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 particle/water/oil three-phase dispersions: Electrostatic vs. capillary bridge forces.

HYPOTHESIS: Particle/water/oil three-phase capillary suspensions possess the remarkable property to solidify upon the addition of minimal amount of the second (dispersed) liquid. The hardening of these suspensions is due to capillary bridges, which interconnect the particles (pendular state). Electrostatic repulsion across the oily phase, where Debye screening by electrolyte is missing, could also influence the hardness of these suspensions. EXPERIMENTS: We present data for oil-continuous suspensions with aqueous capillary bridges between hydrophilic SiO2 particles at particle volume fractions 35-45%. The hardness is characterized by the yield stress Y for two different oils: mineral (hexadecane) and vegetable (soybean oil). FINDINGS AND MODELLING: The comparison of data for the "mirror" systems of water- and oil-continuous capillary suspensions shows that Y is lower for the oil-continuous ones. The theoretical model of yield stress is upgraded by including a contribution from electrostatic repulsion, which partially counterbalances the capillary-bridge attraction and renders the suspensions softer. The particle charge density determined from data fits is close to that obtained in experiments with monolayers from charged colloid particles at oil/water interfaces. The results could contribute for better understanding, quantitative prediction and control of the mechanical properties of solid/liquid/liquid capillary suspensions.

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.