amplification of random fluctuations in the experimental data.…”

“…These four models have been used successfully to describe the interaction behavior between ionic and nonionic surfactants, and are very useful to understand their interacting mechanism in aqueous solution . In addition, other models have also been adopted to predict the interacting behavior between surfactants …”

Markov Chain Modeling of Surfactant Critical Micelle Concentration and Surface Composition

“…There are multiple theoretical models that describe different aspects of surfactant mixing behavior. The most notable include regular solution theory (RST), − molecular thermodynamics, − and recently Markov chain models (MC). , RST is a thermodynamic model that describes nonideal mixing behavior via an interaction parameter. This parameter quantifies the change in the free energy of mixing, G E , from ideal mixing; a system mixes synergistically if G E is negative.…”

A molecular‐thermodynamic approach to predict the micellization of binary surfactant mixtures containing amino sulfonate amphoteric surfactant and nonionic surfactant

“…In many pracitical applications relating to surface active agents, the surfactant mixtures are often used in order to obtain excellent properties of the system, due to their synergistic behavior . Sometimes, the synergistic effect of surfactant mixtures can be observed, which is attributed mainly to the attractive interaction between surfactants and the result of their nonideal mixing . In many models, such as Rubingh model, Rosen model, and so on, the synergistic effect is judged by the interaction parameter between surfactants, β 12 .…”

“…β 12 value near to zero reveals that there is little or no interaction between surfactants. By utilizing the value of β 12 and the fraction of component i in mixed micelle, X i , the activity coefficient of component i in mixed micelle, f i , can be calculated for nonideal mixing case . Herein, to obtain the values of both β 12 and X i , the values of critical micelle concentration ( cmc ) of individual surfactant in mixed system and mixed cmc are usually necessary to be determined by a great deal of burdensome experiments.…”