Quantifying the hydrophobic effect. 2. A computer simulation-molecular-thermodynamic model for the micellization of nonionic surfactants in aqueous solution

In this article, the validity and accuracy of the CS-MT model is evaluated by using it to model the micellization behavior of seven nonionic surfactants in aqueous solution. Detailed information about the changes in hydration that occur upon the self-assembly of the surfactants into micelles was obtained through molecular dynamics simulation and subsequently used to compute the hydrophobic driving force for micelle formation. This information has also been used to test, for the first time, approximations made in traditional molecular-thermodynamic modeling. In the CS-MT model, two separate free-energy contributions to the hydrophobic driving force are computed. The first contribution, gdehydr, is the free-energy change associated with the dehydration of each surfactant group upon micelle formation. The second contribution, ghydr, is the change in the hydration free energy of each surfactant group upon micelle formation. To enable the straightforward estimation of gdehydr and ghydr in the case of nonionic surfactants, a number of simplifying approximations were made. Although the CS-MT model can be used to predict a variety of micellar solution properties including the micelle shape, size, and composition, the critical micelle concentration (CMC) was selected for prediction and comparison with experimental CMC data because it depends exponentially on the free energy of micelle formation, and as such, it provides a stringent quantitative test with which to evaluate the predictive accuracy of the CS-MT model. Reasonable agreement between the CMCs predicted by the CS-MT model and the experimental CMCs was obtained for octyl glucoside (OG), dodecyl maltoside (DM), octyl sulfinyl ethanol (OSE), decyl methyl sulfoxide (C10SO), decyl dimethyl phosphine oxide (C10PO), and decanoyl-n-methylglucamide (MEGA-10). For five of these surfactants, the CMCs predicted using the CS-MT model were closer to the experimental CMCs than the CMCs predicted using the traditional molecular-thermodynamic (MT) model. In addition, CMCs predicted for mixtures of C10PO and C10SO using the CS-MT model were significantly closer to the experimental CMCs than those predicted using the traditional MT model. For dodecyl octa(ethylene oxide) (C12E8), the CMC predicted by the CS-MT model was not in good agreement with the experimental CMC and with the CMC predicted by the traditional MT model, because the simplifying approximations made to estimate gdehydr and ghydr in this case were not sufficiently accurate. Consequently, we recommend that these simplifying approximations only be used for nonionic surfactants possessing relatively small, non-polymeric heads. For MEGA-10, which is the most structurally complex of the seven nonionic surfactants modeled, the CMC predicted by the CS-MT model (6.55 mM) was found to be in much closer agreement with the experimental CMC (5 mM) than the CMC predicted by the traditional MT model (43.3 mM). Our results suggest that, for complex, small-head nonionic surfactants where it is difficult to accurately quantify the hydrophobic driving force for micelle formation using the traditional MT modeling approach, the CS-MT model is capable of making reasonable predictions of aqueous micellization behavior.     

Prediction of conformational characteristics and micellar solution properties of fluorocarbon surfactants

A molecular-thermodynamic theory is developed to model the micellization of fluorocarbon surfactants in aqueous solutions, by combining a molecular model that evaluates the free energy of micellization of fluorocarbon surfactant micelles with a previously developed thermodynamic framework describing the free energy of the micellar solution. In the molecular model of micellization developed, a single-chain mean-field theory is combined with an appropriate rotational isomeric state model of fluorocarbon chains to describe the packing of the fluorocarbon surfactant tails inside the micelle core. Utilizing this single-chain mean-field theory, the packing free energies of fluorocarbon surfactants are evaluated and compared with those of their hydrocarbon analogues. We find that the greater rigidity of the fluorocarbon chain promotes its packing in micellar aggregates of low curvatures, such as bilayers. In addition, the mean-field approach is utilized to predict the average conformational characteristics (specifically, the bond order parameters) of fluorocarbon and hydrocarbon surfactant tails within the micelle core, and the predictions are found to agree well with the available experimental results. The electrostatic effects in fluorocarbon ionic surfactant micelles are modeled by allowing for counterion binding onto the charged micelle surface, which accounts explicitly for the effect of the counterion type on the micellar solution properties. In addition, a theoretical formulation is developed to evaluate the free energy of micellization and the size distribution of finite disklike micelles, which often form in the case of fluorocarbon surfactants. We find that, compared to their hydrocarbon analogues, fluorocarbon surfactants exhibit a greater tendency to form cylindrical or disklike micelles, as a result of their larger molecular volume as well as due to the greater conformational rigidity of the fluorocarbon tails. The molecular-thermodynamic theory developed is then applied to several ionic fluorocarbon surfactant-electrolyte systems, including perfluoroalkanoates and perfluorosulfonates with added LiCl or NH(4)Cl, and various micellar solution properties, including critical micelle concentrations (cmc's), optimal micelle shapes, and average micelle aggregation numbers, are predicted. The predicted micellar solution properties agree reasonably well with the available experimental results.     

Boltzmann distributions and slow relaxation in systems with spherical and cylindrical micelles

Equilibrium and nonequilibrium distributions of molecular aggregates in a solution of a nonionic surfactant are investigated at the total surfactant concentration above the second critical micelle concentration (CMC2). The investigation is not limited by the choice of a specific micellar model. Expressions for the direct and reverse fluxes of molecular aggregates over the potential humps of the aggregation work are derived. These aggregation work humps set up activation barriers for the formation of spherical and cylindrical micelles. With the aid of the expressions for molecular aggregate fluxes, a set of two kinetic equations of micellization is derived. This set, along with the material balance equation, describes the molecular mechanism of the slow relaxation of micellar solution above the CMC2. A realistic situation has been analyzed when the CMC2 exceeds the first critical micelle concentration, CMC1, by an order of magnitude, and the total surfactant concentration varies within the range lying markedly above the CMC2 but not by more than 2 orders of magnitude. For such conditions, an equation relating the parameters of the aggregation work of a cylindrical micelle to the observable ratio of the total surfactant concentration and the monomer concentration is found for an equilibrium solution. For the same conditions, but in the nonequilibrium state of materially isolated surfactant solution, a closed set of linearized relaxation equations for total concentrations of spherical and cylindrical micelles is derived. These equations determine the time development of two modes of slow relaxation in micellar solutions markedly above the CMC2. Solving the set of equations yields two rates and two times of slow relaxation.     

A new pyrene-based fluorescent probe for the determination of critical micelle concentrations

A new pyrene-based fluorescent probe for the determination of critical micelle concentrations (CMC) is described. The title compound 1 is obtained in five steps, starting from pyrene. Fluorescence spectroscopic properties of 1 are studied in homogeneous organic solvents and aqueous micellar solutions. In a wide range of organic solvents, probe 1 exhibits a characteristic monomer emission of the pyrene fluorophore, with three distinct peak maxima at 382, 404, and 425 nm. The spectra change dramatically in aqueous solution, where no monomer emission of the pyrene fluorophore is detected. Instead, only strong excimer fluorescence with a broad, red-shifted emission band at lambda(max) = 465 nm is observed. In micellar aqueous solution, a superposition of the monomer and excimer emission is found. The appearance of the monomer emission in micellar solution can be explained on the basis of solubilization of 1 by the surfactant micelles. The ratio of the monomer to excimer fluorescence intensities of 1 is highly sensitive to changes in surfactant concentration. This renders 1 a versatile and sensitive probe molecule for studying the micellization of ionic and nonionic surfactants. For a representative selection of common surfactants, the critical micelle concentrations in aqueous solution are determined, showing excellent agreement with established literature data.     

Experimental and theoretical investigation of the micellar-assisted solubilization of ibuprofen in aqueous media

Surfactants can be used to increase the solubility of poorly soluble drugs in water and to increase drug bioavailability. In this article, the aqueous solubilization of the nonsteroidal, antiinflammatory drug ibuprofen is studied experimentally and theoretically in micellar solutions of anionic (sodium dodecyl sulfate, SDS), cationic (dodecyltrimethylammonium bromide, DTAB), and nonionic (dodecyl octa(ethylene oxide), C12E8) surfactants possessing the same hydrocarbon "tail" length but differing in their hydrophilic headgroups. We find that, for these three surfactants, the aqueous solubility of ibuprofen increases linearly with increasing surfactant concentration. In particular, we observed a 16-fold increase in the solubility of ibuprofen relative to that in the aqueous buffer upon the addition of 80 mM DTAB and 80 mM C12E8 but only a 5.5-fold solubility increase upon the addition of 80 mM SDS. The highest value of the molar solubilization capacity (chi) was obtained for DTAB (chi = 0.97), followed by C12E8 (chi = 0.72) and finally by SDS (chi = 0.23). A recently developed computer simulation/molecular-thermodynamic modeling approach was extended to predict theoretically the solubilization behavior of the three ibuprofen/surfactant mixtures considered. In this modeling approach, molecular-dynamics (MD) simulations were used to identify which portions of ibuprofen are exposed to water (hydrated) in a micellar environment by simulating a single ibuprofen molecule at an oil/water interface (modeling the micelle core/water interface). On the basis of this input, molecular-thermodynamic modeling was then implemented to predict (i) the micellar composition as a function of surfactant concentration, (ii) the aqueous solubility of ibuprofen as a function of surfactant concentration, and (iii) the molar solubilization capacity (chi). Our theoretical results on the solubility of ibuprofen in aqueous SDS and C12E8 surfactant solutions are in good agreement with the experimental data. The ibuprofen solubility in aqueous DTAB solutions was somewhat overpredicted because of challenges associated with accurately modeling the strong electrostatic interactions between the anionic ibuprofen and the cationic DTAB. Our results indicate that computer simulations of ibuprofen at a flat oil/water interface can be used to obtain accurate information about the hydrated and the unhydrated portions of ibuprofen in a micellar environment. This information can then be used as input to a molecular-thermodynamic model of self-assembly to successfully predict the aqueous solubilization behavior of ibuprofen in the three surfactant systems studied.     

A simulation study of electrostatic effects on mixed ionic micelles confined between two parallel charged plates

Confined colloidal systems have been the subject of extensive theoretical and experimental research, and the recent observation of long-range like-charge attraction in such systems has only highlighted their peculiar behavior. On the other hand, surfactant solutions are often used in small confined space, yet their behavior in confinement has received relatively little attention. A distinct feature of confined self-assembling systems is that the aggregates are capable of adjusting their composition, size, and shape in response to their external environment, which may lead to very different phase characteristics compared to bulk solutions. The primary objective of this study is to explore the effects of varying micelle composition on the structural behavior of a confined mixed ionic micellar solution. Mesoscale canonical Monte Carlo simulations were used to probe the structure of the confined solution, while a molecular-thermodynamic model was used to systematically account for the change in micelle size as we varied its composition. Significant micelle ordering was found under certain conditions, which implies that large deviations from the minimum-energy micelle configuration may not be entropically favorable. Accumulation of micelles along the midplane was observed when the confining walls are weakly charged, suggesting that micelle shape transformation should be considered in more detail. On the other hand, with high wall charge density, apparent attraction was found between like-charged micelles and wall. These findings point to the need for a more quantitative theoretical treatment in describing surfactant self-assembly in confined geometries.     

Micellar effects on the electrochemistry of dopamine and its selective detection in the presence of ascorbic acid

The electrochemistry of dopamine (3-hydroxytyramine) was studied by cyclic voltammetry at a glassy carbon electrode in the presence of cetyltrimethylammonium bromide (CTAB) and sodium dodecyl sulfate (SDS) micelles at different pH. The anodic peak potential (E(pa)) and peak current (I(pa)) were found to be remarkably dependent on the charge and the concentration of the surfactant. The E(pa) and I(pa) change abruptly around the critical micellar concentration (CMC) of the surfactants and reach a plateau above the CMC. The E(pa) at the plateau shifts to more positive values in the cationic CTAB micellar solution, e.g. from 180 mV vs SCE in aqueous solution at pH 6.8 to 410 mV in CTAB micelle, whilst it shifts to less positive values in the anionic SDS micellar solution, e.g. 150 mV at pH 6.8. Therefore, the overlapped anodic peaks of dopamine and ascorbic acid in the mixture of the two compounds in aqueous solutions can be separated in CTAB micelles since the micelle shifts the E(pa) of ascorbic acid to less positive values. The two peaks are separated by ca. 400 mV at pH 6.8 in CTAB micelle, hence dopamine can be determined in the presence of 100 times excess of ascorbic acid. In SDS micelle and in the presence of ascorbic acid, the I(pa) of dopamine is greatly enhanced due to the catalytic oxidation of the latter that enables quantitative determination of both compounds.     

Concentrations of Monomers and Cylindrical Micelles above the Second CMC

Based on thermodynamically substantiated linear dependence of the work of cylindrical micelle formation on the aggregation number within a wide range of aggregation numbers where the cylindrical micelles are accumulated in a surfactant solution, the second critical micellization concentration (CMC) is introduced as an overall surfactant concentration at which the ratio of the total amount of substance in cylindrical micelles to the amount of substance in monomers is equal to 0.1, i.e., it is already noticeable. It is shown that this ratio increases rather rapidly with a monomer concentration. The coefficient of the linear dependence of the work of cylindrical micelle formation on the aggregation number in the important practical situation where the ratios of the total concentration of cylindrical micelles and total amount of substance in these micelles to the monomer concentration are equal by the order of magnitude to 1 and 10⁵, respectively, while disc micelles and extended bilayers are still not appeared. In the same situation, the ratios of the total concentration of spherical micelles and total amount of substance in these micelles to the monomer concentration are equal by the order of magnitude to 1 and 10², respectively. The relationship between the overall surfactant concentration and monomer concentration is found. It is shown that the second CMC exceeds by two orders of magnitude the first CMC corresponding to the onset of the noticeable accumulation of surfactant in spherical micelles. The distribution of cylindrical micelles over the aggregation numbers is analyzed. It is demonstrated that, in agreement with the experiment, the distribution is almost uniform in the considerable part of the wide range of aggregation numbers and drops exponentially in the remaining (right-hand) part of this range. Experimental result is confirmed that the total concentration of cylindrical micelles, the mean value, and the mean statistical scatter of aggregation numbers in a cylindrical micelle is proportional to the square root of the overall surfactant concentration. The balance equation of surfactant amount in the vicinity of the final equilibrium state of a materially isolated solution is linearized. This linearization makes it possible to express the deviations of monomer and aggregate concentrations from their equilibrium values at the lower boundary of the region of the linear dependence of the work of cylindrical micelle formation on the aggregation numbers via the deviations of experimentally observed total concentrations of spherical and cylindrical micelles from their equilibrium values. The case of the solutions of such surfactants, for which spherical shape appeared to be unrealizable due to their molecular structure and packing conditions, is considered separately.     

Spectroscopic studies of interaction of Safranine T with nonionic micelles and mixed micelles

The visible spectra of Safranine T (ST) in micellar solution of Brij 58, Tween 20 and Tween 40 and mixed micellar solution of Brij 58/Tween 20 and Brij 58/Tween 40 indicate formation of 1:1 charge transfer (CT) complex between acceptor ST and donor nonionic micelles and mixed micelles. The experimental CT transition energies are well correlated (through Mulliken's equation) with the vertical ionization potential of the donors. The solvent parameters, i.e. the intramolecular charge transfer energy ET(30) have been determined from the Stokes spectral shift. Variations of ionization potential and micropolarity in the mixed micellar region have been investigated as a function of surfactant composition and the obtained results in mixed micellar medium has been compared to the normal micelles. The critical micelle concentration (CMC) values determined at various surfactant compositions are lower than the ideal values indicating a synergistic interaction. The interaction parameter (beta) and micellar stability has been calculated using regular solution theory.     

Physicochemical studies on the micellization behavior of cetylpyridinium chloride and triton X-100 binary mixtures in aqueous medium

Physicochemistry of micellization of binary mixtures of cetylpyridinium chloride (CPC) and Triton X-100 (TX-100) have been investigated and the data collected have been analyzed and correlated. Tensiometric, conductometric, spectrophotometric, calorimetric and polarographic methods have been employed in the study. Parameters like critical micellar concentration (CMC), counter-ion binding, energetics of micellization, interfacial surfactant adsorption and minimum area of amphiphile head groups at CMC have been determined. The diffusion coefficients of pure and mixed micelles in solution have been determined by the polarographic method. The regular solution theory of Rubingh has been considered to get information on the micellar composition and their mutual interaction (synergistic for the studied system) in solution. The packing of the monomer in micelle has been estimated to witness spherical geometry for CPC and its mixtures with TX-100, whereas the later has been found to be spheroidal. Polarographic measurements have evidenced comparable diffusion coefficients of CPC and TX-100 micelles whereas their mixed micelles have shown lower values with a minimum, at equimolar composition.     

Quantifying the hydrophobic effect. 3. A computer simulation-molecular-thermodynamic model for the micellization of ionic and zwitterionic surfactants in aqueous solution

In this article, the validity and accuracy of the CS-MT model introduced in article 1 for oil aggregates and in article 2 for nonionic surfactants is further evaluated by using it to model the micellization behavior of ionic and zwitterionic surfactants in aqueous solution. In the CS-MT model, two separate free-energy contributions to the hydrophobic driving force for micelle formation are computed using hydration data obtained from computer simulation: gdehydr, the free-energy change associated with dehydration, and ghydr, the change in the hydration free energy. To enable straightforward estimation of gdehydr and ghydr for ionic and zwitterionic surfactants, a number of simplifying approximations were made. Reasonable agreement between the CMCs predicted using the CS-MT model and the experimental CMCs was obtained for sodium dodecyl sulfate (SDS), dodecylphophocholine (DPC), cetyltrimethylammonium bromide (CTAB), two 3-hydroxy sulfonate surfactants (AOS-12 and AOS-16), and a homologous series of four DCNA bromide surfactants with a dimethylammonium head attached to a dodecyl alkyl tail and to an alkyl side chain of length CN, having the chemical formula C12H25CNH2N+1N(CH3)2Br, with N = 1 (DC1AB), 2 (DC2AB), 4 (DC4AB), and 6 (DC6AB). For six of these nine surfactants, the CMCs predicted using the CS-MT model are closer to the experimental CMCs than the CMCs predicted using the traditional molecular-thermodynamic (MT) model. For DC2AB, DC4AB, and DC6AB, which are the most structurally complex of the ionic surfactants modeled, the CMCs predicted using the CS-MT model are in remarkably good agreement with the experimental CMCs, and the CMCs predicted using the traditional MT model are quite inaccurate. Our results suggest that the CS-MT model accurately quantifies the hydrophobic driving force for micelle formation for ionic and zwitterionic surfactants in aqueous solution. For complex ionic and zwitterionic surfactants where it is difficult to accurately quantify the hydrophobic driving force for micelle formation using the traditional MT modeling approach, the CS-MT model represents a very promising alternative.     

A multiscale model for kinetics of formation and disintegration of spherical micelles

Dynamics of self-assembly and structural transitions in surfactant systems often involve a large span of length and time scales. A comprehensive understanding of these processes requires development of models connecting phenomena taking place on different scales. In this paper, we develop a multiscale model for formation and disintegration of spherical nonionic micelles. The study is performed under the assumption that the dominant mechanism of micelle formation (disintegration) is a stepwise addition (removal) of single monomers to (from) a surfactant aggregate. Different scales of these processes are investigated using a combination of coarse-grained molecular dynamics simulations, analytical and numerical solution of stochastic differential equations, and a numerical solution of kinetic equations. The removal of a surfactant from an aggregate is modeled by a Langevin equation for a single reaction coordinate, the distance between the centers of mass of the surfactant and the aggregate, with parameters obtained from a series of constrained molecular dynamics simulations. We demonstrate that the reverse process of addition of a surfactant molecule to an aggregate involves at least two additional degrees of freedom, orientation of the surfactant molecule and micellar microstructure. These additional degrees of freedom play an active role in the monomer addition process and neglecting their contribution leads to qualitative discrepancies in predicted surfactant addition rates. We propose a stochastic model for the monomer addition which takes the two additional degrees of freedom into account and extracts the model parameters from molecular dynamics simulations. The surfactant addition rates are determined from Brownian dynamics simulations of this model. The obtained addition and removal rates are then incorporated into the kinetic model of micellar formation and disintegration.     

Photophysical and Photochemical Processes in Micellar Systems

A fascinating feature inherent to aqueous surfactant solutions is the phenomenon of self-organization: above a certain critical concentration (the critical micelle concentration, CMC) detergent molecules associate spontaneously to build up structural entities of colloidal dimensions called micelles. The architecture of these agglomerates is such that the interior contains the hydrophobic alkyl chain of the amphiphile while the hydrophilic head groups are located at the surface and are in contact with bulk water. In the case of ionic micelles the interface is charged giving rise to an electrical double layer and a potential difference of up to several hundred millivolts between the micellar pseudophase and water. Thus micellar systems are microheterogeneous in character: the electrostatic potential and polarity prevailing in the interior of the aggregate differ from those of the bulk aqueous phase. A particularly attractive aspect of photochemical studies in micellar systems is the possibility of organizing the reactants at a molecular level: by comparison of the data in micelles with similar data in homogeneous solution one can learn about the molecular details of a given reaction and establish which conditions favor one pathway or another. In simple surfactant systems differences in rate and efficiency of a reaction will often be controlled by local electrostatic potentials and the compartmentalization of the reagents within the surfactant aggregates. Through the latter effect the statistics of probe distribution over the micelles becomes important in controlling fast photochemical events. Functional micelles are distinguished by the fact that the surfactant molecule contains a group which itself participates in the photoprocess. These units are unique in that self-assembly often introduces striking cooperative effects.     

Comment on "Determination of the critical micelle concentration of dodecylguanidine monoacetate (dodine)"

In a work published in this journal by J.P.S. Cabral and A.R.W. Smith [J. Colloid Interface Sci. 149 (1992) 27], it is reported that the 1-dodecylguanidinium acetate (dodine) exhibits first CMC at 20-30 microM and second CMC at 110-120 microM in aqueous solution at 22.5 degrees C. Such low CMCs are unusual for ionic surfactants with dodecyl chain, and is quite interesting if this is the case. Thus, we investigated the micelle formation of dodine by electrical conductivity measurements. The specific conductivity, kappa, vs concentration plot showed no evidence for micelle formation up to a few hundreds microM at 25 degrees C. The Krafft temperature of dodine was found to be approx. 52 degrees C. When conductivity measurements were made at 54 degrees C, a clear break point was observed in the kappa vs concentration plot at 9.5 mM, which must correspond to the CMC of dodine. This CMC value is quite normal for cationic surfactant with dodecyl chain.     

Volume study on the exclusion of lithium naphthylsulfonate from lithium decylsulfonate micelles

Densities of aqueous solutions of lithium 1-naphthylsulfonate (1-LiNSO)–lithium decylsulfonate (LiDeSO) and 2-LiNSO–LiDeSO mixtures were measured as a function of total molality and composition of the mixtures. The partial derivative of the solution with respect to the total molality was calculated for the monomer and micellar regions. It was found that the values of the partial derivative are larger for the 2-LiNSO–LiDeSO system than for the 1-LiNSO–LiDeSO system. This fact is attributable to the larger value of the partial molar volume of monomer of 2-LiNSO than that of 1-LiNSO. For the two systems, the micellar molar volume of the mixtures varied linearly with the composition from the partial molar volumes of 1- and 2-LiNSO in their single systems to the micellar molar volume in the single LiDeSO system. Miscibility of the solutes in the mixed micelles was examined by drawing the critical micelle concentration (CMC) vs composition diagrams. The diagrams for the 1- and 2-isomers coincided with each other and showed that molecules of 1- and 2-LiNSO are excluded from the micelles. The contribution of the micelle-unforming component to the volume of micelle formation is positive and large because of the exclusion from the micelles. On the other hand, the contribution of the micelle-forming component to the volume of micelle formation is unchanged. The dependence of the monomer molalities of LiNSO and LiDeSO on the total molality, evaluated by means of the CMC vs composition diagrams, substantiated the validity of the approximations used in the derivation of the equations in this study.     

Second CMC in surfactant micellar systems

Experimental reports of surfactant systems displaying a second critical micelle concentration (second CMC) have been surveyed. It turns out that surfactant micelles usually show a growth behavior with some typical features. (i) Micelles grow weakly at low surfactant concentrations but may switch to a much stronger growth behavior at higher concentrations. The second CMC is defined as the point of transition from weakly to strongly growing micelles. (ii) Micelles are found to be non-spherically shaped below the second CMC. (iii) At the second CMC micelles are found to be much smaller, with aggregation numbers typically 100–200, than expected for flexible micelles. (iv) Micelles of intermediate size are present in a narrow concentration regime close to the second CMC. (v) Micelles grow much stronger above the second CMC than expected from a sphere-to-rod transition. The conventional spherocylindrical micelle model predicts a smooth growth behavior that contradicts the appearance of a second CMC. Modifying the model by means of including swollen end caps neither account for the presence of micelles with intermediate size, nor the strong growth behavior above the second CMC. Taking into account micelle flexibility is not consistent with the rather low micelle aggregation numbers observed at the second CMC. On the other hand, a recently proposed alternative theoretical approach, the general micelle model, have been demonstrated to take into account basically all features that are typical of experimentally observed micellar growth behaviors.