If in analytical glow discharge plasma, two oxygen atoms combine with each other to form oxygen molecule, then what could be the factors which are important in this process?
the question is not very clear. I will try to explain you something about the recombination kinetics.
Let us consider a plasma containing atoms and molecules of oxygen.
You have two kind of processes:
O+O + X -> O2(v) + X
-> O2*+X
where you produce molecules in the ground electronic state in vibrationally excited levels, mostly very highly excited, or you produce electronically excited molecules.
The parameters governing these processes are the pressure, the temperature and the composition.
Things can be more complex in air, finding alternative reaction path.
According to the dissociation degree, the major contribution can come from X=O.
Now you also have electrons and one must consider the dissociation path.
The dissociation mechanisms in a pure oxygen plasma is not well known yet and highly excited molecules can easily dissociate.
Moreover you can produce atoms also by dissociative attachments,
O2+e->O+O-
In conclusion, to understand your project you should consider bnot only recombination, but also atom production mechanisms.
In the case of discharge plasma, X can be the walls of the discharge or any third particle including plasma species. To understand this process, further two questions are arising, 1) what is the role of X in this process? - should the X would be neutral atom or if considered as wall then would it be grounded.? 2) The energy released as the result of recombination (which is equal to the dissociation energy of the molecules) would transfer to excite the molecule as you mentioned above or would be transferred to the third particle?
X can be atom or molecule, or any other species present in the gas (also ions and electrons but usually their contribution is small).
In the case of gas phase recombination, the molecules are produced mainly in highly excited states which are depleted by vT collisions or by dissociation.
Therefore >90 % goes in internal energy (vibration). This is according to the rate coefficients available now. (see publications of Esposito and of Billing)
The behavior of the surface is completely different.
In gas phase processes, the recombination is a 3-body reaction,
Wall recombination follow two different path, if I call O(w) an atom adsorbed on the wall,
the wall recombination can happen as
O(w)+O->O2(v)
O(w)+O(w)->O2(v)
This require an assumption on the covering of the surface by atoms.
In this case the energy of the recombination should also account for the adsorption energy of the atoms. The distribution of molecules depends on the material.
Cacciatore et al made some calculation for oxygen on silica, showing (if I remember well)
an uniform distribution in vibrational levels.
There are some calculations by Armenise et al in the boundary layer of hypersonic flow.
To consider surface processes you ned also e diffusion equation for atoms.