Thermodynamics micelle formation

Therefore, the physical meaning of the solubility curve of a surfactant is different from that of ordinary substances. Above the critical micelle concentration the thermodynamic functions, for example, the partial molar free energy, the activity, the enthalpy, remain more or less constant. For that reason, micelle formation can be considered as the formation of a new phase. Therefore, the Krafft Point depends on a complicated three phase equilibrium. 

Table IX shows the thermodynamic parameters of micellization, calculated from the cmcs and their temperature dependence, for two homologues of each of these types of nonionics. It can be seen that AHm and ASm progressively decrease in the order usual-type > S > L-A > G type for both homologous series. This suggests that the high polarity of the amido linkage causes either less dehydration or exothermic association of the hydrophilic part on micelle formation.

Application of Activity at cmc. The above consideration suggested us to propose a new treatment for ionic micelle formation. According to thermodynamics, the micelle-monomer equilibrium is achieved when the chemical potential of surfactant in the micelle is equal to that in the bulk solution. The free energy of micelle formation can be represented by the use of the critical micelle activity, cma, which is the activity of surfactant at the cmc, as... 

Lipid nanodispersions (SLN and NLC) are complex, thermodynamically unstable systems. The colloidal size of the particles alters physical features (e.g., increasing solubihty and the tendency to form supercooled melts). The complex structured lipid matrix may include hquid phases and various lipid modifications that differ in the capacity to incorporate drugs. Lipid molecules of variant modifications may differ in their mobility. Moreover, the high amount of emulsifier used may result in liposome or micelle formation in addition to the nanoparticles. 

The structure and thermodynamics of formation of mixed micelles is of great theoretical interest. Micelles are also present and often integrally involved in practical processes. For example, in a small pore volume surfactant flooding process (sometimes called micellar flooding), the solution injected into an oil field generally contains 5-12 weight X surfactant (i) and the surfactant is predominately in micellar form in the reservoir water. In detergency, solubilization can be... 

Except for some anionic/cationic surfactant mixtures which form ion pairs, in a typical surfactant solution, the concentration of the surfactant components as monomeric species is so dilute that no significant interactions between surfactant monomers occur. Therefore, the monomer—mi celle equilibria is dictated by the tendency of the surfactant components to form micelles and the interaction between surfactants in the micelle. Prediction of monomer—micelle equilibria reduces to modeling of the thermodynamics of mixed micelle formation. 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

The adsorption of mixed surfactants at the air—water interface (monolayer formation) is mechanistically very similar to mixed micelle formation. The mixed monolayer is oriented so that the surfactant hydrophilic groups are adjacent to each other. The hydrophobic groups are removed from the aqueous environment and are in contact with other hydrophobic groups or air. Therefore, the forces tending to cause monolayers to form are similar to those causing micelles to form and the thermodynamics and interactions between surfactants are similar in the two aggregation processes. 

A brief accounting of the thermodynamics of mixed micelle formation is given here primarily to clarify certain important issues which appear to have been previously overlooked. The necessity for measuring the monomer and micellar composition will be demonstrated. 

The importance of entropic considerations in the formulation of a thermodynamic model for micelle formation in mixtures of ionic and nonionic surfactants has been demonstrated by the ability of the... 

The evaluation of the Interaction parameters is based upon equations (1 and 2), derived by Rubingh (7) for mixed micelle formation from the thermodynamics of the system ... 

Thermodynamic Study of the Surface Adsorption and Micelle Formation of Mixed Surfactants... 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

The mixed admicelle is very analogous to mixed micelles, the thermodynamics of formation of which has been widely studied. If the surfactant mixing in the micelle can be described by ideal solution theory, the Critical Micelle Concentration (CMC) or minimum concentration at which micelles first form can be described by (21) ... 

Critical Micelle Concentration. In order to demonstrate the analogy between our treatment of mixed adsorption and earlier treatments of mixed micellization, we will briefly review the thermodynamics of mixed micelles. The thermodynamics of formation of ideal mixed micelles by two surfactants has been treated by Lange and Beck (9 ) and Cling (10). Rubingh ( ) extended the treatment to account for interactions between the surfactants, essentially by writing the cmc in the mixed surfactant solution as. 

Model Development. There is vast opportunity for development of fundamentally based models to describe the thermodynamics of mixed micelle formation. As discussed in Chapter 1, regular solution theory has yielded useful relations to describe monomer—mi cel 1e equilibrium. 

The same thermodynamic quantities needed for mixed micelle formation (already discussed) are also needed for mixed admicelle formation. Luckily, the monomer-admicelle equilibrium data can be fairly easily and unambiguously obtained (e.g., see Chapter 15). This should be combined with calorimetric data for a more complete thermodynamic picture of the mixed admicelle. As with micelles, counterion bindings on mixed admicelles also need to be obtained in order to account for electrostatic forces properly. Only one study has measured counterion binding on single-component admicelles (3 .), with none reported for mixed admicelles. 

Micelle formation is a nice example of self-organization under thermodynamic control. Following the addition of some liquid soap in water at a concentration higher than the cmc, spherical micellar aggregates spontaneously form. This process takes place with a negative free-energy change - actually the process is attended by an increase of entropy. 

The thermodynamics of micelle formation has been studied extensively. There is for example a mass action model (Wennestrdm and Lindman, 1979) that assumes that micelles can be described by an aggregate Mm with a single aggregation number m, so that the only descriptive equation is mMi Mm. A more complex form assumes the multiple equilibrium model, allowing aggregates of different sizes to be in equilibrium with each other (Tanford, 1978 Wennestrdm and Lindman, 1979 Israelachvili, 1992). 

Carey, M. V. and Small, D. M. (1972). Micelle formation by bile salts. Physical-chemical and thermodynamic considerations. Arc/t. Intern. Med., 130, 506-27. 

In the second item above, the presence of bound and free water molecules was noted. Both bound ions and ionic surfactant groups are hydrated to about the same extent in the micelle as would be observed for the independent ions. The dehydration of these ionic species is an endothermic process, and this would contribute significantly to the AH of micellization if ion dehydration occurred. In the next section we discuss the thermodynamics of micellization, but it can be noted for now that there is no evidence of a dehydration contribution to the AH of micelle formation. The extent of micellar hydration can be estimated from viscosity... 

By comparing the thermodynamic quantities of micellization of both 17R4 and L-64, Zhou and Chu (1994) concluded, that micellization of both surfactants is an endothermic process that accounts for the fact that the CMC decreases as the temperature increases. In both cases, the entropically driven hydrophobic interactions of the polypropylene oxide) blocks in an aqueous environment are mainly responsible for micelle formation. 

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