Surfactant Mixtures Mixed Micelles

The superscript m indicates that the values are inside the micelle. If Xj and are the solution composition, then, 

Xi X2 0.5 that is, at the cmc of the systems the micelles are composed up to 50% of component 2. This illustrates the role of contaminants in surface activity, for example dodecyl alcohol in SDS. 

With many industrial formulations, surfactants of different kinds are mixed together, for example anionics and nonionics. The nonionic surfactant molecules shield the repulsion between the negative head groups in the micelle, and consequently there will be a net interaction between the two types of molecules. Another example is the case when anionic and cationic surfactants are mixed, whereby a very strong interaction will take place between the oppositely charged surfactant molecules. To account for this interaction. Equation (3.25) must be modified by introducing activity coefficients of the surfactants,/j and/2 in the micelle. 

The cmc of the surfactant mixture and the composition are given by the following equations  

(a) Lindman, B. (1984) in Surfactants 7. (ed. Th.F. Tadros), Academic Press, London, NY (b) K. Holmberg, B. Jonsson, 8. B. Kronberg and B. Lindman Surfactants and Polymers in Aqueous Solution, 2nd 

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Anionic/Cationic Surfactant Mixtures. Mixed micelles... 

We continue the surfactant mixture (mixed micelles) solubility example introduced in the first part of this chapter. If only 4 experiments are carried out at the factorial points and the model equation contains 3 coefficients plus the constant term, then the design is saturated. The model will fit the data exactly ... 

Many models have appeared in the literature describing interactions of surfactants in mixed micelles (1-14). For nonionic surfactants mixing nonideally, the key references up to 1984 have been recently summarized (15). Comparatively few models have been developed for ionic surfactants (5,6,10-12) and fewer models which acknowledge ionic/nonionic interactions are available (5-7). Since many practical surfactant mixtures involve ionic and nonionic surfactants which interact with each other and with added salts, it is important to develop explicit ionic/nonionic models. 

Aniansson showed that mixed micellar solutions of binary svuTactant mixtures are characterized by three relaxation processes two fast processes associated with the exchange of the two surfactants between mixed micelles and bvdk phase (Xn and X12) and a slow process associated with the forma-tion/breakdown of the mixed micelles (X2). The basic assumptions and the methods used to derive the expressions of the... 

Brito, R. O., Marques, E. F., Gomes, P. et al. (2006) Self-assembly in a catanionic mixture with an amino acid-derived surfactant from mixed micelles to spontaneons vesicles. J. Phys. Chem. B, 110, 18158-18165. 

Small micelles in dilute solution close to the CMC are generally beheved to be spherical. Under other conditions, micellar materials can assume stmctures such as oblate and prolate spheroids, vesicles (double layers), rods, and lamellae (36,37). AH of these stmctures have been demonstrated under certain conditions, and a single surfactant can assume a number of stmctures, depending on surfactant, salt concentration, and temperature. In mixed surfactant solutions, micelles of each species may coexist, but usually mixed micelles are formed. Anionic-nonionic mixtures are of technical importance and their properties have been studied (38,39). 

The critical micellar concentrations of anionic/nonionic surfactant mixtures examined are low in a saline medium, so that, at the concentrations injected in practice, the chromatographic effects resulting from the respective adsorption of monomers are masked. Such surfactants propagate simultaneously in the medium in the form of mixed micelles. 

The effects of dilution of the micellar surface charge on the rate of alkaline hydrolysis of a betaine ester surfactant have been investigated for a mixture of decyl betainate and a nonionic surfactant with a similar CMC. It was shown that the relation between micellar composition and the hydrolysis rate essentially parallels the relation between micellar composition and counterion binding to mixed micelles made up of ionic and nonionic surfactants [20]. 

Zhang et al. [135] have studied the physicochemical behavior of mixtures of -dodecyl-/l-D-maltoside with anionic, cationic and nonionic surfactants in aqueous solutions. To acquire information on the property of mixed micelles, the characteristic change of pyrene with changes in polarity was monitored. The polarity parameter at low concentrations was found to be 0.5-0.6. 

Except for some anionic/cationic surfactant mixtures which form ion pairs, in a typical surfactant solution, the concentration of the surfactant components as monomeric species is so dilute that no significant interactions between surfactant monomers occur. Therefore, the monomer—mi celle equilibria is dictated by the tendency of the surfactant components to form micelles and the interaction between surfactants in the micelle. Prediction of monomer—micelle equilibria reduces to modeling of the thermodynamics of mixed micelle formation. 

Below the CMC, the surfactant mixing in monolayers composed of similarly structured surfactants approximately obeys ideal solution theory. This means that the total surfactant concentration required to attain a specified surface tension for a mixture is intermediate between those concentrations for the pure surfactants involved. For mixtures of ionic/nonionic or anionic/cationic surfactants, below the CMC, the surfactant mixing in the monolayer exhibits negative deviation from ideality (i.e., the surfactant concentration required to attain a specified surface tension is less than that predicted from ideal solution theory). The same guidelines already discussed to select surfactant mixtures which have low monomer concentrations when micelles are present would also apply to the selection of surfactants which would reduce surface tension below the CMC. 

We may consider precipitation in these systems in the context of competitive aggregate formation between micelles and precipitate. Even systems forming ideal mixed micelles can exhibit synergisms in salinity/hardness tolerance in such systems, the more components present, the higher the tolerance. This is the reason that mixtures of isomeric surfactants generally have Krafft temperatures considerably lower than those of the individual compounds (90). 

If the mixed micelle model already presented is used to predict the ionic surfactant monomer concentration, and a simple concentration—based solubility product is assumed to hold between the unbound counterion and monomer, the salinity tolerance of an anionic/nonionic surfactant mixture can be accurately predicted (91). supporting this view of the mechanism of tolerance enhancement by nonionic surfactant. 

In order to define a ionic/nonionic surfactant solution with high salinity/hardness tolerance, the following criterion should be followed. The mixed micelle should have as large of a negative deviation from ideality as possible. Surfactant mixture characteristics which result in this have already been discussed. The nonionic surfactant should have a high cloud point. Otherwise the amount of nonionic surfactant which can be added to the system is limited to low levels before phase separation occurs. If possible, a mixed ionic surfactant should be used for reasons Just discussed. There is no such benefit to using mixed nonionic surfactants, although this is not necessarily detrimental either. 

This brief review has attempted to discuss some of the important phenomena in which surfactant mixtures can be involved. Mechanistic aspects of surfactant interactions and some mathematical models to describe the processes have been outlined. The application of these principles to practical problems has been considered. For example, enhancement of solubilization or surface tension depression using mixtures has been discussed. However, in many cases, the various processes in which surfactants interact generally cannot be considered by themselves, because they occur simultaneously. The surfactant technologist can use this to advantage to accomplish certain objectives. For example, the enhancement of mixed micelle formation can lead to a reduced tendency for surfactant precipitation, reduced adsorption, and a reduced tendency for coacervate formation. The solution to a particular practical problem involving surfactants is rarely obvious because often the surfactants are involved in multiple steps in a process and optimization of a number of simultaneous properties may be involved. An example of this is detergency, where adsorption, solubilization, foaming, emulsion formation, and other phenomena are all important. In enhanced oil recovery. 

The variation of the mixture critical micelle concentration (CMCf ) with temperature and with overall surfactant composition has been studied using ultrafiltration for two binary mixed nonionic/anionic systems. 

Recently, Rubingh ll) and Scamehorn et al. (9) have shown that the activity coefficients obtained by fitting the mixture CMC data can be correlated by assuming the mixed micelle to be a regular solution. This model proposed by Rubingh for binary mixtures has been extended to include multicomponent surfactant mixtures by Holland and Rubingh (10). Based on this concept Kamrath and Frances (11) have made extensive calculations for mixed micelle systems. 

The mass action model (MAM) for binary ionic or nonionic surfactants and the pseudo-phase separation model (PSM) which were developed earlier (I EC Fundamentals 1983, 22, 230 J. Phys. Chem. 1984, 88, 1642) have been extended. The new models include a micelle aggregation number and counterion binding parameter which depend on the mixed micelle composition. Thus, the models can describe mixtures of ionic/nonionic surfactants more realistically. These models generally predict no azeotropic micellization. For the PSM, calculated mixed erne s and especially monomer concentrations can differ significantly from those of the previous models. The results are used to estimate the Redlich-Kister parameters of monomer mixing in the mixed micelles from data on mixed erne s of Lange and Beck (1973), Funasaki and Hada (1979), and others. 

The purpose of this paper is to develop realistic specific models of mixed micellization which (i) can describe properties of ionic/nonionic surfactant mixtures and effects of salt (ii) lead to tractable calculations and (iii) can be used for extracting information on micelle mixing and monomer concentrations from the limited experimental data which are usually... 

A generalized nonideal mixed monolayer model based on the pseudo-phase separation approach is presented. This extends the model developed earlier for mixed micelles (J. Phys. Chem. 1983 87, 1984) to the treatment of nonideal surfactant mixtures at interfaces. The approach explicity takes surface pressures and molecular areas into account and results in a nonideal analog of Butler s equation applicable to micellar solutions. Measured values of the surface tension of nonideal mixed micellar solutions are also reported and compared with those predicted by the model. 

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

Results for the various binary mixed surfactant systems are shown in figures 1-7. Here, experimental results for the surface tension at the cmc (points) for the mixtures are compared with calculated results from the nonideal mixed monolayer model (solid line) and results for the ideal model (dashed line). Calculations of the surface tension are based on equation 17 with unit activity coefficients for the ideal case and activity coefficients determined using the net interaction 3 (from the mixed micelle model) and (equations 12 and 13) in the nonideal case. In these calculations the area per mole at the surface for each pure component, tOj, is obtained directly from the slope of the linear region in experimental surface tension data below the cmc (via equation 5) and the maximum surface pressure, from the linear best fit of... 

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