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Advances in Colloid and Interface Science (v.119, #1)
Mass transport in micellar surfactant solutions: 1. Relaxation of micelle concentration, aggregation number and polydispersity by K.D. Danov; P.A. Kralchevsky; N.D. Denkov; K.P. Ananthapadmanabhan; A. Lips (pp. 1-16).
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.
Keywords: Micellar surfactant solutions; Kinetics of micelle association and decay; Fast and slow micellization processes; Surfactant adsorption kinetics; Dynamic surface tension
Mass transport in micellar surfactant solutions: 2. Theoretical modeling of adsorption at a quiescent interface by K.D. Danov; P.A. Kralchevsky; N.D. Denkov; K.P. Ananthapadmanabhan; A. Lips (pp. 17-33).
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/ t1/2, 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.
Keywords: Micellar surfactant solutions; Fast and slow micellization processes; Adsorption kinetics of surfactants; Dynamic surface tension; Diffusion in micellar surfactant solutions
Monte Carlo simulation of colloidal membrane filtration: Principal issues for modeling by Jim C. Chen; Albert S. Kim (pp. 35-53).
The principal issues involved in developing a Monte Carlo simulation model of colloidal membrane filtration are investigated in this study. An important object for modeling is the physical dynamics responsible for causing particle deposition and accumulation when encountering an open system with continuous outflow. A periodic boundary condition offers a solution to the problem by recirculating continuous flow back through the system. Scaling to full physical dimensions will allow for release of the model from flawed assumptions such as constant cake layer volume fraction and thickness throughout the system. Furthermore, rigorous modeling on a precise scale extends the model to account for random particle collisions with acute accuracy. A major finding of this study proves that forces within the colloidal filtration system are summed and transferred cumulatively through the inter-particle interactions. The force summation and transfer phenomenon only realizes its true value when the model is scaled to full dimensions. The overall strategy for model development, therefore, entails three stages: first, rigorous modeling on a microscopic scale; next, comprehensive inclusion of relevant physical dynamics; and finally, scaling to full physical dimensions.
Keywords: Monte Carlo simulation; Colloidal membrane filtration; Cake layer formation; Periodic boundary condition; Random particle collisions; Force summation and transfer
Beneficial role of surfactants in electrochemistry and in the modification of electrodes by R. Vittal; H. Gomathi; Kang-Jin Kim (pp. 55-68).
This review deals with the beneficial use of surfactants in various fields of electrochemistry, in general and in the modification of electrodes with immobilized electroactive species, in particular. Special emphasis is laid on the modification of electrodes with metal hexacyanoferrates (MHCFs). After an introduction and brief notes on fundamentals of surfactants, and their applications in electrochemistry, covering some of the very important works in the past two decades involving beneficial use of surfactants, the article gives a brief account on metal hexacyanoferrate modified electrodes and the salient features of our published results on the beneficial role of cetyltrimethylammonium bromide (CTAB), a cationic surfactant, in the modification of electrodes with MHCFs and their derivatized oxides, and with titanium dioxide.
Keywords: Surfactants; Modified electrodes; Micelles; CTAB; Metal hexacyanoferrates