Smooth heterogeneous surfaces

Fig. 6a-d. Schematic view of adsorption from solution onto smooth, planar surfaces where the surface sites are considered to have the same area as the projected area of the solute of interest, a. Top, the ideal (Langmuir) case b. clustering of adsorbed solute due to attractive lateral interactions or positive cooperativity c. heterogeneous surface, i.e., two sets of binding sites d. patchwise heterogeneity or surface domains of different adsorptive properties... 

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... 

This takes us back to the issue of surface heterogeneity. Suspended oxides expose a variety of crystal planes between which the various pK s may vary. Hence, in practice, measurements refer to very heterogeneous surfaces. Accounting for heterogeneity can be done along the same lines as introduced in sec. 1.7 with the potential as an additional parameter but the analysis is very laborious. Perhaps the trend is that the electric potential tends to smooth the... 

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... 

In 1944, Cassie and Baxter derived an equation describing contact angle hysteresis for composite smooth solid surfaces with varying degrees of heterogeneity ... 

There are books on physical electrochemistry, which present electrocatalysis with one of the main influential features left out. I refer to surface heterogeneity. Thus, when a surface is viewed under an electron microscope one can see that the apparently smooth electrode surface is in fact not smooth at all. Because the structure of electrode surfaces is, in fact, very much a part of the interpretation of electrocatalysis, I will give a brief sketch of some of the features of a metal surface that may affect surface reactions. 

Sem micrographs of SCN and SCS synthetic activated carbons are compared with conventional activated carbons " obtained from peat coal or wood in Figure 5.12. The figure clearly shows that the synthetic carbons have a smooth external surface, ensuring favorable conditions for hemocytes membranes that are very sensitive to heterogeneity of the contact surface and that their surface does not need any additional covering by biocompatible polymer films. The bottommost micrographs show that the internal structure of synthetic activated carbon spheres has well-developed channels and pores with sizes considerably smaller than the size of the platelets. The surface characteristics of some hemosorbents are compared in Table 5.11. 

In order to obtain high molecular mobility of polymers, films were swollen until cp decreased to about 5%. At this concentration, the molecules were dishibuted homogeneously and the molecular mobility was high. As the viscosity of such an isotropic solution was comparatively low, surface tension was able to smooth the surface of the film quickly within seconds (heterogeneities in film thickness, as observed by OM on spin-coated films, disappeared). This smoothing process was taken as a clear indication for having reached the isotropic phase. 

Line tension may be important for rough and heterogeneous surfaces. However, the previous relation is applicable for only smooth surfaces and needs further correction for accounting the surface roughness or heterogeneity. Line tension affects the stability of emulsion and foams and would play an important role in microfluidic and nanofluidic devices. As summarized by Amirfazli and Neumann (2004), line tension has been found to be negative as well as positive. 

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. 

In this paper, we suggest a systematic approach that extends the applicability of NLDFT models to heterogeneous surfaces of amorphous and microporous solids. The main idea is to use a multicomponent NLDFT, in which the solid is treated as one of the components with a fixed spatially distributed density. The model, named quenched solid non-local density functional theory (QSNLDFT), is an extension of the quenehed-annealed DFT model of systems with hard-core interactions recently proposed by Schmidt and coworkers [23,24]. Drawing on several prominent examples, we show that the proposed model produces smooth isotherms in the region of multiplayer adsorption. Moreover, the effects of wall microporosity can be naturally incorporated into the model. Although the parameters of the model have not been yet optimized to describe quantitatively a particular experimental system, the model generates adsorption isotherms which are in qualitative agreement with experimental isotherms of N2 or Ar adsorption on amorphous silica materials. 

It is worth noticing that QSNLDFT provides a unified model of adsorption on both smooth and heterogeneous surfaces. QSNLDFT describes the behavior of LJ fluid near a smooth hard wall by employing a uniform solid density distribution with a packing density approaching unity. The behavior of LJ fluid near a smooth attractive wall is approximated by using an appropriate division of the solid-fluid potential into repulsive and attractive parts. Below we consider several prominent examples, which demonstrate that QSNLDFT is capable of describing experimental adsorption isotherms on amorphous and microporous solids. 

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