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1.2 Micelle Formation
ОглавлениеThe necessity of a quantitative measurement of the surface tension of soap solutions was soon evident. By the time that I. Traube published his earliest paper in 1884, significant theories of capillarity from La Place, Poisson, or Gauss were known [31]. Early measurements of the surface tension only imply inorganic salts, acids, and bases. In 1864 Guthrie [32, 33] measured some organic liquids. At the same time, Musculus [34] studied the capillarity of aqueous solution of alcohol observing that “the capillarity of the water decreases considerably with the addition of the least amount of alcohol, in the beginning, much faster than in the presence of more alcohol.” He also noticed that “all derivatives of ethyl alcohol which are soluble in water (as acetic acid) behave like this, and probably this is also the case with the other alcohols,” but substances such as “sugars, and salts if they are not present in a great amount, almost do not influence the capillarity of water.” He proposed the use of capillarity for measuring the concentration of alcohol and acetic acid in water, among other reasons, because “it offers the advantage that one needs only very little fluid for analysis, one drop being enough.” He continued that, as “the animal fluids, such as blood serum, urine, have a capillarity which is equal to that of water, it is possible to detect and quantify substances in the urine,” making reference, for instance, to bile.
Traube started the measurement of the influence of many organic substances on the surface tension of water in the period 1884–1885 [31] and observed that “the surface tension of capillary‐active compounds belonging to one homologous series decreased with each additional CH2 group in a constant ratio which is approximately 3:1,” leading him to propose Traube's Rule.
A nice historical paper was published by Traube [31] in 1940, in which he mentioned previous works related to the investigation of aqueous solutions of inorganic salts, acids, and bases, employing the method of capillary tubes, and, particularly, the dropping method applied by Quinke. Traube developed this method and designed a simple instrument, the stalagmometer – together with the stagonometer – which found general application in science and industry. In the mentioned paper, Traube refers mainly to his publications that appeared in the period 1886–1887. By 1906, the measurement of the surface tension by the capillary rise was so important that it was included in the book Practical Physical Chemistry by A. Findlay. The use of Traube's stalagmometer for such a purpose was proposed in the 3rd edition of the book, published in 1915. The experiment is still proposed in recent textbooks on practical Physical Chemistry [35].
Seventeen of the more important methods of measuring surface tension were described in 1926 by Dorsey [36]. According to his own words, “The list of references does not pretend to be complete but is intended merely to direct the reader to one or more of the sources from which the required information can be obtained most satisfactorily.” Even so, the number of cited papers was greater than 110, while the number of citations corresponding to the nineteenth century was 63 (56%). Eminent scientists such as Bohr, Rayleigh, Thomson, Kelvin, Maxwell, Laplace, and Poisson were among them. Tate [37] published his famous law in 1864 and Wilhelmy in 1863.
Even at low concentrations, surfactants reduce the surface tension of water due to its tendency to migrate toward the air–water interface, forming a monolayer. This was first suggested in 1907 by Milner [38] and, previously, Marangoni in 1871 “suggested that this capability [local variation in the tension of its surface] is due to the presence on the surface of the film of a pellicle, composed of matter having a smaller capillary tension than that of water.” Milner clearly established that “in several organic solutions the surface tension is less than that of water, and there is consequently an excess of solute in the surface.” Later, Langmuir [39] indicated that “the ‐COOH, ‐CO, and –OH groups have more affinity for water than for hydrocarbons… [and] when an oil is placed on water, the –COO– groups combine with the water, while the hydrocarbon chains remain combined with each other.” In other words, the tail of a surfactant (the hydrocarbon chain) must be located at the air interface, with the tail upwards oriented and the head (hydrophilic groups) at the water interface.
Rising the surfactant concentration, the surface concentration increases as well until the full coverage of the interface by the molecules or ions. If the interface is completely covered, further increment of the surfactant concentration does not (almost) modify the surface tension. Furthermore, the additional surfactant molecules (or ions) have to remain in the bulk solution, and following Langmuir “hydrocarbon chains remain combined with each other, thus forming micelles” (or other aggregates).
The term micelle was commonly used by the first years of the twentieth century [40, 41] in relation to colloid solutions (frequently inorganic gels). In 1920 McBain and Salmon [42] (see also [43]) described a brief résumé of previous work, citing, for instance, Krafft's work. From the summary of this paper we extract the following sentences:
3. These colloidal electrolytes are salts in which one of the ions has been replaced by an ionic micelle.
5. This is exemplified by any one of the higher soaps simply on change of concentration. Thus, in concentrated solution there is little else present than colloid plus cation, whereas in dilute solution both undissociated and dissociated soap are crystalloids of simple molecular weight.
8. The ionic micelle in the case of soaps exhibits an equivalent conductivity quite equal to that of potassium ion. Its formula may correspond to but more probably it is , where P − is the anion of the fatty acid in question.
Therefore, the essential definition of the present concept of a micelle was established. IUPAC indicates that “Surfactants in solution are often association colloids, that is, they tend to form aggregates of colloidal dimensions, which exist in equilibrium with the molecules or ions from which they are formed. Such aggregates are termed micelles.”
In 1922, McBain and Jenkins [44] studied solutions of sodium oleate and potassium laurate by ultrafiltration, using this technique for separating the ionic micelle from the neutral colloid. For both surfactants they showed that the proportion (simple potassium laurate or sodium oleate)/(ionic micelle) increases fast at low concentrations and reached a plateau at high concentrations (see graphs of the paper). They also concluded that the diameter of the ionic micelle is only a few times the length of the molecule and “the particles of sodium oleate are about ten times larger than those of potassium laurate.”
By the end of the twenties and the beginning of thirties of the twentieth century, the research activity on micelle‐forming substances experienced an extraordinary blooming spring. The paper by Grindley and Bury [45] is a landmark on the subject, being particularly illustrative for the purposes of this review. They represented the formation of micelles by butyric acid in solution by the equation
(1.2)
where n is “the number of simple molecules in a micelle” or aggregation number (which is a relatively large number) and write the equilibrium constant as
(1.3)
where s and m are the concentrations of butyric acid as monomers and as micelles, respectively. The previous equation can be written as
(1.4)
from which they deduced that if s/K is appreciably smaller than unity, the concentration of micelles will be negligible. Only when s approaches the value K does the concentration of micelles become appreciable, and “will rapidly increase as the total concentration increases.” From this analysis they conclude that “if any physical property of aqueous butyric acid solutions be plotted against the concentration, the slope of the curve will change abruptly near this point.” A few months later, Davies and Bury [46] named that concentration as the critical concentration for micelles.
Previous analysis constitutes the basis of all experimental techniques so far used for determining the critical concentration for micelles (from here cmc). For instance, the association of monomers in micelles reduces the number of particles in the solution and, consequently, colligative properties (freezing point, vapor pressure…) also drastically change at this concentration. Other properties such as solubilization of solutes as dyes or the conductivity of the solution also change significantly. As an example, we shall mention the paper by Powney and Addison [47] who measured the surface tension of aqueous solutions of sodium dodecyl, tetradecyl, hexadecyl, and octadecyl sulfates and plotted the results in the form of vs log (concentration), as we do nowadays. The curves showed breaks at critical concentrations, which correspond to transitions from single ions to micelles, these single ions constituting the surface‐active species. Figure 1.3 shows a typical plot for an unspecified surfactant. Powney and Addison noticed that the magnitude of the surface activity and the critical concentration for micelles were governed by chain length, temperature, and the valency of the added cation.
Figure 1.3 Typical surface tension vs ln (surfactant) plot showing the break point corresponding to cmc.
In 1895, Krafft and Wiglow [48] observed the formation of crystals at 60°, 45°, 31.5°, 11°, 35°, and 0° with hot aqueous solutions (1%) of stearate, palmitate, myristate, laurate, and elaidate sodium salts, respectively. Each of these temperatures is now known as the Krafft point (T k ). IUPAC defines it as the temperature (more precisely, narrow temperature range) above which the solubility of a surfactant rises sharply. At this temperature the solubility of the surfactant becomes equal to the cmc.
In 1955, Hutchinson et al. [49] published the paper “A new interpretation of the properties of colloidal electrolyte solutions” in which “the formation of micelles was treated as a phase separation rather than as an association governed by the law of mass action.” Seven years later, Shinoda and Hutchinson [50] used this model to interpret the Krafft point, associated to the micellization process. These authors proposed micellization as a “similar phase separation, with the important distinction that micellization does not lead to an effectively infinite aggregation number, such as corresponds to true phase separation.” If correct, the model requires that the activity of micelle‐forming compounds should be practically constant above the cmc. Among others, the authors invoke Nilsson results [51] with radiotracers as evidence for their proposition. In a frequently reproduced graph, Shinoda and Hutchinson [50] plotted the concentration vs temperature for sodium decyl sulfonate near the Krafft point. The plot resembles the phase diagram of water near its triple point. If micelles are considered as a phase, by the phase rule, the system should become invariant at constant temperature and pressure [49, 50]. In other words, “the equilibrium hydrated solid monomers micelles is univariant, so that at a given pressure the point is fixed.” As temperature increases, the solubility also increases until T k where the cmc is reached. Above this temperature, the surfactant is dissolved in the form of micelles.
Let us go back to 1915. In this year, Allen [52] published a paper in which he showed the use of the surface tension measurement for the determination of bile salts in urine. In the introduction of his paper, Allen refers to Hay’s method of testing the presence of bile salts in the urine. That method consists in “shaking flowers of sulphur upon the surface of the urine… When the surface tension of the urine is lowered [by bile salts] the powdered sulphur sinks to the bottom, and the lower the surface tension the more rapidly this takes place. [But] The method is very unsatisfactory… and if possible, a quantitative method, would be very desirable.” Thus Allen proposed a very accurate measurement of the surface tension of a solution by the stalagmometric method “to determine the feasibility of estimating the amount of bile salts present in pathological urines from measurements of the surface tension taken with a portable Traube stalagmometer.” He computed the surface tension value of a solution in per cent of that of distilled water according to the formula
(1.5)
The method relies on the fact that bile salts possess the property of lowering the surface tension of a solution very markedly, even when present in small concentrations. Table I of his paper shows some results for sodium glycocholate (NaGC) in distilled water. In a reanalysis of these data by plotting the surface tension vs ln(concentration), it is possible to determine a value of 0.0117 M for the cmc of NaGC, a value in perfect agreement with recent measurements. From the Reis et al. [53] compilation, an average value of (1.04 ± 0.29) × 10−2 M may be estimated for the cmc of this bile salt.
The “excess of solute [surfactant] in the surface” indicated by Milner has traditionally been analyzed through the Gibbs equation [54]
(1.6)
where Γ is the surface excess, ( ∂γ /∂ln c) is the slope of the dependence of γ with the logarithm of the concentration of the surfactant (frequently being linear), R is the ideal gas constant, T the temperature, and n a factor that depends on the nature of the surfactant. The equation allows the determination of the area occupied per molecule at the interface, which is the inverse of the surface excess, i.e.
(1.7)
where N A is Avogadro's number.
Recently Menger et al. [55] have questioned the validity of the Gibbs equation on the basis that in the region of concentration where the equation is applied the adsorption at the interface does not generally reach saturation. This criticism has been supported by measurements from a radioactive surfactant [56], results that suggest that the γ ‐ln c linearity is not indicative of surface saturation, a hypothesis required for the deduction of the Gibbs equation. Neutron reflection measurements also support the fact that there are serious limitations in applying the Gibbs equation accurately to surface tension data [57, 58].
In the late nineteen thirties, other important papers were published. Wright and co‐workers [59–61] measured the conductivity, density, viscosity, and solubility of several sodium alkyl (decyl, dodecyl, and hexadecyl) sulfonates at several temperatures. In all cases breaks at the curves or linear dependences of the property with the sulfonate concentration were observed. They also reported that the addition of sodium chloride to solutions of sodium dodecyl sulfonate lowered the cmc and that the lowering becomes less marked with a rise in temperature. Hartley [62] demonstrated that paraffin chain salts behave as strong electrolytes at low concentrations. For cetane sulfonic acid, a value of about 0.008 N in water at 60 °C was given for cmc and that it increased by about 2% per degree. This is an important question since the formation (or not) of premicellar aggregates is still under debate.
By the end of this decade Hartley [63] reviewed (36 references) the subject, the title of the paper being Ion aggregation in solutions of salts with long paraffin chains. In the abstracts we can read about the structure of micelles which are “aggregates of paraffin‐chain ions with some adsorbed opposite ions,” micelles are spherical with a radius equal to the length of a completely stretched paraffin‐chain and have a liquid interior and the strong dependence of cmc with the length of the hydrocarbon chain and nature of the ionized terminal groups and opposite ions (counterions), and with temperature (in less extension). He also affirmed that “the spherical micelle is more stable than ion pairs.”
Thus, by this time, the essential parameters that define a micelle were introduced or established: change of properties at the cmc, variables that influence the cmc, shape and size, internal and peripheral structures, and the essential thermodynamics (mass action law).
In the period 1946–1947, immediately after the Second World War, the activity on surfactant research experiences an important enhancement.
Corrin and Harkins [64] proposed the equation log(cmc) = − A × log(counterion ±) − B to relate the dependence of the cmc with the concentration of added salts (the sign at the superscript of the counterion is opposite to that of the surfactant ion). Table 1.1 resumes the values for the constants A and B for several surfactants. They also noticed that urea has a negligible effect in lowering the cmc.
Table 1.1 Parameters A and B of the Corrin–Harkins equation. The number of figures on the values of A and B has been reduced.
Source: Corrin and Harkins [64], p. 683 .
| Surfactant | A | B |
|---|---|---|
| Potassium laurate | 0.570 | 2.62 |
| Sodium dodecyl sulfate | 0.458 | 3.25 |
| Dodecyl ammonium chloride | 0.562 | 2.86 |
| Decyltrimethylammonium bromide | 0.343 | 1.58 |
Three years later, Lange [65] applied the mass action law to ionic micelles and wrote the equilibrium of formation of the micelle as
(1.8)
where K is the counterion, A the surfactant ion, and p and q the stoichiometric coefficients. Although Lange considered the activity coefficients of the different species, for simplicity we will ignore them and write the equilibrium constant as
(1.9)
Writing [A] = c k and [K] = c k + N, where N is the equivalent concentration of added salt, it is finally found that
(1.10)
where L = [K p A q ]. Thus with logc k as ordinate and log(c k + N) as abscissa, this is the equation of a straight line with the slope –p/q, which corresponds to the empirical one found by Corrin and Harkins. This point has been discussed in detail by Hall [66] in his theory for dilute solutions of polyelectrolytes and of ionic surfactants.
The effects of solvents (alkyl alcohols C n H2n+1OH, n = 1–4; HOCH2CH2OH, glycerol, 1,4‐dioxane, and heptanol) on the critical concentration for micelle formation of cationic soaps was studied by Corrin and Harkins [67], Herzfeld et al. [68], and Reichenberg [69]. Klevens [70] found that increasing the temperature causes an apparent decrease in the cmc, as determined by spectral changes in various dyes. However, this same author found the opposite effect when the micelles formation was determined by refraction [71].
Simultaneously, other experimental techniques, mainly spectroscopic ones, were introduced for the determination of the cmc. After a paper published by Sheppard and Geddes [72], in which the authors reported that by the addition of cetyl pyridinium chloride, the absorption spectrum of aqueous pinacyanol chloride was shifted from that exhibited in aqueous solutions to that in non‐polar solvents, Corrin et al. [73] used this property to determine the cmc of laurate and myristate potassium salts, giving values of 6 × 10−3 M and 0.023–0.024 M, respectively. The concentration of soap at which this spectral change occurs was taken as the cmc, proposing that the dye is solubilized in a non‐polar environment within the micelle. Klevens [74] performed a similar work by studying the changes in the spectrum of pinacyanol chloride in solutions of myristate, laurate, caprate and caprylate potassium salts, and sodium lauryl sulfate. These studies were extended to other surfactants [75] and other dyes as p‐dimethylaminoazobenzene [76]. By using suitable dyes (Rhodamine 6G, Fluorescein, Acridine Orange, Acridine Yellow, Acriflavine, and Dichlorofluorescein) fluorescence spectroscopy was soon adopted [77, 78].
In 1950, Klevens [79] studied the solubility of some polycyclic hydrocarbons in water and in solutions of potassium laurate (at 25 °C). For all the polycyclic hydrocarbons, he showed that by increasing the concentration of the surfactant, their solubility also increased. Particularly, for pyrene he measured solubilities of 0.77 × 10−6 and 2.24 × 10−3 M in water and potassium laurate (0.50 M), respectively.
One year later, Ekwall [80] studied the sodium cholate association by measuring the fluorescence intensity, and determined that the lowest concentration at which polycyclic hydrocarbons (3,4‐benzopyrene included) are solubilized is 0.018 M. This corresponds to the beginning of the micelle formation, although “at first relatively small amounts of cholate ion aggregates and the actual micelle formation occurs at about 0.040 to 0.044 M.” Foerster and Selinger [81] observed that in micelles of cetyldimethylbenzylammonium chloride, pyrene forms dimers in excited states (excimers).
In the period 1971–1980, the number of papers on solubilized pyrene in micelle solutions increased very quickly. The fluorescence decay of the excited state of pyrene received an important attention. The aggregation number and microviscosities of the micellar interior [82], the permeability of these micelles with respect to nonionic and ionic quenchers [83], oxygen penetration of micelles [84], or the environmental effects on the vibronic band intensities in pyrene monomer fluorescence in micellar systems [85, 86] were published. Kalyanasundaram and Thomas carefully analyzed the lifetime of the monomer fluorescence and the ratio I 3 /I 1 of the third and first vibronic band intensities of pyrene in sodium lauryl sulfate as a function of its concentration. Both curves have a sigmoidal shape (see Figure 1.3 of the paper). A value of 8 × 10−3 M for the cmc of the surfactant was given.
However, Nakajima [86] plotted the ratio I 1 /I 3 and accepted the cmc as the concentration at which the first break is observed (point A in Figure 1.4). At low concentrations of the surfactants the values of the I 1/I 3 ratio are high, typical of a hydrophilic environment for pyrene, the value in water being 1.96 [87] while at high surfactant concentrations the I 1/I 3 ratio tend to typical values of non‐polar solvents. For instance, at high surfactant concentrations of sodium cholate and sodium deoxycholate, the I 1/I 3 ratio is around 0.7 [88] while the value in cyclohexane is 0.61 [89]. This suggests that the polarity of the microenvironment of pyrene is a lipophilic one. Andersson and Olofsson [90], when performing a calorimetric study of nonionic surfactants, also made use of Nakajima’s approach.
Figure 1.4 Typical plot of a sigmoidal curve. Example ϕ = I 1/I 3 (ratio of the intensities of the first and third vibronic peaks of pyrene) vs increasing concentration of a surfactant (left) and its first derivative (right). The shape of curves from isothermal titration calorimetry are similar in shape (see below for a description).
Other authors have proposed the inflection point of the curve (point B) as cmc [91]. As such it fulfills the condition
where ϕ would be the I 1/I 3 ratio. The expression is also valid for any other property that exhibits a sigmoidal behavior as the obtained enthalpograms from isothermal titration calorimetry (ITC) [92]. The plot of (dϕ/dS t ) vs S t is shown in Figure 1.4 (right) and the cmc is easily obtained from the peak.
Aguiar et al. [93] have analyzed both points (A and B) for several surfactants and proposed an approach for choosing between one or the other point. Occasionally, both A and C points have been accepted as an indication that the system has two cmc values. We consider that this is not correct. These different points of view introduce an important question related to the determination of the cmc from sigmoidal curves, which are frequently found when using some experimental techniques.
By now, some different approaches to determine the cmc have already been introduced. Rusanov [94] has reviewed the definitions of cmc based on the application of the mass action law to the aggregation process in surfactant solutions. Among them, we must mention the definition given by the equation
which was proposed by Phillips [95] in 1955 for determining the cmc for an ideal measured property ( ϕ )‐concentration (S t ) relationship. Phillips pretended that Eq. (1.12) corresponds to the point of maximum curvature, but this is not the case. Nakajima's approach fulfills this condition as well as the methodology proposed by Olesen et al. [96] for determining the aggregation number of aggregates from ITC curves. However, the definition of cmc as corresponding to the inflection point in the ϕ vs S t curve has been recommended [97] for the determination of the cmc from ITC curves. For large absolute values of the slope at the inflection point (= ( ϕ C − ϕ A )/(S C − S A )) in previous sigmoidal curves, the difference in the values obtained from any of the two previous equations may be considered negligible for practical purposes. If the cmc is fairly sharp, Hall [98] has proposed that it can be regarded approximately as a second order phase transition.
Among the other definitions for cmc analyzed by Rusanov we would like to remark on the following one. The focus is on a system in which micelles are composed of a single sort of particle. For further details and the analysis of more complex systems, the two papers by Rusanov [94] are recommended.
Let us redefine the Grindley and Bury [45] equilibrium constant as
The equilibrium constant K o would correspond to a hypothetical single step in which a virtual aggregate m j is formed by the binding of an additional monomer to a virtual aggregate of size m j‐1 according to
its equilibrium constant being
(1.15)
The isodesmic model accepts that all K j constants are equal to K o . The difference with the Grindley and Bury equilibrium constant comes from the fact that only (n – 1) steps are required to form a micelle with n monomers. Interestingly, in 1935 Goodeve [99] have pointed out that forming micelles of, say, about 20 molecules must pass through all the intermediate stages of association. The formation of the micelles from the monomer in one stage is, of course, highly improbable as it requires “a collision of 20 molecules at one time.” Goodeve presented Eq. (1.14) as representing the equilibrium according to this point of view.
Equation (1.13) is better understood in the form
where K o and s are both positive, n is usually large, and, independently of the value of n, for K o × s = 1, the concentration of micelles and monomers are the same. Deviations of the product K o × s from that value lead to either m n < s or m n > s. For instance, for n = 50, the ratio m n /s changes by a factor 1.86 × 104 when K o × s varies from 0.9 to 1.1. This is in fact the analysis by Grindley and Bury [45].
This suggests a definition of cmc by the condition
(1.17)
and from the conservation of material (S t = s + n × m n ) it follows that at cmc S t,cmc = (n + 1)s cmc = (n + 1)m n .
From Eq. (1.16) it also follows that
(1.18)
or
In a monodisperse system, this equation may be simplified to
(1.20)
since at cmc, m n = s and n is constant for the whole range of surfactant concentrations. Thus, the larger the rate of change of the micelle concentration is with respect to the change in the monomer concentration, the higher the aggregation number will be.
Once the equilibrium constant and the aggregation number are known, all the thermodynamic functions may be obtained. These thermodynamic quantities have traditionally been determined from the measurement of cmc at different temperatures, the range of temperatures being around 40 °C (or less). The problem is that the dependence of the cmc with temperature is usually low for most of the surfactants and, as the dependence of ΔG o with the concentration is logarithmic, the range of experimental values is even shorter. This introduces an error in the determination of the thermodynamic amounts, which is necessarily rather high.
The commercial introduction of high quality isothermal titration calorimeters has provided a routine way for the determination of previous amounts, which have a much higher precision. In a typical measurement a sample cell is filled with water (or any other appropriate solvent). A surfactant solution is placed in a syringe, which allows the injection of small aliquots into the sample cell at different intervals of time. The solvent of this solution and the one filling the sample cell must be identical to prevent some effects as the dilution heat of inert salts or buffers. The concentration of the surfactant ranges from 10 to 30 times the cmc value. Each injection increases the surfactant concentration in the sample cell from zero to a concentration clearly above the cmc. The heat involved in the process (the concentration in the syringe is always higher than in the sample cell) after each injection is measured and plotted vs the increasing concentration in the sample cell. Figure 1.4 imitates a typical enthalpogram and its derivative. In this case, ϕ = ΔH (in kJ/mol of injectant) is the involved heat after each injection.
An ideal enthalpogram can be subdivided into three concentration ranges. In region I (first injections, till point A in Figure 1.4) the increasing concentration in the cell is still below the cmc. Here, the large enthalpic effects observed are mainly due to breaking micelles into monomers (demicellization process) and dilution of monomers [92]. In region III (final injections, after point C in Figure 1.4), the increasing concentration in the cell is above the cmc. Here, the low enthalpic effects observed are mainly due to dilution of micelles. In the central region (between A and C in Figure 1.4), a sharp decrease is observed and corresponds to a transition from reaching the cmc and exceeding it. Therefore, the cmc corresponds to the inflection point of the curve, which can easily be determined as the first derivative of the curve (Eq. (1.11), 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.
