Heterogenous surface

A somewhat subtle point of difficulty is the following. Adsorption isotherms are quite often entirely reversible in that adsorption and desorption curves are identical. On the other hand, the solid will not generally be an equilibrium crystal and, in fact, will often have quite a heterogeneous surface. The quantities ys and ysv are therefore not very well defined as separate quantities. It seems preferable to regard t, which is well defined in the case of reversible adsorption, as simply the change in interfacial free energy and to leave its further identification to treatments accepted as modelistic. 

In general, one should allow for nonideality in the adsorbed phase (as well as in solution), and various authors have developed this topic [5,137,145-149]. Also, the adsorbent surface may be heterogeneous, and Sircar [150] has pointed out that a given set of data may equally well be represented by nonideality of the adsorbed layer on a uniform surface or by an ideal adsorbed layer on a heterogeneous surface. 

Bowden and Tabor [24] proposed, for such heterogeneous surfaces, that... 

The question is not trivial such agreement is not assured in the case of systems showing hysteresis (see Section XVII-16), and it has been difficult to affirm it on rigorous thermodynamic grounds in the case of a heterogeneous surface. 

The analysis is thus relatively exact for heterogeneous surfaces and is especially valuable for analyzing changes in an adsorbent following one or another treatment. An example is shown in Fig. XVII-24 [160]. This type of application has also been made to carbon blacks and silica-alumina catalysts [106a]. House and Jaycock [161] compared the Ross-Olivier [55] and Adamson-Ling... 

It is generally assumed that isosteric thermodynamic heats obtained for a heterogeneous surface retain their simple relationship to calorimetric heats (Eq. XVII-124), although it may be necessary in a thermodynamic proof of this to assume that the chemical potential of the adsorbate does not show discontinu-... 

Most calculations of f(Q) for a heterogeneous surface, using an adsorption isotherm assume a patchwise distribution of sites. Explain for what kind of local isotherm functions,/((2,P, T) this assumption is not necessary, and for which it is necessary. Give examples. 

As a simple model of a heterogeneous surface, assume that 20% of it consists of sites of Q= 2.5 kcal/mol 45% of sites Q = 3.5 kcal/mol and the remainder, of sites of Q= 4.5 kcal/mol. Calculate Q(P, T) for nitrogen at 77 K and at 90 K, assuming the adsorption to follow the Langmuir equation with bo given by Eq. XVII-15. Calculate qsi for several 6 values and compare the result with the assumed integral distribution hinction. 

Discuss physical situations in which it might be possible to observe a vertical step in the adsorption isotherm of a gas on a heterogeneous surface. 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

Location of Heterogeneous Surface Areas by Measurements of Field Strength... 

Heterogeneous surface areas consist of anodic regions at corrosion cells (see Section 2.2.4.2) and objects to be protected which have damaged coating. Local concentrations of the current density develop in the area of a defect and can be determined by measurements of field strength. These occur at the anode in a corrosion cell in the case of free corrosion or at a holiday in a coated object in the case of impressed current polarization (e.g., cathodic protection). Such methods are of general interest in ascertaining the corrosion behavior of metallic construction units... 

Equation (14), although derived from the approximate random walk theory, is rigorously correct and applies to heterogeneous surfaces containing wide variations in properties and to perfectly uniform surfaces. It can also be used as the starting point for the random walk treatment of diffusion controlled mass transfer similar to that which takes place in the stationary phase in GC and LC columns. 

Dinelli, F, Buenviaje, C. and Ovemey, R.M., Glass transition measurements on heterogeneous surfaces. Thin Solid Films, 396(1-2), 138-144 (2001). 

J. Drelich, J. D. Miller, A. Kumar, G. M. Whitesides. Wetting characteristics of drops at heterogeneous surfaces. Colloids and Surfaces A 95 1-13, 1994. 

Y. K. Tovbin, E. V. Votyakov. Adsorption in pores with heterogeneous surfaces. Langmuir 9 2652-2660, 1993. 

Computer Simulations and Theory of Adsorption on Energetically and Geometrically Heterogeneous Surfaces... 

Another school has also developed and attempted to understand the functional dependence of adsorption on heterogeneous surfaces on the vapor pressure and temperature. Various empirical or semiempirical equations were proposed [24-26] and used later to represent experimental data and to evaluate EADF by inverting Eq. (1), which belongs to the class of linear Fredholm integrals of the first kind [27]. 

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