Non-ideal surface

In reality, solid surfaces are never truly, flat and homogeneous, as assumed in the derivation of Young s equation. Deviation from ideality due to surface roughness and chemical inhomogeneity will now be considered. 

Surface roughness can change the wetting phenomena in two ways. First, roughness will increase the area of contact between solid and liquid. If 

If the liquid resides completely on surface A the contact angle will he 9y- However, if additional liquid is added to the droplet, the triple-point junction will move to the left until it reaches the point N, where the contact angle will still be 6 y and the left-most portion of the liquid/vapor 

Under this condition 0y is established on surface B and the junction can proceed as more liquid is added. 

Conversely, if the junction lies on surface B, e.g. at position 4, and liquid is removed from the droplet, the junction will move up the surface until it reaches position 3. Now the receding junction will be pinned at N until sufficient liquid has been removed to rotate the liquid/vapor interface to position 2. Thus the contact angle on surface B will vary from 6 y to 6 Min, according to 

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An important topic which we have not dealt with at all is the simulation of adsorption on non-ideal surfaces - such as surfaces containing steps , point impurities , etc. 

Such fundamental knowledge about the microscopic processes on the gas-solid interface is also necessary for optimization of many catalytic processes. A statistical mechanical approach, which enables the solution of the many-body problem constituted by the adsorbate layer on the catalytic surface, is essential in the case when lateral interactions between adatoms and molecules are significant. In such cases, non-ideal surface adlayer mixing is often important and the adsorbates form islands on the surface. Hence, microscopic simulations of catalytic processes are necessary to develop an ab-initio approach to kinetics in catalysis. 

Figure 3.14. Dependence of reaction rate on coverage for non-ideal surfaces.

In a similar fashion as for the two-step sequence on non-ideal surfaces, the reaction rate is obtained by multiplication of eq. (7.131) by the distribution function with further integration in the region of medium coverage. Here we present only the result of such treatment, which is an extension of eq. (7.80). 

Assuming ideality of the solution bulk, the equation of state for a non-ideal surface layer can be obtained from Eq. (2.14)... 

This implies that a smaller molecule will expel a larger one from the surface when their total concentration is increased at constant Ci/C2. Thus, a two-dimensional solution treatment which expresses the chemical potentials of the surface layer components by means of Eq. (2.7) enables us to derive equations of state and adsorption isotherms at fluid interfaces depending on the system considered (ideal or non-ideal surface layer, single surfactant or mixture of... 

Lucassen-Reynders). For non-ideal surface layers the following equation of state is obtained... 

The equation of state and adsorption isotherm for a non-ideal surface layer of two surfactants with the same molar areas are Eq. (3.30) and... 

The simplest systems have involved the release of sorbate from coated paper or from polymeric coating (Ghosh et al., 1977 Torres et al., 1985). The latter researchers applied a high surface concentration of sorbate to a model intermediate moisture food using an edible coating of zein as a reservoir. From measurements of the diffusion coefficients of sorbic acid in the coating, and in the food, they concluded that zein was a suitable coating to deliver and maintain the necessary antioxidant level. Non-ideal surface characteristics of the food limited the precision of the results. 

On a non-ideal surface, the static contact angle turns out not to be imique. If, for instance, we inflate a drop (Figure 3.1a), the contact angle 6 can exceed 6e without the line of contact moving at all. Eventually, 6 reaches a threshold value 6a beyond which the line of contact finally does move. 9a is referred to as the advancing angle. 

In this chapter the phenomenon of wetting has been described. The fundamental equations have been developed for the case of non-reactive wetting on ideal perfectly smooth surfaces. The complications introduced by non-ideal surfaces, including rough surfaces and heterogeneous surfaces have been described. Finally, the effects of reactive wetting have been introduced. 

The general conclusions on the thermodynamic restrictions for empty routes are also vahd in the case of surface nonuniformity or appearance of lateral interactions in the adsorbed layer. For the non-ideal surfaces when the nonlinearity of macroscopic rate laws manifests itself, the rate constants of adsorption and desorption depend on surface coverage because of lateral interactions. Imagine that in the reaction mechanism there are steps of types t AZ + Z products and AZ + BZproducts. The reaction rates for steps of type i and j could be given by the following expressions ... 

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