Refining of nonionic surfactant micellization theory based on the law of mass action

Two approaches to determining critical micelle concentration (CMC) are assessed, i.e., from the inflection point in the curve for the concentration dependence of the degree of micellization and as K^1/(1–n), where K is the constant of the law of mass action and n is the aggregation number. The latter approach makes the theory simpler, while the former explicitly expresses the critical degree of micellization via the aggregation number. The concentrations of monomers and micelles are analyzed as functions of the overall concentration of a surfactant in a micellar solution. These functions look much simpler in the graphical form as compared with their complex exact analytical representation. This has resulted in derivation of simple analytical approximations for these functions, with these approximations being useful for calculations. The concentration dependence of the surfactant diffusion coefficient has been considered based on these approximations. It turned out that this dependence not only provides the known method for determining the diffusion coefficient of micelles, but also gives the possibility in principle to determine the aggregation number from the slope of the dependence of the diffusion coefficient on the inverse concentration (counted from the CMC in the CMC units). This new method for determining the aggregation number has been tested using the literature data on the diffusion coefficient of penta(ethylene glycol)-1-hexyl ether in an aqueous solution.     

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.     

Joint solubilization of lipophilic drug amlodipine and glyceryl monolaurate in aqueous micellar solutions of Tween 80

The solubilization of lipophilic amlodipine (Am is a antihypertensive drug) and nonionic surfactant glyceryl monolaurate (GML is a skin permeation enhancer), as well as their joint solubilization (co-solubilization) have been measured by UV spectroscopy and refractometry in aqueous micellar solutions of Tween 80 (Tw). The properties of mixed micelles (Tw + GML, Tw + Am, Tw + GML + Am) have been studied, including the aggregation number of components, the localization of solubilizates, diffusion coefficients, the size and the degree of hydration. As a result of co-solubilization, (Tw + GML + Am) three-component micelles contain 4.2 times more molecules of the drug than (Tw + Am) two-component micelles. The experimental data on the kinetics of mass transfer of Am by micelles based on Tw are in good agreement with the calculations under diffusion theory; furthermore, three-component micelles carry Am more effectively than two-component micelles.     

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.     

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.     

Diffusion of sodium dodecyl sulfate micelles in agarose gels

The gradient diffusion of ionic sodium dodecyl sulfate micelles in agarose gel was investigated at moderate concentrations above the CMC. Of particular interest were the effects of micelle, gel, and sodium chloride concentration on the micelle diffusivity. Holographic interferometry was used to measure the gradient diffusion coefficient at three sodium chloride concentrations (0, 0.03, 0.10 M), three gel concentrations (0, 1, 2 wt%), and several surfactant concentrations. Time-resolved fluorescence quenching was used to measure aggregation numbers both in solution and gel. The micelle diffusivity increased linearly with surfactant concentration at the two larger sodium chloride concentrations and all gel concentrations. In general, the strength of this effect increased with decreasing sodium chloride concentration and increased with gel concentration. This behavior is evidence of decreasing micelle-micelle electrostatic interactions with increasing sodium chloride concentrations, and increasing excluded volume effects and hydrodynamic screening with increasing gel concentration, respectively. The only exception was at 0.1M sodium chloride and 2 wt% agarose, which showed a slight reduction in the slope compared to 1 wt% agarose. It was found that the concentration effect is quite strong for charged solutes: at a NaCl concentration of 0.03 M in a 2% agarose gel, in a solution with 3% SDS micelles by volume, the micelle diffusion coefficient is doubled relative to its value in the same gel at infinite dilution. The extrapolated, infinite-dilution diffusion coefficients and the rate at which the micelle diffusivity increased with surfactant concentration were compared with predictions of previously published theories in which the micelles are treated as charged, colloidal spheres and the gel as a Brinkman medium. The experimental data and theoretical predictions were in good agreement.     

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.     

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.     

The aggregation of the sodium dodecyl sulfate –n - octanol–water system at low concentration

Micelle formation in sodium dodecyl sulfate (SDS)–n-octanol mixtures was studied by several techniques and the results were interpreted using regular solution theory for mixed-micelle formation. Octanol was considered as a nonionic surfactant. The composition of micelles at the critical micelle concentration (cmc) was computed together with the interaction parameter and the activity coefficient of the components of the micelles. The fluorescence quenching technique with pyrene was employed to obtain the SDS and octanol aggregation numbers at the cmc. The results were in agreement with similar studies on other alcohol–SDS systems. At the cmc spherical, almost fully ionized micelles formed, while at a higher concentration there was a transition to anisometric (probably rodlike) micelles which pushed sodium counterions into their Stern double layer. Mixed anisometric micelles were more ionized than pure SDS micelles. When the octanol:SDS total ratio exceeded 0.85:1, an emulsion of octanol appeared in equilibrium with the micelles. Received: 23 December 1998 Accepted in revised form: 3 March 1999     

Length control in rigid cylindrical nanoassembly by tuning molecular interactions in aqueous solutions

We have studied aqueous micellar solutions of nonionic surfactant (pentaethylene glycol mono-n-dodecyl ether, C12E5) doped by cationic surfactant (dodecyl trimethylamoniumbromide, DTAB) as a function of doping level, using small angle neutron scattering. At a doping level of at least 6 mol %, rigid cylindrical micelles formed and the local cylindrical structure of the doped micelles showed no variation across the range of doping levels covered in this study (0-10 mol %). However, the total micellar length decreased rapidly as doping level increased, following well the prediction of micellar aggregation number based on molecular-thermodynamic theory. There was no synergistic interaction between surfactants, leading to monotonically decreasing the micellar aggregation number (shortening of the micellar length).     

Self-aggregation and supramolecular structure investigations of Triton X-100 and SDP2S by NOESY and diffusion ordered NMR spectroscopy

The self-aggregation and supramolecular micellar structure of two surfactants in aqueous solution, the anionic surfactant SDP2S (sodium dodecyl dioxyethylene-2 sulfate) and the nonionic surfactant Triton X-100 (octylphenol-polyoxyethylene ether with 9.5 ethoxy groups), were investigated by NMR spectroscopy. The critical micellar concentration (CMC), the size, and shape of the aggregates were determined by diffusion ordered NMR spectroscopy (DOSY), while 2D NOESY NMR spectra were used to study the mutual spatial arrangement of surfactant molecules in the aggregated state. A nonlinear increase of the micellar hydrodynamic radius, indicating possible sphere-to-rod shape transition, was found for SDP2S at higher surfactant concentrations. Triton X-100 micelles were found to be almost spherical at low surfactant concentrations, but formation of ellipsoid shaped particles and/or micellar aggregation was observed at higher concentrations. The NOESY data show that at low concentration Triton X-100 forms a two-layer spherical structure in the micelles, with partially overlapping internal and external layers of Triton X-100 molecules and no distinct hydrophilic-hydrophobic boundary.     

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.     

Effects of surfactant micelles on viscosity and conductivity of poly(ethylene glycol) solutions

The neutral polymer-micelle interaction is investigated for various surfactants by viscometry and electrical conductometry. In order to exclude the well-known necklace scenario, we consider aqueous solutions of low molecular weight poly(ethylene glycol) (2-20)x10(3), whose radial size is comparable to or smaller than micelles. The single-tail surfactants consist of anionic, cationic, and nonionic head groups. It is found that the viscosity of the polymer solution may be increased several times by micelles if weak attraction between a polymer segment and a surfactant exists, epsilon相似文献   

Contribution of molecular pathways in the micellar solubilization of monodisperse emulsion droplets

It is often proposed that oil solubilization in anionic and nonionic micelles proceeds by different mechanisms, with diffusion of the oil molecule thought to control the former, and the latter interfacially controlled. In order to investigate this hypothesis, the effect of aqueous phase viscosity, salt, and surfactant concentration during the solubilization process was studied. The progressive decrease in average droplet size of nearly monodisperse emulsions during solubilization in SDS or Tween 20 micellar solutions was monitored by light scattering, and the change in turbidity was measured by UV-vis spectrophotometer. The solubilization rates were analyzed using a population balance approach to calculate the mass transfer coefficients. Increasing the aqueous viscosity by adding sucrose reduced the mass transfer coefficients of n-tetradecane and n-dodecane but had a smaller effect on n-hexadecane. The strong dependence of the solubilization rate for the shorter chain length alkanes on aqueous viscosity supported a mechanism in which the oil undergoes molecular diffusion before being taken up by micelles. The dependence of the solubilization kinetics on surfactant concentration appeared consistent with this mechanism but yielded a slower micellar uptake rate than previously predicted theoretically. As the solute chain length increased in nonionic surfactant solutions, an interfacial mechanism mediated by micelles appeared to contribute substantially to the overall rate. Addition of salt only slightly increased the solubilization rate of n-hexadecane in SDS solutions and, thus, indicated a weak role of electrostatic interactions for ionic surfactants on the overall mechanism.     

Use of Micellar-Enhanced Ultrafiltration at Low Surfactant Concentrations and with Anionic-Nonionic Surfactant Mixtures

Micellar-enhanced ultrafiltration is a separation technique which can be used to remove metal ions or dissolved organics from water. Metal ions bind to the surface of negatively charged micelles of an anionic surfactant while organic solutes tend to dissolve or solubilized within the micelles. The mixture is then forced through an ultrafiltration membrane with pore sizes small enough to block passage of the micelles and associated metal ions and/or dissolved organics. Monomeric or unassociated surfactant passes through the membrane and does not contribute to the separation. This paper considers advantages of addition of small concentrations of nonionic surfactant to an anionic surfactant; the resulting anionic-nonionic mixed micelles exhibit negative deviation from ideality of mixing which leads to a smaller fraction of the surfactant being present as monomer and a subsequently larger fraction present in the micellar form. The addition of nonionic surfactant improved the separation of divalent zinc substantially at total concentrations above the critical micelle concentration (cmc) of the anionic surfactant. Both zinc and tert-butylphenol (a nonionic organic solute) show unexpected rejection at surfactant concentrations moderately below the cmc, where micelles are absent. This is considered as due to a higher surfactant concentration in the gel layer adjacent to the membrane where micelles are present. Reduction of this rejection at lower transmembrane pressure drops supports this mechanism. Some rejection of zinc was observed in the absence of surfactant but not of tert-butylphenol, indicating an additional effect of membrane charge for ionic solutes. Copyright 1999 Academic Press.     

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.     

Effect of NaCl on the self-aggregation of n-octyl beta-D-thioglucopyranoside in aqueous medium

This report investigates the effect of sodium chloride (NaCl) on the micellization, surface activity, and the evolution in the shape and size of n-octyl beta-D-thioglucopyranoside (OTG) aggregates. By using surface tension measurements, information was obtained on both changes in the critical micelle concentration and adsorption behavior in the air-liquid interface with the electrolyte concentration. These data were used to obtain the thermodynamic properties of micellization along with the corresponding adsorption parameters in the air-liquid interface. From extended static and dynamic light scattering measurements, the micelle molecular weight, the mean aggregation number, and the second virial coefficient, the apparent diffusion coefficient and the mean hydrodynamic radius of micelles in a range of NaCl concentrations were obtained. The light scattering data have shown that when the surfactant concentration is lower to 4.5 g/L, only spherical micelles are formed. However, an increase in the surfactant concentration induces an increase in micellar size, suggesting a rodlike growth of the micelles. This deviation of micelle geometry from spherical to rodlike is supported both by the ratio between the hydrodynamic radius and the radius of gyration and by the angular dependence of light scattering. On the other hand, the studies performed in the presence of high NaCl concentration (0.2 and 0.5 M) provide strong support for the view that the micelles may overlap together to form an entangled network above certain crossover concentration.     

Dependence of enantioselectivity on the distribution of a chiral hydrogenation catalyst between an aqueous and a micellar phase: investigations using pulsed field gradient spin echo NMR spectroscopy

The enantioselectivity obtained from rhodium complex catalyzed hydrogenations conducted in water can often be increased considerably by the addition of amphiphiles. At present the reasons for this increase in selectivity are not fully understood. The application of pulsed field gradient spin echo NMR (PGSE-NMR) spectroscopy to determine the average diffusion coefficients of the catalysts in both known and novel examples of asymmetric hydrogenation shows definitively that the increase in enantioselectivity is coupled with an aggregation of the catalyst to the micelles. This aggregation or solubilization of the catalyst in the micelles leads to the formation of a new colloidal phase in the aqueous solution. This phase has stronger hydrophobic properties, and thus the hydrogenation is more comparable to those conducted in a hydrophobic or less polar organic solvent. In the case of anionic amphiphiles, which form amphiphilic salts with the cationic catalyst, the embedment of the catalyst complex into the micelle is generally complete. The whole hydrogenation then takes place exclusively inside the micelles, leading to high enantioselectivity. If the catalyst is not completely embedded into the micelle, for example in the cases of nonionic or cationic surfactant solutions, the solubility of the substrate plays an important role. For soluble substrates the hydrogenation of the substrate occurs predominately in the aqueous phase itself, leading to very poor enantioselectivities. In these cases, only the use of a large excess of amphiphile, far above the critical micelle concentration (cmc), will lead to higher enantioselectivities due to a shift of the equilibrium towards the micellar bonded forms of catalyst and substrate. In contrast, poorly soluble substrates exhibit a high tendency to be incorporated into micelles, which leads to much higher enantioselectivities if the cmc of the surfactant is small enough. Changes in the cmc of amphiphiles caused by their aggregation with catalysts could also be estimated. The variation in selectivity observed for the catalysts containing seven-membered, flexible chelate rings is apparently due to changes in their conformation in the less polar micellar medium, and this effect is also seen in organic solvents. As expected, catalysts containing smaller chelate rings show this effect to a considerably lower extent since they are conformationally more rigid.     

Micellization and interaction of anionic and nonionic mixed surfactant systems in water

Interaction between binary surfactant mixtures containing anionic surfactants viz. sodium dodecyl sulphates (NaDS) and magnesium dodecyl sulphates (Mg(DS)₂) and a nonionic surfactants viz. dodecyl dodecapolyethylene glycol ether (C₁₂E₁₂) and dodecyl pentadecapolyethylene glycol ether (C₁₂E₁₅) in water at different mole fractions (0–1) were studied by surface tension, viscometry and dynamic light scattering (DLS) methods. The composition of mixed micelles and the interaction parameter, β evaluated from the CMC data obtained by surface tension for different systems using Rubingh's theory were discussed. Activity coefficient (f₁ and f₂) of metal dodecyl sulphates (MDS)/C₁₂E_m (m = 12, 15) mixed surfactant systems were evaluated, which shows extent of ideality of individual surfactant in mixed system. The estimated interaction parameter indicates an overall attractive interaction in the mixed micelles, which is predominant for NaDS as compared to Mg(DS)₂. Counter ion valency has specific effect on the mixed micelles, as Mg(DS)₂ has less interaction with nonionic surfactants in comparison to NaDS due to strong condensation of counter ion. The stability factors for mixed micelles were also discussed by Maeda's approach, which was justified on the basis of steric factor due to difference in head group of nonionic surfactant. DLS measurements and viscosity data reveals the synergism in mixed micelles, showing typical viscosity trends and linearity in sizes were observed.