Biosurfactants for a Sustainable Future. Группа авторов

Figure 1.4, right). The heat of demicellization ΔH _demic is equal to the enthalpy difference between the two extrapolated lines in Figure 1.4. Thus, the cmc and the enthalpy of micellization are simultaneously determined, but independently to each other.

Repetition of the ITC experiment at other temperatures allows the determination of the change in the heat capacity of the demicellization process,

. The interval of temperatures used in these studies is rarely larger than 30–40 °C. Within this interval, the dependence of ΔH _demic for most of the surfactants is linear with T, meaning that

is constant ([100] and references therein). While ΔH _demic may be either positive (endothermic) or negative (exothermic),

for the demicellization process is always positive. This means that the hydrophobic surface of monomers, being exposed to water, increases upon demicellization. For this reason, it is frequently observed that ΔH _demic is negative at low temperatures and positive at high ones. The formation of a micelle requires that some water molecules surrounding each monomer must be lost in the aggregation process to form the final aggregate. The process also contributes to a favorable entropy term for micellization. Thus, the transfer of surfactant monomers from an aggregate to the bulk water has many facts in common with the dissolution of liquid alkanes into water [101]. Gill et al. [102] have noticed that the experimental heat capacity difference between gaseous and dissolved non‐polar molecules in water is correlated with the number of water molecules in the first solvation shell. They concluded that a two‐state model, in which each water molecule in the solvation shell behaves independently, provides a satisfactory basis to quantitatively describe the heat capacity properties of the solvation shell. For a series of solutes (most of them being hydrocarbon compounds), an average value of ~13.3 J/mol K (see the theoretical line shown in Figure 1.1 at 25 °C of that paper) was estimated for the contribution of each water molecule to

.

      Calorimetric measurements of vapor equilibrium of the system cyclohexane‐heptane were performed almost 70 years ago by Crutzen et al. [103]. These authors observed that between 40 and 60 °C, the increase in the molar free Gibbs energy becomes small because of the partial compensation of the heat of mixing and the entropy of mixing. Since then, many papers have been published in which the concept enthalpy–entropy compensation (EEC) has been taken into consideration. Arguments for or against EEC have been published and, for surfactant systems, EEC has been reviewed several times [100,104–106]. For demicellization (or equivalently micellization), the relationship is written linearly as

      (1.21)

      where T _c = (∂∆H/∂∆S) _P is known as the compensation temperature.

      Recently, Vázquez‐Tato et al. [100] have shown that “it is possible to obtain as many compensation temperature values as the number of temperature intervals in which the dependencies of enthalpy and entropy changes with temperature are analyzed.” Furthermore, “the value of each T _c will agree with the central value T _o of each temperature interval.” These authors concluded that “T _c is simply such experimental T _o ” without any physical meaning and concluded that it “does not provide any additional information about the systems.” In other words, any physical interpretation derived from T _c (and by extension from ΔH _c ) is meaningless.

1.3 Average Aggregation Numbers

      Recently Olesen et al. [96] have published a method for analyzing the ITC curves that allows the determination of the aggregation number. As in previous cases, we will limit the presentation to neutral surfactants. The mass‐action model and monodispersity of micelles are assumed.

Other significant papers for determining the aggregation number of micelles are those by Debye and by Turro and Yekta. After his landmark paper published in 1947 for the molecular weight determination by light scattering, Debye [107] immediately published the first determinations of micellar molecular weights by this technique in 1949 [108], the surfactants being alkyl quaternary ammonium salts and amine hydrochlorides. A few years later, Tartar and Lelong [109] determined the micellar molecular weights of some paraffin chain salts by the same technique. Nowadays, the technique is almost routinely applied in laboratories for determination of molecular weights of polymers, micelles, and so on.

      In 1978, Turro and Yekta [110] presented a simple procedure for determination of the mean aggregation number of micelles by measuring the steady‐state fluorescence quenching of a luminescent probe by a hydrophobic quencher. The Poisson statistics to describe the distribution of the luminescent molecule D and the quencher Q in a solution that contains a well‐defined but unknown micelle concentration [M] was accepted. Both D and Q are selected in such a way that they reside exclusively in the micellar phase. D will partition itself both among micelles containing Q and among “empty” micelles. They also assumed that only excited micelles of D, D*, emit in the micelles containing no Q, i.e. D* is completely quenched when it occupies a micelle containing at least one Q. Under these conditions a “very simple expression” for obtaining the aggregation number is deduced.

In 1899 Biltz [111] published the book Practical Methods for Determining Molecular Weights. The book is a summation of the practical methods for determining molecular weights by vapordensity and other methods based on colligative properties, mainly from the measurement of the increase of the boiling point of a solution with respect to a pure solvent, and the freezing‐point method. Both methods, together with the Nernst method (based upon the principle of lowering of solubility) are the only ones that “find practical application in the laboratory.” When the freezing‐point method is applied to some salts, Biltz accepts the Arrhenius dissociation theory of electrolyte solutions. Otherwise “the electrolytic dissociation in aqueous solutions can lead to smaller molecular weights than would be expected from the formula of the substance.” Earlier in 1896, Krafft [112] noticed that the sodium salts of the shorter fatty acids exist in the “molecular state” (meaning that they are in the state of single molecules, and not in that of molecular aggregates) in aqueous solution and that they give twice the normal rise of boiling point which in fact it would correspond with a hydrolytic decomposition into sodium (hydroxide, in the original) and the fatty acid. Following Biltz, the reverse can take place if “… by condensation several simple molecules form a more complex molecule…. The term association has recently been proposed for this kind of condensation.” Similarly, Kahlenberg and Schreiner [113] observed that the reduction of the freezing point of solutions of sodium oleate resulted in a molecular weight, which is nearly twice as large, like the theoretical formula. Botazzi and d'Errico [114] investigated glycogen of different concentrations by viscosity, freezing point, and electrical conductivity and observed that when the concentration of glycogen solutions reaches a certain maximum it appears that the colloidal particles combine with one another to form micelles. McBain et al. [115] measured the freezing point and the conductivity of sodium and potassium salts of saturated fatty acids that remain liquid at 0°. From this paper we must remark the comment that “free ions of charge equal and opposite to that of the charged colloid are present in the sol or gel.” In 1935 McBain and Betz [116] measured the freezing point of undecyl and lauryl sulfonic acids, expressing the results in terms of the osmotic coefficient. They concluded that in dilute solutions they behave as simple moderately weak electrolytes but with increased concentration molecules and ions associate into neutral and ionic micelles. They also considered that micelles “owing to the wide spacing