Kavssery P. Ananthapadmanabhan

Determination of the aggregation number and charge of ionic surfactant micelles from the stepwise thinning of foam films

The stepwise thinning (stratification) of liquid films, which contain micelles of an ionic surfactant, depends on the micelle aggregation number, N(agg), and charge, Z. Vice versa, from the height of the step and the final film thickness one can determine N(agg), Z, and the degree of micelle ionization. The determination of N(agg) is based on the experimental fact that the step height is equal to the inverse cubic root of the micelle concentration. In addition, Z is determined from the final thickness of the film, which depends on the concentration of counterions dissociated from the micelles in the bulk. The method is applied to micellar solutions of six surfactants, both anionic and cationic: sodium dodecylsulfate (SDS), cetyl trimethylammonium bromide (CTAB), cetylpyridinium chloride (CPC), sodium laurylethersulfates with 1 and 3 ethylene oxide groups (SLES-1EO and SLES-3EO), and potassium myristate. The method has the following advantages: (i) N(agg) and Z are determined simultaneously, from the same set of experimental data; (ii) N(agg) and Z are determined for each given surfactant concentration (i.e. their concentration dependence is obtained), and (iii) N(agg) and Z can be determined even for turbid solutions, like those of carboxylates, where the micelles coexist with acid-soap crystallites, so that the application of other methods is difficult. The results indicate that the micelles of greater aggregation number have a lower degree of ionization, which can be explained with the effect of counterion binding. The proposed method is applicable to the concentration range, in which the films stratify and the micelles are spherical. This is satisfied for numerous systems representing scientific and practical interest.

Control of Ostwald Ripening by Using Surfactants with High Surface Modulus

We describe results from systematic measurements of the rate of bubble Ostwald ripening in foams with air volume fraction of 90%. Several surfactant systems, with high and low surface modulus, were used to clarify the effect of the surfactant adsorption layer on the gas permeability across the foam films. In one series of experiments, glycerol was added to the foaming solutions to clarify how changes in the composition of the aqueous phase affect the rate of bubble coarsening. The experimental results are interpreted by a new theoretical model, which allowed us to determine the overall gas permeability of the foam films in the systems studied, and to decompose the film permeability into contributions coming from the surfactant adsorption layers and from the aqueous core of the films. For verification of the theoretical model, the gas permeability determined from the experiments with bulk foams are compared with values, determined in an independent set of measurements with the diminishing bubble method (single bubble attached at large air-water interface) and reasonably good agreement between the results obtained by the two methods is found. The analysis of the experimental data showed that the rate of bubble Ostwald ripening in the studied foams depends on (1) type of used surfactant-surfactants with high surface modulus lead to much slower rate of Ostwald ripening, which is explained by the reduced gas permeability of the adsorption layers in these systems; (2) presence of glycerol which reduces the gas solubility and diffusivity in the aqueous core of the foam film (without affecting the permeability of the adsorption layers), thus also leading to slower Ostwald ripening. Direct measurements showed that the foam films in the studied systems had very similar thicknesses, thus ruling out the possible explanation that the observed differences in the Ostwald ripening are due to different film thicknesses. Experiments with the Langmuir trough were used to demonstrate that the possible differences in the surface tensions of the shrinking and expanding bubbles in a given foam are too small to strongly affect the rate of Ostwald ripening in the specific systems studied here, despite the fact that some of the surfactant solutions have rather high surface modulus. The main reason for the latter observation is that the rate of surface deformation of the coarsening bubbles is extremely low, on the order of 10(-4) s(-1), so that the relaxation of the surface tension (though also slow for the high surface modulus systems) is still able to reduce the surface tension variations down to several mN/m. Thus, we conclude that the main reason for the reduced rate of bubble Ostwald ripening in the systems with high surface modulus is the low solubility and diffusivity of the gas molecules in the respective condensed adsorption layers (which have solid rather than fluid molecular packing).

Theoretical Model of Viscous Friction inside Steadily Sheared Foams and Concentrated Emulsions

In a recent Letter [N. D. Denkov, Phys. Rev. Lett. 100, 138301 (2008)] we calculated theoretically the macroscopic viscous stress of steadily sheared foam or emulsion from the energy dissipated inside the transient planar films, formed between neighboring bubbles or drops in the shear flow. The model predicts that the viscous stress in these systems should be proportional to Ca 1/2, where Ca is a capillary number and n=1/2 is the power-law index. In the current paper we explain our model in detail and develop it further in several aspects: First, we extend the model to account for the effects of viscous friction in the curved meniscus regions, surrounding the planar films, on the dynamics of film formation and on the total viscous stress. Second, we consider the effects of surface forces (electrostatic, van der Waals, etc.) acting between the surfaces of the neighboring bubbles or drops and show that these forces could be important in emulsions, due to the relatively small thickness of emulsion films (often comparable to the range of action of surface forces). In contrast, the surface forces are usually negligible in steadily sheared foams, because the dynamic foam films are thicker than the extent of surface forces, except for foams containing micrometer-sized bubbles and/or at very low shear rates. Third, additional consideration is made for bubbles or drops exhibiting high surface viscosity, for which we demonstrate an additional contribution to the macroscopic viscous stress, created by the surface dissipation of energy. The new upgraded model predicts that the energy dissipation at the bubble or drop surface leads to power-law index n<1/2 , whereas the contribution of the surface forces leads to n>1/2 , which explains the rich variety of foam or emulsion behaviors observed upon steady shear. Various comparisons are made between model predictions and experimental results for both foams and emulsions, and very good agreement is found.

Solubility limits and phase diagrams for fatty acids in anionic (SLES) and zwitterionic (CAPB) micellar surfactant solutions

The limiting solubility of fatty acids in micellar solutions of the anionic surfactant sodium laurylethersulfate (SLES) and the zwitterionic surfactant cocamidopropyl betaine (CAPB) is experimentally determined. Saturated straight-chain fatty acids with n=10, 12, 14, 16, and 18 carbon atoms were investigated at working temperatures of 25, 30, 35, and 40°C. The rise of the fatty acid molar fraction in the micelles is accompanied by an increase in the equilibrium concentration of acid monomers in the aqueous phase. Theoretically, the solubility limit is explained with the precipitation of fatty acid crystallites when the monomer concentration reaches the solubility limit of the acid in pure water. In agreement with theory, the experiment shows that the solubility limit is proportional to the surfactant concentration. For ideal mixtures, the plot of the log of solubility limit vs. the chainlength, n, must be a straight line, which is fulfilled for n=14, 16, and 18. For the fatty acids of shorter chains, n=10 and 12, a deviation from linearity is observed, which is interpreted as non-ideal mixing due to a mismatch between the chainlengths of the surfactant and acid. The data analysis yields the solubilization energy and the interaction parameter for the fatty acid molecules in surfactant micelles. By using the determined parameter values, phase diagrams of the investigated mixed solutions are constructed. The four inter-domain boundary lines intersect in a quadruple point, whose coordinates have been determined. The results can be applied for the interpretation and prediction of the solubility, and phase behavior of medium- and long-chain fatty acids and other amphiphiles that are solubilizable in micellar surfactant solutions, as well as for determining the critical micellization concentration (CMC) of the respective mixed solution.

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.

The colloid structural forces as a tool for particle characterization and control of dispersion stability

Knowing the size and interactions of colloid particles, one can predict the stepwise thickness transitions and the contact angles of particle-containing liquid films. Here, we consider the inverse problem, viz. how to determine the particle properties by measurements with liquid films. We carried out experiments with films formed from aqueous solutions of two nonionic surfactants, Brij 35 and Tween 20, which contain spherical micelles of diameters in the range 7-9 nm. From the measured contact angles, we determined the micelle aggregation number and volume fraction. In addition, from the measured disjoining-pressure isotherms we determined the micelle diameter. In other words, the liquid-film measurements give information about the micelles, which is analogous to that obtainable by dynamic and static light scattering. Furthermore, we investigate the predictions of different quantitative criteria for stability-instability transitions, having in mind that the oscillatory forces exhibit both maxima, which play the role of barriers to coagulation, and minima that could produce flocculation or coalescence in colloidal dispersions (emulsions, foams, suspensions). The interplay of the oscillatory force with the van der Waals surface force is taken into account. Two different kinetic criteria are considered, which give similar and physically reasonable results about the stability-instability transitions. Diagrams are constructed, which show the values of the micelle volume fraction, for which the oscillatory barriers can prevent the particles from coming into close contact, or for which a strong flocculation in the depletion minimum or a weak flocculation in the first oscillatory minimum could be observed.

The metastable states of foam films containing electrically charged micelles or particles: Experiment and quantitative interpretation

The stepwise thinning (stratification) of liquid films containing electrically charged colloidal particles (in our case - surfactant micelles) is investigated. Most of the results are applicable also to films from nanoparticle suspensions. The aim is to achieve agreement between theory and experiment, and to better understand the physical reasons for this phenomenon. To test different theoretical approaches, we obtained experimental data for free foam films from micellar solutions of three ionic surfactants. The theoretical problem is reduced to the interpretation of the experimental concentration dependencies of the step height and of the final film thickness. The surface charges of films and micelles are calculated by means of the charge-regulation model, with a counterion-binding (Stern) constant determined from the fit of surface tension isotherms. The applicability of three models was tested: the Poisson-Boltzmann (PB) model; the jellium-approximation (JA), and the cell model (CM). The best agreement theory/experiment was obtained with the JA model without using any adjustable parameters. Two theoretical approaches are considered. First, in the energy approach the step height is identified with the effective diameter of the charged micelles, which represents an integral of the electrostatic-repulsion energy calculated by the JA model. Second, in the osmotic approach the step height is equal to the inverse cubic root of micelle number density in the bulk of solution. Both approaches are in good agreement with the experiment if the suspension of charged particles (micelles) represents a jellium, i.e. if the particle concentration is uniform despite the field of the electric double layers. The results lead to a convenient method for determining the aggregation number of ionic surfactant micelles from the experimental heights of the steps.

Effect of Cationic Polymers on Foam Rheological Properties

We study the effect of two cationic polymers, with trade names Jaguar C13s and Merquat 100, on the rheological properties of foams stabilized with a mixture of anionic and zwitterionic surfactants (sodium lauryloxyethylene sulfate and cocoamidopropyl betaine). A series of five cosurfactants are used to compare the effect of these polymers on foaming systems with high and low surface dilatational moduli. The experiments revealed that the addition of Jaguar to the foaming solutions leads to (1) a significant increase of the foam yield stress for all systems studied, (2) the presence of consecutive maximum and minimum in the stress vs shear rate rheological curve for foams stabilized by cosurfactants with a high surface modulus (these systems cannot be described by the Herschel-Bulkley model anymore), and (3) the presence of significant foam-wall yield stress for all foaming solutions. These effects are explained with the formation of polymer bridges between the neighboring bubbles in slowly sheared foams (for inside foam friction) and between the bubbles and the confining solid wall (for foam-wall friction). Upon addition of 150 mM NaCl, the effect of Jaguar disappears. The addition of Merquat does not noticeably affect any of the foam rheological properties studied. Optical observations of foam films, formed from all these systems, show a very good correlation between the polymer bridging of the foam film surfaces and the strong polymer effect on the foam rheological properties. The obtained results demonstrate that the bubble-bubble attraction can be used for efficient control of the foam yield stress and foam-wall yield stress, without significantly affecting the viscous friction in sheared foams.

Disclike vs. cylindrical micelles: generalized model of micelle growth and data interpretation.

Here, we present a detailed theoretical model describing the growth of disclike surfactant micelles. The model is tested against light-scattering data for micellar solutions from mixed conventional surfactants and from fluorinated surfactants. Theoretical expressions are derived for the concentration dependencies of the number and mass average aggregation numbers. Central role in the theory is played by the difference between the chemical potentials of a surfactant molecule in cylindrical and discoidal micelles. This difference, scaled with the thermal energy kT, is denoted p. For p<0, the formation of cylindrical (rather than disclike) micelles is energetically favored. For p>0 disclike micelles are formed, but their growth is limited due to the rise of their positive peripheral energy. Because of that, disclike micelles can be observed in a relatively narrow interval, 0<p<0.1, and in a limited concentration range. Three sets of light-scattering data for different surfactants were processed. It is remarkable that in all cases the best fit gives small positive values of p, in agreement with the theoretical predictions. The model predicts that a strong increase in the viscosity of a surfactant solution should happen upon the transformation of disclike micelles into cylindrical ones at small variations in p. The model can be used for analyzing the shape and size of micelles in various surfactant solutions. The fact that typical disclike micelles form only in the special case 0<p<0.1 shows why such micelles represent a relatively rare form of stable surfactant self-assembly.

Efficient control of the rheological and surface properties of surfactant solutions containing C8-C18 fatty acids as cosurfactants.

Systematic experimental study is performed about the effects of chain length (varied between C8 and C18) and concentration of fatty acids (FAc), used as cosurfactants to the mixture of the anionic surfactant SLES and the zwitterionic surfactant CAPB. The following properties are studied: bulk viscosity of the concentrated solutions (10 wt % surfactants), dynamic and equilibrium surface tensions, surface modulus, and foam rheological properties for the diluted foaming solutions (0.5 wt % surfactants). The obtained results show that C8-C10 FAc induce formation of wormlike micelles in the concentrated surfactant solutions, which leads to transformation of these solutions into viscoelastic fluids with very high apparent viscosity. The same FAc shorten the characteristic adsorption time of the diluted solutions by more than 10 times. In contrast, C14-C18 FAc have small effect on the viscosity of the concentrated solutions but increase the surface modulus above 350 mN/m, which leads to higher friction inside sheared foams and to much smaller bubbles in the formed foams. The intermediate chain C12 FAc combines some of the properties seen with C10 FAc and other properties seen with C14 FAc. These results clearly demonstrate how appropriate cosurfactants can be used for efficient control of the rheological properties of concentrated surfactant solutions and of some important foam attributes, such as bubble size and foam rheology.