Kinetics of micellization: its significance to technological processes

The association of many classes of surface active molecules into micellar aggregates is a well-known phenomenon. Micelles are often drawn as static structures of spherical aggregates of oriented molecules. However, micelles are in dynamic equilibrium with surfactant monomers in the bulk solution constantly being exchanged with the surfactant molecules in the micelles. Additionally, the micelles themselves are continuously disintegrating and reforming. The first process is a fast relaxation process typically referred to as τ₁. The latter is a slow relaxation process with relaxation time τ₂. Thus, τ₂ represents the entire process of the formation or disintegration of a micelle. The slow relaxation time is directly correlated with the average lifetime of a micelle, and hence the molecular packing in the micelle, which in turn relates to the stability of a micelle. It was shown earlier by Shah and coworkers that the stability of sodium dodecyl sulfate (SDS) micelles plays an important role in various technological processes involving an increase in interfacial area, such as foaming, wetting, emulsification, solubilization and detergency. The slow relaxation time of SDS micelles, as measured by pressure-jump and temperature-jump techniques was in the range of 10⁻⁴–10¹ s depending on the surfactant concentration. A maximum relaxation time and thus a maximum micellar stability was found at 200 mM SDS, corresponding to the least foaming, largest bubble size, longest wetting time of textile, largest emulsion droplet size and the most rapid solubilization of oil. These results are explained in terms of the flux of surfactant monomers from the bulk to the interface, which determines the dynamic surface tension. The more stable micelles lead to less monomer flux and hence to a higher dynamic surface tension. As the SDS concentration increases, the micelles become more rigid and stable as a result of the decrease in intermicellar distance. The smaller the intermicellar distance, the larger the Coulombic repulsive forces between the micelles leading to enhanced stability of micelles (presumably by increased counterion binding to the micelles). 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 show relaxation times τ₂ in the range of 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 time τ₂ was related to dynamic surface tension and foaming experiments. A slow break-up of micelles, (i.e. a long relaxation time τ₂) corresponds to a high dynamic surface tension and low foamability, whereas a fast break-up of micelles, leads to a lower dynamic surface tension and higher foamability. In conclusion, micellar stability and thus the micellar break-up time is a key factor in controlling technological processes involving a rapid increase in interfacial area, such as foaming, wetting, emulsification and oil solubilization. First, the available monomers adsorb onto the freshly created interface. Then, additional monomers must be provided by the break-up of micelles. Especially when the free monomer concentration is low, as indicated by a low CMC, the micellar break-up time is a rate limiting step in the supply of monomers, which is the case for many nonionic surfactant solutions. Therefore, relaxation time data of surfactant solutions enables us to predict the performance of a given surfactant solution. Moreover, the results suggest that one can design appropriate micelles with specific stability or τ₂ by controlling the surfactant structure, concentration and physico-chemical conditions, as well as by mixing anionic/cationic or ionic/nonionic surfactants for a desired technological application.     

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.     

Kinetics of the surface tension of micellar solutions: Comparison of different experimental techniques

The kinetics of the surface tension of micellar solutions of nonionic surfactant Triton X-100 is measured experimentally by means of three different techniques: oscillating jet, maximum bubble pressure and inclined plate. They allow to study the micellization kinetics at various time scales (from a few milliseconds to a few seconds) in fairly large concentration region up to 50 times CMC. The experimental data are satisfactorily explained by a theoretical model accounting for the kinetics of micellization, diffusion of surfactant species and expansion of the bubble interface. By this model are computed the characteristic times of diffusion and micellization, which are of comparable magnitude (about 5 to 200 ms), and the Gibbs' elasticity. The micellization time constant corresponds to the slow relaxation process known to coincide with the disintegration of micelles. Comparing our data with other data from literature one can conclude that more realistic information for the micellization kinetics is obtained by the maximum bubble pressure and the oscillating jet method. The inclined plate seems too slow to measure the relaxation processes in micellar solutions of this surfactant.     

Power-law stage of slow relaxation in solutions with spherical micelles

General (independent of models selected for surfactant molecular aggregates) analytical relations are derived to describe the initial stage of slow relaxation in micellar solutions with spherical micelles. This stage precedes the final stage of the relaxation occurring via an exponential decay of disturbances with time. The relations obtained are applicable throughout the interval of micellar solution concentrations from the first to the second critical micellization concentration. It is shown that the initial stage is characterized by power laws of variations in the concentrations of monomers and micelles with time, these laws being different for the relaxation processes proceeding from above and below toward equilibrium values of micellar solution parameters. Relations are derived for the duration of this stage, and the effect of initial conditions is studied. Characteristic times of the power-law stage are determined and compared with the characteristic time of the final exponent-law relaxation stage. The behavior of these times is investigated at surfactant solution concentrations in the vicinity of, and noticeably above, the first critical micellization concentration. On the basis of the droplet and quasi-droplet thermodynamic models of surfactant molecular aggregates, numerical solutions are found for nonlinearized equations of slow relaxation for the time dependence of surfactant monomer concentrations at all stages of the slow relaxation. Numerical results obtained from the models are compared with the results of a general analytical study.     

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.     

Dielectric behavior of aqueous micellar solutions of betaine-type surfactants

Dielectric behavior was examined for aqueous solutions of the betaine-type surfactants dodecyldimethylcarbobetaine (C(12)DCB), tetradecyldimethylcarbobetaine (C(14)DCB), cetyldimethylcarbobetaine (C(16)DCB), and oleyldimethylcarbobetaine (OleyDCB) as a function of frequency from 1.00 x 10(6) to 2.00 x 10(10) Hz (6.28 x 10(6) to 1.26 x 10(11) rad s(-1)) with changing surfactant concentration (c(D)). Rotational relaxation times (tau) of the zwitterionic headgroups of the surfactants in aqueous solutions of C(12)DCB and C(14)DCB, which form spherical micelles, are determined to be 0.26 and 0.30 ns, respectively. Values of tau for aqueous solutions of C(16)DCB and OleyDCB, which form threadlike micelles, are identical at 0.44 ns. The tau values of all micellar solutions are constant irrespective of c(D). The increase in tau with increasing alkyl chain length is assigned to an increase of molecular density at the micellar surface. The magnitude of the relaxation strength for the surfactant solutions increases in proportion to c(D) and is not so different from that of an aqueous solution of glycine betaine (GB), which has the same chemical structure as betaine-type surfactants with zwitterionic headgroups but never forms micelles. This finding suggests that the zwitterionic headgroup rotating on the micellar surface possesses a dipole moment with a magnitude essentially the same as that of GB in aqueous solutions.     

On the theory of surfactant mobility in micellar systems

Specific features of surfactant diffusion in micellar systems are described in terms of mobility, i.e., the limiting velocity of a particle under the action of a unit force. Micellar solutions of nonionic and ionic surfactants are analyzed. A relation is established between average surfactant mobility and the mobilities of individual particles. Although micelles have a lower mobility than monomers have, the average mobility of surfactants is shown to increase rather than decrease upon micellization. In parallel, formulas describing diffusion coefficients are derived, with part of the formulas having been available in the literature.     

Application of a chemical equilibrium model to thermodynamic functions of transfer of alcohols from water to aqueous surfactants

In ternary aqueous solutions, hydrophobic solutes such as alcohols tend to aggregate with surfactants to form mixed micelles. These systems can be studied by meas of the functions of transfer of hydrophobic solutes from water to aqueous solutions of surfactant. These thermodynamic functions often go through extrema in the critical micellar concentration (CMC) region of the surfactant. A simple model based on interactions between surfactant and hydrophobic solute monomers, on the distribution of the hydrophobic solute between water and the micelles and on the shift in the CMC induced by the hydrophobic solute, can simulate the magnitude and trends of the transfer functions using parameters which are mostly derived from the binary systems. In order to check the model more quantitatively, volumes and heat capacities of transfer of alcohols from water to aqueous solutions of a nonionic surfactant, octyldimethylamine oxide, were measured. A quantitative agreement was achieved with three adjustable parameters. Good fits are also obtained for the transfers to the ionic surfactants, octylamine hydrobromide and sodium dodecylsulfate. When the equilibrium displacement contribution is small, the distribution constants and the partial molar properties of the alcohols in the micellar phase agree well with the parameters obtained with similar models.     

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.     

Organization of amphiphiles: XII. Evidence in favor of formation of hydrophobic complexes in aqueous solution

The effects of nonionic surfactants OP-10 and OP-30 (polyoxyethylated octyl phenols with 10 and 30 oxyethylene groups, respectively) in surfactant mixtures with ionic surfactants hexadecyltrimethylammonium bromide (CTAB) and sodium dodecyl sulphate (SDS) have been investigated by a conductometric method in conjunction with fluorescence, surface tension, zeta potential, and DLS measurements. The interactions are found to be antagonistic in nature for each of the systems; i.e., micellization of CTAB as well as SDS is hindered on addition of the nonionic surfactants. The antagonism is found to be more prominent in the presence of OP-10 compared to that of OP-30. Two types of mechanistic paths, path A operating below the critical micellar concentration and path B operating beyond the critical micellar concentration of nonionic surfactants, have been suggested. In path A, the retardation in micellization has been attributed to a decrease in monomeric concentration of the ionic surfactants from solution as a result of the formation of a hydrophobic complex between nonionic and ionic surfactants. In path B, the decrease in monomer concentration is due to the solubilization of the ionic surfactant in micelles of the nonionic surfactants in a 1:1 stoichiometric ratio. A theoretical treatment to the interaction in each ionic-nonionic pair yields a positive value of the interaction parameter supporting the concept of antagonism. The formation of the hydrophobic complex is supported by fluorescence and surface tension measurements. A schematic representation of the stabilization of these hydrophobic complexes has been suggested. The association of ionic surfactants by nonionic micelles is suggested by zeta potential and DLS studies.     

PEP与阴离子表面活性剂复配体系泡沫性能的研究

研究了PEP型非离子表面活性剂分别与十二烷基苯磺酸钠（DBS）,十二烷基硫酸钠（SDS）形成复配体系的泡沫性能,讨论了浓度及配比的变化对泡沫性能的影响,结果表明起泡性和稳泡性皆随混合表面活性剂的浓度的上升而增强;在一定浓度下,随着PEP比例下降,起泡性和稳泡性也随着增大,并达到稳定值。     

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.     

SOLUBILIZATION IN MIXED REVERSE MICELLAR SYSTEMS OF AOT/NONIONIC SURFACTANTS/n-HEPTANE

Solubilization of water and aqueous NaCl solutions in mixed reverse micellar systems of anionic surfactant AOT and nonionic surfactants in n-heptane was studied. It was found that the maximum solubilization capacity of water was higher in the presence of certain concentrations of NaCl electrolyte, and these concentrations increased with the increase of nonionic surfactant content and their EO chain length. Soluibilization capacity was enhanced by mixing AOT with nonionic surfactants. The observed phenomena were interpreted in terms of the stability of the interfacial film of reverse micellar microdroplet and the packing parameter of the surfactant that formed mixed reverse micelles.     

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.     

Micellization kinetics with allowance for fussion and fission of spherical and cylindrical micelles: 1. Set of nonlinear equations describing slow relaxation

Based on the general kinetic equation that describes the aggregation and fragmentation of surfactant molecular aggregates, a closed set of nonlinear equations is derived for the slow relaxation of surfactant monomer concentration and the total concentrations of coexisting spherical and cylindrical micelles to the equilibrium state of a micellar solution. Both the transitions accompanied by the emission and capture of surfactant monomers by micelles and the transitions resulting from the fussion and fission of micelles, are taken into account. The derived set of equations describes all stages of the slow relaxation from the initial perturbance to the final equilibrium state of a micellar solution.     

Micelle dissociation kinetics study by dynamic surface tension of micellar solutions

The dynamic surface of sodium tetradecylsulphate and sodium bexadecylsulphate solutions in water and also in Triton X-100 solutions was measured by the maximum bubble-pressure method, using modern computerized instrumentation, for a wide range of surface lifetimes (from 0.001 to 10 s), temperatures (from 30 to 80°C) and surfactant concentrations (from 1 to 200 CMC). On the basis of a previously suggested adsorption kinetics theory for micellar solutions of ionogenic surfactants (V.B. Fainerman, Colloids Surfaces, 62 (1992) 333) a method was developed for the calculation of the micellar dissociation rate constant k. For the surfactants studied, k increases with increasing concentration. Moreover, for ionic surfactants the dependence of k on concentration (C) becomes more striking for C> (10–30) CMC. This can be explained by a micelle shape transition and by a strengthening of the intermolecular repulsion in micelles. In solutions of the ionic surfactants the constant k increasing with increasing temperature, whereas in Triton X-100 solutions a temperature dependence is absent. This phenomenon is associated with the different nature of the molecular interactions for ionogenic and non-ionogenic surfactants in micelles. The k values, obtained from results of dynamic surface tension measurements, are in satisfactory agreement with the results of a study of the relaxation of micellar solutions published previously.     

Micellar medium effects on the hydrolysis of phenyl chloroformate in ionic,zwitterionic, nonionic,and mixed micellar solutions

The spontaneous hydrolysis of phenyl chloroformate was studied in various anionic, nonionic, zwitterionic, and cationic aqueous micellar solutions, as well as in mixed anionic–nonionic micellar solutions. In all cases, an increase in the surfactant concentration results in a decrease in the reaction rate and micellar effects were quantitatively explained in terms of distribution of the substrate between water and micelles and the first‐order rate constants in the aqueous and micellar pseudophases. A comparison of the kinetic data in nonionic micellar solutions to those in anionic and zwiterionic micellar solutions makes clear that charge effects of micelles is not the only factor responsible for the variations in the reaction rate. Depletion of water in the interfacial region and its different characteristics as compared to bulk water, the presence of high ionic concentration in the Stern layer of ionic micelles, and differences in the stabilization of the initial state and the transition state by hydrophobic interactions with surfactant tails can also influence reactivity. The different deceleration of the reaction observed in the various micellar solutions studied was discussed by considering these factors. Synergism in mixed‐micellar solutions is shown through the kinetic data obtained in these media. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 445–451, 2002     

Aggregation of ionic surfactants to block copolymer assemblies: a simple fluorescence spectral study

A simple and elegant method based on steady-state fluorescence spectral measurement is demonstrated to study the interaction mechanism of copolymers and ionic surfactants with a suitable selection of fluorescent probe and also its general applicability in studying other systems. Three different concentration regions have been indicated from the changes in full width at half-maximum of the emission spectra and fluorescence intensity of coumarin 153 with the molar ratio of ionic surfactant to triblock copolymer (n). At low n values, copolymer-surfactant complexes are basically copolymer-rich micelles with few surfactant molecules, and at very high n values, copolymer-rich micelles are destroyed and surfactant-rich micelles with free copolymer monomers are formed. It has been observed that, in the intermediate surfactant concentration region, the transformation of a dominantly copolymer-rich complex to a mainly surfactant-rich complex can be either gradual incorporation of surfactants into the copolymer-rich micelles with freeing of copolymer units until surfactant-rich micelles are formed (type I) or simultaneous buildup of surfactant-rich micelles together with the destruction of copolymer-rich micelles (type II). The interaction mechanism for nonionic copolymers (P123 and F127) with ionic surfactants (SDS and CTAC) is mainly type II, but at higher copolymer concentrations interaction via the type I mechanism also operates. However, it is dominantly the type I mechanism that operates for common nonionic (TX100) and ionic surfactants.