Effect of Surface Inhomogeneities

The energy to move the interface for a distance, dx, on the solid surface can be written similar to equation (5.16) as 

It may be noted that both material 1 and material 2 participate in work done due to the smaller size of heterogeneities compared to the interaction distance between liquid molecules. The equilibrium is obtained for minimum value of E. Thus, on simplification, we have 

This is known as Cassie Baxter relation. The Teflon layer when deposited on a rough substrate may be porous and inhomogeneous. Hence, the wetting parameter gets modified according to Cassie-Baxter relation, and the gain in hydrophobicity is not as significant as expected. 

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Effect of Surface Inhomogeneity on Ion Penetration into the Pores during Double-Layer Charging/Discharging... 

Self-Poisoning and Aging of Pd-Ag/Al203 in Semi-Hydrogenation of 1,3-Butadiene Effects of Surface Inhomogeneity Caused by Hydrocarbonaceous Deposits... 

Czamecki J (1985) The effects of surface inhomogeneities on the interactions in colloidal systems and colloid stability. Adv Colloid Interface Sci 24 283-319. doi 10.1016/0001-8686 (85)80035-X... 

Scattering techniques have been widely applied to the study of the solid-liquid interface at high resolution. However, such measurements obtain data in frequency space and are thus inherently averaged values, which provide no information on the effect of surface inhomogeneities or defects. Nevertheless such techniques have been extensively applied to investigate the binding of water molecules in the interfacial region. While this can provide information about the nature, orientation, and density of surface... 

M) were typically used for such a comparison to eliminate the influence of possible differences in the inner-layer capacities. However, C of different solid metals, as well as of liquid Ga, In(Ga), and Tl(Ga) alloys have shown such a large variation that this approach can hardly be considered as appropriate. It should be noted that the error in C, which for solid electrodes is much higher than for liquid electrodes, increases with the decrease ofcei further, as shown later (Section II.2 (iv)), the effects of surface crystallographic inhomogeneity also prove especially appreciable.24 67 74... 

It must be stressed that eqn. (72) represents an ideal desorption process, where both v and Ed are coverage-independent parameters. Unfortunately, very few systems behave in this ideal fashion desorption is the reverse process of adsorption and, as has been described above for adsorption, several properties of the adlayer severely affect the kinetics of the basic desorption process. Thus, in the following sections, the effects on desorption kinetics of surface inhomogeneity, changes in desorption mechanism, precursor states and lateral interactions between adspecies, will be considered. The effects which these parameters have are considerable... 

The simplest interpretation of the compact-layer capacitance is represented by the Helmholtz model of the slab filled with a dielectric continuum and located between a perfect conductor (metal surface) and the outer Helmholtz plane considered as the distance of the closest approach of surface-inactive ions. Experimental determination of its thickness, zh, may be based on Eq. (12). Moreover, its dielectric permittivity, h, is often considered as a constant across the whole compact layer. Then its value can be estimated from the values of the compact-layer capacitance, for example, it gives about 6 or 10 (depending on the choice of zh) for mercury-water interface, that is, a value that is much lower than the one in the bulk water, 80. This diminution was interpreted as a consequence of the dielectric saturation of the solvent in contact with the metal surface, its modified molecular structure or the effects of spatial inhomogeneity. The effective dielectric permittivity of the compact layer shows a complicated dependence on the electrode charge, which cannot be explained by the simple hypothesis of the saturation effects on one hand or by the unperturbed bulk-solvent nonlocal polarizability on the other hand. 

In an attempt to choose an adequate treatment, the predictions for both models were compared with experimental data for PC samples of various metals. Qualitatively the conclusions of the model of independent electrodes turned out to be in agreement with experimental data for such metals as Ag, Au, Cu and so on, see reviews in Ref [20, 34], contrary to the failure of the common diffuse layer (CDL) model, Eq. (36a). However, in quantitative terms the effects of crystallographic inhomogeneity were smaller than predicted by the model based on Eq. (34). Eor example, the capacitance at the minimum, for PC Ag diminishes more rapidly than in its theoretical estimates. The experimental slope of the PZ plots calculated with no account for the surface heterogeneity effects is close to 1 for Bi, within a very wide range of the concentration, in contrast to the model analysis. The value of R found from the same plot is close to 1 for some PC Ag electrodes in rather concentrated solutions. 

ANS Yes, that is correct. The potentials on both the epicardium and the surface are determined by the sources and by the effects of the inhomogeneities throughout the entire volume conductor. 

With recent progress in micro- and nanofluidics, new interest has arisen in determining forms of hydrodynamic boundary conditions. In particular, advances in lithography to pattern substrates have raised several questions in the modeling of liquid motions over these surfaces and led to the concept of the effective tensorial slip. These effective conditions capture complicated effects of surface anisotropy and can be used to quantify flow over complex textures without the tedium of enforcing real inhomogeneous boundary conditions. 

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