Gas Phase Decomposition by the Lindemann Mechanism

• Published in: SIAM journal on applied mathematics 1991-12, Vol.51 (6), p.1489-1497
• Main Authors: Cole, S. L., Wilder, J. W.
• Format: Article
• Language: English
• Subjects: Decomposition; Intermediate variables; Mathematical constants; Molecules; Ordinary differential equations; Vapor phases
• ISSN: 0036-1399; 1095-712X
• DOI: 10.1137/0151074

Several mechanisms have been proposed to explain observed phenomenon in gas phase decompositions, yet few theoretical solutions exist. One set of simple mechanisms is proposed by Christiansen and Lindemann [K. J. Laidler, McGraw-Hill, New York, 1950, pp. 76-85], which can be modeled as follows: \begin{equation*}\tag{(i)}A + A \rightleftharpoons A^\ast + A,\end{equation*} \begin{equation*}\tag{(ii)}A + M \rightleftharpoons A^\ast + M,\end{equation*} \begin{equation*}\tag{(iii)}A^\ast \rightarrow P,\end{equation*} where A represents a normal reactant molecule, A* an activated A molecule, M an inert substance, and P the decomposition products. In this mechanism, an A molecule can be activated by collision with another A molecule (step (i)) or an inert molecule M (step (ii)). The activated molecule can deactivate by a collision with an A or M molecule (steps (i) or (ii)) or decompose to form products (step (iii)). This scheme is modeled by a nonlinear set of ordinary differential equations. This paper shows that under normal laboratory conditions these equations can be treated as weakly nonlinear. Perturbation solutions are derived and conclusions given.