Adsorption Heterogeneous surfaces

Van Riemsdijk.W.A. Bolt, G.H. Koopal, L.K. Blakemeer, J. (1986) Electrolyte adsorption on heterogeneous surfaces. Adsorption models. 

Most experimental adsorption isotherms can be considered as a combination of these two ideal types. For heterogeneous surfaces, adsorption isotherms are often modeled as a combination of L and S adsorption isotherms corresponding to a distribution of patches [49, 50]. The many other shapes proposed in the preceding classifications [48] Hke stepwise, high afiinity, or linear can be considered either as the combinations of S- and L-types or as a representation of the phenomenon for a limited range of concentration. For example, the high-affinity type is an extreme form of L-type. A linear adsorption isotherm (if it is not an artefact due to the penetration of the solute in the solid [15] may be the first portion of an L-type observed in the low concentration range. 

FIG. 31 The dependence of the jamming coverage of larger particles X at heterogeneous surfaces (adsorption at active centers having the coverage j). The points denote the numerical RSA simulations performed for curve 1, X = 10 curve 2, X = 5 curve 3, X = 2. The continuous lines denote the interpolating functions. 

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. 

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. 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

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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