Simulations of the Formation of Nitrogen Oxides at the Cooling Stage of a Subthreshold Microwave Discharge in Air with Admixtures of Methane

Abstract—

Studies of the composition of the products of chemical reactions in the afterglow of a new type of atmospheric discharge, the microwave self-non-self-sustained discharge in air with admixtures of methane, were carried out. A detailed kinetic model was developed that describes the kinetics of reactions with polyatomic nitrogen oxides at the stage of intensive cooling of the discharge channel. It was found that the formation of nitrogen oxide NO depends on the percentage of the products of the methane molecule dissociation in the nitrogen–oxygen mixture that, initially, is atomic. The new discharge type can be used for the plasmachemical processing of gaseous media.

APPENDIX

Tables 1–10 show the rate constants and reaction equations used in the model.

Reactions of dissociation and recombination occur with the participation of a third particle (M or M_c). The type of particle M is determined by the chemical compounds listed in Section 2 of this article. The type of particle M_C is given in Tables 1–3.

According to literature, the recommended values of reaction rate constants are given taking into account the temperature range T (in K) in the second column of the table. If the temperature range is not given by the authors or is narrower than the temperature range under study (from 300 to 5000 K), then in the model, the rate constants are extrapolated over the temperature range under study.

For most reactions given in the tables, the dependences on temperature of rate constants ${{k}_{{f,r}}}$ of the forward ( f ) and reverse (r) chemical reactions are approximated using the modified Arrhenius equation [28, 32, 33, 35]

$${{k}_{{f,r}}} = A \times {{T}^{n}} \times {\text{exp}}\left( { - {{E}_{a}}{\text{/}}T} \right).$$

Here, the rate constants are expressed in units of mole^{1 ‒ s} cm^{3(s – 1)} s^–1. The value s determines the order of the reaction. The parameters A, n, and E_a are the constant preexponential factor, the index of power in the temperature factor of the preexponential factor, and the energy threshold of the reaction, respectively [26, 33].

The rate constants for a number of reactions have a more complicated dependence on the translational temperature than the predictions of the modified Arrhenius formula. Their value can be determined not only by the translational temperature, but also by the concentrations of their interaction partners. These rate macroconstants of complicated reactions are given in tables using the approximate expressions from work [32] obtained by the methods of single-quantum step-wise excitation and transitional state [46], the Troe model, the modified Keck’s variational theory [96], and by the scheme of single-step dissociation [97]. Expressions for such constants of forward and reverse reactions contain correction factors d_if and d_ir, respectively. The lower index i stands for the number of the reaction for which the correction factor is in-troduced. For example, for the forward reaction no. 3.15.7, index i is 3157f.

The correction coefficient ${{d}_{{101f}}}$ for reactions 1.0.1–1.0.5 (Table 1) is calculated by the formula

$${{d}_{{101f}}} = 1 - {\text{exp}}\left( { - 3354{\text{/}}T} \right).$$

The coefficients d_101r and d_102r are determined as the product of the correction coefficient ${{d}_{{{\text{101}}f}}}$ and the equilibrium constant K_eq of reactions 1.0.1–1.0.5 (Table 1), respectively.

For reaction 2.0.3 (Table 2), the coefficient d_203f changes is the range from 0.3 to 1.5. Coefficients d_204 f,r and ${{d}_{{{\text{221}}f}}}$ for reactions 2.0.4 and 2.2.1–2.2.5, 2.3 (Table 2), respectively, are determined by expressions

$$\begin{gathered} {{d}_{{{\text{204}}f}}} = {\text{exp}}\left( {{{{\text{170}}} \mathord{\left/ {\vphantom {{{\text{170}}} T}} \right. \kern-0em} T}} \right),\quad {{d}_{{{\text{204}}r}}} = {\text{exp}}\left( {{{{\text{1060}}} \mathord{\left/ {\vphantom {{{\text{1060}}} T}} \right. \kern-0em} T}} \right), \\ {{d}_{{{\text{221}}f}}} = {\text{1}} - {\text{exp}}\left( { - 2240{\text{/}}T} \right). \\ \end{gathered} $$

To determine the values of the correction coefficient ${{d}_{{{\text{301}}f}}}$ (for reactions 3.0.1 and 3.0.2, Table 3) the following relation is used

$${{d}_{{{\text{301}}f}}} = {\text{1}} - {\text{exp}}\left( { - 2700{\text{/}}T} \right).$$

Coefficients ${{d}_{{{\text{331}}f,r}}}$ for reactions of dissociation and recombination (3.3.1–3.3.5, Table 3) are calculated as

$${{d}_{{{\text{331}}f}}} = {{\left[ {1 + 706 \times \exp \left\{ { - \frac{{{\text{2164}}}}{T}} \right\} \times \frac{{{{X}_{{{\text{N}}{{{\text{O}}}_{{\text{2}}}}}}}}}{{\sum\limits_m {{{X}_{m}} \times {{R}_{m}}} }}} \right]}^{{ - 1}}},$$

$${{d}_{{{\text{331}}r}}} = {{\left[ {\frac{{{{K}_{\infty }}}}{{K_{{{\text{Ar}}}}^{{\text{0}}}{{ \times }}\left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,NO,N}}{{{\text{O}}}_{{\text{2}}}}{\text{,}}{{{\text{N}}}_{{\text{2}}}}{\text{O)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{X}_{m}} \times {{R}_{m}}} }}} \right]}^{{ - 1}}}{{ \times }}{{F}^{Y}},$$

$$Y = {{\left\{ {1 + {{{\log }}^{{\text{2}}}}\left[ {\frac{{K_{{{\text{Ar}}}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,NO,N}}{{{\text{O}}}_{{\text{2}}}}{\text{,}}{{{\text{N}}}_{{\text{2}}}}{\text{O)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}{{{{K}_{\infty }}}}} \right]} \right\}}^{{ - 1}}},$$

$$K_{{{\text{Ar}}}}^{{\text{0}}} = 2.3 \times {{10}^{{ - 16}}} \times {{\left( {\frac{T}{{300}}} \right)}^{{ - 1.8}}},\quad {{K}_{\infty }} = 1.8 \times {{10}^{{13}}} \times {{\left( {\frac{T}{{300}}} \right)}^{{0.3}}}.$$

Here, $K_{{{\text{Ar}}}}^{{\text{0}}}$ is the recombination rate constant (on argon atoms) in the low-pressure region (it is measured in cm⁶ s^–1 mol^–2), ${{K}_{\infty }}$ is the recombination rate constant in the high-pressure range (it is measured in cm³ s^–1 mol^–1), ${{X}_{m}}$ are the molar fractions of the chemical compounds of the mixture (m = ${{{\text{N}}}_{{\text{2}}}}{\text{,}}\;{{{\text{O}}}_{{\text{2}}}}{\text{,}}\;{\text{NO,}}\;{{{\text{N}}}_{{\text{2}}}}{\text{O,}}\;{\text{N}}{{{\text{O}}}_{{\text{2}}}}$), N_A is the number of particles in a single mole of the substance, and ${{R}_{m}}$ is the relative efficiency of component m relative to component m = ${{{\text{N}}}_{{\text{2}}}}$:

$$\begin{gathered} {{R}_{{{{{\text{N}}}_{{\text{2}}}}}}} = 1.6;\quad {{R}_{{{{{\text{O}}}_{{\text{2}}}}}}} = 1.3;\quad {{R}_{{{\text{NO}}}}} = 2.8; \\ {{R}_{{{{{\text{N}}}_{{\text{2}}}}{\text{O}}}}} = 7;\quad {{R}_{{{\text{N}}{{{\text{O}}}_{{\text{2}}}}}}} = 10. \\ \end{gathered} $$

The values of coefficients ${{d}_{{{\text{371}}f,r}}}$ (for reactions 3.7.1, Table 3) and ${{d}_{{{\text{311}}f}}}$ (for reaction 3.11, Table 3) are calculated by the formulas

$$\begin{gathered} {{d}_{{{\text{371}}f}}} = {{d}_{{{\text{371}}r}}} = \left( {\sum\limits_m {{{R}_{m}} \times {{X}_{m}}} } \right) \\ \, \times {{\left[ {\left( {1 + 78.3 \times \exp \left( { - 2315{\text{/}}T} \right)} \right) \times {{X}_{{{\text{NO}}}}}{\text{/}}\sum\limits_m {{{R}_{m}} \times {{X}_{m}}} } \right]}^{{ - 1}}}, \\ \end{gathered} $$

$$\begin{gathered} {{d}_{{{\text{311}}f}}} = {{\left[ {{\text{1 + 78}}{\text{.3}} \times \exp \left( { - 2300{\text{/}}T} \right) \times \frac{{{{X}_{{{\text{NO}}}}}}}{{\sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}} \right]}^{{ - 1}}} \\ (m = {{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{N}}}_{{\text{2}}}}{\text{O,}}{{{\text{O}}}_{{\text{2}}}}{\text{,NO}}), \\ \end{gathered} $$

$$\begin{gathered} {{R}_{{{{{\text{N}}}_{{\text{2}}}}}}} = 1.74;\quad {{R}_{{{{{\text{N}}}_{{\text{2}}}}{\text{O}}}}} = 6.9,\quad {{R}_{{{{{\text{O}}}_{{\text{2}}}}}}} = 1.3, \\ {{R}_{{{\text{NO}}}}} = 3,\quad {{R}_{{{\text{C}}{{{\text{O}}}_{{\text{2}}}}}}} = 4. \\ \end{gathered} $$

For reaction 3.11, index m, besides the listed components for the mixture for reactions 3.7.1., additionally includes the denomination for the CO₂ component ($m = {\text{C}}{{{\text{O}}}_{{\text{2}}}}$).

The coefficients ${{d}_{{{\text{3151}}f,r}}}$ and ${{d}_{{{\text{3154}}f,r}}}$ for reactions of dissociation and recombination (3.15.1 and 3.15.4, Table 3) are determined by the expressions

$${{d}_{{{\text{315(1,4)}}f,r}}} = {{\left[ {{\text{1}} + \frac{{{{K}_{{\infty {\text{,}}f,r}}}}}{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,CO,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}} \right]}^{{ - 1}}}{{ \times }}{{F}^{{Y_{{f,r}}^{{(1,4)}}}}},$$

$$F\left( T \right) = \exp \left( { - \frac{T}{{1300}}} \right) + \exp \left( { - \frac{{5200}}{T}} \right),$$

$$\begin{gathered} Y_{{f,r}}^{{{\text{(1,4)}}}} = {{\left\{ {{\text{1}} + {{{\log }}^{{\text{2}}}}\left[ {\frac{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,CO,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}{{{{K}_{{\infty {\text{,}}f{\text{,}}r}}}}}} \right]} \right\}}^{{ - 1}}} \\ (m = {{{\text{N}}}_{2}},{{{\text{O}}}_{2}},{\text{CO}},{\text{C}}{{{\text{O}}}_{2}}), \\ \end{gathered} $$

$${{R}_{{{{{\text{N}}}_{{\text{2}}}}}}} = 1,\quad {{R}_{{{{{\text{O}}}_{{\text{2}}}}}}} = 1,\quad {{R}_{{{\text{CO}}}}} = 2,\quad {{R}_{{{\text{C}}{{{\text{O}}}_{{\text{2}}}}}}} = 2.9,$$

$$K_{{{{{\text{N}}}_{2}},f}}^{0} = 4.45 \times {{10}^{{16}}} \times {{\left( {\frac{T}{{1000}}} \right)}^{{ - 2}}} \times \exp \left( { - \frac{{23{\kern 1pt} 234}}{T}} \right),$$

$$K_{{\infty ,f}}^{{}} = 2 \times {{10}^{{14}}} \times \exp \left( { - \frac{{23{\kern 1pt} 234}}{T}} \right),$$

$$\begin{gathered} K_{{{{{\text{N}}}_{{\text{2}}}},r}}^{{\text{0}}} = 2.93 \times {{10}^{{15}}} \times {{\left( {\frac{T}{{{\text{1000}}}}} \right)}^{{ - 2}}}, \\ K_{{\infty ,r}}^{{}} = 1.32 \times {{10}^{{13}}}. \\ \end{gathered} $$

Here, $K_{{{{{\text{N}}}_{{\text{2}}}},f}}^{{\text{0}}}$ and $K_{{{{{\text{N}}}_{{\text{2}}}},r}}^{{\text{0}}}$ are the rate constants for the reactions of dissociation and recombination in the low-pressure range (their units of measurement are cm³ s^–1 mol^–1 and cm⁶ s^–1 mol^–2, respectively). $K_{{\infty ,f}}^{{}}$ and $K_{{\infty ,r}}^{{}}$ are the rate constants in the high-pressure region (units of measurement s^–1 and cm³ s^–1 mol^–1, respectively). The indices 1 and 4 correspond to molecular components ${{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}$ and ${\text{CO,C}}{{{\text{O}}}_{{\text{2}}}}$.

The coefficients ${{d}_{{{\text{3161}}f,r}}}$ and ${{d}_{{{\text{3162}}f,r}}}$ for reactions of dissociation and recombination (3.16.1 and 3.16.2, Table 3) are found by the expressions

$${{d}_{{{\text{316(1,2)}}f,r}}}{\text{ = }}{{\left[ {{\text{1}} + \frac{{{{K}_{{\infty ,f,r}}}}}{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,CO,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}} \right]}^{{{\text{ - 1}}}}} \times {{F}^{{Y_{{f,r}}^{{{\text{(1,2)}}}}}}},$$

$$F\left( T \right) = \exp \left( { - \frac{T}{{1300}}} \right) + \exp \left( { - \frac{{5200}}{T}} \right),$$

$$Y_{{f,r}}^{{{\text{(1,2)}}}} = {{\left\{ {{\text{1}} + {{{\log }}^{{\text{2}}}}\left[ {\frac{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,CO,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}{{{{K}_{{\infty ,f,r}}}}}} \right]} \right\}}^{{ - 1}}}$$

$$(m = {{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,CO,C}}{{{\text{O}}}_{{\text{2}}}}),\quad {{R}_{{{{{\text{N}}}_{{\text{2}}}}}}} = 1;\quad {{R}_{{{{{\text{O}}}_{{\text{2}}}}}}} = 1;\quad {{R}_{{{\text{CO}}}}} = 2;\quad {{R}_{{{\text{C}}{{{\text{O}}}_{{\text{2}}}}}}} = 2.9,$$

$$K_{{{{{\text{N}}}_{{\text{2}}}},f}}^{{\text{0}}} = 9. \times {{10}^{6}} \times {{\left( {\frac{T}{{{\text{1000}}}}} \right)}^{{ - {\text{2}}}}} \times {\text{exp}}\left( { - \frac{{{\text{23}}{\kern 1pt} {\text{234}}}}{T}} \right),$$

$$K_{{\infty ,f}}^{{}} = 4 \times {{10}^{{14}}} \times \exp \left( { - \frac{{{\text{23}}{\kern 1pt} {\text{234}}}}{T}} \right),$$

$$K_{{{{{\text{N}}}_{{\text{2}}}},r}}^{{\text{0}}} = 5.13 \times {{10}^{{15}}} \times {{\left( {\frac{T}{{{\text{1000}}}}} \right)}^{{ - {\text{2}}}}} \times \exp \left\{ { - \frac{{{\text{23}}{\kern 1pt} {\text{050}}}}{T}} \right\},$$

$$K_{{\infty ,r}}^{{}} = 2.3 \times {{10}^{{13}}} \times \exp \left\{ { - \frac{{{\text{23}}{\kern 1pt} {\text{050}}}}{T}} \right\}.$$

Here, indices 1 and 2 correspond to the ${{{\text{N}}}_{{\text{2}}}}$, O₂ and ${\text{CO,}}\;{\text{C}}{{{\text{O}}}_{{\text{2}}}}$ components of the gas medium.

The coefficients ${{d}_{{{\text{3171}}f,r}}}$ of dissociation and recombination reactions (3.17.1, Table 3) are calculated by the formulas

$${{d}_{{{\text{3171}}f,r}}} = {{\left[ {{\text{1}} + \frac{{{{K}_{{\infty ,f,r}}}}}{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,}}{{{\text{N}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}{\text{,NO,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}} \right]}^{{ - 1}}}{{ \times }}{{F}^{{Y_{{f,r}}^{{}}}}},$$

$$F\left( T \right) = {\text{exp}}\left( { - \frac{T}{{{\text{250}}}}} \right) + {\text{exp}}\left( { - \frac{{{\text{1050}}}}{T}} \right),$$

$$Y_{{f,r}}^{{}} = {{\left\{ {{\text{1}} + {{{\log }}^{{\text{2}}}}\left[ {\frac{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,}}{{{\text{N}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}{\text{,NO,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}{{{{K}_{{\infty ,f,r}}}}}} \right]{\text{/}}{{{\left( {0.75 - \log F{\text{(}}T{\text{)}}} \right)}}^{2}}} \right\}}^{{ - 1}}}$$

$$\begin{gathered} (m = {{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,}}{{{\text{N}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}{\text{,NO,C}}{{{\text{O}}}_{{\text{2}}}}),\quad \\ {{R}_{{{{{\text{N}}}_{{\text{2}}}}}}} = 1,\quad {{R}_{{{{{\text{O}}}_{{\text{2}}}}}}} = 1,\quad {{R}_{{{{{\text{N}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}} = 4.4,\quad {{R}_{{{\text{NO}}}}} = 1.3,\quad {{R}_{{{\text{C}}{{{\text{O}}}_{{\text{2}}}}}}} = 1.7, \\ \end{gathered} $$

$$K_{{{{{\text{N}}}_{{\text{2}}}},f}}^{{\text{0}}} = 1.32 \times {{10}^{{21}}} \times {{\left( {\frac{T}{{{\text{300}}}}} \right)}^{{ - {\text{6}}{\text{.1}}}}} \times {\text{exp}}\left( { - \frac{{{\text{11}}{\kern 1pt} {\text{080}}}}{T}} \right),$$

$$K_{{\infty ,f}}^{{}} = 9.7 \times {{10}^{{14}}} \times {{\left( {\frac{T}{{300}}} \right)}^{{ - 0.9}}} \times {\text{exp}}\left( { - \frac{{{\text{11}}{\kern 1pt} {\text{080}}}}{T}} \right),$$

$$K_{{{{{\text{N}}}_{{\text{2}}}},r}}^{{\text{0}}} = 1.34 \times {{10}^{{18}}} \times {{\left( {\frac{T}{{{\text{300}}}}} \right)}^{{ - 5}}},$$

$$K_{{\infty ,r}}^{{}} = 9.6 \times {{10}^{{11}}} \times {{\left( {\frac{T}{{{\text{300}}}}} \right)}^{{0.2}}}.$$

The coefficient d_323f for reaction 3.23 (Table 3) is the same as coefficient d_331f (dissociation reaction 3.3.1–3.3.5, Table 3). For this reaction, ${{X}_{m}}$ are mole fractions of the mixture components m = ${\text{N}}{{{\text{O}}}_{{\text{2}}}}{\text{,}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,C}}{{{\text{O}}}_{{\text{2}}}}$ and R_m is the relative efficiency of component m relative to the component m = ${\text{N}}{{{\text{O}}}_{{\text{2}}}}$:

$${{R}_{{{\text{N}}{{{\text{O}}}_{{\text{2}}}}}}} = 10;\quad {{R}_{{{{{\text{N}}}_{{\text{2}}}}}}} = 1.6;\quad {{R}_{{{{{\text{O}}}_{{\text{2}}}}}}} = 1.3;\quad {{R}_{{{\text{C}}{{{\text{O}}}_{{\text{2}}}}}}} = 4.3.$$

The values of coefficients ${{d}_{{{\text{3271}}f,r}}}$ for dissociation and recombination reactions (3.27.1, Table 3) are determined by the expressions

$${{d}_{{{\text{3271}}f,r}}} = {{\left[ {{\text{1}} + \frac{{{{K}_{{\infty ,f,r}}}}}{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,N}}{{{\text{O}}}_{{\text{2}}}}{\text{,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}} \right]}^{{ - {\text{1}}}}} \times {{F}^{{Y_{{f,r}}^{{}}}}},$$

$$F\left( T \right) = {\text{exp}}\left( { - \frac{T}{{250}}} \right) + \exp \left( { - \frac{{1050}}{T}} \right),$$

$$Y_{{f,r}}^{{}} = {{\left\{ {{\text{1}} + {{{\log }}^{{\text{2}}}}\left[ {\frac{{K_{{{{{\text{N}}}_{{\text{2}}}}{\text{,}}f,r}}^{{\text{0}}} \times \left( {{{N}_{{{\text{(}}{{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,N}}{{{\text{O}}}_{{\text{2}}}}{\text{,C}}{{{\text{O}}}_{{\text{2}}}}{\text{)}}}}}{\text{/}}N_{{\text{A}}}^{{}}} \right) \times \sum\limits_m {{{R}_{m}} \times {{X}_{m}}} }}{{{{K}_{{\infty ,f,r}}}}}} \right]{\text{/}}{{{\left( {0.75 - \log F{\text{(}}T{\text{)}}} \right)}}^{2}}} \right\}}^{{ - 1}}}$$

$$\begin{gathered} {\text{(}}m = {{{\text{N}}}_{{\text{2}}}}{\text{,}}{{{\text{O}}}_{{\text{2}}}}{\text{,N}}{{{\text{O}}}_{{\text{2}}}}{\text{,C}}{{{\text{O}}}_{{\text{2}}}}),\quad \\ {{R}_{{{{{\text{N}}}_{{\text{2}}}}}}} = 1,\quad {{R}_{{{{{\text{O}}}_{{\text{2}}}}}}} = 1,\quad {{R}_{{{{{\text{N}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{4}}}}}}} = 2,\quad {{R}_{{{\text{N}}{{{\text{O}}}_{{\text{2}}}}}}} = 2,\quad {{R}_{{{\text{C}}{{{\text{O}}}_{{\text{2}}}}}}} = 2. \\ \end{gathered} $$

$$K_{{{{{\text{N}}}_{2}},f}}^{0} = 1.44 \times {{10}^{{18}}} \times {{\left( {\frac{T}{{300}}} \right)}^{{ - 5}}} \times \exp \left( { - \frac{{6392}}{T}} \right),$$

$$K_{{\infty ,f}}^{{}} = 3 \times {{10}^{{15}}} \times {{\left( {\frac{T}{{300}}} \right)}^{{ - 0.8}}} \times \exp \left( { - \frac{{6392}}{T}} \right).$$

To determine the rate constants for reactions 1.0.1–1.0.5 (Table 1), 2.2.1–2.2.5 (Table 2), and 3.22 (Table 3), the detailed equilibrium principle is applied. They are calculated taking into account the equilibrium constant K_eq. The tabulated data for the equilibrium constants are taken from reference book [19]. The dependence of the equilibrium constant on temperature is interpolated by the method of cubic splines.

For the comparative analysis of the rate constants of reactions reverse to dissociation (recombination reactions from Tables 1–3), they were also determined by the model of triple collisions [33]. The collision cross sections of the particles are calculated by the models of elastic collisions: hard spheres, hard spheres with variable diameter; with Lennard-Jones interaction potential; with Born–Mayer repulsion potential.