CMC .

The concentration of free surfactant, counterions, and micelles as a function of overall surfactant concentration is shown in Fig. XIII-13. Above the CMC, the concentration of free surfactant is essentially constant while the counterion concentration increases and... 

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

Practical systems will often have mixtures of surfactants. A useful rule is that the CMC of the mixture. Cm, is given by [196,197]... 

The traditional association colloid is of the M R" type where R" is the surfactant ion, studied in aqueous solution. Such salts also form micelles in nonaqueous and nonpolar solvents. These structures, termed inverse micelles, have the polar groups inward if some water is present [198] however, the presence of water may prevent the observation of a well-deflned CMC [198,199]. Very complex structures may be formed in nearly anhydrous media (see Ref. 200). 

After reviewing various earlier explanations for an adsorption maximum, Trogus, Schechter, and Wade [244] proposed perhaps the most satisfactory one so far (see also Ref. 243). Qualitatively, an adsorption maximum can occur if the surfactant consists of at least two species (which can be closely related) what is necessary is that species 2 (say) preferentially forms micelles (has a lower CMC) relative to species 1 and also adsorbs more strongly. The adsorbed state may also consist of aggregates or hemi-micelles, and even for a pure component the situation can be complex (see Section XI-6 for recent AFM evidence of surface micelle formation and [246] for polymeric surface micelles). Similar adsorption maxima found in adsorption of nonionic surfactants can be attributed to polydispersity in the surfactant chain lengths [247], Surface-active impuri-... 

The CMC for sodium dodecylbenzenesulfonate is about lO Af at 25°C. Calculate K for the preceding reaction, assuming that it is the only process that occurs in micelle formation. Calculate enough points to make your own quantitative plot corresponding to Fig. Xni-13. Include in your graph a plot of (Na )(R ). Note It is worthwhile to invest the time for a little reflection on how to proceed before launching into your calculation ... 

A surfactant solution is a mixture of DTAC (dodecyltrimethylammonium chloride) and CPC (cetyl pyridinium chloride) the respective CMCs of the pure surfactants are 2 X lO M and 9 x IO M (Ref. 140). Make a plot of the CMC for mixtures of these surfactants versus the mole fraction of DTAC. 

Derive Eq. XIV-11 from Eq. XIV-10. State the approximations involved. Explain whether the surface elasticity should be small or large for a surfactant film if the bulk surfactant concentration is about its CMC. 

Figure C2.3.4. Relative surface tension of DTINS at 25 °C. The intersection of tire dotted lines indicates a cmc of 3.0 mM. Reproduced by pennission from figure 1 of 1201.

Such linear free energy relationships are available for alkyl sulphates and for tire C4 to C9 homologues of tire dialkanoyl lecitliins (see table C2.3.3 for stmcture). Most of tire naturally occurring phospholipids are too insoluble to fonn micelles, but tire lower alkanoyl lecitliins, also known as phosphotidylcholines, do fonn micelles. The ernes for tliese homologues are listed in table C2.3.6. The approximately linear free energy relationship between tire alkyl chain iengtli and log cmc is given by ... 

Here (log cmc) is tire log cmc in tire absence of added electrolyte, is related to tire degree of counterion binding and electrostatic screening and c- is tire ionic strengtli (concentration) of inert electrolyte. Effects of added salt on cmc are illustrated in table C2.3.7. 

Eriksson M A L, J Pitera and P A Kollman 1999. Prediction of the Binding Free Energies of New TIBO-like HIV-1 Reverse Transcriptase Inhibitors Using a Combination of PROFEC, PB/SA, CMC/MD, and Free Energy Calculations. Journal of Medicinal Chemistry 42 868-881. 

The concentration of surfactant was 3.89 mM above the cmc in each case. Values taken from Chapter 2 and determined at a constant ionic strength of 2.0 M using KNOj as background electrolyte. 

At low concentrations surfactant molecules adsorbed at the surface are in equilibrium with other molecules in solution. Above a threshold concentration, called the critical micelle concentration (cmc, for short), another equilibrium must be considered. This additional equilibrium is that between individual molecules in solution and clusters of emulsifier molecules known as micelles. 

When micelles are formed just above the cmc, they are spherical aggregates in which surfactant molecules are clustered, tails together, to form a spherical particle. At higher concentrations the amount of excess surfactant is such that the micelles acquire a rod shape or, eventually, even a layer structure. 

With this picture in mind, let us consider what happens when monomer is stirred into a surfactant solution-which also contains a water-soluble initiator-above the cmc. 

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