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.     

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.     

Aggregation work at polydisperse micellization: ideal solution and "dressed micelle" models comparing to molecular dynamics simulations

General thermodynamic relations for the work of polydisperse micelle formation in the model of ideal solution of molecular aggregates in nonionic surfactant solution and the model of "dressed micelles" in ionic solution have been considered. In particular, the dependence of the aggregation work on the total concentration of nonionic surfactant has been analyzed. The analogous dependence for the work of formation of ionic aggregates has been examined with regard to existence of two variables of a state of an ionic aggregate, the aggregation numbers of surface active ions and counterions. To verify the thermodynamic models, the molecular dynamics simulations of micellization in nonionic and ionic surfactant solutions at two total surfactant concentrations have been performed. It was shown that for nonionic surfactants, even at relatively high total surfactant concentrations, the shape and behavior of the work of polydisperse micelle formation found within the model of the ideal solution at different total surfactant concentrations agrees fairly well with the numerical experiment. For ionic surfactant solutions, the numerical results indicate a strong screening of ionic aggregates by the bound counterions. This fact as well as independence of the coefficient in the law of mass action for ionic aggregates on total surfactant concentration and predictable behavior of the "waterfall" lines of surfaces of the aggregation work upholds the model of "dressed" ionic aggregates.     

Abnormal micellar growth in sugar-based and ethoxylated nonionic surfactants and their mixtures in dilute regimes using analytical ultracentrifugation

To develop structure-property relationships for surfactants that control their adsorption, solubilization, and micellization behavior in mixed systems and to develop predictive models based on such relationships, it is necessary to acquire quantitative information on various species present in these complex systems. The analytical ultracentrifugation technique is selected for the first time to characterize the species present in mixed micellar solutions due to its powerful ability to separate particles on the basis of their size and shape. Two nonionic surfactants, n-dodecyl-beta-D-maltoside (DM) and nonyl phenol ethoxylated decyl ether (NP-10), and their 1:1 molar ratio mixture were investigated in this study. Micelles of the nonionic surfactants and their mixture are asymmetrical in shape at the critical micelle concentration (cmc). Interestingly, unlike ionic surfactants, the micellar growths of the nonionic surfactants were found to occur at concentrations immediately above the cmc. The results from both sedimentation velocity and sedimentation equilibrium experiments suggest coexistence of two types of micelles in nonyl phenol ethoxylated decyl ether solutions and in its mixture with n-dodecyl-beta-D-maltoside, while only one micellar species is present in n-dodecyl-beta-D-maltoside solutions. Type 1 micelles were primary micelles at the cmc, while type 2 micelles were elongated micelles. The differences in the micellar shapes of n-dodecyl-beta-D-maltoside and nonyl phenol ethoxylated decyl ether are attributed to packing parameters detected by their molecular structures.     

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.     

Molecular thermodynamics for micellar branching in solutions of ionic surfactants

We develop an analytical molecular-thermodynamic model for the aggregation free energy of branching portions of wormlike ionic micelles in 1:1 salt solution. The junction of three cylindrical aggregates is represented by a combination of pieces of the torus and bilayer. A geometry-dependent analytical solution is obtained for the linearized Poisson-Boltzmann equation. This analytical solution is applicable to saddle-like structures and reduces to the solutions known previously for planar, cylindrical, and spherical aggregates. For micellar junctions, our new analytical solution is in excellent agreement with numerical results over the range of parameters typical of ionic surfactant systems with branching micelles. Our model correctly predicts the sequence of stable aggregate morphologies, including a narrow bicontinuous zone, in dependence of hydrocarbon tail length, head size, and solution salinity. For predicting properties of a spatial network of wormlike micelles, our aggregation free energy is used in the Zilman-Safran theory. Our predictions are compared with experimental data for branching micelles of ionic surfactants.     

Importance of micellar kinetics in relation to technological processes

The association of many classes of surface-active molecules into micellar aggregates is a well-known phenomenon. Micelles are in dynamic equilibrium, constantly disintegrating and reforming. This relaxation process is characterized by the slow micellar relaxation time constant, tau(2), which is directly related to the micellar stability. Theories of the kinetics of micelle formation and disintegration have been discussed to identify the gaps in our complete understanding of this kinetic process. The micellar stability of sodium dodecyl sulfate micelles has been shown to significantly influence technological processes involving a rapid increase in interfacial area, such as foaming, wetting, emulsification, solubilization, and detergency. First, the available monomers adsorb onto the freshly created interface. Then, additional monomers must be provided by the breakup of micelles. Especially when the free monomer concentration is low, which is the case for many nonionic surfactant solutions, the micellar breakup time is a rate-limiting step in the supply of monomers. The Center for Surface Science & Engineering at the University of Florida has developed methods using stopped flow and pressure jump with optical detection to determine the slow relaxation time of micelles of nonionic surfactants. The results showed that the ionic surfactants such as SDS exhibit slow relaxation times in the range from milliseconds to seconds, whereas nonionic surfactants exhibit slow relaxation times in the range from seconds (for Triton X-100) to minutes (for polyoxyethylene alkyl ethers). The slow relaxation times are much longer for nonionic surfactants than for ionic surfactants, because of the absence of ionic repulsion between the head groups. The observed relaxation times showed a direct correlation with dynamic surface tension and foaming experiments. In conclusion, relaxation time data of surfactant solutions correlate with the dynamic properties of the micellar solutions. Moreover, the results suggest that appropriate micelles with specific stability or tau(2) can be designed by controlling the surfactant structure, concentration, and physicochemical conditions (e.g., salt concentration, temperature, and pressure). One can also tailor micelles by mixing anionic/cationic or ionic/nonionic surfactants for a desired stability to control various technological processes.     

Dimeric and oligomeric surfactants. Behavior at interfaces and in aqueous solution: a review

Dimeric and oligomeric surfactants are novel surfactants that are presently attracting considerable interest in the academic and industrial communities working on surfactants. This paper first presents a number of chemical structures that have been reported for ionic, amphoteric and nonionic dimeric and oligomeric surfactants. The following aspects of these surfactants are then successively reviewed the state of dimeric and oligomeric surfactants in aqueous solutions at concentration below the critical micellization concentration (cmc); their behavior at the air/solution and solid/solution interfaces; their solubility in water, cmc and thermodynamics of micellization; the properties of the aqueous micelles of dimeric and oligomeric surfactants (ionization degree, size, shape, micropolarity and microviscosity, solution microstructure, solution rheology, micelle dynamics, micellar solubilization, interaction between dimeric surfactants and water-soluble polymers); the mixed micellization of dimeric surfactants with various conventional surfactants; the phase behavior of dimeric surfactants and the applications of these novel surfactants.     

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.     

Kinetic study in water-ethylene glycol cationic, zwitterionic, nonionic, and anionic micellar solutions

The spontaneous hydrolysis of phenyl chloroformate was studied in water-ethylene glycol, EG, cationic, zwitterionic, nonionic, and anionic micellar solutions, the surfactants being tetradecyltrimethylammonium bromide, tetradecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate, tricosaoxyethylene glycol ether, and sodium dodecyl sulfate. The dependence of the observed rate constant on surfactant concentration as well as on the percentage by weight of EG, varying from 0 to 50 wt %, was investigated. Information about changes in the critical micelle concentrations, in the micellar ionization degrees (for ionic surfactants), in the aggregation numbers, and in the polarity of the interfacial region of the micelles upon changing the weight percent of EG was obtained through conductivity, surface tension, spectroscopic, and fluorescence measurements. A simple pseudophase model was adequate to rationalize the kinetic data. Micellar medium effects were explained by considering charge-charge interactions and polarity, ionic strength, and water content in the micellar interfacial region. The acceleration of the reaction produced by an increase in the amount of EG present in the mixture was explained on the basis of the substantial decrease in the equilibrium binding constant of phenyl chloroformate molecules to the micelles, resulting in the contribution of the reaction taking place in the bulk water-EG phase being more important. The weight percent of EG did not substantially influence the rate constant in the micellar pseudophase.     

Toward a Theory of Diffusion of a Nonionic Surfactant with Variable Aggregation Number in a Micellar System

Since the aggregation number of micelles always grows with concentration, and, in some cases this dependence is noticeable even for spherical micelles, there is a need to revise the theory of micellization, in which the aggregation number is assumed to be constant. This work reformulates the theory of diffusion of nonionic surfactants in micellar solutions with regard to the variability of the aggregation number. A new formula, which expresses the diffusion coefficient of a surfactant via the diffusion coefficients of monomers and micelles, contains an additional factor capable of increasing the diffusion coefficient with the surfactant concentration. However, this factor is not overly strong, and the “old” part of the formula acts in the opposite direction; as a result, the conventional decrease in the diffusion coefficient of a nonionic surfactant remains prevailing. The analytical consideration has been supplemented with numerical calculations, the results of which are presented in the tables.     

Lattice Monte Carlo simulations of phase separation and micellization in supercritical CO2/surfactant systems: effect of CO2 density

Lattice Monte Carlo simulations are used to study the effect of nonionic surfactant concentration and CO2 density on the micellization and phase equilibria of supercritical CO2/surfactant systems. The interaction parameter for carbon dioxide is obtained by matching the critical temperature of the model fluid with the experimental critical temperature. Various properties such as the critical micelle concentration and the size, shape, and structure ofmicelles are calculated, and the phase diagram in the surfactant concentration-CO2 density space is constructed. On increasing the CO2 density, we find an increase in the critical micelle concentration and a decrease in the micellar size; this is consistent with existing experimental results. The variation of the micellar shape and structure with CO2 density shows that the micelles are spherical and that the extension of the micellar core increases with increasing micellar size, while the extension of the micellar corona increases with increasing CO2 density. The predicted phase diagram is in qualitative agreement with experimental phase diagrams for nonionic surfactants in carbon dioxide.     

Thermodynamic characterization of 3-[(3-cholamidopropyl)-dimethylammonium]-1-propanesulfonate (CHAPS) micellization using isothermal titration calorimetry: temperature, salt, and pH dependence

A systematic investigation of the micellization process of a biocompatible zwitterionic surfactant 3-[(3-cholamidopropyl)-dimethylammonium]-1-propanesulfonate (CHAPS) has been carried out by isothermal titration calorimetry (ITC) at temperatures between 278.15 K and 328.15 K in water, aqueous NaCl (0.1, 0.5, and 1 M), and buffer solutions (pH = 3.0, 6.8, and 7.8). The effect of different cations and anions on the micellization of CHAPS surfactant has been also examined in LiCl, CsCl, NaBr, and NaI solutions at 308.15 K. It turned out that the critical micelle concentration, cmc, is only slightly shifted toward lower values in salt solutions, whereas in buffer media it remains similar to its value in water. From the results obtained, it could be assumed that CHAPS behaves as a weakly charged cationic surfactant in salt solutions and as a nonionic surfactant in water and buffer medium. Conventional surfactants alike, CHAPS micellization is endothermic at low and exothermic at high temperatures, but the estimated enthalpy of micellization, ΔHM0, is considerably lower in comparison with that obtained for ionic surfactants in water and NaCl solutions. The standard Gibbs free energy, ΔGM0, and entropy, ΔSM0, of micellization were estimated by fitting the model equation based on the mass action model to the experimental data. The aggregation numbers of CHAPS surfactant around cmc, obtained by the fitting procedure also, are considerably low (nagg ≈ 5 ± 1). Furthermore, some predictions about the hydration of the micelle interior based on the correlation between heat capacity change, Δcp,M0, and changes in solvent-accessible surface upon micelle formation were made. CHAPS molecules are believed to stay in contact with water upon aggregation, which is somehow similar to the micellization process of short alkyl chain cationic surfactants.     

Effect of head group polarity and spacer chain length on the aggregation properties of gemini surfactants in an aquatic environment

The aggregation behavior of cationic gemini surfactants with respect to variation in head group polarity and spacer length is studied through conductance, surface tension, viscosity, and small-angle neutron-scattering (SANS) measurements. The critical micellar concentration (cmc), average degree of micelle ionization (beta(ave)), minimum area per molecule of surfactant at the air-water interface (A(min)), surface excess concentration (gamma(max)), and Gibb's free energy of micellization (delta G(mic)) of the surfactants were determined from conductance and surface tension data. The aggregation numbers (N), dimensions of micelles (b/a), effective fractional charge per monomer (alpha), and hydration of micelles (h(E)) were determined from SANS and viscosity data, respectively. The increasing head group polarity of gemini surfactant with spacer chain length of 4 methylene units promotes micellar growth, leading to a decrease in cmc, beta(ave), and delta G(mic) and an increase in N and b/a. This is well supported by the observed increase in hydration (h(E)) of micelles with increase in aggregation number (N) and dimension (b/a) of micelle.     

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 simple rule for describing the composition dependence of the aggregation number of mixed micelles

The mean aggregation numbers of mixed micelles composed of hydrocarbon surfactants (nonionic/nonionic and ionic/nonionic surfactants) have been determined by the intensity light-scattering method, in order to compare them with the values calculated by using the equations derived. The equations have been derived for representative micellar shapes (disk-like, rod-like, and spherical shapes) by making the assumptions that (i) the surface area of the hydrocarbon core of a mixed micelle is built up by independent contributions from each surfactant monomer, and (ii) the dimension of the hydrocarbon core is determined by the number of carbon atoms of a surfactant. The closest agreement of the observed aggregation numbers with the calculated ones has been obtained for the mixed micelle of an oblate ellipsoidal shape as a geometrical model for a disk-like micelle. This suggests that an oblate ellipsoidal shape may be more probable for a micelle formed at a moderate range of surfactant concentration than a prolate ellipsoidal (a rod-like) and a spherical shape if the assumptions (i) and (ii) hold. The equations presented here are useful, since they make it possible to calculate an accurate aggregation number of the mixed micelle of any composition from the aggregation numbers of the pure micelles of the components and the number of carbon atoms of component surfactants as long as there is no highly specific interaction between different surfactant components.     

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.