Transcript ME 533 Lecture 6 Pla..

Plasma Physics & Engineering
Lecture 6
THE ION-MOLECULAR REACTIONS.
• This is another group of fast processes taking place in
collisions of heavy particles.
• Some briefly discussed
– The positive ion-conversion A+ + B + M → AB+ + M, was
considered as a preliminary stage of the dissociative electron-ion
recombination.
– Clusterization of negative ions, using important
examples of the formation of stable complex ions
from a negative oxygen ion: O   C 2    C 3  
    2     3  
– The fast ion-molecular reactions, as discussed, make
an important contribution in the balance of charged
particles. These also can provide plasma-chemical
processes by themselves.
Ion-Molecular Polarization Collisions, the
Langevin Rate Coefficient.
• If a neutral particle itself has no permanent
dipole moment, the ion-neutral charge-dipole
interaction and scattering is due to the dipole
moment pm , induced in the neutral particle by
the electric field E of an ion:
e
p m   0   
2
4r
(2.81)
typical orbits of relative ion and
neutral motion during polarization
scattering
• when the impact parameter is high, the orbit has a
hyperbolic character
• when the impact parameter is sufficiently low, the
scattering leads to the Langevin polarization capture.
• the spiral trajectory results in “closer interaction” and
formation of the ion-molecular complex, which then can
either spiral out or provide inelastic changes of state and
formation of different secondary products.
• ion-molecular capture process based on polarization
occurs when
m   
e
e
4r 2 4 0 r 2
~ O(
1
 2 )
2
From this qualitative equality,→Langevin Cross Section
e 2
L 
 0  2
Langevin capture rate coefficient
kL   Lv
rewrite
≠f(T)
k Lion / neutral  2.3 *10 9 cm
 ,10 24 cm 3
3
sec *
, amu
• If an ion interacts with a molecule having
an induced dipole plus a permanent dipole
moment then the Langivin capture cross
section becomes larger.
• For molecules like H20 or HF, having large a
permanent dipole moment, the Langevin cross
sections and rate coefficients for the dipole
molecules and radicals can exceed by a factor of
10 the numerical values obtained for pure
polarization collisions
The Ion- Atom Charge Transfer Processes
• During a collision An electron can transfer from
– a neutral particle →a positive ion, or
– from negative ion to a neutral particle.
– charge transfer or charge exchange process.
• The charge exchange reaction without significant defect
of the electronic state energy during collision →
resonant charge transfer. Otherwise charge transfer
→ non-resonant.
•
• The resonant charge transfer is a non-adiabatic process
and usually has a very large cross section..
• charge exchange between a neutral particle B and a
positive ion A+
      
the Coulomb potential energy of an electron in
the Coulomb field of A+ and B+:
e2
e2
U ( z)  

4 0 z 4 0 rAB  z
•
e2
U max  
0 rAB
charge transfer is possible in the framework of classical
mechanic if the maximum of potential energy Umax <
initial energy EB of an electron which is going to be
transferred from level n of particle B:
IB
e2
B   2 
 U max
40 rAB
n
• What is the maximum distance between the interacting
heavy particles when the charge transfer is still permitted
by classical mechanics?
max
rAB
3e 2 n 2

4 0 I B
• If the charge exchange is resonant and therefore
not limited by the defect of energy, the classical
class
2

reaction cross section chtr can be found -- rAB
• actual cross section of a resonant charge transfer >>
when taking into account the quantum mechanical effect
of electron tunneling from B to A+
•
This effect can be estimated by calculating the
electron tunneling probability Ptunn across a
potential barrier of height about IB and width d:
tunn  exp( 
 chtunn
.tr
2
 chtunn
cm

.tr
1
I B eV
2d

2meI B
IBd
1  2
 (
)(ln
_ ln v) 2
I B 8me

(6.5 *10 7  3 *10 8 ln v,
cm
)
sec
Non-Resonant Charge Transfer Processes.
        ,
  0.9eV
The principal potential curves, illustrating the
non-resonant charge transfer
Io=13.6 eV < IN=14.5 eV).
electron transfer from oxygen to nitrogen is an
exothermic process
and the separated N+O+ energy level is located
0.9 eV lower than the separated O+N+ energy
level.
• The endothermic reactions of charge
exchange, like the reverse process
N + O+ →N+ + O,
are usually very slow at low gas
temperatures with low energies of the
colliding ions and heavy neutral particles.
acidic behavior of non-thermal air plasma
• Ionization of air in non-thermal discharges
→N2+ ions
• low ionization potential and high dipole moment of water
molecules → fast charge exchange

 2   2   2   2 ,
can be significantly focused on
formation of water ions H2O+
• these ions can then react with neutral water molecules
in the quite fast ion-molecular reaction
 2     2    3   ,
• The selective generation of OH- radicals in non-thermal
air discharges is the fundamental basis for employing
discharges for purifying air from different pollutants.
Ion-Molecular Processes of Cluster Growth,
the Winchester Mechanism
• Ion-molecular reactions are very favorable to clusterization
• Besides Langevin capture -- Winchester Mechanism of ionmolecular cluster growth
• A key point of Winchester Mechanism is thermodynamic
advantage of the ion-cluster growth processes.
• Consider a sequence of negative ions defining the cluster
growth
(2.106)
1   2   3  ...   n  ...
• the corresponding electron affinities 1 ,  2 , 3 ,...,  n ,...
are usually increasing, ultimately reaching the value of the
work function (electron extraction energy), which is
generally larger than the electron affinity for small
molecules.
• Each elementary step reaction of the cluster growth has an
apriori tendency to be exothermic.
• Exothermic ion-molecular reactions have no activation
barrier and are usually very fast,
– thus the Winchester Mechanism explains effective
cluster growth based on ion-molecular processes.
• The phenomenon is important until the cluster becomes
too large and the difference in electron affinities becomes
negligible.
• Each elementary step includes cluster rearrangements
with an electron usually going to the furthest end of the
complex.
• Valid also for positive ion-clusters
– thermodynamic advantage also holds.
1   2   3  ...   n  ...
• Corresponding ionization energies I (1 ), I ( A2 ), I ( A3 ),..., I ( An ),...
are usually decreasing
• Each elementary step reaction of the cluster growth also
has apriori tendency to be exothermic for positive ions
as well
Dusty plasma formation in low-pressure silane
SiH4 and silane-argon SiH4 – Ar discharges
• nucleation process can be initiated by a dissociative
attachment to a silane molecule: e  SiH 4  SiH 3  H
•
then continues by the sequence
Sin H 2n 1  SiH 4  Sin 1 H 2n 3  H 2
e
e
SiH 4
SiH3
Si2 H 5
Si3 H 7
SiH 4*
SiH 4*
SiH 4*
• Thermal effects of the first 4 reactions of
in silane plasma
SiH 3  SiH 4  Si2 H 5  H 2  0.07eV
Si2 H 5  SiH 4  Si3 H 7  H 2  0.07eV
Si3 H 7  SiH 4  Si4 H 9  H 2  0.07eV
Si4 H 9  SiH 4  Si5 H 11  H 2  0.00eV
• Winchester mechanism shows the tendency of energy
effects on ion-cluster growth
ELEMENTARY PROCESSES OF
EXCITED MOLECULES
AND ATOMS IN PLASMA.
ELECTRONICALLY EXCITED ATOMS AND
MOLECULES IN PLASMA.
• Excited species, in particular vibrationally excited
molecules, are of special importance
•
Most of discharge energy in molecular gases focused on
vibrational excitation of molecules by electron impact.
– Often >more than 95% of electron gas energy →
vibrational excitation.
• Excited species subdivided into three groups:
– electronically excited atoms and molecules,
– vibrationally excited molecules and
– rotationally excited molecules
Electronically Excited Particles, Resonance
and Metastable States
• High Te in electric discharges provide high excitation rate
electronically excited states by electron impact.
• Energy of the electronically excited particles -- high
(about 5-10 eV),
• lifetime is generally very short (usually about 10-8 - 10-6
sec).
• If radiative transition to the ground state is not forbidden
by quantum mechanical selection rules, -- resonance
excited state.
– shortest lifetime ( about 10-8 sec) with respect to
radiation,
– direct contribution in plasma kinetics is usually small.
• If the radiative transition is forbidden by selection rules,
--metastable excited states.
– no spontaneous transition; lifetime of the excited
particles can be much longer .
– can also lose their energy by means of different
collisional relaxation processes
Atom and it’s
Ground State
First Resonance
Excited States
Resonance
Energy
Low Energy
Metastable States
Metastable’s
Energy
Metastable’s
Lifetime
He (1s2 1S0 )
2p 1P10
21.2 eV
2s 3S1
19.8 eV
2*10-2 sec
2s 1S0
20.6 eV
9*103 sec
4s 3P2
16.6 eV
4*102 sec
4s 3P0
16.7 eV
20 sec
He(1s2 1S0 )
Ne (2s2p6 1S0 )
3s 1P10
16.8 eV
Ne (2s2p6 1S0 )
Ar (3s2p6 1S0 )
4s 2P10
11.6 eV
4s 2P0,20
11.6 eV
40 sec
Kr (4s2p6 1S0 )
5s 3P10
10.0 eV
5s 3P2
9.9 eV
2 sec
5s 3P0
10.6 eV
1 sec
Kr (4s2p6 1S0 )
H (1s 2S1/2 )
2p 2P1/2,3/20
10.2 eV
2s 2S1/2
10.2 eV
0.1 sec
N (2s2p3 4S3/2 )
3s 4P1/2,3/2,5/20
10.3 eV
2p3 2D3/2
2.4 eV
6*104 sec
N (2s2p3 4S3/2 )
2p3 2D5/2
2.4 eV
1.4*105 sec
N (2s2p3 4S3/2 )
2p3 2P1/20
3.6 eV
40 sec
N (2s2p3 4S3/2 )
2p3 2P3/20
3.6 eV
1.7*102 sec
2p4 3P1
0.02 eV
-
O (2s2p4 3P2 )
2p4 3P0
0.03 eV
-
O (2s2p4 3P2 )
2p4 1D2
2.0 eV
102 sec
O (2s2p4 3P2 )
2p4 1S0
4.2 eV
1 sec
O (2s2p4 3P2 )
3s 3S10
9.5 eV
Electronically Excited Atoms
• Collision of a high-energy plasma electron with a
neutral atom in a ground state can result in
energy transfer from the free plasma electron to
a bound electron in the atom. --- main source of
electronically excited atoms in plasma.
• The most important growth of energy of a
bound electron during the excitation is due to an
increase in the principal quantum number
“n”, but it also usually also grows with the value
of angular momentum quantum number
“l”.
• In general, energy levels of excited atoms
depend not only on the principal quantum
number “n” of the excited electrons and the
total angular orbital momentum “L”, but
also on the total spin number“S” and total
momentum quantum number “J”. Thus,
typically, the triplet terms (S = 1) lie below the
correspondent singlet terms (S = 0). Hence the
energy levels in corresponding excited, atomic
states are lower for the higher total spin
numbers.
• The total orbital angular momentum (L) and the total
spin momentum (S) are coupled by weak magnetic
forces.
• This results in splitting of a level with fixed values of L
and S into group of levels with different total momentum
quantum numbers J from a maximum J = L + S to a
minimum J = │L - S│(altogether there are 2S+1 energy
levels in the multiplet, if S , L.
• Also the energy difference inside of the multiplet
between two levels J+1 and J (with the same L and S) is
proportional to J+1.
• L-S coupling
• j-j coupling --- Nobel gases
standard designation of atomic levels
• N (2s2p3 4S3/2 )
-- ground state atomic nitrogen
• 2s2p3 --outer shell with the principal quantum number n=2
there are 2 s-electrons (l=0) and 3 p-electrons (l=1)
•
4S
3/2
--- the outer electrons of the ground state atomic
nitrogen not individually, but collectively
– “4” denotes the multiplicity 2S+1, which corresponds, to the
number of energy levels in a multiplet, if S ≤ L.
– S --denotes the total angular orbital momentum L=0 (other values
of L=1,2,3,4 corresponds to capital letters P, D, F and G).
– subscript “3/2” denotes the total momentum quantum number
J=3/2.
• From the Table, some additional term-symbols
• 2p 1P10
----
1st excited state of helium
– also contains a right-hand superscript “o”.
– is the designation of parity, which can be
either odd (superscript “o”) or even (no righthand superscript),
– depending on the odd or even value of the
sum of angular momentum quantum numbers
for individual electrons in the atom.
– For completed shells the parity is even.
Selection Rules
•
•
•
indicate whether an electric dipole
transition (and hence radiation emission
or absorption) is allowed or forbidden.
The parity must change. -- ground states
and first resonance excited states have
different parity.
The multiplicity must remain unchanged.
– Note: rule can not be applied to noble
gases,
•
Quantum numbers J and L must change
by +1, -1 or 0 (however transitions 0→0
are forbidden).
Electronic States of Molecules and Their
Classification
• Classification of electronically, excited states of diatomic
and linear polyatomic molecules is somewhat similar to
atoms.
• quantum number Λ =0,1,2,3 (corresponding Greek
symbols Σ, Π, Δ, Φ), describes the absolute value of the
component of the total orbital angular momentum along
the internuclear axis.
• If Λ ≠0, , the states are doubly degenerate because of
two possible directions of the angular momentum
component. Molecular terms are then specified by a
quantum number S, which designates the total electron
spin angular momentum and defines the multiplicity
2S+1.
• Similar to atomic terms, the multiplicity is written here
as a prefixed superscript. Thus, the designation 2Π
means Λ =1, S=1/2.
• In the case of Σ-states (e.g. Λ =0 ),
• To designate whether the wave function is symmetric or
antisymmetric WRT reflection at any plane including the internuclear
axis,- in the case of Σ-states (so when Λ=0), the right hand
superscripts “+” and “-” are used.
• ,Further, to designate whether the wave function is symmetric or
antisymmetric WRT the interchange of nuclei in homonuclear
molecules like such as N2, H2 , O2, F2 etc., the right hand
subscripts “g” or “u” are written.
– Remember, this type of symmetry also can be applied only for diatomic
molecules. Thus, the molecular term designation 1   means , S=0 and
g
the wave function is symmetric WRT both reflections at any plane
including the internuclear axis and to interchange of nuclei.
• Finally, to denote the normal ground state electronic term, the
capital X is usually written before the symbol of the term symbol.X 1 g
Capital letters A, B, C etc. before the main symbol denote
consequence of excited states having the same multiplicity as a
ground state. Small letters a, b, c, etc. before the main symbol
denote vice versa, the consequence of excited states having
multiplicity different from that of a ground state.
• Electronic terms of ground states of some diatomic molecules and
radicals are given in the Table 3.3 of the text together with
specification of electronic states of atoms, corresponding to
dissociation of the diatomic molecules.
• From this Table, the majority of chemically stable (saturated)
diatomic molecules have completely symmetrical normal electronic
state with S=0. In other words, a ground electronic state for the
majority of diatomic molecules is X 1 
or X 1 g in for the case of
homonuclear molecules. Exceptions of this rule, includes O2 (normal
term X 3 g ) and NO (normal term X 2 ). Obviously, this rule can
not be applied to radicals.