Adsorption kinetics of ionic surfactants

As shown in paragraph 4.2.6. the adsorption process of ionic surfactants is much more complicated that that of a nonionic one. Although ionics are widely used in practical applications, there are not many experimental data on their adsorption dynamics. The reason maybe the lack of quantitative theories to describe the effect of the ionic charge on the adsorption process. 

As an example the dynamic surface tensions of three SDS solutions are given in Fig. 4.33 measured in presence of 0.5 M NaCl. The presence of the electrolyte makes the alkyl sulphate more surface active than in pure water (cf paragraph 2.7.2. and Chapter 3). 

The analysis of the kinetic data was performed on the basis of the diffusion-controlled model, using the Langmuir and the aggregation isotherm, given by Eq. (2.16) and Eqs. (2.107) -(2.111), respectively. As one can see, the agreement with the theory is not satisfactory. The models developed mainly by the Bulgarian school [33] requires extensive numerical calculations so that its application to experimental data will be possible only after the elaboration of effective computer programmes. 

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In an approximate relation of the equilibrium difhise layer, the characteristic time T, of adsorption kinetics of ionic surfactants is estimated from... 

The ratio Tj/Tj characterises the role of a non-equilibrium DL on the adsorption kinetics of ionic surfactants. If for example vj7s,g 8-10, z=2 and C(, Cj the deviation of c(x, t) from equilibrium can retard the adsorption kinetics by two orders of magnitude. However, an addition of electrolyte can suppress this effect. 

Experimental Investigations of Adsorption Kinetics of Ionic Surfactants... 

Systematic investigations of the adsorption kinetics of ionic surfactants does not exist. In comparison to nonionics very small attention was paid to the peculiarities of ionic surfactants adsorption. Therefore, a quantitative comparison of the developed theory with experimental... 

In the models described in Sections 7.2. through 7.5., equilibrium between the adsorption layer and the adjacent subsurface is assumed. A generalisation, taking into account a Henry transfer mechanism as the relation between surface and subsurface concentration (cf Section 4.4), is given in Section 7.6. The special problems connected with the adsorption model of ionic surfactants as well as macro-ions is discussed in Sections 7.7. and 7.8. and an attempt to solve the boundary value problem numerically is demonstrated in Section 7.9. The few experimental results on ionic adsorption kinetics are reported in Section 7.10. 

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 adsorption kinetics of a surfactant to a freshly formed surface as well as the viscoelastic behaviour of surface layers have strong impact on foam formation, emulsification, detergency, painting, and other practical applications. The key factor that controls the adsorption kinetics is the diffusion transport of surfactant molecules from the bulk to the surface [184] whereas relaxation or repulsive interactions contribute particularly in the case of adsorption of proteins, ionic surfactants and surfactant mixtures [185-188], At liquid/liquid interface the adsorption kinetics is affected by surfactant transfer across the interface if the surfactant, such as dodecyl dimethyl phosphine oxide [189], is comparably soluble in both liquids. In addition, two-dimensional aggregation in an adsorption layer can happen when the molecular interaction between the adsorbed molecules is sufficiently large. This particular behaviour is intrinsic for synergistic mixtures, such as SDS and dodecanol (cf the theoretical treatment of this system in Chapters 2 and 3). The huge variety of models developed to describe the adsorption kinetics of surfactants and their mixtures, of relaxation processes induced by various types of perturbations, and a number of representative experimental examples is the subject of Chapter 4. 

Although large number of studies have been reported on the equilibrium adsorption of ionic surfactants at the interfaces, very little attention has been paid to the adsorption kinetics. Only a few attempts have been made to follow the time evolution of the process from the initial adsorption to the equilibrium configuration and to understand the role of the diffusion [24,25,31]. 

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. 

The theoretical models proposed in Chapters 2-4 for the description of equilibrium and dynamics of individual and mixed solutions are by part rather complicated. The application of these models to experimental data, with the final aim to reveal the molecular mechanism of the adsorption process, to determine the adsorption characteristics of the individual surfactant or non-additive contributions in case of mixtures, requires the development of a problem-oriented software. In Chapter 7 four programs are presented, which deal with the equilibrium adsorption from individual solutions, mixtures of non-ionic surfactants, mixtures of ionic surfactants and adsorption kinetics. Here the mathematics used in solving the problems is presented for particular models, along with the principles of the optimisation of model parameters, and input/output data conventions. For each program, examples are given based on experimental data for systems considered in the previous chapters. This Chapter ean be regarded as an introduction into the problem software which is supplied with the book an a CD. 

In the case of ionic surfactants the existence of a diffuse EDL essentially influences the kinetics of adsorption. The process of adsorption is accompanied by a progressive increase in the surface-charge density and electric potential. The charged surface repels the incoming surfactant molecules, which results in a deceleration of the adsorption process (54). Theoretical studies on the dynamics of adsorption encounter difficulties with the nonlinear set of partial differential equations, whieh deseribes the electrodiffusion process (55). 

We turn to the more complicated but important problem of ionic surfactant adsorption, and start with the salt-free case where strong electrostatic interactions are present. In Fig. 3 we have reproduced experimental results published by Bonfillon-Colin et al. for SDS solutions with (open circles) and without (full circles) added salt [13]. The salt-free ionic case exhibits a much longer process with a peculiar intermediate plateau. Similar results were presented by Hua and Rosen for DESS solutions [21]. A few theoretical models were suggested for the problem of ionic surfactant adsorption [22-24], yet none of them could produce such dynamic surface tension curves. It is also rather clear that a theoretical scheme such as the one discussed in the previous section cannot fit these experimental results. On the other hand, addition of salt to the solution screens the electrostatic interactions and leads to a behavior very similar to the non-ionic one. We shall return to this issue in Section 4. We thus infer that strong electrostatic interactions affect drastically the adsorption kinetics. Let us now study this effect in more detail. We follow the same lines presented in the previous section while adding appropriate terms to account for the additional interactions. 

The drop shape method is possibly the most useful one for the investigation of the adsorptive transfer, i.e. the adsorption kinetics at the interface between two liquid phases containing the surfactant from the partition equilibrium. This phenomenon is particularly significant when situations far from the partition equilibrium are considered, in systems characterised by a high solubility of the surfactant in the recipient phase or by a large solubility of the surfactant in both phases. The latter case represents a typical situation for many types of ionic surfactants in water-oil and water-alkane systems, as demonstrated by the partition coefficients measured for various solvents [52, 53, 54, 55, 56]. 

More recently, this topic has been revisited by Daikhin and Urbakh [88] who presented a kinetic description of ionic surfactant transfer across an ITIES that includes the charging of the interface, adsorption, and transfer as well as characteristics of the electrical circuit. This model showed that the irregular current oscillations are due to a dynamic instability induced by the interplay between the potential-dependent adsorption and direct transfer across the interface. In particular, this model showed that current anomalies occur in a potential range close to the standard ion-transfer potential. 

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. 

The effect of adsorption of phospholipids [57-59] and non-ionic surfactants [60-62] on ET kinetics has been investigated. These studies would shed light on the ET mechanisms in biological systems. 

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... 

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. 

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). 

To get the main idea of the charge effect on adsorption kinetics, it is sufficient to consider an aqueous solution of a symmetric (z z) ionic surfactant in the presence of an additional indifferent symmetric (z z) electrolyte. When a new interface is created or the equilibrium state of an interfacial layer disturbed a diffusion transport of surface active ions, counterions and coions sets in. This transport is affected by the electric field in the DEL. According to Borwankar and Wasan [102], the Gouy plane as the dividing surface marks the boundary between the diffuse and Stem layers (see Fig. 4.10). When we denote the surfactant ion, the counterion and the coion, respectively, with the indices / = 1, 2 and 3, the transport of the ionic species with valency Z/ and diffusion coefficient A, under the influence of electrical potential i, is described by the equation [2, 33] ... 

Besides this bulk phase elfects surfactants will adsorb at the liquid-liquid interface. Their influence on mass transfer may then be on different mechanism. A blocking effect of adsorption layers in a diffusional transport regime is well known and results in a reduction of mass transfer [54-57] and even Marangoni instabilities [58,59] are found. However, in the kinetical mass-transfer regime, both an enhancement and retartion of mass transfer [59] is with Gibbs surfactant layers. With extracting ionic species, ionic surfactants will induce an electrostatic double layer, which can be related to the -potential. As a result, there exists, in addition to the chemical potentials, an... 

Abstract We review a new theoretical approach to the kinetics of surfactant adsorption at fluid-fluid interfaces. It yields a more complete description of the kinetics both in the aqueous solution and at the interface, deriving all equations from a free-energy functional. It also provides a general method to calculate dynamic surface tensions. For non-ionic surfactants, the results coincide with previous models. Non-ionic surfactants are shown to usually undergo diffusion-limited adsorption, in agreement with the experiments. Strong electrostatic interactions in salt-free ionic surfactant solutions are found to... 

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