Micellization entropy

The small and positive values of enthalpy of solution of water in AOT-reversed micelles indicate that its energetic state is only slightly changed and that water solubilization (unfavorable from an enthalpic point of view) is driven mainly by a favorable change in entropy (the destructuration of the water at the interface and its dispersion as nanodroplets could be prominent contributions) [87],... 

Usually the discussion of the ODT of highly asymmetric block copolymers in the strong segregation limit starts from a body-centred cubic (bcc) array of the minority phase. Phase transitions were calculated using SOFT accounting for both the translational entropy of the micelles in a disordered micelle regime and the intermicelle free energy [129]. Results indicate that the ODT occurs between ordered bcc spheres and disordered micelles. 

Guillaume et al. [69] presented a high performance liquid chromatographic method for an association study of miconazole and other imidazole derivatives in surfactant micellar using a hydrophilic reagent, Montanox DF 80. The thermodynamic results obtained showed that imidazole association in the surfactant micelles was effective over a concentration of surfactant equal to 0.4 pM. In addition, an enthalpy-entropy compensation study revealed that the type of interaction between the solute and the RP-18 stationary phase was independent of the molecular structure. The thermodynamic variations observed were considered the result of equilibrium displacement between the solute and free ethanol (respectively free surfactant) and its clusters (respective to micelles) created in the mobile phase. 

Electronically excited states of organic molecules, acid-base properties of, 12,131 Energetic tritium and carbon atoms, reactions of, with organic compounds, 2, 201 Enolisation of simple carbonyl compounds and related reactions, 18,1 Entropies of activation and mechanisms of reactions in solution, 1,1 Enzymatic catalysis, physical organic model systems and the problem of, 11, 1 Enzyme action, catalysis of micelles, membranes and other aqueous aggregates as models of, 17. 435... 

First, micelles have very loose, mobile, structures and there are considerable entropy costs in a concerted reaction. These costs are much less serious in enzymic systems where conformation at the active site is tailor-made to fit the transition state. Secondly, the sites of micellar reactions are very wet and omnipresent water molecules are available to transfer protons. 

Exchange of unimers between two different types of block copolymer micelles has often been referred to as hybridization. This situation is more complex than for the case described above because thermodynamic parameters now come into play in addition to the kinetic ones. A typical example of such hybridization is related to the mixing of micelles formed by two different copolymers of the same chemical nature but with different composition and/or length for the constituent blocks. Tuzar et al. [41] studied the mixing of PS-PMAA micelles with different sizes in water-dioxane mixtures by sedimentation velocity measurements. These authors concluded that the different chains were mixing with time, the driving force being to reach the maximum entropy. 

Excellent reviews on micelles formed in organic solvents have been published by Hamley [2], Chu et al. [86], and Riess [14]. From these overviews it appears that a wide range of styrene-, (meth)acrylates-, and dienes-based block copolymers were investigated and that the formation of micelles in organic solvents can generally be considered as an entropy-driven process. AB diblock and ABA triblock architectures were systematically compared. All these previous investigations have been summarized by Hamley [2], We will therefore not perform an extensive review of all these systems, since this information has already been provided by others, but we will briefly outline some selected examples. 

Standard entropies and enthalpies of micellization, AS°. and AH°-c, can be calculated from the relationships ... 

Althogh, AG evaluated by Equation 9 takes into account the loss in translational entropy of counter ions upon micellar assoclatlon(3,4), it is doutfull that the term (m/n) RT ln[X], can Include all the effects of interionic interaction in micelle formation. 

As mentioned above, a substantial part of the electrical charge of the micelle surface has been shown to be neutralized by the association of the counter ions with the micelle. In the calculation based on Equation 12, however, the loss in entropy arising from this counter ion association is not taken into account. This is by no means insignificant in comparison to of Equation 12 (4). A major part of the counter ions are condensed on the ionic micelle surface and counteract the electrical energy assigned to the amphiphilic ions on the micellar surface. The minor part of the counter ions,in the diffuse double layer, are also restricted to the vicinity of the micellar surface. 

This conclusion implies that the excess entropy of mixing is non-zero and that the mixed micelles presumably acquire more internal order than they would by random mixing. An examination of the magnitude of the deviations from the regular solution approximation shows that there must be a large TS contribution to the excess free energy of mixing. 

This transition may j-.e. reducing the specific surface energy, f. The reduction of f to sufficiently small values was accounted for by Ruckenstein (15) in terms of the so called dilution effect". Accumulation of surfactant and cosurfactant at the interface not only causes significant reduction in the interfacial tension, but also results in reduction of the chemical potential of surfactant and cosurfactant in bulk solution. The latter reduction may exceed the positive free energy caused by the total interfacial tension and hence the overall Ag of the system may become negative. Further analysis by Ruckenstein and Krishnan (16) have showed that micelle formation encountered with water soluble surfactants reduces the dilution effect as a result of the association of the the surfactants molecules. However, if a cosurfactant is added, it can reduce the interfacial tension by further adsorption and introduces a dilution effect. The treatment of Ruckenstein and Krishnan (16) also highlighted the role of interfacial tension in the formation of microemulsions. When the contribution of surfactant and cosurfactant adsorption is taken into account, the entropy of the drops becomes negligible and the interfacial tension does not need to attain ultralow values before stable microemulsions form. 

FORMATION. Aqueous solutions of highly surface-active substances spontaneously tend to reduce interfacial energy of solute-solvent interactions by forming micelles. The critical micelle concentration (or, c.m.c.) is the threshold surfactant concentration, above which micelle formation (also known as micellization) is highly favorable. For sodium dodecyl sulfate, the c.m.c. is 5.6 mM at 0.01 M NaCl or about 3.1 mM at 0.03 M NaCl. The lower c.m.c. observed at higher salt concentration results from a reduction in repulsive forces among the ionic head groups on the surface of micelles made up of ionic surfactants. As would be expected for any entropy-driven process, micelle formation is less favorable as the temperature is lowered. 

Note the change of sign.) Likewise, we can define the standard entropy and enthalpy for micellization as follows ... 

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. 

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