Surfaces in multicomponent systems

We assume that the surface is planar and horizontal and that the surface region extends from zi to Z2- We place a dividing plane at a location zo inside the surface region. The volume of each phase is assigned to be the volume that extends to the 

Rgure 5.19 A Typical Density Profile Through a Surface Region (Schematic). 

The thermodynamic variables of each phase are defined as though the phase were uniform up to the dividing plane. They obey all of the equations of thermodynamics without surface contributions. For phase I, 

Let us subtract Eq. (5.6-2) for phase I and for phase II from the expression for dG in the version of Eq. (5.5-3) that applies to a multicomponent system  

The surface tension y is an intensive variable, depending only on T, P, and the composition of the phases of the system. Although is not proportional to the size of the system, we assume that there is a contribution to G equal to so that Euler s theorem, instead of the version in Eq. (4.6-4), is 

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The situation becomes most complicated in multicomponent systems, for example, if we speak about filling of plasticized polymers and solutions. The viscosity of a dispersion medium may vary here due to different reasons, namely a change in the nature of the solvent, concentration of the solution, molecular weight of the polymer. Naturally, here the interaction between the liquid and the filler changes, for one, a distinct adsorption layer, which modifies the surface and hence the activity (net-formation ability) of the filler, arises. Therefore in such multicomponent systems in the general case we can hardly expect universal values of yield stress, depending only on the concentration of the filler. Experimental data also confirm this conclusion [13],... 

In multicomponent systems, large solutes with lower diffusivity polarize more and exclude smaller solutes from the membrane surface, decreasing their passage. Operation at the knee of the flex curve reduces this effect. 

Implies participation in multicomponent systems, generally involving also water, an alcohol, and a surface active agent, to produce a useful agent... 

When all the SE s of a solid with non-hydrostatic (deviatoric) stresses are immobile, no chemical potential of the solid exists, although transport between differently stressed surfaces takes place provided external transport paths are available. Attention should be given to crystals with immobile SE s which contain an (equilibrium) network of mobile dislocations. In these crystals, no bulk diffusion takes place although there may be gradients of the chemical free energy density and, in multicomponent systems, composition gradients (e.g., Cottrell atmospheres [A.H. Cottrell (1953)]). 

In addition to its capability of imaging the topography of polymer surfaces with virtually eliminated shear forces, intermittent contact (tapping) mode AFM, can also be useful to probe various surface properties, such as adhesive or surface mechanical properties. Thereby AFM can help to identify and quantify the abundance and distribution of the phases present in multicomponent systems. As shown already... 

To calculate thermodynamic equilibrium in multicomponent systems, the so-called optimization method and the non-linear equation method are used, both discussed in [69]. In practice, however, kinetic problems have also to be considered. A heterogeneous process consists of various occurrences such as diffusion of the starting materials to the surface, adsorption of these materials there, chemical reactions at the surface, desorption of the by-products from the surface and their diffusion away. These single occurrences are sequential and the slowest one determines the rate of the whole process. Temperature has to be considered. At lower substrate temperatures surface processes are often rate controlling. According to the Arrhenius equation, the rate is exponentially dependent on temperature ... 

In multicomponent systems, surface segregation of the constituent with the lowest surface free energy occurs. 

Even though these isotherms presumably account for nonuniform surfaces, they have primarily been developed for single adsorbing components. Thus, the rational extensions to interactions in multicomponent systems is not yet possible, as with the Langmuir isotherm. This latter point is important for our further applications, and so we essentially use only the Langmuir isotherms for developing kinetic rate expressions. However, not all adsorption data can be represented by a Langmuir isotherm, and this is still an unresolved problem in catalytic kinetics. 

Other groups have developed alternative models in order to explain the surface segregation in multicomponent systems, briefly discussed in the next part. However, it is outside the scope of this chapter to thoroughly describe the theoretical models developed in this topic but rather provide a simple overview of the main aspects involved in the surface segregation of polymer blend. Those readers interested in the theoretical approaches reported to understand the surface segregation phenomena are referred to the following references [18, 38 1]. 

Theories for adsorption equilibria in multicomponent systems are not as advanced as those for single component systems. This slow progress in this area has been due to a number of reasons (i) lack of extensive experimental data for multicomponent systems, (ii) solid surface is too complex to model adequately. However, some good progress has been steadily achieved in this area. 

Another potential difficulty with dynamic SIMS is that, in multicomponent systems, various elements may sputter at different rates. This will lead to segregation of the more slowly sputtering component at the surface. At steady state this surface segregation must exactly compensate for the lower sputtering rate, so that the ratio of sputtered ions will accurately reflect the composition of the material, but transient effects will occur before this steady state is reached. This is a problem if one is interested in the composition profile immediately beneath the surface. What can be done is to coat the sample with a thin, sacrificial layer of polymer (typically about 50 nm thick) steady state is then reached by the time etching has reached the sample... 

In multicomponent systems (e.g., surfactant solutions), surface tension gradients usually are due to adsorption-related phenomena or, where possible, to different rates of evaporation from the system (although simple temperature variations can also be important). If the system contains two liquid components of differing volatility, the more volatile liquid may evaporate more quickly from the LV interface, resulting in localized compositional—and therefore surface tension—differences. It is also commonly found that when two or more components are present, one will be preferentially adsorbed at the LV interface and lower ctlv of the system. If a surface-active component... 

The surface tension of water diminishes when a surfactant, even in small quantities, is added. Similarly, an adsorbed gas reduces the surface energy of a solid. The Gibbs equation provides a relation between surface tension and surface concentration in multicomponent systems. 

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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