On the origin of power-law kinetics in carbon oxidation

Many experimental studies report high fractional orders for the global carbon/oxygen reaction, including several studies that cover wide ranges in oxygen partial pressure and observe power-law kinetics with a constant apparent order over the entire range. This persistent nth-order behavior is inconsistent with the simple Langmuir kinetic model and is also a challenge for more elaborate multi-step models of elementary reactions on ideal surfaces. The power law form is a simple and attractive rate law, but without a fundamental basis, it will remain empirical and ultimately controversial. The present paper evaluates the effect of surface or site heterogeneity as an explanation for the paradox of persistent power-law behavior. Simple models of intrinsic and induced heterogeneity are used to show that power-law kinetics are indeed expected when desorption or adsorption activation energy distributions are broad. Examination of experimental TPD data shows that desorption activation energy distributions are broad enough for global power-law kinetics to be generally expected for disordered carbons. The particular formulation of Haynes was evaluated as a candidate framework for describing the main features in the carbon oxidation database at temperatures below 1000 K and oxygen pressures above 0.01 bar. The Haynes turnover model predicts persistent power-law behavior and gives a promising description of the absolute reaction orders, activation energies, and near-atmospheric rates for several coal and polymer chars. It also predicts the low reaction order and its weak variation with pressure in the graphitized carbon black data of Tyler and coworkers. The origin of power-law kinetics is discussed in terms of the detailed behavior of three classes of active sites: reactive bare sites, partially covered sites, and stable oxide, and an approximate analytical expression is derived that relates global order features in the desorption activation energy distribution.