Dynamic adsorption layer

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. 

Since the first work by Nikolov et al. [44] in 1981 on the possibility of coexisting states in a soluble surfactant monolayer, mainly qualitative discussions on this subject have been published [39, 45]. The systematic thermodynamic work by Fainerman then gives a new understanding of the surface state of soluble surfactants at liquid interfaces [46, 47, 48, 49] as reviewed recently [50, 51]. The impact of these new ideas on adsorption dynamics is immense and up to now has been started only. It appears to be possible to answer to many open questions still existing in the interpretation of surfactant adsorption layer dynamics, and even of protein layers. 

In the potential region where nonequilibrium fluctuations are kept stable, subsequent pitting dissolution of the metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption allows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. 

Miller, R., Fainerman, V.B., Makievski, A.V., Kragel, J., Grigoriev, D.O., Kazakov, V.N., Sinyachenko, O.V. (2000a). Dynamics of protein and mixed protein + surfactant adsorption layers at the water-fluid interface. Advances in Colloid and Interface Science, 86, 39-82. 

Another dynamic factor affecting the rate of diffusion transfer, mentioned long ago by Gibbs [9], is the elasticity of the surfactant monolayers which decreases the capillary pressure in small bubbles during their compression and increases it in large bubbles during their expansion. This effect is most pronounced in bubbles whose adsorption layers contain insoluble surfactants. Analysis of the influence of this factor on diffusion transfer has been reported in [486], However, no experimental verification has been performed so far. 

The dynamic origin of the adsorption layer which provides physical network junctions... 

The influence of hydrophilic Aerosil on the chain dynamics in the adsorption layer becomes evident with the help of comparison of solid-echo spectra for a series of filled PDMS samples containing different amounts of Aerosil as shown in Fig. 3 [21]. 

The Ti relaxation in this sample is characterized by two relaxation times, which indicate the dynamical heterogeneity of the sample. In order to assign the two T components to the chain units inside and outside the adsorption layer, solid-echo spectra at different stages of T] relaxation have been... 

Finally, the NMR and the dynamic mechanical study show that two regions are present in filled silicone rubbers above the Tg, which differ significantly in local chain mobility immobilized chain units adsorbed at the filler surface and mobile chain units outside the adsorption layer. The local chain motions outside the adsorption layer are similar to those for unfilled rubbers. Chain motions in the adsorption layer however are strongly restricted. The frequency of chain motions in the adsorption layer at 300 K is comparable to the fi-equency of chain motions in a crosslinked PDMS containing 3-4 elementary chain units between network junctions [26]. 

The thickness of the adsorption layer was estimated from the fraction of adsorbed chain units measured by means of h Ty, Tj and H relaxation studies [7, 8, 10, 12]. From the known value of the specific surface of Aerosil, its volume fraction in mixtures and the fraction of low mobile chain units at the Aerosil surface, the thickness of the adsorption layer is estimated assuming imiform coverage of the filler particles by a PDMS layer of constant thickness. This calculation leads to a value of about 0.8 run [7]. This value is increased by a factor 1.5-2, if a part of the filler surface will not be accessible for PDMS chains due to direct contacts between the primarily filler particles in aggregates [27]. Thus, the chain adsorption causes a significant restriction of local motions only in one or two monolayers adjacent to the filler surface. A similar estimation of the adsorption layer thickness has been obtained by other methods such as, e.g. dielectric experiment [27], adsorption study [3], the viscosity of the boundary layer for silicon liquids at the surface of a glass [5], molecular dynamics simulations [6], and C NMR relaxation experiments [22]. 

Summarizing this section it can be stated that the adsorption bonds in filled PDMS have a dynamic origin. With increasing temperature, the frequency of adsorption-desorption processes in the adsorption layer increases and the adsorption-desorption equilibrium shifts to the chain desorption. At room temperature, the lifetime for the dimethylsiloxane chain units in the adsorption state is very short chain units adhere to the filler surface only for tens of microseconds. 

Fast relaxation processes ( , 0) show a Williams-Landel-Ferry (WLF) type temperature dependence which is typical for the dynamics of polymer chains in the glass transition range. In accordance with NMR results, which are shown in Fig. 9, these relaxations are assigned to motions of chain units inside and outside the adsorption layer (0 and , respectively). The slowest dielectric relaxation (O) shows an Arrhenius-type behavior. It appears that the frequency of this relaxation is close to 1-10 kHz at 240 K, which was also estimated for the adsorption-desorption process by NMR (Fig. 9) [9]. Therefore, the slowest relaxation process is assigned to the dielectric losses from chain motion related to the adsorption-desorption. 

Considerable effort has been spent to explain the effect of reinforcement of elastomers by active fillers. Apparently, several factors contribute to the property improvements for filled elastomers such as, e.g., elastomer-filler and filler-filler interactions, aggregation of filler particles, network structure composed of different types of junctions, an increase of the intrinsic chain deformation in the elastomer matrix compared with that of macroscopic strain and some others factors [39-44]. The author does not pretend to provide a comprehensive explanation of the effect of reinforcement. One way of looking at the reinforcement phenomenon is given below. An attempt is made to find qualitative relations between some mechanical properties of filled PDMS on the one hand and properties of the host matrix, i.e., chain dynamics in the adsorption layer and network structure in the elastomer phase outside the adsorption layer, on the other hand. The influence of filler-filler interactions is also of importance for the improvement of mechanical properties of silicon rubbers (especially at low deformation), but is not included in the present paper. 

A consideration of the adsorption kinetics is very important m an estimation of the effectiveness of surfactants under the dynamic conditions of emulsion polymerization. In a stalagmometric study of dynamic and static adsorption of emulsifiers of various structure at the air-water interface, it was established that adsorption values of micelle-forming sui c-tants differ significantly in the period of drop formation (Nikitina et ai, 1961). This was explained by the considerable period needed for establishment of adsorption equilibrium connected with the kinetics of adsorption layer formation. The authors concluded tirat for usual concentrations of surfactant solutions the period of estaUishm t of adsorption equilibrium can be taken as equal to 2 min. Figure 2 shows the adsorption isotherms of... 

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

The use of an evanescent wave to excite fluorophores selectively near a solid-fluid interface is the basis of the technique total internal reflection fluorescence (TIRF). It can be used to study theadsorption kinetics of fluorophores onto a solid surface, and for the determination of orientational order and dynamics in adsorption layers and Langmuir-Blodgett films. TIRF microscopy (TIRFM) may be combined with FRAP ind FCS measurements to yield information about surface diffusion rates and the formation of surface aggregates. 

G. Kretzschmar and R. Miller. Dynamic Properties of Adsorption Layers of Amphiphilic Substances at Fluid Interfaces, Adv. Colloid Interface Set 36 (1991) 65. See also R. Miller, G. Kretzschmar, Ibid 37 (1991) 97. 

The most frequently used parameter to characterize the dynamic properties of liquid adsorption layers is the dynamic surface tension (a time-dependent quantity). Various techniques are available to measure Y y as a function of time (which ranges from a fraction of a millisecond to minutes and hours or even days). 

Here is the activity of the surfactant molecule in the subsurface layer is scaled with the volume per molecule in a dense (saturated) adsorption layer, Vj = where bj is interpreted as the thickness of the adsorption layer, or the length of an adsorbed molecule. In terms of the subsurface activity, Equation 5.9 can be applied to ionic surfactants and to dynamic processes. In the simplest case of nonionic surfactants and equilibrium processes, we have Cj, where Cj is the bulk surfactant concentration. 

Miller R, Fainerman VB, Aksenenko EV, Makievski AV, Kraegel J, Liggieri L, Ravera F, Wuestneck R, and Loglio G (2000) "Surfactant Adsorption Kinetics and Exchange of Matter for Surfactant Molecules with Changing Orientation within the Adsorption Layer" in Emulsion, Foams, and Thin Films, Mittal and Kumar Editors, Ch. 18, Marcel Dekker, pp. 313-327 Miller R, Fainerman VB, Makievski AV, Leser M, Michel M and Aksenenko EV (2004) Determination of Protein Adsorption by Comparative Drop and Bubble Profile Analysis Tensiometry. Colloids Surfaces B 36 123-126 Neumann AW and Spelt JK Eds., Applied Surface Thermodynamics, Surfactant Science Series, Vol. 63, Marcel Dekker Inc., New York, 1996 Noskov B and Logho G (1998) Dynamic surface elasticity of surfactant solutions. Colloids Surfaces A 143 167-183... 

Elastic properties of interface. The surface tension of the solution interface is less than the surface tension of the pure solvent interface. The difference is equal to the surface pressure of surfactant molecules [9, 109, 414], This does not contradict the fact that the films forming the skeleton of the foam possess increased strength and elasticity. The equilibrium surface layer of a pure liquid is ideally inelastic. Under the action of external forces, the free surface increases not because of extension (an increase in the distance between the molecules in the near-surface layer) but because new molecules are coming from the bulk. A decrease in the equilibrium tension as some amount of surfactant is added does not mean that the elasticity of the surface decreases, since this surface does not possess elastic properties under slow external actions. Nevertheless, we point out that even surfaces of pure liquids possess elastic properties [465] (dynamic surface tension [232]) under very rapid external actions whose characteristic time is less than the time of self-adsorption relaxation of the surface layer. This property must not depend on the existence of an adsorption layer of surfactant. At the same time, surfactants impart additional elastic properties to the surface both at low and high strain rates. 

The first term on the right-hand side determines the surface (equilibrium or dynamic) tension a, and the second term is the modulus of elasticity of the adsorption layer... 

Equation of dynamics of the adsorption layer. In the case of foams, the main interface consists of films in which the liquid is virtually stagnant. The film surface is even more constrained. Therefore, Eq. (7.3.1) describes the molecular (or Brownian) diffusion in the bulk of liquid, and Eq. (7.3.2), under the additional assumption that the specific adsorption is rapidly smoothed along the interface (i.e., T = r(t)), describes the dynamics of a localized (or ideal) adsorption layer [119, 250,511] ... 

Dynamics of the adsorption layer for the foam film. Taking into account the fact that in actual foam of high multiplicity the film thickness h usually does not exceed 10 micrometers, the time td = h2/D of diffusion relaxation in the film is a fraction of a second, and hence the concentration is equalized throughout the film thickness almost instantaneously. For this reason, we can omit the subscripts S on Cs indicating the corresponding surface and assume that... 

Here D is the diffusion coefficient, t is the time, t is a dummy integration variable. Using Equation (8), respective T(t) dependencies can be obtained, while the Equations (l)-(7) serve as boundary condition for the diffusion model. This set of equations yield a quasi-equilibrium diffusion model which means that at a given surface pressure the composition of the surface layer under dynamic conditions is equal to that in the equilibrium. Another regime of adsorption kinetics, called kinetic model, can also be described by assuming compositions of the adsorption layer that can differ from the equilibrium state. The deviation of the adsorption layer from the equilibrium composition is the result of the finite rate of the transition process between the adsorption states. In case of two adsorption states we have6... 

Dynamic properties of interfaces have attracted attention for many years because they help in understanding the behaviour of polymer, surfactant or mixed adsorption layers.6 In particular, interfacial rheology (dilational properties) is crucial for many technological processes (emulsions, flotation, foaming, etc).1 The present work deals with the adsorption of MeC at the air-water interface. Because of its amphiphilic character MeC is able to adsorb at the liquid interface thus lowering the surface tension. Our aim is to quantify how surface active this polymer is, and to determine the rheological properties of the layer. A qualitative and quantitative evaluation of the adsorption process and the dilata-tional surface properties have been realised by dynamic interface tension measurements using a drop tensiometer and an axisymmetric drop shape analysis. 

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. 

Adsorption isotherms can be applied to any surface. In the following we focus our attention on surfaces covered with adsorption layers under dynamic conditions, the kinetics of adsorption and desorption of surfactants to and from soluble adsorption layers for example. Another phenomenon is the spread of surfactant molecules tangential to the surface that effect takes place if the adsorption layer is inhomogeneous (cf. Fig. 1.1). 

Adsorption Dynamics and Dynamic Adsorption Layers. Qualitative... 

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