Electrostatic retardation of adsorption

From the theoretical point of view a similarity exists between electrostatic retardation of ion transport and coagulation retardation, known as slow coagulation (Fuchs, 1934). Both phenomena arise from electrostatic repulsion caused by the existence of the diffuse part of the DL. In the slow coagulation theory, the electric field if the DL is derived from the Gouy-Chapman model (cf. Chapter 2). This model does not consider a deviation of the diffuse layer from equilibrium. Initially, the same simplification was used by Dukhin et al. (1973) in describing the DL effect on the electrostatic retardation of adsorption. 

Electrostatic retardation of adsorption kinetics of surfactant anions is expected in the case... 

The calculation of the flow of surfactant anions to the surface of a bubble can be performed under the condition of electrostatic retardation of adsorption kinetics. It follows from Eq. (7.30),... 

The limiting stage is the overcoming of the electric double layer, with electrostatic retardation of adsorption, the value of j is given by Eq. (7.36). 

Now the condition under which, electrostatic retardation of adsorption kinetics of surfactant anions appears at the main part of the siuface, is determined. Substituting the estimate for T from Eq. (9.34) into (7.26) and (7.29) yields the following condition. 

An estimate of the total desorption flow from the surface of a strongly retarded region in the neighbourhood of the rear pole of the bubble is derived as follows. When electrostatic retardation of adsorption-desorption kinetics does not exists, the results of Chapter 8 [Eq. (8.145)] can be applied. For ionic surfactant, the equation for surface tension variation somewhat differs from that for non-ionic surfactant. With regard to these differences, the following estimate of desorption flow results. 

At a given electrostatic retardation of adsorption-desorption kinetics of the surfactants, its approximate anion flux to the bubble surface is... 

The electrostatic retardation of the adsorption kinetics of ionic siufactants is one of these nonequilibrium surface phenomena to be described on the basis of this physical model, consisting of the electrochemical macro-kinetic equations used in theoretical and colloid electrochemistry. This approach describes the flux of ions in terms of their spatial distribution. The equations were first developed by Overbeek (1943) and later proved to be valid for the theory of different... 

Fuchs theory is restricted to a quasi-steady process, where the time dependence is neglected. The quasi-steady state approach of electrostatic retardation in adsorption will be described in Section 7.3. 

First models of electrostatic retardation of ion adsorption used the boundary condition of slow coagulation (Dukhin et al. 1973, Glasman et al. 1974, Michailovskij et al. 1974, Dukhin et al. 1976). These models are discussed in Section 7.5. In later models the derivation of the theory was performed by expressing c(0,t) through c , which is a more general case (Dukhin et al. 1983, 1990). This approach is described in detail in the following Section 7.2. The more complicated non-steady ion adsorption is considered in Section 7.3. 

It follows from (7.26) that at small Stem potentials at the bubble surface, the ratio K(vj7s,) / 6 is a quantity of the order of (1/(k8d), i.e., it is much less than unity. The new effect, the electrostatic retardation of kinetics of surfactant anions adsorption becomes visible when the dimensionless parameter exp(-v /sj) equals or exceeds (kSq). ... 

The aim of this section is to consider the dynamic adsorption layer structure of ionic surfactant on the surface of rising bubbles. Results obtained in the previous section cannot be transferred directly to this case. The theory describing dynamic adsorption layers of ionic surfactant in general should take into accoimt the effect of electrostatic retardation of the adsorption kinetics of surfactant ions (Chapter 7). The structure of the dynamic adsorption layer of nonionic surfactants was analysed in the precedings section in the case when the adsorption process is kinetic controlled. In this case, it was assumed that the kinetic coefficients of adsorption and desorption do not depend on the surface coverage. On the other hand, the electrostatic barrier strongly depends on F , and therefore, the results of Section 9.1. cannot be used for the present case.. 

The first factor in the left-hand side is greater than unity and the second one is less than unity. Hence, the realization of conditions for the dynamic adsorption layer formation is possible both with electrostatic retardation of the adsorption and without, depending on the system parameters. Note that condition (9.35) can be fulfilled only for multiple-charged anions. Conditions considered in the present section correspond to the situation where the dynamic... 

Therefore, the first necessary condition of realization of the regime under consideration has the same form as in the case of a non-ionic surfactant [Eq. (8.103)]. To derive the second condition, the bubble surface velocity v (0) has to be estimated. In the absence of electrostatic retardation of surfactant anion adsorption kinetics, the estimate derived in Section 8.6. is valid and the condition is identical to (8.105). 

Electrostatic retardation of surfactant anion adsorption is realized in the region above the dotted lines. 

Diffusion of the products of reaction away from the surface is slow enough to be important if there is attraction due either to electrostatic or to adsorption forces. The first observation of this effect seems to be that of Alexander and Rideal (30), who found that in the alkaline hydrolysis of trilaurin the soap produced was liable to remain in the film. This complicated the kinetics of the reaction to such an extent that it was found necessary to work under conditions such that the laurate ions were more rapidly expelled. Without this precaution, the negative potential which built up on the interface considerably retarded the reaction by offering a barrier to the approaching catalytically active hydroxyl ions. 

Since this book is dedicated to the dynamic properties of surfactant adsorption layers it would be useful to give a overview of their typical properties. Subsequent chapters will give a more detailed description of the structure of a surfactant adsorption layer and its formation, models and experiments of adsorption kinetics, the composition of the electrical double layer, and the effect of dynamic adsorption layers on different flow processes. We will show that the kinetics of adsorption/desorption is not only determined by the diffusion law, but in selected cases also by other mechanisms, electrostatic repulsion for example. This mechanism has been studied intensively by Dukhin (1980). Moreover, electrostatic retardation can effect hydrodynamic retardation of systems with moving bubbles and droplets carrying adsorption layers (Dukhin 1993). Before starting with the theoretical foundation of the complicated relationships of nonequilibrium adsorption layers, this introduction presents only the basic principles of the chemistry of surfactants and their actions on the properties of adsorption layers. 

The adsorption of ionic surfactants as carrier of electrical charges leads to the built-up of a surface charge. The kinetics of adsorption is coupled with the formation of an electrical double layer at the interface. There is evidence that the electrical double layer can retard the adsorption flux of the surface active ions with an electrostatic barrier. 

If kinetic processes of adsorption or desorption were observed in time scales t lOO tg, it is difficult to distinguish between impurity effects and specific effects of the surfactant system, such as electrostatic retardation, phase transitions in adsorption layers, conformational changes, structure formations etc. 

The Manifestation of Electrostatic Retardation in Transient Adsorption processes... 

The non-steady diffusion of surfactant ions is a problem similar to the non-steady diffusion of non-ionic surfactant, which was described in Chapter 4. There is a specific distinction caused by the electrostatic retardation effect. The non-steady transport of ionic surfactants to the adsorption layer is a two-step process, consisting of the diffusion outside and inside the DL. 

For simplification, in the following an equilibrium between the adsorption layer and the subsurface is assumed. The retardation by the electric double layer can be considered as a process analogous to the kinetic retardation of molecular adsorption discussed in Section 4.4. With respect to the latter mechanism, the physical picture of the electrostatic retardation is clear, while the nature of the adsorption barrier, leading to a deviation from equilibrium between the surface and the subsurface, has multiple origins. 

In the following an estimate will be given to distinguish between electrostatic retardation and bulk diflusion as time-controlling steps of the adsorption process. 

To incorporate the electrostatic retardation effect into the adsorption-desorption exchange of matter at harmonically disturbed surfaces, the amount of ions is described by... 

On the basis of the Henry mechanism, given in Section 4.4, and the classification of stages of the adsorption process of the previous section, the simultaneous influence of electrostatic retardation and a specific barrier can be regarded for. To do so, the expression for c(0,t) given in Eq. (7.22) is inserted into the Henry rate equation (4.32), which leads to. 

In the presented theories of electrostatic retardation, very simple models are used to enable an analytical solution of the different problems and to clarify the physics of the mechanisms. The objective of further work is of course the generalisation of models with respect to the adsorption isotherm, content of background electrolyte, and ion transport properties. 

The importance of electrostatic retardation increases with the surface potential, i.e. with the adsorption surfactant molecules. Especially in some practical systems of high background electrolyte, only at densely packed adsorption layers the electrostatic retardation will set in. This state of adsorption has not been taken into consideration so far. With increasing background electrolyte concentration counterions build the Stem layer. The charge of the adsorption layer is compensated partially by the diffuse layer and the Stem layer (Eq. 2.5) which decrease with the increased amount of counterions in the Stem layer. Simultaneously, the Stem potential is lowered and the electrostatic retardation becomes less effective. This aspect was discussed already by Kretzschmar et al. (1980). Consequently, the electrostatic retardation can exist in NaCl solution while it can disappear under certain conditions in CaCl2 solutions. 

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