Enthalpy and Entropy of Micellization

S.2.2.3 Thermodynamic Parameters The CMC value dependence on temperature is used for the determination of thermodynamic parameters applying models [60]. The mass action model, apparent and partial model, and phase separation model [14,59,60] are apphed to estimate the thermodynamic parameters Gibbs energy, enthalpy, and entropy of micelle formation. The enthalpy and entropy change for the miceUization can be determined using the Gibbs-Helmholtz equation [55]. 

As mentioned above, the process of micellization is one of the most important characteristics of surfactant solution and hence it is essential to understand its mechanism (the driving force for micelle formation). This requires analysis of the dynamics of the process (i.e. the kinetic aspects) as well as the equilibrium aspects whereby the laws of thermodynamics may be applied to obtain the free energy, enthalpy and entropy of micellization. Below a brief description of both aspects will be given and this will be followed by a picture of the driving force for micelle formation. 

The influence of alkyl chain length of the surfactant on the free energy, enthalpy and entropy of micellization has been demonstrated by Rosen [19] who listed these parameters as a function of alkyl chain length for sulphoxide surfactants. The results given in Table 2.3 show that the standard free energy of micellization... 

Calculate the values of the thermodynamic properties, Gibbs free energy, enthalpy and entropy of micellization, for the following surfactants from the information below for T = 298 K. 

Enthalpies and Entropies of Mixing in Micelles. Next to monomer activities, the most needed data on mixed micelles are the enthalpy (heat) and entropy of mixing... 

It is generally accepted that the hydrophobicity of alcohols is enhanced when the hydrogenated alkyl chain is fluorinated. Only a few such systems have been studied,but it appears that AG is more negative for the fluorinated alcohols, whereas the enthalpies and entropies of transfer are more positive. The effect on TAS is larger than that on AH. It thus seems that the difference between the hydrogenated and fluorinated alcohols largely stems from a more pronounced hydro-phobic effect of the fluorinated chain in the aqueous phase, and is not an effect of a larger affinity toward the micelles. 

Shinoda, K., Kobayashi, M., and Yamaguchi, N., Effect of iceberg formation of water on the enthalpy and entropy of solution of paraffin chain compounds the effect of temperature on the critical micelle concentration of lithium perfluorooctane sulfonate, J. Phys. Chem., 91, 5292, 1987. 

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. 

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). 

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). 

The enthalpy of micellization A H° can be measured either from the variation of cmc with temperature or directly by microcalorimetry. From AG° and AH0, one can obtain the entropy of micellization AS0,... 

The free energy change of a system is dependent on changes in both the entropy and enthalpy that is, AG = AH-T AS. For a micellar system at normal temperatures the entropy term is by far the most important in determining the free energy changes (T AS constitutes approximately 90-95% of the AG value). Micelle formation entails the transfer of a hydrocarbon chain from an aqueous to a nonaqueous environment (the interior of the micelle). To understand the changes in enthalpy and entropy that accompany this process, we must first consider the structure of water itself. 

The main waterlike properties of EAN are that it can promote the formation of micelles, has a high cohesive energy density," is highly polar with solvophobic behavior, and has waterlike properties in its enthalpy and entropy changes for the transfer of nonpolar gases to BAN. ... 

Standard free energies of micellization AG and their enthalpy and entropy —TAS ... 

Nuclear magnetic resonance is a very powerful tool for investigating micellar structures of fluorinated surfactants. NMR spectroscopy yields values of the free energy of micellization, AG,° and the corresponding enthalpy and entropy changes, AH° and AS° [26-32]. 

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