Weak Heterogeneity

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. 

According to the analysis of Cerofolini [33], in the weak heterogeneity limit, i.e. for 9m — 9m bTf, the adsorption isotherm behaves in the high pressure region as... 

Olson and Innes, who observed tht B- - X system of in absorption, studied the extensively predissociated level v = 3 of the B state by observations of line broadening in the 3-1 absorption band, using Fabry-Perot interferometry. (The gross perturbation in the v = 3 level was first identified by Brown and Oibson. ) An estimated B state radiative lifetime of (0.98 0.10) /Fluorescence decay gives a non-collisional lifetime of 0.5 /us for v = 1,2. ... 

Singular perturbation analysis was employed to study the velocity of pulled fronts, and it was shown that the solvability integrals diverge [103, 104, 448]. Therefore we will use this method only for non-KPP kinetics. We assume 5 = 0(e), weak heterogeneities, i.e., S = as in (6.51) with a = 0(1). Equation (6.51), together with the corresponding boundary conditions, becomes... 

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... 

Weak Heterogeneity.—In this case (qM qm >> kaTf/a,) the upper bound of integration can be ignored, r=l, and distribution (28) can reasonably be supposed to hold in the whole range (qm,+°°)- Putting Tp= xo = i/ 2, equation (28) becomes... 

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...

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. 

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. 

These slight differences undoubtedly came from weak heterogeneity remaining in the liquids it is probable that, in the first case, neither of the two liquids was absolutely homogeneous, and that the two contrary effects which resnlted therefrom ( 30 and notes current), partly neutralized each other, while, in the second case, the alcoholic liquid being made completely homogeneous, the effect of the small heterogeneity of the oil appeared in its entirety. 

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