Surfactants total monomer concentrations

Ideal Mixed Micelles. The Critical Micelle Concentration (CMC) is the lowest surfactant concentration at which micelles form the lower the CMC, the greater the tendency of a system to form micelles. When the total surfactant concentration equals the CMC, an infintesimal fraction of surfactant is present as micelles therefore, the CMC is equal to the total monomer concentration in equilibrium with the micellar pseudo—phase. The CMC for monomer—micelle equilibrium is analogous to the dew point in vapor—liquid equilibrium. 

Table 1. Total Monomer Concentrations and Micellar Compositions For a Binary SurFactant System at Various Deviations From Ideality...

Beyond the CMC the addition of surfactant leads mainly to the increase of the number of micelles and the total monomer concentration is practically constant. Furthermore, the first forming micelles will have a composition close to the optimum value yA because the free energy of micellisation has a minimum at this composition. As it follows from Eq. (5.110) the mole fraction of these micelles x i at yA is finite and becomes small only when xi expfgm/kuT). Further approximation of the CMC at this concentration and application of Eq. (5.124) for the optimum composition yA allows us to get finally the relation for the CMC of the mixture as... 

Fig. 5.15 presents the results obtained for sodium octylsulfate. This surfactant has a high cmc (as 0.135M). The agreement between the theory and experiment [57] is satisfactory below the cmc. Above the cmc, experimental and calculated values deviate rapidly. Finally Fig. 5.16 presents the results obtained for sodium octanoate as a function of total monomer concentration. The cmc is very high ( i 0.4M) and there is also a divergence between experiment and theory above the cmc. There is one fitting parameter the charge of the micelle. 

A variant of the Stober synthesis, in which the only reaction medium used was water, was presented by Miller et al. [12]. The surfactant-free synthetic route for the fabrication of silicone nanospheres via a two-step process was developed (1) acid-catalyzed hydrolysis and condensation of 3-mercap-topropyltrimethoxysilane, followed by (2) base-catalyzed condensation [12]. This procedure resulted in a rapid formation of emulsion droplets with a narrow size distribution, which undergo further condensation with the formation of soUd spheres with an equcdly narrow size distribution. By Vcuying the total monomer concentration the control over the pcuTicle size in the rjuige of 50 nm - 3 pm cm be achieved [13]. 

In an ideal system of two similar surfactants of like charge, the total monomer concentration is between the cmc values of the two surfactants, if the total surfactant concentration is at or above the mixture cmc (Fig. 7.4) [64]. At equilibrium [64],... 

Monomer concentrations as a function of total surfactant concentration. Experimental CMC s are marked by arrows. At 0.01 o total surfactant levels, the monomer concentrations will be approximately given by the CMC values except for Cj E g whose CMC is 0.06.. Inset shows absorption profile if values of partition coefficient (P) shown apply. From Florence (1982). 

In order to illustrate the eFFect oF micellar nonidealities oF mixing on total surFactant monomer concentrations and micelle compositions in a system at the CHC, consider a hypothetical binary surFactant pair, A and B. Assume CMCa = 1 mli and CMCb = 2 mil. For a equimolar mixture oF A and B as monomer, the values oF Cn and micelle compositions are tabulated in Table I at various values oF W/RT. 

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. 

In the case of non—eutectic systems, the solid phase shows nearly ideal mixing, so that the surfactant components distribute themselves between the micelle and the solid in about the same relative proportions (i.e., both the mixed micelle and mixed solid are approximately ideal). However, in the case of the eutectic type system, the crystal is extremely non-ideal (almost a single component), while the micelle has nearly ideal mixing. As seen in earlier calculations for ideal systems, even though the total surfactant monomer concentration is intermediate between that of the pure components, the monomer concentration of an individual component decreases as its total proportion in solution decreases. As the proportion of surfactant A decreases in solution (proportion of surfactant B increases) from pure A, there is a lower monomer concentration of A. Therefore, it requires a lower temperature or a higher added electrolyte level to precipitate it. At some... 

The equilibrium in these systems above the cloud point then involves monomer-micelle equilibrium in the dilute phase and monomer in the dilute phase in equilibrium with the coacervate phase. Prediction o-f the distribution of surfactant component between phases involves modeling of both of these equilibrium processes (98). It should be kept in mind that the region under discussion here involves only a small fraction of the total phase space in the nonionic surfactant—water system (105). Other compositions may involve more than two equilibrium phases, liquid crystals, or other structures. As the temperature or surfactant composition or concentration is varied, these regions may be encroached upon, something that the surfactant technologist must be wary of when working with nonionic surfactant systems. 

Micelles are often present in surfactant systems. In some processes, such as solubilization, they are directly involved. Micelles indirectly affect many other processes because monomer concentrations or activities of the surfactant components are dictated by the monomer— micelle equilibrium at total surfactant concentrations above the CMC. Therefore, interest in mixed micelle formation will continue to grow. 

If one considers solely the consecutive equilibria, the concentration of monomer can only increase with increasing total amphiphile concentration even above the CMC. (Apart from the trivial decrease in the monomer concentration calculated on the total volume which may arise when the micelles occupy a substantial volume fraction). However, if one realizes that micelles are not only composed of amphiphile, the result may be different. Thus counterion binding helps to stabilize the micelles and for ionic surfactants it can be predicted that the monomer activity may decrease with increasing surfactant concentration above the CMC. Good evidence for a decreasing monomer concentration above the CMC has been provided in the kinetic investigations of Aniansson et al.104), and recently Cutler et al.46) demonstrated, from amphiphile specific electrode studies, that the activity of dodecylsulfate ions decreases quite appreciably above the CMC for sodium dodecylsulfate solutions (Fig. 2.14). 

It is desirable to obtain an a priori predictio of the total equilibrium monomer concentration (CAC ) at set levels of adsorption based on the mixture feed mole fractions, instead of the equilibrium monomer mole fractions (Y.). The equilibrium monomer mole fractions will differ from the feed mole fractions because of the preferential adsorption of some of the surfactants in the mixture. A mass balance on component i in the feed, equilibrium solution, and adsorbed phase is solved for the equilibrium monomer mole fraction to obtain Equation 4 ... 

Monomer molecular weight (kg/mol) Average number of radicals per particle Surfactant agglomeration number Number of moles of monomer Total number concentration of particles (1/L)... 

Micelles of cationic surfactants have been found to form both in glycerol [44] and in ethylene glycol [18], The micelle formation of Ci6PyBr in ethylene glycol and glycerol was studied with surfactant-selective electrodes [45,46], The monomer concentration could in this way be measured at different total surfactant concentrations, and it was concluded that there is some premicellar aggregation... 

FIG. 6.2 Calculated dependence of (a) the monomer concentration C and (b) the weight average aggregation number gw on the total surfactant concentration Ctot for decyl, dodecyl, tetradecyl, and cetyl trimethylammonium bromides in ethylene glycol solutions. (From Nagarajan, R. and Wang, C.-C., J. Colloid Interface Sci., 178, 471, 1996.)... 

It is well-established now that the concentration of surfactant ions in micellar solutions changes when the total surfactant concentration c is increased. This leads to changes in the adsorption value and, consequently, to changes in the surface tension. These alterations, however, are small, even for ionic surfactants. For relatively dilute solutions, i.e. c< 10 CMC, as a first approximation one can consider that the monomer concentration ci is constant (ci CMC). Actually, for c > CMC surface tension changes are usually low and in the range of accuracy of conventional methods. This fact evidences an approximate constancy of the adsorption. 

The Eqs. (5.210) and (5.211) describe the diffusion of monomers and micelles as before. The physical meaning of Eq. (5.212) is not so obvious. It can be regarded as the equation of the local balance of surfactants in micelles. If the initial distribution of micelles is homogeneous and only the monomer concentration is perturbed, the first relaxation proeess can lead to the dependence of the aggregation numbers on space coordinates and time even in absence of a concentration gradient of the total number of micelles. Surfactants can be transferred not only as a result of the monomer diffusion but due to the diffusion of aggregates of different aggregation numbers. This effect is described by equation (5.212). 

Surfactant solutions above the cmc may be considered as made up of two species in equilibrium, i.e. monomers and micelles. Chromatographic methods may indicate how the monomer concentration, C., varies with the total concentration above the cmc. The concentration of monomers, C, above cmc is often assumed to be constant, as indicated surface tension [54] or from equilibrium dialysis [55]. This question was recently investigated by the use of chromatography [47]. In Fig. 14 the equilibria between the various species are depicted. Before elution the surfactant solution above cmc consists of micelles and monomers. These investigations were carried out where the eluant contained only monomers, C, somewhat lower than cmc. In order to calculate the magnitude of the monomer concentration, C, in equilibrium with micelles, when the total surfactant concentration, C, is larger than cmc, the following analytical procedure was carried out. The situation of the elution process is shown in Fig. 14b. 

The concentration of the surfactant in micellar and in complex form (in monomer units) is plotted against the equilibrium surfactant concentration in Fig. 3. The critical micelle formation concentration is around 0.42 mM. When the total surfactant concentration reaches this value the excess surfactants form micelles at almost constant equilibrium monomer concentration. Cp cannot increase to 0.47-0.48 mM where... 

Figure 1 Plot of binding ratio against the free detergent concentration. The binding ratio is defined as the quantity [conci of bound surfactant/total number of monomer units in the polymer].

The cmc of a surfactant is commonly defined as being that total detergent concentration at which micelle formation is already considerable (experimentally detectable) but most of the surfactant is still monomeric D > ) ), so that the concentration of monomers is still close to the total detergent concentration (D D[ = cmc ). It is therefore convenient to define cmc [1] by the equation... 

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