On the Applicability of the Regular Solution Theory to Multicomponent Systems

Abstract

The critical micelle concentration (CMC) of aqueous mixtures of decyl-(C 10 TAB), dodecyl-(C 12 TAB), and tetradecyl trimethyl ammonium (C 14 TAB) bromides has been studied in the complete triangular diagram. The results have been analyzed on the basis of the multicomponent regular solution theory for mixed micelles (MRST). It has been found that the mixtures of both, two or three components, contrary to the MRST theory assumptions, have a nonideal behavior. Both the experimental CMC, (CMC ijk ) exp , and that computed with the MRST, (CMC ijk ) calc ), were lower than the ideal one, (CMC ijk ) id , indicating an attractive interaction. Moreover, in the majority of the triangular diagram (CMC ijk ) exp differs significantly from (CMC ijk ) calc . This suggests that the assumption in the MRST that the interaction among the three different homologue molecules in the mixed micelle computed using the binary regular solution theory interaction parameters obtained from binary mixtures may be an oversimplification. This has been reinforced by analysis of the intramicellar activity coefficients of components, indicating differences in the surrounding of the component molecules when they are in bi-or tricomponent micelles. The excess free energy of micellization in three-component systems indicates that the more stable mixed micelles are those having an excess of the shorter components (C 10 TAB-C 12 TAB) and \50 % of the longer one (C 14 TAB). Furthermore, the common statement that mixtures of homologue surfactants are ideal is not supported by this work.

The aqueous Triton X-100 – dodecyltrimethylammonium bromidemicellar mixed system. Experimental results and thermodynamic analysis

“…The RST has received severe criticism [25,26]. In particular, its extension to multicomponent surfactant mixtures gives completely unrealistic results [27]. Since it is based in the regular solution theory, it is supposed that the energy if introducing a molecule of surfactant 1 in a micelle of pure surfactant 2, W12, is equal to that of introducing a molecule of 2 in a micelle of pure 1, W21, i.e., that the system is thermodynamically symmetric.…”

Theoretical Approaches on the Synergistic Interaction between Double‐Headed Anionic Amino Acid‐Based Surfactants and Hexadecyltrimethylammonium Bromide

“…From the RST model, (Rubingh and Mittal, 1979) different thermodynamic parameters can be derived (Das et al, 2018), assuming that the excess entropy of mixing is zero, as has been performed for other surfactant mixtures (Patel et al, 2017;Ren et al, 2017aRen et al, , 2017bRosen and Kunjappu, 2012;Schulz et al, 2013;Sikorska et al, 2016). Gibbs excess free energy (G Ex ), excess enthalpy (H Ex ), and enthalpy of micellization (ΔH m ) can be calculated using Equation 13 (Patel et al, 2017;Ren et al, 2017aRen et al, , 2017b:…”

“…There are two opposing factors that contribute to ΔH m : (i) the energy released due to the loss of translational energy of surfactant monomers as a result of electrostatic and hydrophobic interaction for the micellization, and (ii) energy required to break the organized structure of bulk water. (Schulz et al, 2013;Fig. 4 Variation of f 1 , f 2 and CMC values calculated by SPB model, X SPB and β R values calculated by SPB model with the mole fraction of α AAS at 298 K. systems: Ο, C 12 MalNa 2 -HTAB; Δ, C 12 AspNa 2 -HTAB and □, C 12 GluNa 2 -HTAB Sikorska et al, 2016).…”

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.…”