Adsorption kinetics model surfactant mixture

The adsorption kinetics of surfactant mixtures is a field rarely investigated. Systematic studies do not exist at all and therefore, we can give here only few information. As it was shown by the generalised model of Sutherland of Eq. (4.19) the adsorptions of the components of a mixture are independent at sufficiently low concentrations so that the dynamic surface tension y(t) can be calculated easily. The concentrations of the three compounds calculated for Fig. 4.34 differ... 

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. 

The aim of this chapter is to present the fundamentals of adsorption kinetics of surfactants at liquid interfaces. Theoretical models will be summarised to describe the process of adsorption of surfactants and surfactant mixtures. As analytical solutions are either scarcely available or very complex and difficult to apply, also approximate and asymptotic solutions are given and their ranges of application demonstrated. For particular experimental methods specific initial and boundary conditions have to be considered in these theories. In particular for relaxation theories the experimental conditions have to be met in order to quantitatively understand the obtained results. In respect to micellar solutions and the impact of micelles on the adsorption layer dynamics a detailed description on the theoretical basis as well as a selection of representative experiments will follow in Chapter 5. 

As it was shown in Chapter 2 there are thermodynamic models that allow a quantitative description of the adsorption behaviour of surfactant mixtures in the equilibrium state. Using such isotherms a correct description of the adsorption kinetics is also possible, however, sophisticated numerical procedures are required as analytical solutions will not be available. 

The graph in Fig. 41 shows the dynamic surface tensions of a mixtured solution of CioDMPO and C14DMPO measured with the maximum bubble pressure method BPAl (O) and profile analysis tensiometer PATl ( ). The theoretical curves shown were calculated due to the adsorption kinetics model for surfactant mixtures discussed above (Miller et al. 2003). 

Most spraying processes work under dynamic conditions and improvement of their efficiency requires the use of surfactants that lower the liquid surface tension yLv under these dynamic conditions. The interfaces involved (e.g. droplets formed in a spray or impacting on a surface) are freshly formed and have only a small effective age of some seconds or even less than a millisecond. The most frequently used parameter to characterize the dynamic properties of liquid adsorption layers is the dynamic surface tension (that is a time dependent quantity). Techniques should be available to measure yLv as a function of time (ranging firom a fraction of a millisecond to minutes and hours or days). To optimize the use of surfactants, polymers and mixtures of them specific knowledge of their dynamic adsorption behavior rather than equilibrium properties is of great interest [28]. It is, therefore, necessary to describe the dynamics of surfeictant adsorption at a fundamental level. The first physically sound model for adsorption kinetics was derived by Ward and Tordai [29]. It is based on the assumption that the time dependence of surface or interfacial tension, which is directly proportional to the surface excess F (moles m ), is caused by diffusion and transport of surfeictant molecules to the interface. This is referred to as the diffusion controlled adsorption kinetics model . This diffusion controlled model assumes transport by diffusion of the surface active molecules to be the rate controlled step. The so called kinetic controlled model is based on the transfer mechanism of molecules from solution to the adsorbed state and vice versa [28]. 

The kinetics of adsorption from solutions of surfactant mixtures are described on the basis of a generalised Langmuir isotherm. The simultaneous adsorption leads to the replacement of less surface active compounds by those of higher surface activity, which are usually present in the bulk at much lower concentration. More general descriptions of the process are possible on the basis of the Frumkin and Frumkin-Damaskin isotherms, which include specific interfacial properties of the individual surface active species. Quantitative studies of such very complex models can be performed only numerically. 

The graphs shown in Fig. 4.35 are the dynamic surface tensions of three mixtures of CioDMPO and CmDMPO measured with the maximum bubble pressure method MPT2 (O) and ring tensiometer TE2 (O). Although there is a general theoretical model to describe the adsorption kinetics of a surfactant mixture, model calculations are not trivial and a suitable software does not exists. 

The equilibrium and dynamics of adsorption processes from micellar surfactant solutions are considered in Chapter 5. Different approaches (quasichemical and pseudophase) used to describe the micelle formation in equilibrium conditions are analysed. From this analysis relations are derived for the description of the micelle characteristics and equilibrium surface and interfacial tension of micellar solutions. Large attention is paid to the complicated problem, the micellation in surfactant mixtures. It is shown that in the transcritical concentration region the behaviour of surface tension can be quite diverse. The adsorption process in micellar systems is accompanied by the dissolution or formation of micelles. Therefore the kinetics of micelle formation and dissociation is analysed in detail. The considered models assume a fast process of monomer exchange and a slow variation of the micelle size. Examples of experimental dynamic surface tension and interface elasticity studies of micellar solutions are presented. It is shown that from these results one can conclude about the kinetics of dissociation of micelles. The problems and goals of capillary wave spectroscopy of micellar solutions are extensively discussed. This method is very efficient in the analysis of micellar systems, because the characteristic micellisation frequency is quite close to the frequency of capillary waves. 

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. 

Fainerman and Miller [35] found that displacement of an initially adsorbed surfactant by a second, more surface-active species allowed measurement of the desorption rate of the former. For example, competitive adsorption of sodium decyl sulfate and the nonionic Triton X-165 gave a desorption rate constant for the former of 40 s". Mul-queen and coworkers [36] recently developed a diffusion-based model to describe the kinetics of surface adsorption in multicomponent systems, based upon the Ward-Tor-dai equation. Experimental work with a binary mixture of two nonionic alkyl ethoxy-late surfectants [37] showed good agreement with the model, demonstrating a similar temporal adsorption profile to that found by Diamant and Andehnan [34],... 

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