Electrostatic retardation

Fig. 10. Photoeleotron spectrum of oxygen using the helium resonance line (21-21 e.v.) obtained with a magnetic electron energy analyser (May and Turner, unpublished work). Ionization energy increasing from left to right. The spectrum reveals four levels of ionization and the vibrational structure associated with each state of the ion can be clearly distinguished. This spectrum may be compared with that obtained using an electrostatic retarding field analyser (Al-Joboury et al., 1965).

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. 

In this book we are only concerned with the electrostatic repulsion aspect of the surface behaviour of charged surfactants, and then, as shown later, their electrostatic retardations effects. Such kinetic effects are in some cases decisive dynamic properties of a liquid interface and therefore significant for applications in colloid science and technology. 

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. 

To draw a clear picture of the physical mechanism of the electrostatic retardation effect any existence of additional non-electrostatic barriers, such as discussed in Section 4.4, or other mechanisms influencing the transfer of surfactant molecules between the subsurface and the interface, are avoided. Thus, the electrostatic retardation effect is considered under the assumption of local equilibrium between the subsurface, defined as the bulk layer adjacent to the interface (cf. Chapter 2), and the interface. 

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... 

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. 

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. 

The unknown function c(0,t) is expressed by the theory of electrostatic retardation, containing the bulk concentration c . 

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. 

Favourable conditions for the manifestation of electrostatic retardation effects are met in the exchange of ionic surfactants at surfaces under harmonic disturbances. This process is outlined in Section 7.4. 

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

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 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 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. 

Analysis of the two relations (7.51) and (7.52) allow favourable conditions for a manifestation of the electrostatic retardation effects at oscillating surfaces to be defined. At first, the diffusion layer thickness has to be small and decreases with increasing frequency. Secondly, the deviation from equilibrium during the oscillation process must be small, 8r 1. 

Under the condition a l the electrostatic retardation controls the periodic transport of the surfactant ions. During the period of the oscillation the diffusion layer thickness is even smaller than 8q and, therefore, Eq. (7.54) holds for the whole oscillation 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... 

From the analysis of this expression, comparison of the terms containing 8F, the condition can be derived at which the exchange of matter is prevented by electrostatic retardation. If the term on the right hand side of Eq. (7.57) is negligible, the exchange of matter does not influence the adsorbed amount of ions at the interface. For a harmonic deformation of the surface, the relation... 

Adsorption Kinetics Model, Taking Into Account the Electrostatic Retardation and a Specific Adsorption Barrier... 

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. 

As discussed already in Section 7.6. the transfer of molecules or ions from the subsurface to the interface can be controlled by another, specific barrier which does not coincide with the electrostatic retardation arising from the transport of ions through the electric double layer. The maximum of electrostatic repulsion is located at a distance to the interface approximately equal to the radius of the adsorbing macro-ions. 

The equation derived for the transport of surfactant ions through the DL describes the adsorption kinetics as a reversible process. The qualitatively new result in the theory of ionic adsorption kinetics is the incorporation of electrostatic retardation for both the adsorption and desorption process, which is of essential importance for processes close to equilibrium. Such a situation exists at harmonically disturbed surfaces, used in investigations of adsorption dynamics like the damping of capillary waves or oscillating bubbles. At sufficiently high frequencies the diffusion layer becomes very thin and the adsorption-desorption exchange is controlled only by the ion transport through the DL, i.e. by the electrostatic retardation. At... 

Any type of specific barriers hinder the adsorption/desorption exchange of ionic and nonionic surfactants between the subsurface and the adsorption layer. In contrast to these specific barriers the electrostatic retardation influences the exchange at the boundary between diffuse and diffusion layer. Thus, the effects of specific and electrostatic retardation do not overlap but multiply each other. This means, that the collective effect of both can be measurable even when the separate effects are insignificant. The amplification of one retardation by the other is quantitatively expressed in the present theory. Varying the electrostatic conditions by electrolyte concentration and pH changes systematic studies of specific barriers and electrostatic retardations can be performed. 

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 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. 

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... 

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