Entropy of micelles

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 first version of Equation (17) suggests that a plot of In cCMC versus 1/Tis a straight line of slope A// ,c/[/ (l + m/n)] if AH°mtc and m/n are independent of T. Backtracking to Equation (9) or (15) shows that n must also be constant with respect to temperature for this to be valid. In fact, n increases with temperature for polyoxyethylene nonionics any temperature dependence of n is generally assumed to be absent in ionic systems. Even if the In cCMC versus /T plot is nonlinear, the second form of Equation (17) allows a value of AH°mc to be evaluated from the slope of a tangent to a plot of In cCMC versus T at a particular temperature. Once AG°ic and AH°mjc are known, the entropy of micellization is readily obtained from AG = AH — TAS. Example 8.4 illustrates the use of these relationships. 

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,... 

A frequently used simplifying approximation is based on neglecting the translational entropy of micelles (i.e., the second term in (1) is omitted). This approximation is justified as long as the aggregation number in an equilibrium micelle is large. Then, (2)-(4) reduce to ... 

A comparison of (10) and (14) indicates that because of the stability condition, (8), the exact CMC [defined by (10)] is smaller than the CMC obtained from the approximate analytical model, (14). Accounting for the translational entropy of micelles leads, therefore, to a lower value of the aggregation number, Peq(c) < po, and a lower CMC. 

The free energy, (1), complemented by the contribution due to counterions, cf. (15), can be minimized with respect to Cmic nd P- When the translational entropy of micelles is neglected, the optimal aggregation number, p = po, is still given by (11). The concentration of unimers that coexist with micelles, and thus the CMC, is, however, significantly larger than for neutral (uncharged) amphiphiles ... 

Translational entropy of micelles Dead time of mixing Flory exponent Volume of component i Sample volume in cm ... 

Determinations of the thermodynamic parameters for micellization in the vicinity of room temperature support the above interpretation. The major contributor to the free energy of micellization, AG per unimer, is from the entropy of micellization, AS, Table Note that... 

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 entropy of micellization can then be calculated from the relationship between AG° and AH°, i.e.,... 

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... 

Finally the standard entropy of micellization per mole of monomer, niay be obtained from... 

A and B are two constants and cmco is the cmc in the absence of salt. The value of B is close to the degree of counterion association to the micelle. ds Thermodynamic studies showed that the formation of micelles is entropy-driven.The large positive value of the entropy of micellization reflects a change affecting water molecules surrounding surfactant alkyl chains when the chains are transferred from the aqueous phase to the micelle core. s... 

Micellization is (almost always) an entropic effect, I.e. the driving force behind aggregation of surfactant molecules Is a large positive value of entropy of micellization why ... 

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. 

Data published on thermodynamic properties of fluorinated surfactants are scarce. Shinoda and Hutchinson [42] treated the micelle as a separate pseudophase of very small dimensions. The phase-separation model describes the micelle as a separate phase which begins to form at cmc. If micelle formation is analogous to phase separation, the heat and entropy of micellization can be calculated from the temperature dependence of the activities of micelle-forming species. 

Shinoda and Katsura [126] calculated the entropy of micellization from the temperature dependence of cmc for potassium perfluorooctanoate under the con-... 

The standard free entropy of micellization, Sh, was calculated from AG = AHl, - TASlt... 

Although the very existence of CMC of surfactant dissolved in nonpolar has been questioned, the UV absorption and fluorescence emission measurements of AOT-solubilized solubilizates, such as tert-butylphenol, pyrene, and hemi-Mg salt of 8-anilino-l-naphthalenesulfonic acid, in isooctane provided evidence for the existence of CMC at different values of R = [H20]/[A0T] (with R < 3) and CMC value increases with increase in R. The values of CMC, obtained at different temperatures, were used to calculate standard enthalpy of micellization (AH j°) from Equation 1.13 and standard entropy of micellization (AS j ) from Equation 1.14, and these respective values vary from 38.07 to 44.81 kJ mol and 184.60 to 202.60 JK moE with increase in temperature from 20 to 45°C. The positive AH j values arise mainly from the dismantling of hydrated ions in the quasi-lattice of AOT interior. 

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