Master Equation Analysis of Thermal Activation Reactions: Reversible Isomerization and Decomposition

Abstract

We present the full solution of the master equation for the system with reversible isomerization and decomposition channels at low pressures. As an example of such a system we consider the cis-trans isomerization of 2-butene. At high temperatures cis-Zbutene decomposes into butadiene and hydrogen. The effect of isomerization on the decomposition rate coefficient was studied and indicated multiple steady-state behavior. At 1200 K, for example, a true steady state is achieved only after 75% of the product has been formed. This behavior is explained in terms of relaxation to the equilibrium distribution between cis and trans isomers. The first plateau in the rate coefficient corresponds to the irreversible regime of isomerization when two isomers are far from equilibrium, while the second plateau or true steady state is established after equilibrium between isomers has been reached. The effect is not observed at either low temperatures or high pressures.

Master Equation Analysis of Thermal Activation Reactions: Energy-Transfer Constraints on Falloff Behavior in the Decomposition of Reactive Intermediates with Low Thresholds

“…20 The reaction thresholds for such processes are frequently in the 40-90 kJ/mol range. Of course, reversible isomerizations have certain unique problems, 14 and it would be extremely interesting and important to consider the situation where such processes are coupled with decomposition. This is the actual situation with n-hexyl radicals.…”

“…Note that for the treatment of an extra decomposition channel one needs only add an additional term for decomposition into the master equation. In an earlier paper 14 we described our procedure for solving the master equation. The solution in terms of F i (t) is expressed in terms of the eigenvalues λ i and eigenvectors S i of the relaxation matrix J:…”

Communication: Thermal unimolecular decomposition of syn-CH3CHOO: A kinetic study

“…Using the calculated PES properties, anharmonic constants, and rovibrational parameters obtained with mHEAT (see above), a simplified two-dimensional-(E,J)-grained master equation was solved using an eigenvalue-eigenvector matrix technique [51][52][53][54][55][56][57][58][59][60][61] to obtain the time evolution of various intermediates as well as phenomenological rate constants as functions of pressure (P = 10 −3 to 10 4 Torr) and temperature (T = 200-400 K) that cover atmospheric conditions. Figure 2 displays the time evolution of various species as a function of pressure at 300 K, while Figure 3 shows the time evolution of various species as a function of temperature at 1 atm.…”

When Rate Constants Are Not Enough

“…the cis-and trans-wells with index numbers #1 and #2, respectively, in this model), the fragmentation products (1,3-butadiene + H2, with index #3), and transition states for cis/trans isomerization and for fragmentation of cis-butene-2, and, as shown in Figure 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For the parameters needed to model this system, we used most of the same principal sources as Bedanov et al 8 Harmonic vibration frequencies for cis-and trans-butene-2 were taken from Richards and Nielsen 22 and rotational constants computed at the B3LYP/aug-cc-pVTZ level of theory were obtained from the NIST Computational Chemistry Comparison and Benchmark Database. 23 The harmonic frequencies for the cis/trans isomerization transition state were taken from Lin and Laidler 24 and the rotational constants were assumed to the be the same as those for cis-butene-2.…”