Adsorption from micellar solutions

Most of the traditional adsorption studies of surfactants correspond to dilute systems without aggregation in the bulk phase. At the same time micellar solutions are much more important from a practical point of view. To estimate the equilibrium adsorption, neglecting the effect of micelles can usually lead to reasonable results. However, the situation changes for nonequilibrium systems when the adsorption rate can increase by orders of magnitude when the of surfactant concentration is increased beyond the CMC. Current interest in the adsorption from micellar solutions is mainly caused by recent observations that the stability of foams and emulsions depends strongly on the concentration in the micellar region [1]. This effect can be explained by the influence of the micellisation rate on the adsorption kinetics. 

Both problems, changes of the equilibrium adsorption with micellar concentration and the influence of micelles on the adsorption rate, are the subjects of this review. Various definitions of the CMC are represented at the outset. Nowadays the thermodynamics of micellisation is the most developed part of modem theories of micellar systems. Two main approaches ( quasichemical and pseudophase ) are discussed in the second section of this chapter. In section 3 the thermodynamic equations for the Gibbs adsorption of surfactants in the micellar region are considered together with corresponding experimental data. The subsequent sections are devoted to non-equilibrium micellar systems. First, section 4 delineates briefly the theory of 

This definition of the CMC originates from the qualitative analysis of experimental concentration dependencies of physico-chemical properties, and is not quite strict. Indeed, the limits of the concentration range corresponding to the CMC depend on the error limits of the applied experimental method and on its sensitivity to micellar concentration. For instance, the equivalent conductivity of aqueous solutions of ionic surfactants decreases drastically just above the CMC. Sometimes other properties of surfactant solutions, for example, the intensity 

A and B are constant factors, and cu and cm are the concentrations of monomers and micelles, respectively. However, it was noted later that the condition (5.1) corresponds only to the inflection point of the dependence d([)/dctoti = fictoii) but not to the point of maximum curvature of the function ) = ())(ctoti) [9]. The latter point is characterised mathematically by the following condition 

According to Hall and Pethica [10] the CMC can be identified as the total concentration where 

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An analysis of the maximum bubble pressure method including all known theoretical approaches was given only recently so that data from literature are only of approximate character [160]. Therefore, the current level of kinetic theories of adsorption from micellar solutions and the corresponding experimental technique is still insufficient for investigations of the micellisation kinetics with a precision comparable to that of bulk relaxation methods. This pessimistic conclusion, however, relates to a less extent to methods based on small (mainly periodic) perturbations of the adsorption equilibrium. 

Noskov, B.A., Kinetics of adsorption from micellar solutions, Adv. Colloid Interface Sci., 95, 237, 2002. 

The first theoretical model of surfactant adsorption from micellar solutions, proposed by Lucassen [142], uses the simplifying assumptions that the micelles are monodisperse and that the micellization happens as a single step, which is described as a reversible reaction of order n (the micelle aggregation number). Later, more realistic models, which account for the multi-step character of the micellar process, were developed [143-145]. The assumption for a complete local dynamic equilibrium between monomers and micelles makes possible to use the equilibrium mass action law for the micellization reaction [142,146,147]. In such a case, the surfactant transfer corresponds to a conventional diffusion-limited adsorption characterized by an effective diffusion coefficient, Deff, which depends on the micelle diffusivity, concentration, and aggregation number. Dgff is independent of the rate constants of the fast and slow demicellization processes and k. Joos et al. [146,147] confirmed experimentally that in some cases the adsorption from micellar solutions could be actually described as a diffusion-limited process characterized by an apparent diffusivity,... 

In other experiments, Joos et al. [95,148] established that sometimes the dynamics of adsorption from micellar solutions exhibits a completely different kinetic pattern the interfacial relaxation is exponential, rather than inverse square root, as it should be for diffusion-limited kinetics. 

The Four Kinetic Regimes of Adsorption from Micellar Solutions In the theoretical model proposed in Refs. [149,150], the use of the quasi-equilibrium approximation (local chemical equilibrium between micelles and monomers) is avoided. The theoretical problem is reduced to a system of four nonlinear differential equations. The model has been applied to the case of surfactant adsorption at a quiescent interface [150], that is, to the relaxation of surface tension and adsorption after a small initial perturbation. The perturbations in the basic parameters of the micellar solution are defined in the following way ... 

In summary, four distinct kinetic regimes of adsorption from micellar solutions exist, called AB, BC, CD, and DE see Figures 4.8 and 4.10. In regime AB, the fast micellar process governs the adsorption kinetics. In regime BC, the adsorption occurs under diffusion control because the... 

Adsorption from micellar solution In this case, both surfactant monomers and micelles are involved in the diffusion process. Thus, the micelles serve as carriers of surfactant from the bulk to the surface and vice versa. The reactions of micelle formation and decay should be necessarily taken into account see Sec. III.E for details. 

Noskov, B.A. and Grigoriev, D.O. (2001) Adsorption from micellar solutions, in Surfactants - Chemistry, Interfacial... 

To date, almost all AFM work has focused on adsorption from micellar solution or from solutions just below the cmc. Below the cmc, the chemical potential of the surfactant is a much stronger function of solution concentration, so it should be possible to form a larger variety of surfactant structures. There is hope that new structures might be observed in this more dilute regime. 

Danov, K.D., Adsorption from micellar surfactant solutions nonlinear theory and experiment, J. Colloid Interface ScL, 183, 223, 1996. 

Fig. 4.11 Schematic of an adsorption process from micellar solutions...

The aggregation number also plays an important role in the total rate of the adsorption process from micellar solutions. The presence of dimers, which are assumed not to adsorb, increases the adsorption rate remarkably, although only 10% of the surfactant is aggregated in dimers (Fig. 4.14). 

The first attempt to take into account the two-step kinetic theory of micellisation was made by Fainerman [147]. With that end in view two pairs of diffusion equations (for micelles and monomers) were written down for two situations eorresponding to the fast and slow proeesses. Approximate solutions of the boundary problems for these equations were used subsequently in the course of analysis of experimental data on the adsorption kinetics from micellar solutions [77, 85, 87, 88]. However, as it has been shown by Dushkin et al. [137], this approaeh is equivalent to the PFOR model for the slow proeess and probably eannot be applied to the description of the adsorption kinetics for the fast process. 

Another difficulty arising from this comparison is connected with the mathematical complexity of the corresponding boundary problems even if only linear diffusion equations are used. The mathematical description of the adsorption kinetics from micellar solutions is essentially more complicated in comparison with the case of the adsorption process from sub-micellar solutions. Analytical solutions of the corresponding boundary problems using rather poor approximations have been obtained only for a small number of situations. A sufficiently general solution cannot be obtained analytically and the deficiency of the rather well elaborated numerical methods often compel experimentalists to apply approximate solutions. Therefore, it seems important to consider the main equations proposed for the description of kinetic dependencies of the surface tension and adsorption, and to elucidate the limits of their application before the discussion of experimental results. 

Application of numerical methods have been rather seldom in studies of adsorption kinetics from micellar solutions. The main difficulties are probably connected with the large number of independent parameters. The first work belongs to Miller [146]. Fainerman and Rakita also published numerical results of the solution of the boundary value problem (5.236), (5.237), (5.245) [85]. Recently Danov et al. proposed an original method for solving the boundary value problem for the diffusion of micelles and monomers [92]. The system of equations was reduced to a system of ordinary differential equations by using a model concentration profile in the bulk phase. The obtained results agree better with dynamic surface tensions of micellar solutions than equation (5.248). 

One of the reasons of the insufficient reliability of micellisation kinetics data determined from dynamic surface tensions, consists in the insufficient precision of the calculation methods for the adsorption kinetics from micellar solutions. It has been already noted that the assumption of a small deviation from equilibrium used at the derivation of Eq. (5.248) is not fulfilled by experiments. The assumptions of aggregation equilibrium or equal diffusion rates of micelles and monomers allow to obtain only rough estimates of the dynamic surface tension. An additional cause of these difficulties consists in the lack of reliable methods for surface tension measurements at small surface ages. The recent hydrodynamic analysis of the theoretical foundations of the oscillating jet and maximum bubble pressure methods has shown that using these techniques for measurements in the millisecond time scale requires to account for numerous hydrodynamic effects [105, 158, 159]. These effects are usually not taken into account by experimentalists, in particular in studies of micellar solutions. A detailed analysis of... 

This relation describes not only periodic deformations of a liquid surface. Using methods of integral transformations it is possible to show that the dynamic surface elasticity is a fundamental surface property and its value determines the system response to a small arbitrary surface dilation [161]. With this method it is also possible to determine the dynamic elasticity of liquid-liquid interfaces where the surfactant is soluble in both adjacent phases [133]. Moreover, similar transformations lead to an expression for the dynamic surface elasticity for the case when the mechanism of the slow step of micellisation is determined by scheme (5.185) or for frequencies corresponding to the fast step of micellisation [133,134]. However, as stated above, it is the slow process which mainly influences the adsorption kinetics from micellar solutions. 

Vlahovska, PM., Horozov, T., Dushkin, CD., Kralchevsky, P.A., Mehreteab, A., and Broze, G., Adsorption from micellar surfactant solutions nonlinear theory and experiment, J. Colloid Interface Sci., 183, 223, 1997. 

Adsorption isotherms from surfactant solutions have been reported to often exhibit maximum and sometimes even minimum in the region around critical micelle concentration (1-4). The phenomenon of maximum and minimum is of such theoretical interest as well as practical importance in such areas as enhanced oil recovery using surfactant flooding. The presence of maximum has been attributed in the past to mechanisms involving micellar exclusion from interfacial region due to electrostatic repulsion or structural incompatibility, presence of impurities, surfactant composition, adsorbent morphology, etc. (1,2). None of these mechanisms is, however, fully substantiated to be considered as a confirmed mechanism for surfactant adsorption from concentrated solutions particularly due to serious possibilities for experimental arti-... 

Adsorption at the Air-Water Interface from Micellar Solutions... 

Dynamics of Adsorption from Micellar Surfactant Solutions.276... 

As already mentioned, the surfactants are used to stabilize the liquid films in foams, in emulsions, on solid surfaces, and so forth. We will first consider the equilibrium and kinetic properties of surfactant adsorption monolayers. Various two-dimensional equations of state are discussed. The kinetics of surfactant adsorption is described in the cases of dijfusion and barrier control. Special attention is paid to the process of adsorption from ionic surfactant solutions. Theoretical models of the adsorption from micellar surfactant solutions are also presented. The rheological properties of the surfactant adsorption mono-layers, such as dilatational and shear surface viscosity and suiface elasticity, are introduced. The specificity of the proteins as high-molecular-weight surfactants is also discussed. 

As mentioned earlier, below we focus om attention on the kinetics of surfactant adsorption. First, we introduce the basic equations. Next, we consider the two alternative cases of surfactant adsorption under diffusion and barrier control. Special attention is paid to the adsorption of ionic surfactants, whose molecules are involved in long-range electrostatic interactions. Finally, we consider the adsorption from micellar surfactant solutions, which is accompanied by micelle diffusion, assembly, or disintegration. 

In addition to the factors listed in Table VIII, the nature of the surfactant-modified stationary phase affects P (partition coefficient for distribution of solute between bulk solvent and modified stationary phases) and thus will influence the retention observed. It should be realized that most of the normal and reversed-phase packing materials will adsorb/absorb surfactant molecules from the mobile phase solution and become coated to different degrees when surfactant mobile phases are passed through them. Numerous adsorption isotherms have been reported for various surfactant - stationary phase combinations illustrating this point (82,85,106,115-128,206). The presence of additives can mediate the amount of surfactant surface coverage obtained (110-129,175,206). It has been postulated that the architecture which adsorbed surfactant molecules can assume on conventional stationary phases can range from micellar, hemi-micellar, or admicellar to mono-,bi-, or multilayered, and/or other liquid crystalline-type structures (93,106,124,128,129,... 

There are a number of different factors which may affect the level of uptake and the energetics of adsorption from solution the chemistry and electrical properties of the solid surface and the molecular/micellar/polymeric structure of the solution must all be taken into account. Whenever possible, a study of both adsorption isotherms and enthalpies of displacement is worthwhile, but it is often necessary to complement these measurements with others including electrophoretic mobilities, FI7R spectra-and various types of microscopy. 

Bijsterbosch, H.D. Stuart, M.A.C. Fleer, G.J. Adsorption kinetics of diblock copolymers from a micellar solution on silica and titania. Macromolecules 1998, 31, 9281-9294. lijima, M. Nagasaki, Y. Okada, T. Kato, M. Kataoka, K. Core-polymerized reactive micellesm from heterotelechelic amphiphilic block copolymers. Macromolecules 1999, 32, 1140-1146. 

Figure 18.12 Representation of the adsorption process from a micellar solution.

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