Micelle–monomer equilibria in solutions of ionic surfactants and in ionic–nonionic mixtures: A generalized phase separation model

On the basis of a detailed physicochemical model, a complete system of equations is formulated that describes the equilibrium between micelles and monomers in solutions of ionic surfactants and their mixtures with nonionic surfactants. The equations of the system express mass balances, chemical and mechanical equilibria. Each nonionic surfactant is characterized by a single thermodynamic parameter — its micellization constant. Each ionic surfactant is characterized by three parameters, including the Stern constant that quantifies the counterion binding. In the case of mixed micelles, each pair of surfactants is characterized with an interaction parameter, β, in terms of the regular solution theory. The comparison of the model with experimental data for surfactant binary mixtures shows that β is constant — independent of the micelle composition and electrolyte concentration. The solution of the system of equations gives the concentrations of all monomeric species, the micelle composition, ionization degree, surface potential and mean area per head group. Upon additional assumptions for the micelle shape, the mean aggregation number can be also estimated. The model gives quantitative theoretical interpretation of the dependence of the critical micellization concentration (CMC) of ionic surfactants on the ionic strength; of the CMC of mixed surfactant solutions, and of the electrolytic conductivity of micellar solutions. It turns out, that in the absence of added salt the conductivity is completely dominated by the contribution of the small ions: monomers and counterions. The theoretical predictions are in good agreement with experimental data.     

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.     

Mixed micellization of a nonionic-cationic surfactant system constituted by n-octyl-beta-D-glucopyranoside/dodecyltrimethylammonium bromide/H2O. An electrochemical, thermodynamic, and spectroscopic study

The mixed micelles constituted by a nonionic surfactant widely used in the biochemical field, n-octyl-beta-D-glucopyranoside, and a cationic surfactant with 12 carbon atoms on the hydrophobic tail, dodecyltrimethylammonium bromide, have been studied in aqueous solution, at 298.15 K, by means of conductivity, speed of sound, density, and fluorescence spectroscopy experiments. From these data, the monomeric and micellar phases of the mixed aggregates were fully analyzed through the determination of the total and partial critical micellar concentrations, the dissociation degree of the mixed micelle, the total and partial aggregation numbers, the apparent molar volumes and isentropic compressibilities, the hydration numbers, and the corresponding changes in these thermodynamic properties due to the mixed aggregation process. The experimental findings have been compared with those obtained with several theoretical models, some of them modified in this work to take into account the specific characteristics of the aggregates studied herein.     

Thermodynamic and kinetic theory of ionic micellar systems: 1. Work of aggregation

The previously developed approach to the thermodynamics of molecular aggregates based on the methods of the nucleation theory is extended to including ionic aggregative systems with the choice of the real concentration of monomeric ions of surfactants as a standard concentration of aggregates. Results are also generalized to multicomponent systems and a new expression for the work of aggregation is derived. Three models of ionic aggregates are analyzed, i.e., bare aggregate (containing no counterions), fully dressed aggregate (with maximal number of counterions), and dressed aggregate with arbitrary numbers of counterions. In the consideration of the ionic aggregate as a complex ion that yields simpler ions upon dissociation, the notion of the average activity coefficient of the ionic aggregate is introduced. Characteristics of real dressed ionic aggregates are studied. Restrictions in the use of the model of the dressed ionic aggregate are revealed.     

Micelle formation of N-(1,1-dihydroperfluorooctyl)- and N-(1,1-dihydroperfluorononyl)-N,N,N-trimethylammonium chlorides

Micelle formation of N-(1,1-dihydroperfluorooctyl)-N,N,N- and N-(1,1-dihydroperfluorononyl)-N,N,N-trimethylammonium chloride was investigated by analyzing the concentration dependence of the electric conductivity and of the activity of the counterion (Cl(-)) of the solution. The three micellization parameters for ionic surfactants, the micellization constant K(n), the micelle aggregation number n, and the number of counterions per micelle m, were determined by combination of electric conductivity and counterion concentration. The present analysis employed two slopes of the plots of specific conductivity against surfactant concentration below and above the critical micelle concentration and the mass action model of micelle formation. The aggregation numbers thus obtained were relatively small, while the degrees of counterion binding to the micelle (m/n) were found to be quite large, much larger than expected from the small aggregation numbers. Thermodynamical parameters of the micellization were evaluated from the temperature dependence of the three parameters, and the micellization of the fluorinated surfactant was found to be enthalpy-driven. A CF(2) group in the perfluorocarbon chain was found to be 1.44 times larger in hydrophobicity for micellization than a CH(2) group in the hydrocarbon chain.     

Activity Coefficients of Aqueous Mixed Ionic Surfactant Solutions from Osmometry

Osmotic techniques for measuring thermodynamic activities, such as isopiestic equilibration, are well established for multicomponent solutions, especially mixed salt solutions. Surprisingly, these techniques have not yet been applied to mixed ionic surfactants, despite the numerous practical applications of these systems and the importance of the Gibbs free energy for micelle stability. In this study, mass-action equations are developed for the osmotic coefficients of solutions of ionic surfactant CA + ionic surfactant CB, with common counterion C. Extended Debye–Hückel equations are used for the ionic activity coefficients. The equilibrium constants for mixed micelle formation are evaluated by Gibbs–Duhem integration of critical micelle concentrations. Fitting the derived equations to the osmotic coefficients of aqueous sodium decanoate + sodium dodecylsulfate solutions measured by freezing-point osmometry is used to evaluate the activities of the total surfactant components. Very large departures from ideal solution behavior are indicated, including stoichiometric surfactant activity coefficients and micelle activity coefficients that drop below 0.05 and 10^?8, respectively, relative to unity for ideal solutions. Osmometry offers many interesting and unexplored possibilities for studies of mixed surfactant thermodynamics.     

Micellar solutions of ionic surfactants and their mixtures with nonionic surfactants: Theoretical modeling vs. Experiment

Here, we review two recent theoretical models in the field of ionic surfactant micelles and discuss the comparison of their predictions with experimental data. The first approach is based on the analysis of the stepwise thinning (stratification) of liquid films formed from micellar solutions. From the experimental step-wise dependence of the film thickness on time, it is possible to determine the micelle aggregation number and charge. The second approach is based on a complete system of equations (a generalized phase separation model), which describes the chemical and mechanical equilibrium of ionic micelles, including the effects of electrostatic and non-electrostatic interactions, and counterion binding. The parameters of this model can be determined by fitting a given set of experimental data, for example, the dependence of the critical micellization concentration on the salt concentration. The model is generalized to mixed solutions of ionic and nonionic surfactants. It quantitatively describes the dependencies of the critical micellization concentration on the composition of the surfactant mixture and on the electrolyte concentration, and predicts the concentrations of the monomers that are in equilibrium with the micelles, as well as the solution’s electrolytic conductivity; the micelle composition, aggregation number, ionization degree and surface electric potential. These predictions are in very good agreement with experimental data, including data from stratifying films. The model can find applications for the analysis and quantitative interpretation of the properties of various micellar solutions of ionic surfactants and mixed solutions of ionic and nonionic surfactants.     

Micellization theory based on the law of mass action with a variable aggregation number

Variations in the aggregation number of spherical micelles are considered within the micellization theory based on the law of mass action. The mechanism of micellization in a polydisperse aggregated system and the transition to a monodisperse model are explained. A relation between aggregation numbers and chemical potentials of molecules or ions is determined using the curve for equilibrium distribution of aggregates over the aggregation numbers. It is shown that the aggregation numbers of nonionic surfactants unambiguously grow with concentration; however, such a conclusion cannot be drawn for ionic surfactants. For the explicit concentration dependence of the aggregation number, two versions of an analog of the Langmuir equation are proposed to be used, i.e., versions comprising the total surfactant concentration and the concentration of monomers. Comparison with experimental data is carried out by the example of conventional surfactants, namely, sodium dodecyl sulfate and hexadecyltrimethylammonium bromide.     

Micellization of cationic gemini surfactant and its interaction with DNA in dilute brine

The micellization of cationic gemini surfactant trimethylene-1,3-bis (dodecyldimethylammonium bromide) (12-3-12·2Br) was investigated and critical micelle concentrations (CMC) and thermodynamic parameters were evaluated as functions of ionic strength and temperature. The micellization of 12-3-12·2Br is entropically driven and thermodynamically favored. Raising the temperature slightly increases the CMC, while increasing the ionic strength lowers the CMC. A multi-technique study of the 12-3-12·2Br/DNA interaction and its dependence on ionic strength, temperature and DNA concentration were presented. DNA with loose coil conformation, necklace-like structure, highly ordered toroidal aggregates and coexisting of large aggregates and small structures in DNA/12-3-12·2Br system were observed. Critical aggregation concentrations (CAC), interaction saturation concentrations (C(2)), and associated thermodynamic parameters were determined. The screening effect of salt decreases the DNA/12-3-12·2Br electrostatic attraction, but favors the formation of free 12-3-12·2Br micelles or aggregates on the DNA chain. DNA acts as a separate phase contacting with the surfactant molecules and therefore CAC is independent of DNA concentration. Increasing DNA concentration postpones the appearance of free micelle in bulk phase, consequently increases the C(2). Finally an interaction mechanism between 12-3-12·2Br and DNA was proposed.     

Structure of mixed anionic/nonionic surfactant micelles: experimental observations relating to the role of headgroup electrostatic and steric effects and the effects of added electrolyte

The structures of the mixed anionic/nonionic surfactant micelles of SDS/C12E6 and SDS/C12E8 have been measured by small angle neutron scattering (SANS). The variations in the micelle aggregation number and surface charge with composition, measured in D2O and in dilute electrolyte, 0.01 and 0.05 M NaCl, provide data on the relative roles of the surfactant headgroup steric and electrostatic interactions and their contributions to the free energy of micellization. For the SDS/C12E8 mixture, solutions increasingly rich in C12E8 show a modest micellar growth and an increase in the surface charge. The changes with increasing electrolyte concentration are similarly modest. In contrast, for the SDS/C12E6 mixture, solutions rich in C12E6 show a more significant increase in aggregation number. Furthermore, electrolyte has a more substantial effect on the aggregation for the nonionic (C12E6) rich mixtures. The experimental results are discussed in the context of estimates of the steric and electrostatic contributions to the free energy of micellization, calculated from the molecular thermodynamic approach. The variation in micelle surface charge is discussed in the context of the "dressed micelle" theory for micelle ionization, and other related data.     

A Viscometric and Conductometric Investigation of the Micellar and Solution Properties of Two-Headed Surfactant Systems, the Disodium 4-Alkyl-3-sulfonatosuccinates

A family of two-headed surfactants, the disodium 4-alkyl-3-sulfonatosuccinates, has been prepared by reacting maleic anhydride with the appropriate chain-length alcohol and subsequent addition of sodium bisulfite to the corresponding monoester. The properties of the micelles formed by these compounds in aqueous solution (aggregation numbers, degrees of counterion binding, and the cmc values) have been investigated as a function of temperature and surfactant chain length using viscosity, density, and conductance measurements. The critical micelle concentrations (cmc's) and the aggregation numbers appear to indicate that, in agreement with the earlier literature on other two-headed surfactants systems, these amphiphiles have higher cmc and lower aggregation numbers when compared to single-headed surfactants of comparable chain length. In addition, viscosity B coefficients and the thermodynamic parameters of activation of viscous flow have been determined. These results are interpreted in terms of the structure-making or -breaking properties of the surfactant amphiphiles below the cmc region. Finally, the thermodynamic properties of micelle formation have been estimated from the dependence of the cmc on the absolute temperature according to the charged pseudo-phase separation model of micelle formation. All these results are discussed in terms of how the addition of the second charged surfactant headgroup alters the micellar and solution properties of two-headed surfactants vs. their single-headed counterparts.     

Thermodynamic Characteristics of Micellization in the Droplet Model of Surfactant Spherical Molecular Aggregate

The dependence of the work of the molecular aggregate formation on the aggregation number and surfactant monomer concentration in solution that has the key role for the theory of micellization was studied on the basis of a simple realistic droplet model of spherical aggregate composed of surfactant molecules (the o/w micelle type). Analytical formulas were derived for the coordinates of maximum and minimum of aggregate formation work on the aggregation number axis arising with an increase in the concentration of micellar solution. Model calculations of the thermodynamic characteristics of the kinetics of micellization were performed for premicellar and micellar regions of aggregate sizes within a wide range of solution concentration including the critical micellization concentration.     

Thermodynamic and Kinetic Foundations of the Micellization Theory: 5. Hierarchy of Kinetic Times

The characteristic kinetic times of micellization in the solution of a nonionic surfactant: the times of establishment of quasi-equilibrium concentrations of molecular aggregates in micellar, subcritical, and overcritical regions, times of establishment of quasi-equilibrium concentrations of molecular aggregates in the near-critical region of their sizes, the average time between two successive acts of emission of surfactant monomers by a micelle, the average value of micelle lifetime, the time of establishment of quasi-stationary mode of matter exchange between the solution and molecular aggregate, as well as the times of fast and slow relaxation in a solution were analyzed. The hierarchy of these times disclosing complex multistage kinetic process of micelle formation and decomposition and the establishment of equilibrium in the micellar solution was revealed. It was shown that this hierarchy is provided by the small parameters of the kinetic theory. The inverse problem of micellization kinetics was discussed; this problem allows us to find the characteristics of the formation work for micellar aggregate from the experimental data on the relaxation time of micellar solution.     

Premicellar and micelle formation behavior of dye surfactant ion pairs in aqueous solutions: deprotonation of dye in ion pair micelles

The premicellar and micelle formation behavior of dye surfactant ion pairs in aqueous solutions monitored by surface tension and spectroscopic measurements has been described. The measurements have been made for three anionic sulfonephthalein dyes and cationic surfactants of different chain lengths, head groups, and counterions. The observations have been attributed to the formation of closely packed dye surfactant ion pairs which is similar to nonionic surfactants in very dilute concentrations of the surfactant. These ion pairs dominate in the monolayer at the air-water interface of the aqueous dye surfactant solutions below the CMC of the pure surfactant. It has been shown that the dye in the ion pair deprotonates on micelle formation by the ion pair surfactants at near CMC but submicellar surfactant concentrations. The results of an equilibrium study at varying pH agree with the model of deprotonated 1:1 dye-surfactant ion pair formation in the near CMC submicellar solutions. At concentrations above the CMC of the cationic surfactant the dye is solubilized in normal micelles and the monolayer at the air-water interface consists of the cationic surfactant alone even in the presence of the dyes.     

Thermodynamic Characteristics of a Spherical Molecular Surfactant Aggregate in a Quasi-Droplet Model

The model of spherical molecular aggregate of nonionic surfactant is proposed. This model allows for the maximal (in accordance with packing rules) penetration of water molecules into an aggregate and is an alternative to the droplet model of molecular aggregate. Necessary conditions for the applicability of a model named quasi-droplet model are formulated. Based on this model, the dependence of the work of molecular aggregate formation on the aggregation number and surfactant monomer concentration in solution that plays the key role for the theory of micellization is studied. The equation is derived for the coordinates of maximum and minimum of aggregate formation work on the aggregation number axis arising with an increase in the concentration of micellar solution. Model calculations of the thermodynamic characteristics of the kinetics of micellization are performed. The approximation of the work of molecular aggregate formation allowing for the analytical study is constructed.     

Thermodynamics of micellization of ionic surfactant/alkoxyethanol mixed micelles as a function of temperature

Estimates of the thermodynamic parameters of micellization ((_micG°, (_micH°, and (_micS°) have been determined for a series of mixed micelles consisting of ionic surfactants (sodium dodecylsulfate and dodecyltrimethylamonium bromide) and medium chain length alkoxyethanols as the co surfactant. The enthalpies of micellization have been measured directly for the above systems using isoperibol solution calorimetry; the Gibbs energies and entropies of micellization are obtained by application of the mass-action model to the critical micelle concentration values from the calorimetric titration experiments. The thermodynamic properties of mixed micelle formation with alcohol concentration and temperature are in excellent agreement with our previous results. However, there does appear to be some dependence of the thermodynamic properties of mixed micelle formation on the charge of the ionic surfactant. These dependencies are discussed in terms of the manner in which the ethylene oxide group of the alcohol interacts with the ionic head groups and the location of the solubilizates in the micellar interior.     

Interfacial and aggregation properties of the binary mixture of decanoyl-N-methyl-glucamide and hexadecyltriphenylphosphonium bromide

The interfacial and aggregation behavior of the nonionic surfactant decanoyl-N-methyl-glucamide (Mega-10) with the cationic surfactant hexadecyltriphenylphosphonium bromide (HTPB) have been studied using interfacial tension measurements and fluorescence techniques. From interfacial tension measurements, the critical micellar concentrations (cmc) and various interfacial thermodynamic parameters have been evaluated. The experimental results were analyzed in the context of the pseudophase separation model, the regular solution theory, and the Maeda’s approach. These approaches allowed us to determine the interaction parameter and composition in the mixed state. By using the static quenching method, the mean micellar aggregation numbers of pure and mixed micelles of HTPB+Mega-10 were obtained. It was found that that the aggregation number decreases with increasing mole fraction of HTPB. This behavior is attributed to the presence of the bulky head group of HTPB, which creates steric head group incompatibility and/or electrostatic repulsion. The micropolarity of the micelle was monitored with pyrene fluorescence intensity ratio. It was observed that the increasing participation of HTPB induces the formation of micelles with a hydrated structure. The polarization of the fluorescent probe Rhodamine B was monitored in micellar medium and found to increase with the increase of ionic content. This behavior suggests the formation of mixed micelles with a more ordered or rigid structure.