Weakly Heterogeneous Surfaces

Weakly Heterogeneous Surfaces.—In this case, qM Qm ksTp, the expression of the energy distribution function is given by equation (29). In addition, and in order to simplify the computations, it is supposed here that lateral interactions are negligible (xo very high). The energy distribution function reduces to the exponential distribution (30), which under equilibrium conditions leads to Freundlich behaviour. 

As soon as t t the kinetics of (42) become p(t) = s/t. This behaviour is well known as Elovich behaviour it takes place at low temperature on the same heterogeneous surfaces which, under equilibrium condition, obey the Freund-lich isotherm. The kinetics of (42) hide a difficulty indeed, if it held true exactly, the total desorbed quantity would diverge at t — oo. This difficulty can be overcome by introducing a finite upper adsorption energy. 

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Figure 3 Log-log plot of the adsorption isotherms which should be observable on weakly heterogeneous surfaces grown at Tp= 1000 K and frozen to T= 50 K. The figure shows that the Freundlich range gradually extends as Xo increases...

A simplified model of equilibrium surface suggests that the DR behaviour is observed in low-pressure adsorption on patchwise, weakly heterogeneous surfaces which were grown in equilibrium conditions and hence were quenched at the adsorption temperature. At higher pressures, these surfaces should exhibit the Freundlich behaviour, while in the case of strong heterogeneity adsorption should be described by the Temkin isotherm. The three classic empirical isotherms, Freundlich, Dubinin-Radushkevich, Temkin, seem therefore to be related to adsorption on equilibrium surfaces, and the explanation of these experimental behaviours can be seen as a new chapter of the theory of adsorption the theory of physical adsorption on equilibrium surfaces. 

Another special case of weak heterogeneity is found in the systems with stepped surfaces [97,142-145], shown schematically in Fig. 3. Assuming that each terrace has the lattice structure of the exposed crystal plane, the potential field experienced by the adsorbate atom changes periodically across the terrace but exhibits nonuniformities close to the terrace edges [146,147]. Thus, we have here another example of geometrically induced energetical heterogeneity. Adsorption on stepped surfaces has been studied experimentally [95,97,148] as well as with the help of both Monte Carlo [92-94,98,99,149-152] and molecular dynamics [153,154] computer simulation methods. 

This explains the success of the well-known B.E.T. method for this analysis. After the excellent discussion by Hill (244) of the B.E.T. and the Hiittig theories, in which he points out the weaknesses of the first and the fallacy of the latter, and after the analysis by Halsey (245), who indicates when a B.E.T. isotherm of satisfactory character is obtained on a heterogeneous surface, little need be said here. 

The kinetic theory of interface processes, including the adsorption one, on heterogeneous surfaces was constructed in Refs. [80,85,89]. An example of an application of the theory taking into account both lateral interactions and surface heterogeneity is the TDS for H2 on Ir(110)-2 x 1 described in Refs. [127,128]. The elementary lattice consists of three sites (Fig. 8.8) one strong (site of the first type) and two weak (sites of the second and third types). The sites of the third type are separated only formally for an easier presentation of the distribution function - the molecular characteristics of these sites are the same as those of the sites of second type. 

Deactivate the original heterogeneous surface of the silica surface to avoid matrix effects. As silica has a weak acidic surface basic solutes are strongly adsorbed, which should be minimized by surface modification. 

Function (28) inserted into integral (4) allows the computation of the overall adsorption isotherm on equilibrium surfaces. Two cases are conveniently distinguished weak heterogeneity (qM qm keTf/ai) and strong... 

As the Elovich behaviour is observed both for weakly and strongly heterogeneous surfaces grown under equilibrium conditions, the reasons for... 

This surface modification does not influence the pore structure of support. The modifier molecules do not cover all the surface of Ti02. Only 29% of surface of Ti02 is occupied by PPA, which is considered to be a heterogenous surface modification. Furthermore, this surface modification also does not change the dispersion of active species on the support due to the same morphology of active species and interaction between active species and support according to the results of transmission electron microscopy (TEM) and TPR analysis (Li et al, 2012). However, there is only one obvious influence by surface modification on the H2S desorption from different supports. The H2S-TPD patterns show that there are two absorption modes of H2S on the Ti02 The lower peak at 254 °C indicates weak adsorption... 

The results of such experiments typically fall on a rather broad distribution curve that reflects the formation of microcontacts between geometrically and energetically heterogeneous surfaces of the two particles. For this reason, the results are typically presented as differential distribution histograms, which typically contain two maxima one corresponding to the weak (coagulation)... 

Hence, if (C1)<46.4%, two types of structural units exist, both non-chlorinated and monochlorinated but if 46.4% < o(Cl) < 64%, then both mono- and dichlorinated products are formed. In the present case (Figure 60), o(Cl) = 54.6% can be introduced into PP film during 4 hours of continuous chlorination, which corresponds to TV (Cl) = 1.376 per structural unit, supposing that chlorination proceeds uniformly in the whole volume of PP film. Despite small film thickness, this is not completely true (as well as all above-described heterogeneous transformations) however, it is warranted by the fact that the refractive index change is measured interferometrically along the whole optical thickness of the film. Real saturation at o(Cl) = 54.6% (instead of o(Cl) = 70% according to [140]) is explained by the weakly developed surface of film PP samples. 

The way in which these factors operate to produce Type III isotherms is best appreciated by reference to actual examples. Perhaps the most straightforward case is given by organic high polymers (e.g. polytetra-fluoroethylene, polyethylene, polymethylmethacrylate or polyacrylonitrile) which give rise to well defined Type III isotherms with water or with alkanes, in consequence of the weak dispersion interactions (Fig. S.2). In some cases the isotherms have been measured at several temperatures so that (f could be calculated in Fig. 5.2(c) the value is initially somewhat below the molar enthalpy of condensation and rises to qi as adsorption proceeds. In Fig. 5.2(d) the higher initial values of q" are ascribed to surface heterogeneity. 

Sorption of nonionic, nonpolar hydrophobic compounds occurs by weak attractive interactions such as van der Waals forces. Net attraction is the result of dispersion forces the strength of these weak forces is about 4 to 8 kj/mol ( 1 2 kcal/mol). Electrostatic interactions can also be important, especially when a molecule is polar in nature. Attraction potential can develop between polar molecules and the heterogeneous sod surface that has ionic and polar sites, resulting in stronger sorption. 

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