Analytical modeling of micelle growth. 5. Molecular thermodynamics of micelles from zwitterionic surfactants.

HYPOTHESIS: The critical micelle concentration, aggregation number, shape and length of spherocylindrical micelles in solutions of zwitterionic surfactants can be predicted by knowing the molecular parameters and surfactant concentrations. This can be achieved by upgrading the quantitative molecular thermodynamic model with expressions for the electrostatic interaction energy between the zwitterionic dipoles and micellar hydrophobic cores of spherical and cylindrical shapes. THEORY: The correct prediction of the mean micellar aggregation numbers requires precise calculations of the free energy per molecule in the micelles. New analytical expressions for the dipole electrostatic interaction energy are derived based on the exact solutions of the electrostatic problem for a single charge close to a boundary of spherical and cylindrical dielectric media. The obtained general theory is valid for arbitrary ratios between dielectric constants, radii of spheres and cylinders, positions, and orientations of dipoles. FINDINGS: The detailed numerical results show quantitatively the effects of the micelle curvature and dielectric properties of the continuum media on the decrease of the dipole electrostatic interaction energy. Excellent agreement was achieved between the theoretical predictions and experimental data for the critical micelle concentration, size and aggregation number of zwitterionic surfactant micelles. This study can be extended to mixed micelles of zwitterionic and ionic surfactants in the presence of salt to interpret and predict the synergistic effect on the rheology of solutions.

Rheology of mixed solutions of sulfonated methyl esters and betaine in relation to the growth of giant micelles and shampoo applications.

This is a review article on the rheological properties of mixed solutions of sulfonated methyl esters (SME) and cocamidopropyl betaine (CAPB), which are related to the synergistic growth of giant micelles. Effects of additives, such as fatty alcohols, cocamide monoethanolamine (CMEA) and salt, which are expected to boost the growth of wormlike micelles, are studied. We report and systematize the most significant observed effects with an emphasis on the interpretation at molecular level and understanding the rheological behavior of these systems. The experiments show that the mixing of SME and CAPB produces a significant rise of viscosity, which is greater than in the mixed solutions of sodium dodecyl sulfate and CAPB. The addition of fatty alcohols, CMEA and cationic polymer, leads to broadening of the synergistic peak in viscosity without any pronounced effect on its height. The addition of NaCl leads to a typical salt curve with high maximum, but in the presence of dodecanol this maximum is much lower. At lower salt concentrations, the fatty alcohol acts as a thickener, whereas at higher salt concentrations - as a thinning agent. Depending on the shape of the frequency dependences of the measured storage and loss moduli, G' and G", the investigated micellar solutions behave as systems of standard or nonstandard rheological behavior. The systems with standard behavior obey the Maxwell viscoelastic model (at least) up to the crossover point (G' = G") and can be analyzed in terms of the Cates reptation-reaction model. The systems with nonstandard rheological behavior obey the Maxwell model only in a restricted domain below the crossover frequency; they can be analyzed in the framework of an augmented version of the Maxwell model. The methodology for data analysis and interpretation could be applied to any other viscoelastic micellar system.

Properties of the micelles of sulfonated methyl esters determined from the stepwise thinning of foam films and by rheological measurements.

HYPOTHESES: The micellar solutions of sulfonated methyl esters (SME) are expected to form stratifying foam films that exhibit stepwise thinning. From the height of the steps, which are engendered by micellar layers confined in the films, we could determine the micelle aggregation number, surface electric potential, and ionization degree. Moreover, addition of the zwitterionic surfactant cocamidopropyl betaine (CAPB) is expected to transform the small spherical micelles of SME into giant wormlike aggregates. EXPERIMENTS: Stratifying films from SME solutions are formed and the heights of the steps are recorded. The viscosity of mixed SME + CAPB solutions is measured at various concentrations and weight ratios of the two surfactants. FINDINGS: By theoretical analysis of the foam film data, we established that at 30-100 mM SME spherical micelles are formed and their aggregation number was determined. The addition of calcium ions, as in hard water, does not produce significant effect. However, SME and CAPB exhibit a strong synergism with respect to micelle growth as indicated by the high solution's viscosity. For this reason, the SME + CAPB mixtures represent a promising system for formulations in personal-care and house-hold detergency, having in mind also other useful properties of SME, such as high hard water tolerance, biodegradability and skin compatibility.

Hardening of particle/oil/water suspensions due to capillary bridges: Experimental yield stress and theoretical interpretation.

Suspensions of colloid particles possess the remarkable property to solidify upon the addition of minimal amount of a second liquid that preferentially wets the particles. The hardening is due to the formation of capillary bridges (pendular rings), which connect the particles. Here, we review works on the mechanical properties of such suspensions and related works on the capillary-bridge force, and present new rheological data for the weakly studied concentration range 30-55 vol% particles. The mechanical strength of the solidified capillary suspensions, characterized by the yield stress Y, is measured at the elastic limit for various volume fractions of the particles and the preferentially wetting liquid. A quantitative theoretical model is developed, which relates Y with the maximum of the capillary-bridge force, projected on the shear plane. A semi-empirical expression for the mean number of capillary bridges per particle is proposed. The model agrees very well with the experimental data and gives a quantitative description of the yield stress, which increases with the rise of interfacial tension and with the volume fractions of particles and capillary bridges, but decreases with the rise of particle radius and contact angle. The quantitative description of capillary force is based on the exact theory and numerical calculation of the capillary bridge profile at various bridge volumes and contact angles. An analytical formula for Y is also derived. The comparison of the theoretical and experimental strain at the elastic limit reveals that the fluidization of the capillary suspension takes place only in a deformation zone of thickness up to several hundred particle diameters, which is adjacent to the rheometer's mobile plate. The reported experimental results refer to water-continuous suspension with hydrophobic particles and oily capillary bridges. The comparison of data for bridges from soybean oil and hexadecane surprisingly indicate that the yield strength is greater for the suspension with soybean oil despite its lower interfacial tension against water. The result can be explained with the different contact angles of the two oils in agreement with the theoretical predictions. The results could contribute for a better understanding, quantitative prediction and control of the mechanical properties of three-phase capillary suspensions solid/liquid/liquid.

Shear rheology of mixed protein adsorption layers vs their structure studied by surface force measurements.

The hydrophobins are proteins that form the most rigid adsorption layers at liquid interfaces in comparison with all other investigated proteins. The mixing of hydrophobin HFBII with other conventional proteins is expected to reduce the surface shear elasticity and viscosity, E(sh) and η(sh), proportional to the fraction of the conventional protein. However, the experiments show that the effect of mixing can be rather different depending on the nature of the additive. If the additive is a globular protein, like ß-lactoglobulin and ovalbumin, the surface rigidity is preserved, and even enhanced. The experiments with separate foam films indicate that this is due to the formation of a bilayer structure at the air/water interface. The more hydrophobic HFBII forms the upper layer adjacent to the air phase, whereas the conventional globular protein forms the lower layer that faces the water phase. Thus, the elastic network formed by the adsorbed hydrophobin remains intact, and even reinforced by the adjacent layer of globular protein. In contrast, the addition of the disordered protein ß-casein leads to softening of the HFBII adsorption layer. Similar (an even stronger) effect is produced by the nonionic surfactant Tween 20. This can be explained with the penetration of the hydrophobic tails of ß-casein and Tween 20 between the HFBII molecules at the interface, which breaks the integrity of the hydrophobin interfacial elastic network. The analyzed experimental data for the surface shear rheology of various protein adsorption layers comply with a viscoelastic thixotropic model, which allows one to determine E(sh) and η(sh) from the measured storage and loss moduli, G' and G″. The results could contribute for quantitative characterization and deeper understanding of the factors that control the surface rigidity of protein adsorption layers with potential application for the creation of stable foams and emulsions with fine bubbles or droplets.

Shear rheology of hydrophobin adsorption layers at oil/water interfaces and data interpretation in terms of a viscoelastic thixotropic model.

Here, we investigate the surface shear rheology of class II HFBII hydrophobin layers at the oil/water interface. Experiments in two different dynamic regimes, at a fixed rate of strain and oscillations, have been carried out with a rotational rheometer. The rheological data obtained in both regimes comply with the same viscoelastic thixotropic model, which is used to determine the surface shear elasticity and viscosity, E(sh) and η(sh). Their values for HFBII at oil/water interfaces are somewhat lower than those at the air/water interface. Moreover, E(sh) and η(sh) depend on the nature of oil, being smaller for hexadecane in comparison with soybean-oil. It is remarkable that E(sh) is independent of the rate of strain in the whole investigated range of shear rates. For oil/water interfaces, E(sh) and η(sh) determined for HFBII layers are considerably greater than for other proteins, like lysozyme and ß-casein. It is confirmed that the hydrophobin forms the most rigid surface layers among all investigated proteins not only for the air/water, but also for the oil/water interface. The wide applicability of the used viscoelastic thixotropic model is confirmed by analyzing data for adsorption layers at oil/water interfaces from lysozyme and ß-casein - both native and cross-linked by enzyme, as well as for films from asphaltene. This model turns out to be a versatile tool for determining the surface shear elasticity and viscosity, E(sh) and η(sh), from experimental data for the surface storage and loss moduli, G' and G''.

Surface shear rheology of hydrophobin adsorption layers: laws of viscoelastic behaviour with applications to long-term foam stability.

The long-term stabilization of foams by proteins for food applications is related to the ability of proteins to form dense and mechanically strong adsorption layers that cover the bubbles in the foams. The hydrophobins represent a class of proteins that form adsorption layers of extraordinary high shear elasticity and mechanical strength, much higher than that of the common milk and egg proteins. Our investigation of pure and mixed (with added beta-casein) hydrophobin layers revealed that their rheological behavior obeys a compound rheological model, which represents a combination of the Maxwell and Herschel-Bulkley laws. It is remarkable that the combined law is obeyed not only in the simplest regime of constant shear rate (angle ramp), but also in the regime of oscillatory shear strain. The surface shear elasticity and viscosity, E(sh) and eta(sh), are determined as functions of the shear rate by processing the data for the storage and loss moduli, G' and G''. At greater strain amplitudes, the spectrum of the stress contains not only the first Fourier mode, but also the third one. The method is extended to this non-linear regime, where the rheological parameters are determined by theoretical fit of the experimental Lissajous plot. The addition of beta-casein to the hydrophobin leads to softer adsorption layers, as indicated by their lower shear elasticity and viscosity. The developed approach to the rheological characterization of interfacial layers allows optimization and control of the performance of mixed protein adsorption layers with applications in food foams.

Surface shear rheology of adsorption layers from the protein HFBII hydrophobin: effect of added ß-casein.

The surface shear rheology of hydrophobin HFBII adsorption layers is studied in angle-ramp/relaxation regime by means of a rotational rheometer. The behavior of the system is investigated at different shear rates and concentrations of added ß-casein. In angle-ramp regime, the experimental data comply with the Maxwell model of viscoelastic behavior. From the fits of the rheological curves with this model, the surface shear elasticity and viscosity, E(sh) and η(sh), are determined at various fixed shear rates. The dependence of η(sh) on the rate of strain obeys the Herschel-Bulkley law. The data indicate an increasing fluidization (softening) of the layers with the rise of the shear rate. The addition of ß-casein leads to more rigid adsorption layers, which exhibit a tendency of faster fluidization at increasing shear rates. In relaxation regime, the system obeys a modified Andrade's (cubic root) law, with two characteristic relaxation times. The fact that the data comply with the Maxwell model in angle-ramp regime, but follow the modified Andrade's low in relaxation regime, can be explained by the different processes occurring in the viscoelastic protein adsorption layer in these two regimes: breakage and restoration of intermolecular bonds at angle-ramp vs solidification of the layer at relaxation.