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5.3. VIBRATIONAL DISTRIBUTIONS other molecules gaining in energy. Such collisional exchange of energy becomes espe- cially important at high pressures where collisional frequency is high. These exchanges fall under two main categories [210]: Vibrational-Vibrational relaxation (V-V relax- ation), if vibrationally excited molecules collide with each other and exchange energy such that one gains the energy while the other loses the energy A(m)+A(n) −→ A(m+1)+A(n−1); (R2) Vibrational-Translational relaxation (V-T relaxation), if vibrationally excited molecules collide with the ground state molecule and lose the excess energy into translational en- ergy (kinetic energy or heat) A(m) + A(0) −→ A(m − 1) + A(0) (R3) It has to be noted that, in harmonic oscillators in each collision only one quantum can be changed (e.g m −→ m + 1 in reaction R2). Multi-quantum transitions are possible in anharmonic oscillators however, the probability of such a transition is in the range of 10−9 per collision and therefore can be neglected. Generally, VT relaxation is extremely slow when compared with creation by electron impact which helps in storing energy in vibrations in non-thermal discharges [36]. For all the processes discussed so far the reverse processes also exist the rate coefficients of which can be calculated using the principle of detailed balancing [211]. 5.3 Vibrational distributions To study the role of vibrational excitation in dissociation of a molecule, the population of vibrationally excited molecules as a function of the vibrational energy (E), the vibra- tional distribution f(E) has to be studied. In general a distribution is calculated by setting up a "master equation" – a set of differential equations describing competing processes and solving it as a function of time [210–212]. In addition to the processes discussed in section 5.2, dissociation of highly excited states is also a very important loss process that affects the vibrational distribution. When the system under consideration is in thermal equilibrium, f(E) can be de- scribed with a Maxwellian distribution with the same temperature (Tv) as that of gas temperature (T0). However, the main attraction of a non thermal plasma is deviation from equilibrium thus driving the system into a desired state – for example enhancing dissociation rates than dictated by thermal rates. Treanor et al [211] considered one ex- ample of such a non thermal distribution where VV relaxation between the molecules is 113PDF Image | Understanding CO2 containing non-equilibrium plasmas
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