Calculation of Reactive Cross Sections and Microcanonical Rates from Kinetic and Thermochemical Data

Abstract

In general, kinetic rate data may be represented by van't Hoff's four-parameter equation. When this is true, the mathematical properties of the Laplace transform may be used to derive phenomenological equations that describe the energy-dependent reactive cross sections and microcanonical rates in terms of the same four parameters. Since the macroscopic rate data and microscopic expressions are related by the Laplace transform, these microscopic descriptions do not imply new information; they simply express the information contained in the rate data in another form. The Monte Carlo techniques used to determine confidence envelopes for the rate data may also be used to provide confidence envelopes or “bounds” for the energy-dependent properties. These microscopic expressions may be used to compare and contrast theoretical calculations or as a starting point in RRKM or master equation calculations. Both the forward and reverse H + O2 ↔ OH + O reactions and the associative reaction CH3 + CH3 → C2H6 are used to illustrate the above ideas. In the first example, the cross section for the reverse reaction shows that it is not dominated by the dipole−quadrupole interaction. The cross section for the forward reaction is obtained by fitting rate data from 158 to 5300 K and peaks just above the threshold of 8354 K. In the second example, comparison to recent theoretical calculations highlights the importance of angular momentum and the centrifugal barrier.

An updated comprehensive kinetic model of hydrogen combustion

“…As shown in Figure 2, over this temperature range, the prediction of Hessler [16] is close to those of [25] and [28] (within 15%). The reasons driving us to choose the correlation of Hessler [16] over others will become clear below.…”

“…Yu et al [28] analyzed the shock tube experimental data of [25] and [29], and used an H 2 /O 2 mechanism to derive the rate constant of reaction (R1) over 1336-3370K. As shown in Figure 2, over this temperature range, the prediction of Hessler [16] is close to those of [25] and [28] (within 15%). The reasons driving us to choose the correlation of Hessler [16] over others will become clear below.…”

“…Since the publication of [1], there have been several important elementary kinetic publications further addressing two of the most important reactions involving the hydrogen radical, i.e., the branching reaction [16],…”

“…Mueller et al [1] used the rate constant expression of Pirraglia et al [24] for the reaction (R1) and noted that while the expression over-predicts the recent high temperature data above 1700 K [25][26][27], it more properly predicts the rate at low temperatures. The recent analysis of Hessler [16] excluded consideration of certain sets of available elementary rate data [27] based upon a defined uncertainty envelope.…”

“…In the present mechanism, the rate constant of reaction (R1) is updated to that in Hessler [16]. Figure 2 compares the predictions of the rate constant of reaction (R1) available in literature.…”