Interpretation of surface-tension isotherms of n-alkanoic (fatty) acids by means of the van der Waals model.

Here we apply the two-dimensional van der Waals model to interpret surface-tension isotherms of aqueous solutions of n-alkanoic (fatty) acids. We processed available experimental data for a homologous series of eight acids, from pentanoic to dodecanoic (lauric). Only three adjustable parameters have been varied to fit simultaneously all experimental curves. Excellent agreement between the theoretical model and the experiment has been obtained. The determined parameter values comply well with the molecular properties and allow one to calculate the surfactant adsorption, surface elasticity, and the surface pressure vs area isotherms. For the dodecanoic acid, the van der Waals model indicates the existence of a surface phase transition.

Mass transport in micellar surfactant solutions: 1. Relaxation of micelle concentration, aggregation number and polydispersity.

The surfactant transfer in micellar solutions includes transport of all types of aggregates and the exchange of monomers between them. Such processes are theoretically described by a system containing tens of kinetic equations, which is practically inapplicable. For this reason, one of the basic problems of micellar kinetics is to simplify the general set of equations without loosing the adequacy and correctness of the theoretical description. Here, we propose a model, which generalizes previous models in the following aspects. First, we do not use the simplifying assumption that the width of the micellar peak is constant under dynamic conditions. Second, we avoid the use of the quasi-equilibrium approximation (local chemical equilibrium between micelles and monomers). Third, we reduce the problem to a self-consistent system of four nonlinear differential equations. Its solution gives the concentration of surfactant monomers, total micelle concentration, mean aggregation number, and halfwidth of the micellar peak as functions of the spatial coordinates and time. Further, we check the predictions of the model for the case of spatially uniform bulk perturbations (such as jumps in temperature, pressure or concentration). The theoretical analysis implies that the relaxations of the three basic parameters (micelle concentration, mean aggregation number, and polydispersity) are characterized by three different characteristic relaxation times. Two of them coincide with the slow and fast micellar relaxation times, which are known in the literature. The third time characterizes the relaxation of the width of the micellar peak (i.e. of the micelle polydispersity). It is intermediate between the slow and fast relaxation times, in the case of not-too-low micellar concentrations. For low micelle concentrations, the third characteristic time is close to the fast relaxation time. Procedure for obtaining the exact numerical solution of the problem is formulated. In addition, asymptotic analytical expressions are derived, which compare very well with the exact numerical solution. In the second part of this study, the obtained set of equations is applied for theoretical modeling of surfactant adsorption from micellar solutions under various dynamic conditions, corresponding to specific experimental methods.

Particle-interface interaction across a nonpolar medium in relation to the production of particle-stabilized emulsions.

Quantitative theory of the particle-interface interaction across a nonpolar medium is developed. We consider a spherical dielectric particle (phase 1), which is immersed in a nonpolar medium (phase 2), near its boundary with a third dielectric medium (phase 3). The interaction originates from electric charges at the particle surface (e.g., the surface of a silica particle immersed in oil). The theoretical problem is solved exactly, in terms of Legendre polynomials, for arbitrary values of the dielectric constants of the three phases. As a result, expressions for calculating the interaction force and energy are derived. These expressions generalize the known theory of the electrostatic image force (acing on point charges) to the case of particles that have finite size and uniform surface charge density. For typical parameter values (silica or glass particles immersed in tetradecane), the image-force interaction becomes significant for particles of radius R > 30 nm. At fixed relative particle-to-interface distance, the force increases with the cube of the particle radius. In general, this is a strong and long-range interaction. For micrometer-sized particles, the interaction energy could be on the order of 10(5) k(B)T at close contact, and, in addition, the interaction range could be about 10(5) particle radii. The sign of the interaction depends on the difference between the dielectric constants of phases 2 and 3. When phase 3 has a smaller dielectric constant (e.g., air), the interface repels the particle. In contrast, when phase 3 has a greater dielectric constant (e.g., water), the interaction is attractive. Especially, water drops attract charged hydrophobic particles dispersed in the oily phase, and thus favor the formation of reverse particle-stabilized (Pickering) emulsions. The particle-interface interaction across the oily phase is insensitive to the concentration of electrolyte in the third, aqueous phase.

Mass transport in micellar surfactant solutions: 2. Theoretical modeling of adsorption at a quiescent interface.

Here, we apply the detailed theoretical model of micellar kinetics from part 1 of this study to the case of surfactant adsorption at a quiescent interface, i.e., to the relaxation of surface tension and adsorption after a small initial perturbation. Our goal is to understand why for some surfactant solutions the surface tension relaxes as inverse-square-root of time, 1/t(1/2), but two different expressions for the characteristic relaxation time are applicable to different cases. In addition, our aim is to clarify why for other surfactant solutions the surface tension relaxes exponentially. For this goal, we carried out a computer modeling of the adsorption process, based on the general system of equations derived in part 1. This analysis reveals the existence of four different consecutive relaxation regimes (stages) for a given micellar solution: two exponential regimes and two inverse-square-root regimes, following one after another in alternating order. Experimentally, depending on the specific surfactant and method, one usually registers only one of these regimes. Therefore, to interpret properly the data, one has to identify which of these four kinetic regimes is observed in the given experiment. Our numerical results for the relaxation of the surface tension, micelle concentration and aggregation number are presented in the form of kinetic diagrams, which reveal the stages of the relaxation process. At low micelle concentrations, "rudimentary" kinetic diagrams could be observed, which are characterized by merging of some stages. Thus, the theoretical modeling reveals a general and physically rich picture of the adsorption process. To facilitate the interpretation of experimental data, we have derived convenient theoretical expressions for the time dependence of surface tension and adsorption in each of the four regimes.

On the mechanism of stomatocyte-echinocyte transformations of red blood cells: experiment and theoretical model.

This study represents an attempt to achieve a better understanding of the stomatocyte-echinocyte transition in the shape of red blood cells. We determined experimentally the index of cell shape at various ionic strengths and osmolarities for native and trypsin-treated human erythrocytes. For every given composition of the outer phase, we calculated the ionic strength in the cells and the transmembrane electric potential using a known theoretical model. Next, we described theoretically the electric double layers formed on both sides of the cell membrane, and derived expressions for the tensions of the two membrane leaflets. Taking into account that the cell-shape index depends on the tension difference between the two leaflets, we fitted the experimental data with the constructed physicochemical model. The model, which agrees well with the experiment, indicates that the tension difference between the two leaflets is governed by the different adsorptions of counterions at the two membrane surfaces, rather than by the direct contribution of the electric double layers to the membrane tension. Thus, with the rise of the ionic strength, the counterion adsorption increases stronger at the outer leaflet, whose stretching surface pressure becomes greater, and whose area expands relative to that of the inner leaflet. Hence, there is no contradiction between the bilayer-couple hypothesis and the electric double layer theory, if the latter is upgraded to account for the effect of counterion-adsorption on the membrane tension. The developed quantitative model can be applied to predict the shape index of cells upon a stomatocyte-discocyte-echinocyte transformation at varying composition of the outer medium.

Mixed solutions of anionic and zwitterionic surfactant (Betaine): surface-tension isotherms, adsorption, and relaxation kinetics.

Here, we present experimental surface-tension isotherms of mixed solutions of two surfactants, sodium dodecyl sulfate (SDS) and cocoamidopropyl betaine (Betaine), measured by means of the Wilhelmy plate method. The kinetics of surface-tension relaxation exhibits two characteristic time scales, which have been distinguished to determine correctly the equilibrium surface tension. The transition from the zwitterionic to the cationic form of Betaine is detected by surface-tension measurements. Synergistic dependence of the critical micellization concentration on the composition of the surfactant blend is established. The experimental surface-tension isotherms are fitted by means of the two-component van der Waals model, and an excellent agreement between theory and experiment was achieved. Having determined the parameters of the model, we calculated different properties of the mixed surfactant adsorption layer at various concentrations ofSDS, Betaine, and salt. Such properties are the adsorptions ofthe two surfactants, the surface dilatational elasticity, the occupancy of the Stern layer by bound counterions, the surface electric potential, and so forth. In particular, the addition of a small amount of Betaine to SDS significantly increases the surface elasticity. The results could be further applied to predict the thickness and stability of foam films or the size of the rodlike micelles in the mixed solutions of SDS and Betaine.

Spontaneous detachment of oil drops from solid substrates: governing factors.

We carried out experiments on detachment of oil drops from glass substrates in solutions of an anionic surfactant. The three-phase contact line shrinks spontaneously, and eventually the oil drop detaches from the substrate. Consecutive video frames of such drops are digitized, and the time dependencies of the contact radius and angle are determined. Three stages of detachment of a drop, situated above a horizontal substrate, can be distinguished. They correspond to three different driving factors: (1) the interfacial tension decrease because of surfactant adsorption, (2) the aqueous meniscus spontaneously advances owing to the penetration of water between the oil and solid phases, and (3) at sufficiently small contact radius the shape of the oil-water interface becomes unstable and the drop detaches under the action of buoyancy. Analyzing the experimental data, we identified two important characteristics of the drop-detachment process: the velocity of spontaneous advance of the contact line and the line drag coefficient. In the case of moving contact line, a dynamic Young equation must be used, which takes into account the line drag force. The latter is proportional to the velocity of contact-line motion. The experimental data agree with the latter dependence, from whose slope the line drag coefficient is determined.