Thermodynamics of micellization

According to the original mass action model, micellization is a reversible association of micelles [20,116)  

Assuming ideal behavior, the chemical potentials, and ixm, of the surfactant monomers and micelles respectively are 

The free energy of micellization, AG°, is then given by AG = RTId Ca - In c  

If the aggregation number n varies with temperature or, as in some cases, with surfactant concentration, Eq. (20) is not valid. If the variation of the aggregation number n with temperature is assumed to be small and can be neglected [27,45,47,54,105,115,117-122], an equation of the Clausius-Clapeyron type can be written 

Equation (21) is not strictly valid for calculating the heat of micellization because certain assumptions made in its derivation do not hold here. The equation implies that the micelle is at equilibrium near cmc in a standard state [27,54]. However, micelles are not definite stoichiometric entities but aggregates of different sizes that are in dynamic equilibrium with themselves and surfactant monomers. The aggregation number may vary with temperature. An extended mass action model describes micellization as a multiple equilibrium characterized by a series of equilibrium constants (see Section 6.2). Because these equilibrium constants cannot be determined, the micellar equilibrium is usually described by 

There are several approaches to derive the Gibbs free energy of micellization. We only discuss one of them which is called the phase separation model. Even this approach only leads to approximate expressions for nonionic surfactants. More detailed discussions of the thermodynamics of micellization can be found in Refs. [3,528,529], 

In the phase separation model we take advantage of the fact that micellization has much in common with the formation of a separate liquid phase. At low concentration the chemical potential of the dissolved surfactants can be described by 

The molar Gibbs energy of micelle formation is the Gibbs energy difference between a mole of monomers in micelles and the standard chemical potential in dilute solution  

For nonionic surfactants we can use this equation to calculate the change in Gibbs free energy of micellization. For ionic surfactants the change of dissociation of charges from the head groups effects the result. 

CMCs are usually below 1 M. For this reason Gibbs free energies for micellization are negative i.e. it is a spontaneous process. For example, the CMC of CioE is 1 mM. The Gibbs free energy of micellization is AG C = RT In 0.001 = —17.1 kJ per mol surfactant at 25°C. 

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In general, the standard enthalpy of micellization is large and negative, and an increase in temperature results in an increase in the c.m.c. the positive entropy of micellization relates to the increased mobility of hydrocarbon side chains deep within the micelle as well as the hydrophobic effect. Hoffmann and Ulbricht have provided a detailed account of the thermodynamics of micellization, and the interested reader will find that their tabulated thermodynamic values and treatment of models for micellar aggregation processes are especially worthwhile. 

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). 

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... 

One important point to recognize about the Stern layer in ionic micelles is that the bound counterions help overcome the electrostatic repulsion between the charged heads of the surfactant molecules. For nonionics no such repulsion exists. It is incorrect to think that ionic micelles form and then adsorb counterions. The Stern layer is part of the micelle, and the energetics of its formation are part of the thermodynamics of micellization. 

In this section we consider the thermodynamics of micellization from two points of view the law of mass action and phase equilibrium. This will reveal the equivalency of the two approaches and the conditions under which this equivalence applies. In addition, we define the thermodynamic standard state, which must be understood if derived parameters are to be meaningful. 

The micellization of surfactants has been described as a single kinetic equilibrium (10) or as a phase separation (11). A general statistical mechanical treatment (12) showed the similarities of the two approaches. Multiple kinetic equilibria (13) or the small system thermodynamics by Hill (14) have been frequently applied in the thermodynamics of micellization (15, 16, 17). Even the experimental determination of the factors governing the aggregation conditions of micellization in water is still a matter of considerable interest (18, 19) and dispute (20). 

This two-state model, which assumes that surfactant exists either as monomers or micelles, is almost certainly an oversimplification. The mass action model assumes an equilibrium between monomers, n-mers and micelles, with the proviso that the bulk of the surfactant is present as monomers or micelles. In other words micelliza-tion is considered to occur over a narrow range of surfactant concentration, at least for aqueous micelles [1,2,23]. The thermodynamics of micellization have been discussed in terms of the hydrophobic interactions and the electrostatic interactions of the head groups, and, for ionic micelles, of the counterions with the ionic head groups [18,22,24],... 

The effects of a variety of added organic solvents upon the thermodynamics of micellization have been investigated by lonescu and Fung [129],... 

Reviews of globular aggregates can be found in Statistical Thermodynamics of Micelles and Microemulsions, eds. S. Chen and R. Ra-jagopalan (Springer-Verlag, New York, 1990). 

Goodman JF, Corkill JM, and Harrold SP. (1964). Thermodynamics of micellization of non-ionic detergents. Transactions of the Faraday Society, 60, lOl-Kfl. 

There are two basic approaches to modeling the thermodynamics of micelle formation. The mass action model views the micelles as reversible complexes of the monomer that are aggregating and predicts the sharp change in tendency of incremental surfactant to form micelles instead of monomer at the CMC this sharp transition is a consequence of the relatively large number of molecules forming the aggregate. The mass action model predicts that micelles are present below the CMC but at very low concentrations. The ocher major model used to describe micelle formation is the pseudophase separation model, which views micelles as a separate thermodynamic phase in equilibrium with monomer. Because micelle formation is a second-order phase transition, micelles are not a true thermodynamic phase, and this model is an approximation. However, the assumption that there are no mi-celies present below the CMC, and that the surfactant activity becomes constant above the CMC. is close to reality. and the mathematical simplicity of the pseudophase... 

The structure and the basic thermodynamics of micelles formed by amphiphilic block copolymers with a PE coronal block A can be analyzed using the blob model. However, the ionization of block A in a polymeric amphiphile introduces long-ranged repulsive interactions in the corona of a micelle. As a result, the blob picture for the micellar corona has to be modified, as explained in this section. 

Tanford, C. 1974. Thermodynamics of micelle formation Prediction of micelle size and size distribution. Proceedings of the National Academy of Sciences. 71, 1811. 

N. Funasaki, Thermodynamics of Micellization of Surfactants in Presence or Absence of Salts, J. Colloid Interface Sci., 67 384 (1978). 

The thermodynamics of micelle formation can be analyzed with varying degrees of complexity. The simplest is to consider that a phase separation into... 

Experimental data indicate that the changes in rates of variation of physical properties near the CMC actually occur over a narrow range of concentrations and not discontinuously at a single concentration. Hraice a chemical reaction or mass action model should be more realistic than the phase separation model for describing the thermodynamics of micellization. That is, we consider that micelle formation occurs as follows ... 

R. NAGARAJAN is currently Assistant Professor of Chemical Engineering at the Pennsylvania State University. He received his Ph.D. degree in 1979 from the State Unviersity of New York at Buffalo. His research interests focus on surfactants, their mechanism of action and their applications. He has published more than 30 papers in the areas of thermodynamics of micelles, vesicles, solubilization, enhanced oil recovery and surfactant-polymer interactions. 

Chaterjee, A. Moulik, S.P. Sanyal, S.K Mishra, B.K. Puri, P.M. Thermodynamics of Micelle Formation of Ionic Surfactants A Critical Assessment for Sodium Dodecyl Sulfate, Cetyl Pyridinium Chloride and Dioctyl Sulfosuccinate (Na Salt) by Microcalorimetric, Conductometric, and Tensiometric Measurements. /. Phys. Chem. 

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