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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 4r (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 4r 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) 40 z 40 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 40 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( 2d 2meI B 2 IBd 1 tunn ch.tr ( )(ln _ ln v) 2 I B 8me 2 chtunn cm .tr 1 I B eV (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 2n 1 SiH 4 Sin 1 H 2n 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.