Abstract
The chemical reaction + H_{2} → H_{2} + is the simplest bimolecular reaction involving a polyatomic, yet is complex enough that exact quantum mechanical calculations to adequately model its dynamics are still unfeasible. In particular, the branching fractions for the “identity,” “proton hop,” and “hydrogen exchange” reaction pathways are unknown, and to date, experimental measurements of this process have been limited. In this work, the nuclear-spin-dependent steady-state kinetics of the + H_{2}reaction is examined in detail, and employed to generate models of the ortho:para ratio of formed in plasmas of varying ortho:para H_{2} ratios. One model is based entirely on nuclear spin statistics, and is appropriate for temperatures high enough to populate a large number of rotational states. Efforts are made to include the influence of three-body collisions in this model by deriving nuclear spin product branching fractions for the + H_{2}reaction. Another model, based on rate coefficients calculated using a microcanonical statistical approach, is appropriate for lower-temperature plasmas in which energetic considerations begin to compete with the nuclear spin branching fractions. These models serve as a theoretical framework for interpreting the results of laboratory studies on the reaction of with H_{2}.
The authors thank Kisam Park for providing code for calculating the rate coefficients used in our modeling work. This work has been supported by NSF PHY 08-55633.
I. INTRODUCTION
II. NUCLEAR SPIN SELECTION RULES
A. + H_{2}
B. + H_{2}
III. HIGH TEMPERATUREMODEL
A. Two-body high temperaturemodel
B. Three-body high temperaturemodel
IV. LOW TEMPERATUREMODEL
V. CONCLUSIONS
Key Topics
- Nuclear spin
- 59.0
- Hydrogen reactions
- 42.0
- Nuclear reactions
- 40.0
- Classical spin models
- 21.0
- Plasma temperature
- 19.0
Figures
The two-body high temperature model [Eq. (17)] for values of α ranging from 0 (purple, horizontal) to ∞ (red, steepest slope).
The two-body high temperature model [Eq. (17)] for values of α ranging from 0 (purple, horizontal) to ∞ (red, steepest slope).
The three-body high temperature model [Eq. (19)] for various values of Φ_{2}, α_{2}, and α_{3}. For reference, the gray dotted lines are the two-body high temperature model [Eq. (17)] for α = {0, 0.5, 2.0, ∞} from shallowest to steepest slope.
The three-body high temperature model [Eq. (19)] for various values of Φ_{2}, α_{2}, and α_{3}. For reference, the gray dotted lines are the two-body high temperature model [Eq. (17)] for α = {0, 0.5, 2.0, ∞} from shallowest to steepest slope.
Low temperature model [Eq. (20)] results for a variety of temperatures and branching fractions. The gray dotted lines are the two-body high temperature model [Eq. (17)] for α = {0, 0.5, 2.0, ∞} from shallowest to steepest slope.
Low temperature model [Eq. (20)] results for a variety of temperatures and branching fractions. The gray dotted lines are the two-body high temperature model [Eq. (17)] for α = {0, 0.5, 2.0, ∞} from shallowest to steepest slope.
Tables
Total nuclear spin statistical weights for the + H_{2} reaction (see Ref. 10). The table rows correspond to the nuclear spin configuration of reactant (,H_{2}) pairs, and the table columns correspond to the product pairs.
Total nuclear spin statistical weights for the + H_{2} reaction (see Ref. 10). The table rows correspond to the nuclear spin configuration of reactant (,H_{2}) pairs, and the table columns correspond to the product pairs.
Mechanism-specific nuclear spin branching fractions for the formation of o- and p- from the + H_{2} reaction with the (,H_{2}) reactant nuclear spin configurations.
Mechanism-specific nuclear spin branching fractions for the formation of o- and p- from the + H_{2} reaction with the (,H_{2}) reactant nuclear spin configurations.
As Table I, for the + H_{2} reaction.
As Table I, for the + H_{2} reaction.
Values of g _{ pI } for product pair p and intermediate angular momentum representation .
Values of g _{ pI } for product pair p and intermediate angular momentum representation .
Angular momentum substates for each I _{5} state of .
Angular momentum substates for each I _{5} state of .
Mechanism-specific cumulative nuclear spin modification probabilities for .
Mechanism-specific cumulative nuclear spin modification probabilities for .
Fractional spin product outcomes of the + H_{2} reaction.
Fractional spin product outcomes of the + H_{2} reaction.
Reactions and rates used in the three-body high temperature model. The nuclear spin dependence of each reaction is not listed explicitly here. The final reaction is written so as to only allow for ()^{*} to undergo at most one collision with H_{2}. The superscript L refers to a Langevin rate coefficient, and the superscript u refers to a unimolecular dissociation rate coefficient.
Reactions and rates used in the three-body high temperature model. The nuclear spin dependence of each reaction is not listed explicitly here. The final reaction is written so as to only allow for ()^{*} to undergo at most one collision with H_{2}. The superscript L refers to a Langevin rate coefficient, and the superscript u refers to a unimolecular dissociation rate coefficient.
Branching fractions for the spin configuration of ()^{*} formed in collisions of and H_{2}.
Branching fractions for the spin configuration of ()^{*} formed in collisions of and H_{2}.
Branching fractions for the spin configuration of formed upon dissociation of ()^{*}.
Branching fractions for the spin configuration of formed upon dissociation of ()^{*}.
Mechanism-specific nuclear spin branching fractions for resulting from the three-body reaction + 2H_{2}. Reactant is the H_{2} that collides with ()^{*}.
Mechanism-specific nuclear spin branching fractions for resulting from the three-body reaction + 2H_{2}. Reactant is the H_{2} that collides with ()^{*}.
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