Diffusion-controlled adsorption mechanism

Some consequences which result from the proposed models of equilibrium surface layers are of special practical importance for rheological and dynamic surface phenomena. For example, the rate of surface tension decrease for the diffusion-controlled adsorption mechanism depends on whether the molecules imdergo reorientation or aggregation processes in the surface layer. This will be explained in detail in Chapter 4. It is shown that the elasticity modulus of surfactant layers is very sensitive to the reorientation of adsorbed molecules. For protein surface layers there are restructuring processes at the surface that determine adsorption/desorption rates and a number of other dynamic and mechanical properties of interfacial layers. 

Calculations show that the model of a non-equilibrium surface layer is an alternative to kinetic-controlled adsorption models. On the basis of the purely diffusion-controlled adsorption mechanism the proper consideration of a non-equilibrium diffusion layer leads to a satisfactory agreement between theory and experimental data for various studied systems, systematically demonstrated for the short-chain alcohols [132], The non-equilibrium model is applicable in the concentration range from 10 to 10 mol/cm at different values of the Langmuir constant at- For l < 10 mol/cm a consideration of non-equilibrium layer effects is not necessary. For ai > 10 mol/cm and large surfactant concentration the Ay values calculated from the proposed theory do not compensate the discrepancy to the experimental data so that other mechanisms have to be taken into account. An empirical formula also proposed in [132] for the estimation of the non-equilibrium surface layer thickness leads to a better agreement with experimental data, however this expression restricts the validity of the non-equilibrium surface layer model as alternative to non-diffusional adsorption kinetics. 

For several non-ionic surfactants Fainerman and Miller [46] published dynamic surface tension data which can be interpreted in terms of a diffusion controlled adsorption mechanism easily. The experimental results obtained for different Triton solutions (octylphenyl poly -oxyethylene ether (C,4Hj 0(C2H40) H) with different numbers n of ethylene oxide groups Triton X-100 (n=10), Triton X-114 (n=11.4), Triton X-165 (n=16.5), Triton X-305 (n=30.5) and Triton X-... 

For a modelling of adsorption processes the well-known integro-differential equation (4.1) derived by Ward and Tordai [3] is used. It is the most general relationship between the dynamic adsorption r(t) and the subsurface concentration e(0,t) for fresh non-deformed surfaces and is valid for kinetic-controlled, pure diffusion-controlled and mixed adsorption mechanisms. For a diffusion-controlled adsorption mechanism Eq. (4.1) predicts different F dependencies on t for different types of isotherms. For example, the Frumkin adsorption isotherm predicts a slower initial rate of surface tension decrease than the Langmuir isotherm does. In section 4.2.2. it was shown that reorientation processes in the adsorption layer can mimic adsorption processes faster than expected from diffusion. In this paragraph we will give experimental evidence, that changes in the molar area of adsorbed molecules can cause sueh effectively faster adsorption processes. 

Fig. 5.17. Dependence of the damping coefficient ot capillary waves on DACh concentration at the frequency of 200 Hz [168] curves are calculated according to Eq. (5.256) for the diffusion - controlled adsorption mechanism (solid line), for the mixed adsorption mechanism (dotted line), and for the barrier -controlled adsorption mechanism (dashed line).

For various non-ionic surfactants the dynamic surface tension data can be interpreted in terms of a diffusion controlled adsorption mechanism easily (Fainerman and Miller 1995). Some selected experimental results for different Triton solutions (C14H20O (C2H40)mH) with different numbers m of ethylene oxide groups are shown as a y(Vt) -plot. For all solutions we get a surface tension y(t) = Yo at t=0 which is the condition for the application of Eq. (46). 

The interfacial tension response to transient and harmonic area perturbations yields the dilational rheological parameters of the interfacial layer dilational elasticity and exchange of matter function. The data interpretation with the diffusion-controlled adsorption mechanism based on various adsorption isotherms is demonstrated by a number of experiments, obtained for model surfactants and proteins and also technical surfactants. The application of the Fourier transformation is demonstrated for the analysis of harmonic area changes. The experiments shown are performed at the water/air and water/oil interface and underline the large capacity of the tensiometer. 

We obtain a linear dependence with a slope of about — 2, which is exactly what was expected from the theory. Hence, we can conclude that at least in the short time range, until there is enough material adsorbed so that the surface tension starts to decrease, the controlling adsorption mechanism is diffusion. 

Besides the diffusion-controlled adsorption theory other mechanisms are presented, comprising transport processes in the bulk solution and transfer mechanisms from the subsurface to the interface (Chang Franses 1992). 

The quantitative analysis of the adsorption mechanism (cf Miller Kretzschmar 1991) shows a diffusion controlled adsorption over the whole concentration range with a slight change of the diffusion coefficient D with adsorption time and surfactant concentration. A detailed data analysis with butyl phenols of different chemical structure is in progress. 

The diffusion controlled adsorption model is the most useful one as it is at present the main basis for all particular adsorption kinetics theories. It has also been demonstrated that for most of the systems for which an adsorption barrier controlled mechanism was discussed surface active impurities had been detected. These impurities can simulate a kinetic controlled adsorption mechanism [53, 54, 55]. 

In diffusion-controlled adsorption models, one assumes that there is no activation energy barrier to the transfer of surfactant molecules between the subsurface and the surface [85]. Thus diffusion is the only mechanism needed in establishing adsorption equilibrium. The time required for the molecules to transfer from the bulk to the subsurface is much longer than the time required for equilibration between the surface and the subsurface. On the contrary, if the adsorption or desorption rate at the interface is slow or comparable to the diffusion rate, the adsorption process is significant. This model is called the mixed-kinetic adsorption model. This condition may depend not only on the properties of the system but also on the diffusion length and possibly on convection conditions. The diffusion-controlled model of Eqs. (3) and (4) have been given by Fainerman et al. [86,87]. 

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]. 

Limitations on neutron beam time mean that only selected surfactants can be investigated by OFC-NR. However, parametric and molecular structure studies have been possible with the laboratory-based method maximum bubble pressure tensiometry (MBP). This method has been shown to be reliable for C > 1 mM.2 Details of the data analysis methods and limitations of this approach have been covered in the literature. Briefly, the monomer diffusion coefficient below the cmc, D, can be measured independently by pulsed-field gradient spin-echo NMR measurements. Next, y(t) is determined by MBP and converted to F(0 with the aid of an equilibrium equation of state determined from a combination of equilibrium surface tensiometry and neutron reflection. The values of r(f) are then fitted to a diffusion-controlled adsorption model with an effective diffusion coefficient which is sensitive to the dominant adsorption mechanism 1 for... 

Separation through zeohte membranes proceeds through three different mechanisms (i) molecular sieving, (ii) diffusion-controlled permeation, (iii) adsorption-controUed permeation [7, 8]. Figure 10.5 gives examples of common zeohte separations that fall within each category. The simplest of the three is molecular... 

In weak-strong separations, one component does not strongly adsorb but has a high diffusivity the other component is slow but strongly adsorbs. In this case, the separation mechanism exhibited is either diffusion-controlled permeation or adsorption-controlled permeation, depending on the operating conditions [39]. 

A perspective based on kinetics leads to a better understanding of the adsorption mechanism of both ionic and nonionic compounds. Boyd et al. (1947) stated that the ion exchange process is diffusion controlled and the reaction rate is limited by mass transfer phenomena that are either film diffusion (FD) or particle diffusion (PD) controlled. Sparks (1988) and Pignatello (1989) provide a comprehensive overview on this topic. 

According to their analysis, if is zero (practically much lower than 1), then the liquid-film diffusion controls the process rate, while if tfis infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the so-called mechanical parameter represents the ratio of the diffusion resistances (solid and liquid film). The authors did not refer to any assumption concerning the type of isotherm for the derivation of the above-mentioned criterion it is sufficient to be favorable (not only rectangular). They noted that for >1.6, the particle diffusion is more significant, whereas if < 0.14, the external mass transfer controls the adsorption rate. 

The slope is indicative of the type of release mechanism. A slope of 0.5 indicates a diffusion-controlled release a slope of 1.0 indicates that a corrosion-related mechanism is operable.The diffusion release mechanism is characterized by surface adsorption, ion exchange, and migration. Chemical corrosion, or alteration of the silicate lattice, is characterized by hydroxyl attack on silicon or by hydrogen attack on bridging oxygens. 

A very important feature of chronopotentiometry is the characteristic variation in ix1/2 that occurs for certain electrode reactions when i is varied over a wide range by varying i. The behavior of ix1/2 can be effectively used to diagnose certain mechanisms of electrode reactions. Diagnostic curves for ix1/2 versus i are shown in Figure 4.4 for several mechanistic situations. A constant value of ix1/2 over a wide range of x (Fig. 4.4A) is characteristic of an uncomplicated, diffusion-controlled electrode reaction with no kinetic or adsorption phenomena at a planar electrode. 

The form of eqn. (204) is expected from both adsorption- and surface diffusion-controlled reactions and also from the site-blocking mechanism. Therefore, the agreement with this form of equation is of limited help in understanding the underlying mechanism of growth. This requires a detailed examination of the kinetics without inhibitors. 

---