Fridman-Macheret a-model

Reaction type Simple exchange Simple exchange Simple exchange Double exchange 

Simple geometry (Fig. 2-37) shows that an effective decrease of activation energy related to vibrational excitation is eqnal to 

In this relation, Aa+bc and Aab+c are characteristic slopes of the terms A + BC and AB + C (Fig. 2-37B). If these energy terms depend exponentially on reaction coordinates with decreasing parameters yi and y2 (reverse radii of corresponding exchange forces), then 

The subscripts 1 and 2 stand for direct (A + BC) and reverse (AB + C) reactions. Formulas (2-210) and (2-211) not only explain the main kinetic relation (2-205) for reactions of vibrationally excited molecules but also determine the value of the coefficient a (which is actually equal to a = hE /E y. 

Usually the exchange force parameters for direct and reverse reactions yi and yi are close yi/yi 1), which leads to the approximate but very convenient main formula of the Fridman-Macheret a-model  

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ELEMENTARY CHEMICAL REACTIONS OF EXCITED MOLECULES FRIDMAN-MACHERET a-MODEL... 

Note ttexp. coefficient obtained experimentally, amp, coefficient calculated from Fridman-Macheret a-model. 

Accuracy of Frldman-Macheret a-Model. Based on Table 2-26 for the a-efficiency coefficients, determine the relative accuracy for application of the Fridman-Macheret a-model to (1) endothermic, (2) exothermic, and (3) thermo-neutral reactions. 

The difference between vibrational and translational CO2 temperatures (Tv > 7 o)results in a maximum energy efficiency increase to 60% even in the case of the quasi-equilibrium balance of direct and reverse reactions (Evseev, Eletsky, Palkina, 1979), because direct endothermic reactions are mostly stimulated by molecular vibration, whereas reverse exothermic reactions are mostly stimulated by translational temperature (see the Fridman-Macheret a-model in Chapter 2). This efficiency corresponds to the case of super-ideal non-equilibrium (TV > To) quenching of the CO2 thermal plasma dissociation products (Potapkinetal., 1983). 

The vibrational energy of CO2 molecules is the most effective means for stimulation of endothermic reactions related to CO2 dissociation, in particular reactions (5-6) and (5-7) see the Fridman-Macheret a-model in Chapter 2. 

Table 2-26 permits one to classify chemical reactions into groups with specific probable values of the a-coefficients in each class. Such a classification (Levitsky, Macheret, Fridman, 1983) is presented in Table 2-27. Reactions are divided in this table into endothermic, exothermic, and thermoneutral categories and into simple- and double-exchange elementary processes. The classification also separates reactions with breaking bonds into excited or non-excited molecules. This classification table approach is useful for determining the efficiency of vibrational energy a in elementary reactions if it is not known experimentally or from special detailed modeling.

Figure 2- 1. Experimental and theoretieal values of the non-equilibrium dissoeiation factor Z as function of translational gas temperature in (a) molecular oxygen, (b) molecular nitrogen, and (c) molecular iodine (1) Macheret-Fridman model, (2) Kuznetsov model, and (3) Losev model.

The factor 5 is a fitting parameter of the Park model, which is recommended to be taken as 5 = 0.7. In initial publications, the effective temperature was taken approximately as Teff = V oTv. The Macheret-Fridman model permits the Park parameter to be found theoretically ... 

The negative temperature -U is a fitting parameter of the model with recommended values U = 0.6 77 - 3 77. The Macheret-Fridman model permits us to find theoretically the Marrone-Treanor parameter... 

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