A Quantitative Approach to Calculating the Energetic Heterogeneity of Solid Surfaces from an Analysis of TPD Peaks:  Comparison of the Results Obtained Using the Absolute Rate Theory and the Statistical Rate Theory of Interfacial Transport

Abstract

We present a comparison of the quantitative information obtained about the energetic heterogeneity of silicasupported nickel catalysts by an analysis of an experimental TPD peak using the absolute rate theory, in the form of the Wigner-Polanyi equation, and the statistical rate theory of interfacial transport. A new method of evaluating the desorption energy distribution, based on an improved condensation approximation approach and applicable to thermodesorption kinetics in both the above approaches, has been developed for this purpose. To make the comparison, a literature report of a study of adsorption equilibria in the hydrogen/SiO 2 -Ni system is used together with a TPD study of our own sample of the catalyst. The use of the Wigner-Polanyi approach resulted in the recovery of energy distribution functions showing the solid surface to be more energetically heterogeneous than it is when one uses the SRTIT approach on the same data. The broader surface energetic heterogeneity calculated using the Wigner-Polanyi approach is especially dramatic in the systems where significant readsorption occurs. This is because readsorption affects TPD peaks in a similar way to that due to surface heterogeneity. Despite this, the Wigner-Polanyi approach is commonly applied, neglecting the readsorption term, because of fundamental problems connected with using the full ART formulation, with the readsorption term included. We find that in general, for the same set of physical parameters characterizing a given gas/solid adsorption system, the Wigner-Polanyi approach will generate theoretical TPD peaks which are narrower, and shifted toward lower temperatures, compared with matching theoretical TPD peaks generated by the SRTIT approach. Clearly, one of these approaches is misleading, and on the basis of various considerations presented below, arguments are put forward favoring the use of the SRTIT approach for the interpretation of TPD peaks.

Theoretical description of the kinetics of solute adsorption at heterogeneous solid/solution interfaces

“…Ward and co-workers were the first to show how the SRT approach can be applied to describe the kinetics of isothermal adsorption at the gas/solid interfaces [26][27][28][29], and the kinetics of thermodesorption [30]. Then a series of papers has been published during the last decade by Rudzinski and co-workers, showing how that new description can be generalized further to describe the kinetics of isothermal gas adsorption/desorption on/from energetically heterogeneous surfaces [31][32][33][34][35] as well as the kinetics of thermodesorption [36][37][38][39].…”

Adsorption and Desorption of H2 on Graphite by Molecular Dynamics Simulations

“…Kreuzer and co-workers 8,[13][14][15][16][17][18] used nonequilibrium statistical thermodynamics and developed rate expressions from the statistical lattice-gas model. Many experiments, like temperatureprogrammed desorption 6,8,9,15 or sorption experiments with different sorbents 10 have been successfully described by these theories. The choice of one equation instead of another one is not trivial, however; see Ho et al 10 In this context and despite the work of Kreuzer and co-workers, 8,[13][14][15][16][17][18] it is fair to say that nonequilibrium thermodynamics 19 has not been popular.…”

A quantitative study of solid surface heterogeneity based on the statistical rate theory for analyzing spectra of controlled-rate thermal analysisThe work was carried out at both ICSC-PAS Krakow (Poland) and LEM-INPL Nancy (France).

“…In a series of our recent works we have discussed that problem for the case of TPD spectra obtained by applying a linearly programmed thermodesorption (a linear increase of temperature with time). [36][37][38][39] There we discussed the fundamental difficulties which one comes across while applying the classical TAAD approach for the theoretical interpretation of TPD spectra. At the same time, we have proposed new theoretical interpretation based on the statistical rate theory (SRT) approach.…”