Surface roughness and heterogeneity

For not too rough surfaces2 we can describe the effect of surface roughness by the so-called Wenzel equation [260]  

Most solid surface are also chemically inhomogeneous. Cassie considered a smooth but chemically patchwise heterogeneous surface. If there are two different kinds of region with 

2 Not too rough here refers to surfaces which look smooth and glossy. Such an optical appearance implies, that the roughness is significantly below the wavelength of fight. 

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The overall conclusion is that the present problem is not solved the main culprit is a lack of information on the submicroseopic properties of the solid surface, and the real world is very mueh more complex than discussed so far think of the influences of the line tension (which intermingles in a complicated fashion with surface roughness and heterogeneity) and surfactants (which may lead to continuing changes even after the application of a force has been stopped). 

The model (2)-(4) is referred to as the quenched solid non-local density functional theory (QSNLDFT). There are several advantages in considering the solid as a quenched component of the system rather than a source of the external field. On the one hand, this approach offers flexibility in the description of the fluid-solid boundary by varying the solid density and the thickness of the diffuse solid surface layer. On the other hand, it retains the main advantage of NLDFT computational efficiency because even a one-dimensional solid density distribution ceui include the effects of surface roughness and heterogeneity. For example, the solid density distribution can be taken from simulations of amorphous silica surfaces [29,30]. 

One other caveat concerning the approach used here must be made. This discussion, and the studies to which it relates, are based on some version of the Stern model for the oxide-electrolyte interface. Oxide surfaces are rough and heterogeneous. Even for the mercury-electrolyte interface, or single crystal metal-electrolyte interfaces, the success of some form of the Stern model has been less than satisfactory. It is important to bear in mind the operational nature of these models and not to attach too much significance to the physical picture of the planar interface. 

X-ray diffractograms (Fig. 4) and petrographic analyses (scanning electron microscopy also used for estimating the surface roughness and micro-heterogeneity of samples) indicate the presence of diverse silicates and oxides on the surface and in the bulk of the vitrocrystalline samples. In addition to the nearly ubiquitous quartz, other minerals were found in several samples gehlenite, albite, diopside, portlandite, pyroxenes... 

Both roughness and heterogeneity may be present in real surfaces. In such a case, the correction factors defined by Equations (45) and (46) are both present. Although such modifications adapt Young s equation to nonideal surfaces, they introduce additional terms that are difficult to evaluate independently. Therefore the validity of Equation (44) continues to be questioned. 

In a praetical sense, it is not necessary to eliminate completely all evidence of roughness and heterogeneity. If the average contact angle and liquid surface tension measurements for a variety of liquids all give the same solid surface tension via the equation of state (11. then effectively the surface is sufficiently smooth and homogeneous. The required level of accuracy will determine the acceptable solid surface quality. 

In a series of mostly theoretical model studies Marmur et al. - ) Investigated the role of the drop volume for smooth surfaces, containing oscillatory chemical heterogeneities. The idea, that many metastable states may exist for rough and heterogeneous surfaces, was pushed ahead by showing that the dependence of the... 

Recent analyses of contact angle hysteresis has treated surface heterogeneity in terms of random fluctuations see the excellent review by deGennes The approach is to treat both surface roughness and variations in surface composition as weak fluctuations, i.e. deviations from the ideally smooth surface, du/dy (Fig. 11) and from the difference in solid/liquid and solid/vapor surface energies, — yj - Both fluctuations are considered to be equivalent in perturbing the contact line and are analyzed in terms of their effect on the elastic line energy. 

A stable equilibrium is obtained if the surface is ideally smooth, imiform and non-deformable. If the surface is rough or heterogeneous, the system may reside in one of many metastable states, and the measured angle is a metastable contact angle. In this instance, the contact angle is not only dependent of surface tension, but also on the surface roughness and the drop volume [98]. 

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