Elementary plasma-chemical reactions can be described by micro-kinetic characteristics like cross-sections and reaction probabilities. There are several types of ionization processes including direct electron impact ionization, stepwise ionization, and ionization by photons or heavy particles. Collision parameters include the cross-section, probability, mean free path, and reaction rates. Direct ionization follows the Thomson formula at high energies. Molecular ionization is affected by the Frank-Condon principle where atomic positions remain fixed. Stepwise ionization occurs through excitation to an energy above the ionization potential. High-energy electrons like in beams follow the Bethe-Bloch formula for energy loss per unit length.

1. Plasma Chemistry
Chapter 2 Elementary Plasma-Chemical
Reactions
Presentation & Online Discussion
Si Thu Han
Date – 19.04.2020

2. Reference Book - Plasma Chemistry
Chapter 2 Elementary Plasma-Chemical Reactions
Page 12 ~ 20, A. 2.1.1 - 2.1.8

3. Contents
1. Elementary Charged Particles in Plasma
2. Elastic and Inelastic Collisions and Their Fundamental Parameters
3. Classification of Ionization Processes
4. Elastic Scattering and Energy Transfer in Collisions of Charged Particles: Coulomb Collisions
5. Direct Ionization by Electron Impact: Thomson Formula
6. Specific Features of Ionization of Molecules by Electron Impact: Frank-Condon Principle and Dissociative
Ionization
7. Stepwise Ionization by Electron Impact
8. Ionization by High-Energy Electrons and Electron Beams: Bethe-Bloch Formula
9. Conclusion

4. 2.1.1 Mechanism of the plasma-chemical process.
• Elementary reaction rates are determined by the micro-kinetic characteristics of
individual reactive collisions (like, for example, reaction cross-sections or
elementary reaction probabilities) as well as by relevant kinetic distribution
functions (like the electron energy distribution function [EEDF], or population
function of excited molecular states).
• Topic – on the micro-kinetics of the elementary reactions – on their cross
sections and probabilities – assuming, if necessary, conventional Maxwellian or
Boltzmann distribution functions.
• Elementary Charged Particles in Plasma
• the number densities of electrons and positive ions are equal or close in
quasineutral plasmas, but in “electronegative” gases (like O2, Cl2, SF6, UF 6,
TiCl4,etc.) with high electron affinity, negative ions are also effectively formed.
• Electrons are first in getting energy from electric fields, because of their low mass
and high mobility

5. 2.1.2. Elastic and Inelastic Collisions and Their Fundamental Parameters
The elastic collisions are those in which the internal energies of colliding particles do not change;
therefore, total kinetic energy is conserved.
Most in elastic collisions, like ionization, result in energy transfer from the kinetic energy of
colliding partners into internal energy
the internal energy of excited atoms or molecules can be transferred back into kinetic energy (in
particular, into kinetic energy of plasma electrons).
These elementary processes referred to as superelastic collisions.

6. The elementary processes can be described in terms of six major collision parameters: cross section,
probability, mean free path, interaction frequency, reaction rate, and finally reaction rate coefficient.
The crosssection,which can be interpreted as an imaginary circle of area σ
If two colliding particles can be considered hard elastic spheres of radii r1 and r2, their
collisional cross section is equal to π(r1 + r2)^2.
where nB is the number density (concentration) of the particles B.

7. The number of elementary processes, w, which take place per unit volume per unit time
is called the elementary reaction rate.
For bimolecular processes A + B, the reaction rate
can be calculated by multiplication of the interaction frequency of partner A with partner B,
νA, and by the number of particles A in the unit volume (their number density, nA):

11. 2.1.3. Classification of Ionization Processes
1. Direct ionization by electron impact is ionization of neutral and previously unexcited atoms,
radicals, or molecules by an electron whose energy is high enough to provide the ionization act in
one collision.
2. Stepwise ionization by electron impact is ionization of preliminary excited neutral species.
3. Ionization by collision of heavy particles takes place during ion–molecule or ion–atom collisions,
as well as in collision of electronically or vibrationally excited species, when the total energy of the
collision partners exceeds the ionization potential
4. Photo-ionization takes place in collisions of neutrals with photons, which result in the formation of
an electron–ion pair. Photo-ionization is mostly important in thermal plasmas and in some
mechanisms of propagation of non-thermal discharges.
5. Surface ionization (electron emission) is provided by electron, ion, and photon collisions with
different surfaces or simply by surface heating. This ionization mechanism is quite different from
the first four and will be considered separately later on in this chapter.

12. 2.1.4. Elastic Scattering and Energy Transfer in Collisions of Charged Particles: Coulomb Collisions
Electron–electron, electron–ion, and ion–ion scattering processes are the so-called Coulomb
collisions.
In an elastic collision of electrons with heavy neutrals or ions, m M and, hence,
γ = 2m/M, which means that the fraction of transferred energy is very small (γ ∼
10−4).

13. 2.1.5. Direct Ionization by Electron Impact: Thomson Formula
At high electron energies, ε >>I,
In this relation, the cross section σ0 = Zv πe^4/ (I^2 * (4πεo)^2) is about
the geometric atomic cross section (for molecular nitrogen, 10−16 cm2,
and for argon, 3 · 10−16 cm2).

14. 2.1.6. Specific Features of Ionization of Molecules by Electron Impact: Frank-Condon Principle and
Dissociative Ionization
Non-dissociative ionization of molecules by direct electron impact can be presented for the
case of diatomic molecules AB as
This process takes place when the electron energy does not greatly exceed the ionization potential.
Motion in atoms molecular vibrations
Time for atom motion >> plasma electron and molecule
As a result, all the atoms inside a molecule can be considered as being frozen during the process of electronic
transition,
This fact is known as the Frank-Condon principle.
When the electron energy is relatively high and substantially exceeds the ionization
potential, the dissociative ionization process can take place:
This ionization process corresponds to electronic excitation into a repulsive state of the
ion, (AB+)∗, followed by a decay of this molecular ion.

16. 2.1.7. Stepwise Ionization by Electron Impact
When the plasma density and, therefore, the concentration of excited neutrals are high
enough, the energy (I) necessary for ionization can be provided in two different ways.
First, like in the case of direct ionization, it could be provided by the energy of plasma electrons.
Second, the high energy of preliminary electronic excitation of neutrals can be converted in
the ionization act, which is called stepwise ionization.
If the level of electronic excitation is high enough, stepwise ionization is much faster than direct ionization,
because the statistical weight of electronically excited neutrals is greater than that of free plasma electrons.
At first, electron–neutral collisions prepare highly excited species, and then
a final collision with a relatively low-energy electron provides the actual ionization event.

17. The stepwise ionization rate coefficient ks can be found by the summation of partial rate coefficients ks,n i ,
corresponding to the nth electronically excited state, over all states of excitation, taking into account their
concentrations:
In this relation, Nn, gn, and εn are number densities, statistical weights, and energies of the electronically
excited atoms, radicals, or molecules, respectively; the index n is the principal quantum number.
From statistical thermodynamics, the statistical weight of an excited particle gn = 2gin2, where gi is the
statistical weight of an ion; N0 and g0 are concentration and statistical weights of ground-state particles,
respectively.
This means that excited particles with energy about εn = I − Te make the major contributions

18. This means that excited particles with energy about εn = I − Te
make the major contributions into sum . Taking into account that In ∼ 1/n^2, the
number of states with energy about εn = I − Te and ionization potential about In = Te
has
an order of n.
Sigma = e4/Te^ 2 (4πε0)^2,

19. 2.1.8. Ionization by High-Energy Electrons and Electron Beams: Bethe-Bloch Formula
The electron energy in electron beams applied today usually varies from 50 KeV to 1–2 MeV.
Typical energy losses of the beams in atmospheric-pressure air are about 1 MeV per
1 m (≈ 1 keV/mm).
Electron energy losses per unit length, dE/dx, can be
evaluated in the non-relativistic case by the Bethe-Bloch formula:
Z is the atomic number of neutral particles, providing the beam stopping; n0 is
their number density; and v is the stopping electron velocity.
Source -Heavy particles and rate coefficients in HF and MW discharges in Argon at
atmospheric pressure

20. Conclusion
• Elastic: momentum is redistributed between particles and the total kinetic energy remains
unchanged
• Inelastic: momentum is redistributed between particles but a fraction of the initial kinetic energy
is transferred to internal energy in one or more of the particles
• Superelastic: a third class also needs to be anticipated— here there is more kinetic energy
after the collision. Momentum is conserved and internal energy in the particles entering into a
collision is transferred into kinetic energy
• Electron and ion temperature can be measured by Langmuir Probe and by using these values,
plasma density can be calculated
• V-I curve is also important in studying the characteristics of plasma.
• ionization rate coefficient value determine which gas species can be produced from the specific
type of plasma

21. Thank you for your attention!