Micelles and critical micelle concentration

The properties of surfactant at low concentration in water are similar to those of simple electrolytes except that the surface tension decreases sharply with increase in concentration. At a certain concentration, surfactant monomers assemble to form a closed aggregate (micelle) in which the hydrophobic tails are shielded from water while the hydrophilic heads face water. The critical aggregation concentration is called the critical micelle concentration (CMC) when micelles form in an aqueous medium. The CMC is a property of the surfactant. It indicates the point at which monolayer adsorption is complete and the surface active properties are at an optimum. Above the CMC, the concentrations of monomers are nearly constant. Hence, there are no significant changes in the surfactant properties of the solution since the monomers are the cause of the surface activity. Micelles have no surface activity and any increase in the surfactant concentration does not affect the number of monomers in the solution but affects the structure of micelles. 

The typical CMC values at room temperature are 10-3-10-2 M for anionic surfactants, 10—3—10 1 M for amphoteric and cationic surfactants and 10—5—10 4 M for non-ionic surfactants. The CMC of several surfactants in aqueous media can be found in [2,23]. 

Surfactant structure, temperature, the presence of electrolyte, existence of organic compounds and the presence of a second liquid have an effect on the CMC. The following factors contribute to CMC decrease [1, 2, 24-30]  

The CMC decreases with temperature to a minimum and then increases with further increase in temperature. The minimum appears to be around 25°C for ionic surfactants and 50°C for non-ionic surfactants [31, 32]. 

Several empirical correlations are available for the estimation of CMC values. For straight and saturated single tail ionic surfactants, the CMC can be calculated from [33]  

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For a cationic (CTABr) and an anionic (NaLS) surfactant in a variety of dipolar aprotic solvents, e.g., dimethyl sulfoxide, dimethyl formamide, the variation of conductance with surfactant concentration is characteristic of micellization, and critical micelle concentrations were reported, which tend to be higher than those in water, especially for CTABr [144]. 

Fig. 3.1 Illustration of the critical micelle concentration (cmc) and critical gel concentration (cgc) in a block copolymer solution.

VIII. MICELLE FORMATION AND CRITICAL MICELLAR CONCENTRATION (CMC) OF BILE SALTS... 

Hydroxypropylmethyl cellulose, HPMC, (trade name Methocel K4M CR, methoxyl content 22.7%, hydroxypropyl content 8.9%) was obtained from Colorcon Ltd., England. Viscosity average molecular mass was Mv=91,500 g/mol, determined at 20 °C. Critical overlap concentration of HPMC was c =0.1269%. Sodium carboxymethyl cellulose, NaCMC, degree of substitution DS=0.77, purity >96%, was obtained from Milan Blagojevic , Serbia. Viscosity average molecular mass of NaCMC was Mv=121,000 g/mol, determined at 25 °C, and critical overlap concentration c =0.1927%. Sodium dodecylsulfate, SDS, purity >99%, was obtained from Merck, Germany. Critical micelle concentration was... 

The issue of water in reverse micellar cores is important because water swollen reverse micelles (reverse microemulsions) provide means for carrying almost any water-soluble component into a predominantly oil-continuous solution (see discussions of microemulsions and micellar catalysis below). In tire absence of water it appears tliat premicellar aggregates (pairs, trimers etc.) are commonly found in surfactant-in-oil solutions [47]. Critical micelle concentrations do exist (witli some exceptions). 

Additives, whether hydrophobic solutes, other surfactants or polymers, tend to nucleate micelles at concentrations lower than in the absence of additive. Due to this nucleating effect of polymers on micellization there is often a measurable erne, usually called a critical aggregation concentration or cac, below the regular erne observed in the absence of added polymer. This cac is usually independent of polymer concentration. The size of these aggregates is usually smaller than that of free micelles, and this size tends to be small even in the presence of added salt (conditions where free micelles tend to grow in size). 

Mukeqee P and Mysels K J 1970 Critical Micelle Concentrations of Aqueous Surfactant Systems (National Standard Reference Data System, National Bureau of Standards Circular No 36) (Springfield, VA National Teehnieal Information Serviee)... 

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. 

During Stage I the number of polymer particles range from 10 to 10 per mL. As the particles grow they adsorb more emulsifier and eventually reduce the soap concentration below its critical micelle concentration (CMC). Once below the CMC, the micelles disappear and emulsifier is distributed between the growing polymer particles, monomer droplets, and aqueous phase. 

Emulsification is the process by which a hydrophobic monomer, such as styrene, is dispersed into micelles and monomer droplets. A measure of a surfactant s abiUty to solubilize a monomer is its critical micelle concentration (CMC). Below the CMC the surfactant is dissolved ia the aqueous phase and does not serve to solubilize monomer. At and above the CMC the surfactant forms spherical micelles, usually 50 to 200 soap molecules per micelle. Many... 

Fig. 3. Schematic diagram of anionic surfactant solution at equiUbrium above its critical micelle concentration, where M = micelle and 0 are counterions ...

Critical Micelle Concentration. The rate at which the properties of surfactant solutions vary with concentration changes at the concentration where micelle formation starts. Surface and interfacial tension, equivalent conductance (50), dye solubilization (51), iodine solubilization (52), and refractive index (53) are properties commonly used as the basis for methods of CMC determination. 

P. Mukerjee and M. J. Mysels, Critical Micelle Concentration ofMqueous Suf actant Systems, NSROS-NBS 36, U.S. Dept, of Commerce, Washiagton, D.C., 1971. 

MeutralSoluble Salts. So dium sulfate [7757-82-6] and, to a considerably lesser extent, sodium chloride [7647-14-5] are the principal neutral soluble salts used in laundering compositions. They are often considered to be fillers although they perform an important standardizing function enabling the formulator to manufacture powders of a desired, controlled density. Sodium sulfate, in addition, lowers the critical micelle concentration of organic surfactants and thus the concentration at which effective washing can be achieved. 

Surfactants lower the surface tension of water, typically from 72 to ca 30—35 mN/m (= dyn/cm), and many surfactants have a strong effect on the contact angle when used at low concentrations. Both changes help dewatering. Too much surfactant, near or above the critical micelle concentration... 

K is K, just below the collectors critical micelle concentration, C,. Ko is Ki at some higher cohector concentration, C,. E is the relative effectiveness, in adsorbing cohigend, of surface cohector versus micehar collector. Generally, E > 1. F, is the surface excess of collector. More about each K is avahable [Lemhch, Adsubble Methods, in Li (ed.). Recent Developments in Separation Science, vol. 1, CRC Press, Cleveland, 1972, pp. 113-127 Jashnani and Lemlich, Ind. Eng. Chem. Process Des. Dev., 12, 312 (1973)]. 

Beyond the CMC, surfactants which are added to the solution thus form micelles which are in equilibrium with the free surfactants. This explains why Xi and level off at that concentration. Note that even though it is called critical, the CMC is not related to a phase transition. Therefore, it is not defined unambiguously. In the simulations, some authors identify it with the concentration where more than half of the surfactants are assembled into aggregates [114] others determine the intersection point of linear fits to the low concentration and the high concentration regime, either plotting the free surfactant concentration vs the total surfactant concentration [115], or plotting the surfactant chemical potential vs ln( ) [119]. 

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