Critical micelle concentration defined

Changes in surface pressure with time or concentration can be used to measure various fundamental properties. Changes in surface pressure versus protein concentration curves can be used to determine the excess surface concentration (critical micelle concentration), defined as the amount of protein at the surface divided by the surface area. Indicates minimum amount of protein needed to form an emulsion. 

One of the most important characteristics of the emulsifier is its CMC, which is defined as the critical concentration value below which no micelle formation occurs. The critical micelle concentration of an emulsifier is determined by the structure and the number of hydrophilic and hydrophobic groups included in the emulsifier molecule. The hydrophile-lipophile balance (HLB) number is a good criterion for the selection of proper emulsifier. The HLB scale was developed by W. C. Griffin [46,47]. Based on his approach, the HLB number of an emulsifier can be calculated by dividing... 

The curve shown in Fig. 6 for sodium dodecyl sulfate is characteristic of ionic surfactants, which present a discontinuous and sharp increase of solubility at a particular temperature [80]. This temperature is known as the Krafft temperature. The Krafft temperature is defined by ISO as the temperature [in practice, a narrow range of temperatures] at which the solubility of ionic surface active agents rises sharply. At this temperature the solubility becomes equal to the critical micelle concentration (cmc). The curve of solubility vs. temperature intersects with the curve of the CMC vs. temperature at the Krafft temperature. 

Micelles the mostly spherical nanoscale aggregates formed by amphiphilic compounds above their critical micelle concentration in aqueous solution have a narrow size distribution and are dynamic, because there is a fast exchange of amphiphiles in solution and those incorporated in micelles. However, micelles are defined as self-assembled structures, since the structure is in thermodynamical equilibrium. 

The critical concentration at which the first micelle forms is called the critical micelle concentration, or CMC. As the concentration of block copolymer chains increases in the solution, more micelles are formed while the concentration of nonassociated chains, called unimers, remains constant and is equal to the value of the CMC. This ideal situation corresponds to a system at thermodynamic equilibrium. However, experimental investigations on the CMC have revealed that its value depends on the method used for its determination. Therefore, it seems more reasonable to define phenomenologically the CMC as the concentration at which a sufficient number of micelles is formed to be detected by a given method [16]. In practical terms, the CMC is often determined from plots of the surface tension as a function of the logarithm of the concentration. The CMC is then defined as the concentration at which the surface tension stops decreasing and reaches a plateau value. 

The Krafft Point may be defined as the temperature above which the solubility of a surfactant increases steeply. At this temperature, the solubility of the surfactant becomes equal to the critical micelle concentration (Cj ) of the surfactant. Therefore, surfactant micelles only exist at temperatures above the Krafft Point. This point is a triple point at which the surfactant coexists in the monomeric, the micellar, and the hydrated solid state (, ). 

Critical Micelle Concentration. Figure 1 shows the cmc as a function of the surfactant composition, a, defined as. 

FIG. 8.2 Schematic illustration of variation of properties of a surfactant solution with surfactant concentration. Note the change in behavior at the critical micelle concentration (CMC). The shading emphasizes the fact that the CMC is not necessarily sharply defined. 

Micelles. Surfactant molecules or ions at concentrations above a minimum value characteristic of each solvent-solute system associate into aggregates called micelles. The formation, structure, and behavior of micelles have been extensively investigated. The term critical micelle concentration (CMC) denotes the concentration at which micelles start to form in a system comprising solvent, surfactant, possibly other solutes, and a defined physical environment. 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

The state of the hydrocarbon chains in mesophases and micelles is reflected in the Krafft phenomena. In aqueous solutions of surfactants the Krafft point is defined as the temperature at which the solubility reaches the critical micelle concentration when the temperature is increased further, the solubility rises rapidly since the monomers form micelles (Figure 5) (10). Lipids that do not form micelles frequently start to swell by the uptake of water at a well-defined temperature they are transformed into a mesomorphous state (Figure 6) (11) The relation between these two Krafft phenomena is explained to some extent by the... 

Block copolymers of polystyrene (PSt, hydrophobe) and polyoxyethylene (PEO, hydrophile) form spherical micelles in water when the length of water soluble PEO is significantly larger than that of the insoluble PSt portion of the molecule [62]. In analogy with low molecular weight surfactants, one defines the onset of intermolecular association as the critical micelle concentration (CMC). Theories of polymer micellization predict that the concentration of free, unassociated block copolymers is close to that of the CMC. 

One characteristic property of surfactants is that they spontaneously aggregate in water and form well-defined structures such as spherical micelles, cylinders, bilayers, etc. (review Ref. [524]). These structures are sometimes called association colloids. The simplest and best understood of these is the micelle. To illustrate this we take one example, sodium dode-cylsulfate (SDS), and see what happens when more and more SDS is added to water. At low concentration the anionic dodecylsulfate molecules are dissolved as individual ions. Due to their hydrocarbon chains they tend to adsorb at the air-water interface, with their hydrocarbon chains oriented towards the vapor phase. The surface tension decreases strongly with increasing concentration (Fig. 3.7). At a certain concentration, the critical micelle concentration or... 

In spite of many favorable examples of coincidence between the conventionally defined CMC-values obtained by this method and, for example, spectroscopic or other techniques, it appears a priori not advisable to assign these breaks directly to critical micelle concentrations without further analyses of these systems. 

The enthalpy and entropy changes of micellization have been calculated for benzenesulfonate and alkylammonium salts in low-polar solvents suggesting that micellization is essentially an enthalpy-driven effect. The aggregation can take place at low concentrations of surfactant and can have different aggregation numbers. The absence of well-defined critical micelle concentrations (CMC) for some systems in the low-polar solvents was observed (Kertes and Gutman, 1976). 

There is a vast body of diblock copolymer studies since block choice can be such that they resemble amphiphilic surfactants. For the sake of brevity, we will skip them. Instead, we present an interesting case of triblock copolymers of poly(ethylene oxide), PEO, and poly(propylene oxide), PPO, commonly known by one of its trade names, Pluronics [117]. They have been used as non-ionic surfactants for a variety of applications such as in emulsification and dispersion stabilization. In aqueous solutions, these copolymers form micelles, and there exists a well-defined critical micelle concentration that is experimentally accessible. Several groups have investigated colloidal suspensions of these polymers [118-122], The surface properties of the adsorbed monolayers of the copolymers have been reported with respect to their structures and static properties [123-126]. 

The critical concentration, Ccrit, is defined as the concentration at which there is a change in the size distribution of the surfactant aggregates from a monotonically decreasing curve (below Ccrit), to one that possesses a maximum and aminimum above the critical concentration. The transition in shape occurs at a size distribution that displays an horizontal inflexion point. The critical micelle concentration (CMC) has a value close to the critical value Ccrit [3.1 ] and [3.2],... 

In dilute aqueous solutions, surfactants have normal electrolyte or solute characteristics and are formed at the interface. As the surfactant concentration increases beyond the well-defined concentrations (i.e., critical micelle concentration, c.m.c.), the surfactant molecules become more organized aggregates and form micelles. At the c.m.c., the physicochemical characteristics of the system (osmotic pressure, turbidity, surface tension, and electrical conductivity) are suddenly changed, as shown in Figure 4.19. 

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