Scattering theory for threadlike micellar solutions

Association-dissociation equilibria and the static scattering function were formulated using precise thermodynamic functions for nonionic surfactant solutions including long, stiff, threadlike micelles. The present theory is applicable for micellar solutions with the surfactant concentration much higher than the critical micelle concentration and containing highly growing threadlike micelles. The scattering function formulated was compared with experimental light scattering data for aqueous solutions of a nonionic surfactant, penta(oxyethylene glycol) n-decyl ether (C12E5), at different surfactant concentrations and also temperatures.     

The mass action law theory of micellar solutions

Theories of micellization based on the application of the mass action law to aggregation processes in surfactant solutions are reviewed. The rigorous thermodynamic justification of the approach, explanation of the critical micelle concentration, inter-relations between the main micellization parameters, and an analysis of the surface tension isotherm of a micellar solution are given. Properties of ionic micellar systems, including counterion binding and the behavior of free monomeric ions, are discussed in detail with illustrative estimations for sodium dodecylsulfate and other surfactants.     

Kinetic micellar effects in tetradecyltrimethylammonium bromide-pentanol micellar solutions

The reactions 1,1,1-trichloro-2,2-bis(p-chlorophenyl)ethane + OH(-) and 2-(p-nitrophenyl)ethyl bromide + OH(-) were studied in tetradecyltrimethylamonium bromide, TTAB, and TTAB-pentanol micellar solutions. The influence of changes in the surfactant concentration as well as changes in the hydroxide ion concentration on the observed rate constant was investigated. If changes in the cmc and ionization degree provoked by the presence of the different amounts of n-pentanol in the micellar solutions are taken into account, the experimental kinetic data can be rationalized quantitatively by using the PIE model. Assuming that the ion-exchange equilibrium constant, K(OH(-)/Br(-)), for the competition between the bromide and the hydroxide ions in all TTAB and in TTAB-pentanol micellar solutions studied is the same, a good agreement between the theoretical and the experimental kinetic data was found in all the micellar media for the two processes studied. This assumption was checked by experimentally determining the ion-exchange equilibrium constant K(OH(-)/Br(-)) in TTAB and TTAB-pentanol micellar solutions through a spectroscopic method, results showing that the presence of n-pentanol does not affect substantially the value of K(OH(-)/Br(-)). The second-order rate constants obtained from the fittings decrease slightly when the amount of pentanol increases, being greater than that in aqueous solution. This acceleration can be explained considering that micelles accelerate the reactions in which the charge is delocalized in the transition state.     

Counterion condensation and release in micellar solutions

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with ion-selective electrode. Monte Carlo simulations based on the cell model are also performed to analyze the experimental results. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, alpha< or =1. The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is exceeded, the free counterion ratio alpha declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. A simple model is developed to obtain the true degree of ionization, which agrees with our Monte Carlo results. Upon addition of neutral polymer or monovalent salts, some of the surfactant counterions are released to the bulk. The former is due to the decrease of the intrinsic charge (smaller aggregation number) and the degree of ionization is increased. The latter is attributed to competitive counterion condensation, which follows the Hefmeister series. This consequence indicates that the specific ion effect plays an important role next to the electrostatic attraction.     

Slow water diffusion in micellar solutions

Slowly diffusing water molecules were found by quasi-elastic neutron scattering (QENS) in a sodium dodecyl sulfate (SDS) micellar solution, and both their diffusion coefficient (4.33 x 10(-6) cm2 x s(-1)) and mole fraction (0.057) were determined. After successfully checking the mean slowing down of solvent molecules by the gradient compensated stimulated spin-echo (GCSTE) pulse sequence NMR method, a similar effect was observed with this technique in the solvent phase of dodecyl trimethylammonium bromide (DTAB) and differing chain length (X = 12, 20, 30, and 40) ethoxylated nonyl phenol (9NX) micellar systems. Following the literature, the experimental results are qualitatively explained by assuming that, apart from ionic hydration, H-bonds may form between the solvent molecules and the O or N atoms present in the hydrophilic (head)groups of the micelle-forming monomers.     

Two-photon absorption in aqueous micellar solutions

Addition of the surfactant sodium dodecyl sulfate at concentrations above the critical micelle concentration increases the fluorescence quantum yield and the two-photon absorption cross-section of charged [2.2]paracyclophane chromophores containing pairs of D-pi-D chromophores. The resulting spectra in the micellar solutions are very similar to those obtained for neutral isostructural analogues in toluene. The measured etadelta values are 1300 GM for 1C and 1920 GM for 2C, which are comparable or larger to those in toluene. These results highlight possible misleading interpretation of two-photon-induced emission for evaluating the concentration of labeled substrates used in two-photon microscopy and provide guidelines for designing molecular structures with optimized two-photon action cross-sections in water.     

Size distribution of aggregates in micellar solutions

A general expression for the equilibrium size distribution of polydisperse ionic aggregates in micellar solutions is proposed. This expression accounts for the interactions between the micelles. The interaction is modeled via screened electrostatic potential. Asymptotic formulae for nearly monodisperse case and for high polydispersity of the micelles are presented. The results show that the interactions lead to the stabilization of the monodispersity in the first case. In the second case the interactions cause an increase in the polydispersity of the micellar solution.     

The solubilization of alcohols in micellar solutions

The specific conductivities of dodecyldimethylbenzylammonium bromide (C12BBr) have been determined in aqueous butanol and aqueous benzyl alcohol solutions in the temperature range of 5-40°C. From these data the temperature dependent critical micelle concentration (cmc) was determined. The molar fraction of alcohol in the micelle was estimated using the theory suggested by Motomura et al. for surfactant binary mixtures. The thermal properties such as standard Gibbs free energy, enthalpy and entropy of solubilization of alcohols in the micelles were estimated for the phase separation model. The change in heat capacity upon solubilization of alcohol in the micelle has been estimated form the above properties. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamics of molecular oxygen in micellar solutions

Fluorescence quenching by molecular oxygen has been employed to estimate dynamic parameters and solubility characteristics of molecular oxygen in micelle forming detergent solutions. A kinetic model which assumes that oxygen quenching occurs only in the micellar phase is employed to analyze the data.     

SANS-measurements on micellar solutions of perfluoro-detergents

Small-angle-neutron-scattering-(SANS)-measurements were carried out with soulutions of Tetramethylam-moniumperfluoroctanesulfonate (TMAFOS) and Diethylammoniumperfluorononanoate (DEAFN) in pure D₂O and in mixtures of D₂O and H₂O. For the TMAFOS-solutions the experimentally observed scattering functions, i.e. the coherent scattering intensity as a function of the scattering angles, could be fitted very well for large scattering angles with the theoretically calculated scattering function for rodlike particles and the dimensions of the rods could be evaluated from these fits. The radius of the rods was independent of the detergent concentration and equal to the double length of a detergent molecule. For small scattering angles the scattering function showed a maximum which was due to nearest neighbour order between the aggregates resulting from the intermicellar interaction. From this maximum a mean distance between the aggregates and hence the lengths L of the rods could be calculated.For the DEAFN-solutions the observed scattering function showed no maximum what clearly indicates the absence of nearest neighbour order between the aggregates. The experimentally observed scattering functions could not be fitted on the basis of rodlike aggregates, but agreed rather well with the theoretically calculated scattering functions for disclike aggregates and also for vesicle-like double layers. The dimensions for the discs could be evaluated from the fits.     

Microfluidic flows of wormlike micellar solutions

The widespread use of wormlike micellar solutions is commonly found in household items such as cosmetic products, industrial fluids used in enhanced oil recovery and as drag reducing agents, and in biological applications such as drug delivery and biosensors. Despite their extensive use, there are still many details about the microscopic micellar structure and the mechanisms by which wormlike micelles form under flow that are not clearly understood. Microfluidic devices provide a versatile platform to study wormlike micellar solutions under various flow conditions and confined geometries. A review of recent investigations using microfluidics to study the flow of wormlike micelles is presented here with an emphasis on three different flow types: shear, elongation, and complex flow fields. In particular, we focus on the use of shear flows to study shear banding, elastic instabilities of wormlike micellar solutions in extensional flow (including stagnation and contraction flow field), and the use of contraction geometries to measure the elongational viscosity of wormlike micellar solutions. Finally, we showcase the use of complex flow fields in microfluidics to generate a stable and nanoporous flow-induced structured phase (FISP) from wormlike micellar solutions. This review shows that the influence of spatial confinement and moderate hydrodynamic forces present in the microfluidic device can give rise to a host of possibilities of microstructural rearrangements and interesting flow phenomena.     

Thermal analysis of aqueous micellar solutions

A micro differential temperature scanning calorimeter was used to characterize the structural changes between different types of micelles in aqueous solutions of ionic surfactants: anionic — sodium dodecylsulfate (SDS) — and cationic — hexadecyltrimethyl ammonium bromide (CTAB). Moreover, this technique allowed to confirm the existence of peculiar types of complexes between surfactants and selected solutes. In SDS solutions containing polyethylene glycols (PEG), the presence of complexes formed by small micelles adsorbed along the chains of the polymers was evidenced in the case of long enough polymer chains. In CTAB-phenol solutions, due to strong interactions between the polar heads of surfactant and phenol, molecular complexes of a composition of 1:1 molar ratio have been characterized. Depending on the ratio [phenol]/[CTAB], the rheological behaviour was found to change from fluid to viscoelastic and gel-like solutions, owing to the growth of elongated rod-like micelles. With entangled worm-like micelles, the important role of kinetics to reach the thermodynamic equilibria was shown.     

Fast dynamics of wormlike micellar solutions

We present the first measurements of the fast dynamics of cationic wormlike micelles (WLM) using neutron spin echo (NSE). The comparison with theory [Zilman, A.; Granek, R. Phys. Rev. Lett. 1996, 77, 4788. Granek, R. J. Phys. II 1997, 7, 1761]1,2 enables coarse grained parameters to be identified. We propose and validate a calibration procedure to extract the bending constant kappa from NSE measurements.     

Kinetics of adsorption from micellar solutions

Previous studies on surfactant adsorption mostly deal with dilute systems without aggregation in the bulk phase. At the same time, micellar solutions can be more important from the point of view of applications. If one attempts to estimate the equilibrium adsorption, neglecting the influence of micelles can lead to reasonable results. The situation differs for non-equilibrium systems when the adsorption rate can increase by an order of magnitude at the increase of the surfactant concentration beyond the CMC. A critical survey of various models describing the influence of micelles on adsorption kinetics at the liquid-gas interface is given and the theoretical results are compared with existing experimental data. The theories proposed for the case of large deviations from the equilibrium are usually based on some unjustifiable assumptions and can describe the kinetic dependencies of adsorption in only a limited number of situations. Consequently, only rough estimates of the kinetic coefficients of micellization can be obtained from experimental data on dynamic surface tension. More rigorous equations can be derived if the system only deviates slightly from equilibrium. In the latter case, the agreement between theoretical and experimental results is essentially better and measurements of the dynamic surface elasticity of micellar solutions allow us to study the micellization kinetics.     

Composition of sodium cholate micellar solutions

To study the composition of sodium cholate solutions, an investigation was carried out at 25 degrees C and in N(CH3)4Cl, as a constant ionic medium, at three different concentrations (W = 0.100; 0.500 and 0.800 mol dm(-3)). Electromotive force measurements of three different galvanic cells, the first involving a glass electrode for hydrogen ions, the second an electrode for sodium ions and the third a lead amalgam electrode, were performed. Independently, lead (II) cholate solubility measurements in the presence of sodium ions were performed, as well. The experimental results obtained from both approaches were explained by assuming the formation of aggregates in cholate and sodium of different composition depending on W and on the cholate concentration. The maximum aggregation found number for cholate was 24 and even aggregation numbers were markedly predominant. Only two species with odd aggregation number were found, but at a low percentage. The assumed species and the relative constants were compared with those found for the other sodium salt of cholanic acids.     

Cryo-TEM studies of worm-like micellar solutions

Solutions of worm-like micelles display a rich rheological behavior that makes them useful as, for example, drag-reducing agents or viscosity enhancers. The properties of these solutions depend on the morphology and interactions between the micelles, both of which can be tuned by changing solution conditions. Although there has been extensive theoretical study of these solutions, there are often conflicting explanations, or no explanation, of an observed trend. Application of cryogenic transmission electron microscopy (cryo-TEM) for the direct visualization of the micelles can help correlate microstructure to rheology. Of particular interest is the cause of a maximum in viscosity as a function of increasing surfactant or salt concentration. Several studies support the theory of a transition from linear to branched micelles, while other studies report no change in microstructure or no connection between structure evolution and changes in viscosity. More systematic and thorough studies that combine cryo-TEM with other experimental techniques are needed.     

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.     

Shear banding structure in viscoelastic micellar solutions

 Theoretically, it has been shown that worm-like micellar solutions of surfactant can, for a shear rate γ˙ greater than a critical value γ˙_c, undergo a transition giving a plateau evolution (σ=σ_c) of the shear stress σ against shear rate γ˙. We report here on a experimental study of the linear and nonlinear rheological behaviour of aqueous CTAB solutions with NaNO₃ as added salt. With this system, it is possible to observe the evolution of the fundamental characteristics of the flow curve, i.e., the shear rate γ˙_1c at which a shear banding structure appears and the second critical shear rate γ˙_2c characterizing the end of the shear stress plateau followed by a new increased shear stress. For the first time, experimentally, we obtained evidence for the existence and the evolution of γ˙_2c against CTAB and salt concentrations and temperature variations. Experimental results are compared to theoretical predictions correlating σ_c, γ˙_1c and G ₀ (the shear modulus) for Maxwellian micellar solutions. Received: 4 July 1996 Accepted: 19 November 1996     

Temperature dependence of the thermodynamics and kinetics of micellar solutions

We predict theoretically the thermodynamics and relaxation kinetics of solutions of cylindrical branched micelles. Using a recently developed theory in combination with the experimental data, we explain the unusual, inverted temperature dependence of the phase separation observed in wormlike micelles and dilute microemulsions. We extend the model to treat the temperature dependence of the relaxation kinetics and explain the observations.