Micellization and the Critical Micelle Concentration

The hydrophilic-hydrophobic nature of amphiphilic molecules leads to their self-assembly into a variety of structures in aqueous solution, as will be discussed further in Section 4.10.2. Micelles are one of the main types of structure formed by the association of amphiphiles. They consist of a core of hydrophobic chains (often alkyl chains) shielded from contact with water by hydrophilic head groups, which may be ionic or nonionic. The hydrophilic units of surfactants form a micellar corona. Micelles can either be spherical or extended into an ellipsoidal or rod-like shape. This depends on the packing of the molecules, as discussed further in Section 4.10.1. In this section we consider spherical micelles, since these are usually the type formed at the critical micelle concentration. A spherical micelle is sketched in Fig. 4.14. Unassociated molecules coexisting with micelles are often called unimers, and this nomenclature is used here. 

The critical micelle concentration (CMC) occurs at a fixed temperature as amphiphile concentration increases. The CMC is not a thermodynamic phase transition. It is defined phenomenologically from a sharp increase in the number of molecules associated into micelles. The precise location of the CMC thus depends on the technique used to measure it. Many physical properties exhibit abrupt changes at the CMC, as illustrated in Fig. 4.15. Some of these are colligative properties such as osmotic pressure or ionic conductivity. Other techniques are sensitive to changes in the dynamics of molecules at the CMC. For example, the self-diffusion coefficient measured by dynamic light scattering decreases discontinuously 

Micellization can also occur upon varying temperature at fixed concentration above or below a critical micelle temperature (CMT), depending on whether the self-assembly process is endothermic or exothermic. However, it is most common to determine the CMC rather than the CMT, since this enables comparison of CMC values at a fixed temperature (often 25 °C). 

Addition of many organic molecules such as alcohols causes a decrease in the surface tension of an aqueous solution, because they are adsorbed preferentially at the air-water interface as they are, to some extent, hydrophobic. In contrast, the surface tension of most electrolyte solutions increases with concentration, because ions are depleted from the surface due to attractive interactions in the bulk solution. The same behaviour is observed for hydrophilic solutes such as sugars. 

The concentration dependence of surface tension for a surfactant solution is distinctive because it is sensitive to the formation of micelles. Unlike non-amphiphilic molecules, the decrease of surface tension with increasing concentration is non-monotonic. Upon increasing the concentration of a pure amphiphile, the surface tension decreases rapidly from the value y = 72 mN m for pure water until a point at which it levels off and becomes almost independent of concentration (Fig. 4.16). This point is the CMC. Note that the concentration is plotted on a logarithmic scale in Fig. 4.16. The reason for this will become apparent when we consider Eq. (4.27). The limiting value of surface tension above the CMC is typically around 35 mN m. That the surface tension is independent of concentration above the CMC is sometimes ascribed to saturation of the surfactant in the surface monolayer. However, it is actually due to a chemical potential that is almost independent of concentration above the CMC, as discussed in the following section. 

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PEG and poly(2-methyl-2-oxazoline) (PMeOx) with amine end groups were used to polymerize BLG-NCA and 5-benzyloxy carbonyl-L cysteine NCA. The resulting copolymers were compared with regard to their aggregation behavior. There is not very much influence on the aggregation behavior caused by the hydrophilic polymer (PEG or PMeOx), whereas the peptide block has a substantial influence on the size of the micelles and the critical micelle concentration. The authors ascribe this to the different secondary structure and hydrophobicity of the polypeptide blocks [52]. 

The major reasons for the divergence of theory (Harkins Smith Ewart) and practice, involve the much lower degrees of conversion of the experiments on which the academic studies were based, and the much higher concentrations of surfactant (and their method of addition) commonly employed commercially. The latter play a major role in effecting the behaviour of the micelles and the critical micelle concentration (CMC) both factors on which the classical theories were built. 

The determination of nonionic surfactants has been demonstrated using mixed micelle formation. This relies on the principle that, to a great extent, micelle formation is additive, i.e., if two surfactants are present, each will be present in the micelles, and the critical micelle concentration (CMC) is the sum of the concentrations of the two surfactants. A dye is chosen which has an absorbance which changes if surfactant micelles are present in solution. A blank solution is titrated with a surfactant, usually an anionic, to determine the CMC. A solution of the unknown surfactant is then titrated, giving an apparent CMC lower than the blank. The difference in the two values represents the contribution of the unknown surfactant, a contribution which is additive over a useful concentration range (85). 

However, in the case of Na tetradecyl dioxy-ethylene sulfate, the surface tension and the critical micelle concentration will be reduced in the presence of water hardness. If a complexing agent is added, the effect is weakened because of the complexing of the... 

Micelles tend to aggregate, and there are many ways to measure their concentration, including surface tension measurements. The midpoint of the concentration range over which micellar aggregation occurs is called the critical micellar concentration (CMC). Below the CMC, added bile-salt molecules dissolve in the form of monomers above the CMC, added bile-salt molecules form micelles, leaving the monomeric concentration essentially constant. The pH at which CMC formation occurs is called the critical micellar pH, (CMpH). Table 1.1 lists values for some of the bile acids mentioned in this review. 

There are several possibilities for the determination of the critical micellar concentration. If the micelles are formed from charged surfactants, a plot of the electrophoretic current at constant high voltage against the surfactant concentration shows an inflection point at the ccmc. It should be noted that the critical micellar concentration changes with temperature, the kind and concentration of counterions, and other buffer ingredients. 

Vpsp and Vip are the volumes of the micellar and aqueous (liquid) phase, respectively Csf is the concentration of the surfactant in the BGE V is the partial specific volume of the micelle CMC is the critical micellar concentration... 

With short chain derivatives, the forces of repulsion are higher than the ones of attraction the curvature is high and spherical micelles are formed at a concentration called the critical micellar concentration (cmc). This concentration can be detected by a change in the physico-chemical properties of the solution (e.g. surface tension, Fig. 3 a). Above a characteristic temperature (referred as Krafft temperature), the tensio-active molecules are infinitely soluble in the form of micelles (Fig. 3 b). 

Most of the studies on thermodynamics of mixed micellar systems are based on the variation of the critical micellar concentration (CMC) with the relative concentration of both components of the mixed micelles (1-4). Through this approach It Is possible to obtain the free energies of formation of mixed micelles. However, at best, the sign and magnitude of the enthalpies and entropies can be obtained from the temperature dependences of the CMC. An Investigation of the thermodynamic properties of transfer of one surfactant from water to a solution of another surfactant offers a promising alternative approach ( ), and, recently, mathematical models have been developed to Interpret such properties (6-9). 

Surface aggregates formed by ionic surfactant adsorption on oppositely charge surfaces have been shown to be bi layered structures (1.) and are called admicelles<2) in this paper, though they are sometimes referred to as hemimicelles. The concentration at which admicelles first form on the most energetic surface patch is called the Critical Admicellar Concentration (CAC) in analogy to the Critical Micelle Concentration (CMC), where micelles are first formed. Again, in much of the literature, the CAC is referred to as the Hemimicellar Concentration (HMC). 

Long-chain fatty acids are insoluble in water, and their titration curves are concentration-dependent because of the formation of organized aggregates (acid soaps, soap micelles, fatty acid precipitates) which concentrate protons at the surface. At concentrations above the critical micellar concentration, solutions of long-chain fatty acid soaps manifest a diprotic curve when they are titrated from pH 10 to 4 (23). The first... 

The polymerizability of R-(EO)n-VB macromonomers has its maximum (Rp) around n=15-20 [51]. This finding was related to the micelle formation which is expected to be unfavored for either too long or too short chain length of PEO. The macromonomers and their polymacromonomers with very short R are soluble in water and therefore they lose their amphiphilic nature. The parameters of R and n of macromonomer (R-(EO)n-VB) were found to correlate with the formation of micelles and their structure. In the aqueous phase the scattering intensity increased with the concentration of macromonomer above the CMC. The critical micellar concentration in water was found to be in the range from 3.3 xl0 5to 7.1xl0 5 mol dm-3 for several R-(EO)n-VB macromonomers. 

Mixed micelles, comprising both polymerized and free surfactants, are formed once the critical association concentration (CAC) of the free am-phiphiles is reached. The CAC is typically much smaller than the CMC for the formation of free micelles. As the fraction of unpolymerized surfactants within the mixed micelles grows, their structure approaches that of free micelles. 

Plots of surface tension versus concentration for n-pentanol [49], LiCl (based on Ref. [50]), and SDS in an aqueous medium at room temperature are shown in Fig. 3.7. The three curves are typical for three different types of adsorption. The SDS adsorption isotherm is typical for amphiphilic substances. In many cases, above a certain critical concentration defined aggregates called micelles are formed (see Section 12.1). This concentration is called the critical micellar concentration (CMC). In the case of SDS at 25°C this is at 8.9 mM. Above the CMC the surface tension does not change significantly any further because any added substance goes into micelles not to the liquid-gas interface. 

A temperature-composition phase diagram for a surfactant solution is a characteristic phase diagrarr that delineates the conditions under which crystalline surfactant, monomers, or micelles will exist. On the phase diagram shown in Figure 12.5 (Smirnova, 1995), L represents the liquid phase, S the solid phase, and )(the surfactant mole fraction. The critical micellar temperature, CMT, is deLned as the line between the crystalline and micellar phases. Micelle formation occurs at temperatures greater than the CMT. The critical micellar concentration, CMC, line separates the micellar and... 

Amphiphilic molecules (surfactants) can assemble into nanoscopic supramolecular structures with a hydrophobic core and a hydrophilic shell micellar arrangement. As surfactant concentration is increased in aqueous solutions, the separated molecules aggregate into micelles upon reaching a concentration interval known as the critical micellar concentration (CMC). 

Chlorhexidine is a strong base (Lewis acid-base theory) because it reacts with acids to form salts of the RX2 type, and it is practically insoluble in water (<0.008% wt/vol at 20°C). The water solubility of the different salts varies widely as demonstrated in Table 2.13. Chlorhexidine is moderately surface-active (a net+chare over its surface) and forms micelles (molecular aggregates form colloidal particles) in solution the critical micellar concentration of the acetate is 0.01% wt/vol at 25°C (Heard and Ashworth 1969). Aqueous solutions of chlorhexidine are most stable within the pH range of 5-8, and above pH 8.0 chlorhexidine is precipitated because conditions for a base (>pH 7) reaction are present. 

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