Lecture 9. Detailed Balance, and Nonreactive Scattering of Molecules

Transcription

1 Lecture 9 Detailed Balance, and Nonreactive Scattering of Molecules 2014 D.J. Auerbach All rights reserved

2 Reading List 1. Cardillo, M.J., M. Balooch, and R.E. Stickney, Detailed Balancing and Quasi- Equilibrium in Adsorption of Hydrogen on Copper. Surface Science, 50(2): p (1975) 2. Rettner CT, Schweizer EK, Mullins CB Desorption and Trapping of Argon at a 2H-W(100) Surface and a Test of the Applicability of Detailed Balance to a Nonequilibrium System. J. Chem. Phys. 90: (1989) 3. Kleyn AW, Luntz AC, Auerbach DJ Rotational Energy-Transfer in Direct Inelastic Surface Scattering - No on Ag(111). Phys. Rev. Lett. 47: (1981) 4. Luntz AC, Kleyn AW, Auerbach DJ Observation of Rotational Polarization Produced in Molecule-Surface Collisions. Physical Review B 25: (1981) 5. Sitz, G.O., et al., Direct Inelastic-Scattering of N 2 from Ag(111).2. Orientation. Journal of Chemical Physics, 89(4): p (1988) 6. Kay BD, Raymond TD, Coltrin ME, Observation of direct multiquantum vibrational excitation in gas-surface scattering: NH3 on Au(111). PRL 59: (1987) 2

3 Summary Lecture 7-8 Smooth PES in surface plane (x-y) Nearly impulsive scattering If there is sufficient energy loss particles trap Scattering divides into two channels: Direct inelastic Trapping followed by desorption Predictive semi-empirical theory of trapping is available 3

4 What does Impulsive Scattering Mean Impulsive scattering means the time of a collision is infinitesimal. Nearly impulsive scattering means the time scale for a collision is short compared to the time the surface atoms need to respond Argon atom approaches a Pt atom Argon atom collides Collision is over before the Pt atom has time to move much Collision is like collision of billiard balls. 4

5 Billiard Ball Collisions Conservation of momentum and Energy Solution mv = mv + M v 1i 1f 2 f mv = mv + M v i 2 1f 2 2 f ( m M ) v1 i 2mv 1i v1f = v2 f = m+ M m+ M 2 ( m M) E1f = E1 i 2 ( m + M ) 5

6 Trapping probability vs. E i Hard Cube model with attractive well E f = (E i + ε)(m M) 2 /(m + M) 2 Solve for when E f = ε Critical energy for trapping ε E i ε c E i = ε 4mMε ( m M) 2 c atoms trap 6

7 Hard Cube Model with Attractive Well at Zero Kelvin surface temperature E I ε c = 4mMε ( m M ) 2 7

8 Glossary Ad-atom An atom that is adsorbed on a surface Ad-particle A single atom, cluster of atoms, molecule that is adsorbed on a surface. Chemisorption or Chemical Adsorption The binding of an atom or molecule to a surface with the formation of a new chemical bond between the adsorbed species and the surface. Chemisorption bond energies are usually 0.5 ev or stronger, although the term weak chemisorption is used to describe bonds of energies ~ 0.3 ev Good reference: Norskov, J.K. (1990). "Chemisorption on metal surfaces". Reports on Progress in Physics 53 (10):

9 Glossary Physisorption or Physical Adsorption The binding of an atom or molecule to a surface by van der Waals forces. Typical binding energies are mev 7

10 Glossary Adsorption The process where an atom or molecule goes from the gas phase to being physisorbed or chemisorbed on a surface Sticking Atom or molecule adsorbs for a long time Trapping Atom or molecule adsorbs for a short time 7

11 Summary 2: Why only 2 channels not many We can understand this by examining the simulated trajectories for Xe scattering from Pt(111) The trajectories show that once a Xe atom makes more than 2 bounces on the surface, it almost always goes on to trap rather than desorbing before it equilibrates. Thermal motion of the lattice is not sufficient to make up for the energy lost after more than 2 bounces. This picture obviously could change if T S is increased enough 11

12 Schematic view of trapping Atom bounces when it s electron cloud overlaps with that of metal Multiple bounces almost always lead to trapping 12

13 Trapping-Desorption: Mysteries Desorption appears to be nonequilibrium 13

14 Angular distribution of the trapping desorption component Ar/ 2H-W(100) A broad angular distribution is observed for trappingdesorption component. Approximately Cos(θ f ) But it is actually somewhat broader How can that be? Shouldn t desorption follow the equilibrium cosine law Rettner, Schweizer, Mullins, JCP, 90(7), (1989) 14

15 The temperature of desorbing Ar lags T S Ar / 2H-W(100) ϑ ι =60 o ϑ f =-25 o E i =35 mev T trans 182K 130K 80K Is this consistent with equilibrium? Shouldn t T desorb = T S 15

16 Principle of Detailed Balance We shall see that All of the properties of desorption can be predicted from a knowledge of the properties of adsorption And vice versa Incidence angle dependence of the trapping dictates the favored angles of desorption And vice versa Incidence energy dependence of trapping dictates the translational energies found in desorption And vice versa All the mysteries are resolved 16

17 Principle of Detailed Balance At equilibrium the flux of each distinguishable incident state is matched by an equal but opposite flux of that state leaving the surface. f desorption = f adsorption 17

18 But can we assume equilibrium??? UHV surface science or surface scattering experiments are not conducted at equilibrium. Can we use detailed balance??? Consider the following thought experiment Flux Leaving without gas = equilibrium flux if Structure doesn t change when removing gas Distribution of the states of adsorbed molecules doesn t change 18

19 Adsorption Flux The adsorption flux is the product of the equilibrium distribution in the gas and the adsorption or sticking probability Incidence angle Incidence velocity equlibrium f = S( θ, v, V, J, T,...) f ( θ, v, V, J, T = T,...) adsorb i i i i S incident i i i i Gas S Vibrational Quantum Number Rotational Quantum Number 19

20 Desorption Distributions Detailed balance: f desorption = f adsorption f ( θ, v, V, J, T,...) = f ( θ, v, V, J, T,...) desorption f f f f adsorption i i i i equlibrium = S( θ, v, V, J,...) f ( θ, v, V, J, T,...) i i i i incident i i i i Adsorption distribution depends on the properties of gas in equilibrium at T S and on the sticking probability as a function of incidence conditions. Therefore, the desorption distribution depends on sticking probability as a function of the incidence conditions, S( θ, v, V, J, T,...) i i i i S 20

21 Example 1: Detailed balance between adsorption and desorption when S= constant In adsorption: Flux is number density * velocity φ in = ρ v Flux to a flat surface is φ to-a-flat-surface = ρ v = ρ v cos θ If there is no dependence of the sticking on θ Flux away from a flat surface is φ away-from-a-flat-surface cos θ Cosine Law for desorption Similarly if the adsorption probability is independent of velocity, the outgoing flux will follow a Maxwell- Boltzmann velocity distribution 21

22 Example 2 Activated Adsorption If adsorption has an activation barrier, the sticking probability will increase with incidence energy Only high energy molecules stick. The corresponding desorption distribution will be hyperthermal. 22

23 Example 3 Trapping If adsorption has no activation barrier, the sticking probability will decrease as the incidence energy gets larger than the well depth Only low energy molecules stick. Therefore the desorption distribution will be sub-thermal. 23

24 Ar/2H-W(100): The mysteries TOF Data: sub-thermal desorption Angular Distributions: Broader the cos(θ) T trans 182K 130K 80K 2013 D.J. Auerbac h 24

25 Resolution: Detailed Balance By multiplying the trapping probability function by a Boltzmann translational energy function at T S, one obtains the desorption translational energy function Agrees with the experimental result T desorb =183 K for T S =273 K 25

26 Detailed Balance Ar / 2H-W(100) Take trapping probability function from experiments Multiply by incident Boltzmann distribution to get the adsorption distribution and hence the predicted desorption distribution Convert to TOF space and compare directly to the experiments Look carefully there is a solid line under these points which is the result of this procedure 26

27 What About the Angular distributions? At larger incidence angles, higher velocities can be trapped. T S low This reflects the fact that the parallel momentum need only be partly dissipated to promote trapping T S high So at larger angles one has higher velocities, which means higher flux. These higher angles play an increasing role at elevated temperatures October 14, 2014 Chemical Dynamics at Surfaces Dalian - Lecture 9 27

28 Detailed Balance for Angular distributions Notice that the curve converges on cos(θ) in the limit of low T s where the sticking probability is approximately 100% regardless of angles and energies October 14, 2014 Chemical Dynamics at Surfaces Dalian - Lecture 9 28

29 Experimental Results: Angular distributions broaden with increasing T S Chemical Dynamics at Surfaces Dalian - October 14, 2014 Lecture 9 29

30 Conclusions Ar / 2H-W(100) Principle of Detailed Balance works for Ar / 2H-W(100) Cos(θ) distribution is a dynamical signature of trapping/desorption for unit (or constant) sticking probability. Quasi equilibrium desorption angular distributions depend on dynamical factors May be broader or narrower then Cos(θ) Quasi equilibrium velocity distributions depend on dynamical factors May be sub-thermal or hyperthermal 30

31 Apparent Violations of the Principle of Detailed Balance Naive application of the detailed balance can give the wrong results 31

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33 Naive application of detailed balance S( E ) = H( E E ) = H( E cos ( θ ) E ) 2 n n 0 i i 0 MB SE ( n ) θ = 0 θ = 45 i i Energy of desorbing D 2 increases strongly with θ f 33

34 Naive application of detailed balance Energy of desorbing D 2 increases strongly with θ f 34

35 Detailed balance with a realistic S(En) Michelsen and Auerbach, JCP 94, 7502 (1991) 35

36 Naive application of detailed balance 36

37 Naive application of detailed balance Large energetic barrier to adsorption desorption at high energy 37

38 Detailed Balance with Measured S0(Ei) Measured S 0 (Dürr et al.) Detailed balance prediction, Dürr et al. Measured desorption energy, Matsuno et al. Dürr, Rashke, Höfer, JCP 111, 10411, (1999) Matsuno et al., JCP, 122, (2005) 38

39 Summary The principle of detailed balance is based on an assumption of thermal equilibrium Nonetheless, detailed balance makes correct predictions for adsorption and desorption under the quasi equilibrium conditions of real experiments It is easy to get it wrong. Key to proper use of detailed balance: compare adsorption and desorption under the same conditions, e.g. same Ts use a realistic form of SE (, θ, T) based on experiment i i S 39

40 Homework Problem Detailed Balance a) Calculate the energy distribution of desorbed particles using the principle of detailed balance, surface temperature = 300 K sticking probability is given by S (E) = exp [- (E / E 0 ) 2 ] with E 0 = 40 mev. b) Compare the result with a thermal distribution. What temperature leads to the best fit? c) Why do the desorbed particles come off colder than the surface? d) What happens when the parameter E 0 is decreased? 40

41 Scattering of Molecules from Surface Coupling to Phonons, Molecular Rotation, and Vibration, 41

42 State Resolved Measurements are Needed to Observe Rotational or Vibrational excitation N 2 / Pt(111): No sign of new peaks due to rotational or vibrational excitation 42

43 Laser Induced Fluorescence Laser Excitation to Excited electronic state Fluorescence observed by Photomultiplier tube Requirements Long lived excited electronic state High fluorescence quantum yield High sensitivity 10 6 molecules/cm 3 43

44 Resonance Enhanced Multiphoton Ionization Multiphoton Laser Excitation to Excited Electronic State Subsequent Ionization Advantages Excited state can be short lived 100% ion collection efficiency Sensitivity higher than LIF 10 3 molecules/cm 3 44

45 Scattering Machine with State Specific Detection 45

46 Rotational Excitation Seeded supersonic beam of NO incident on clean Ag(111) Few rotational states Facile rotational excitation Direct T R transfer Unexpected peak in population vs. rotational state Rotational Rainbow Kleyn, Luntz, Auerbach, PRL (1981) 46

47 Data presented on linear scale without degeneracy weighting 47

48 Rotational Rainbows N 2 / Ag(111) Kummel, Sitz, Zare, JCP

49 Optical Rainbows 49

50 Optical Rainbow 50

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52 Simulations of Scattering of NO + Ag(111) Analysis: Rotational Rainbow results from strong orientation dependence to energy transfer Prediction: There will be a strong orientation dependence to the trapping (adsorption) probability J.C. Tully and M.J. Cardillo, Science, 223, 445 (1984) Muhlhausen, Williams, Tully, J. Chem. Phys. 83, 2594 (1985) 53

53 Orientated Beams Oriented Beam Scattering Instrument NO / Pt(111) Ei =.18 ev, Ts= 573 K E.W. Kuipers, M.G. Tenner, A.W. Kleyn (1989) 54

54 Rotational Polarization We can learn about the direction the molecule is rotating by using the dependence on LIF signal on the direction of polarization of the exciting radiation. Distribution of orientations of J LIF intensity 55

55 Polarization Anisotropy 56

56 Observed Rotational Polarization LIF Intensity varies strongly with the direction of polarization of the exciting radiation Strong Polarization with J perpendicular to n Cartwheel motion not Helicopter motion Luntz, Kleyn, Auerbach, Phys. Rev B, (1982) 57

57 N2 / Ag(111) 2 + 1REMPI Detection Sitz, Kummel, Zare, JCP 89, 2559 (1988) 58

58 Rotational Polarization: N 2 / Ag(111) Quadrupole Alignment Parameter: -1 Perfect Cartwheel Motion Sitz, Kummel, Zare, JCP 89, 2559 (1988) 59

59 Determining Orientation: N 2 / Ag(111) Polarization Which way does J point Orientation Which way is the molecule rotating With 2 photon excitation with elliptically polarized light, it is possible to determine orientation Sitz, Kummel, Zare, Tully, JCP 89, 2572 (1988) 60

60 Dependence of Signal on Polarization Asymmetry about β = 0 indicates orientation 61

61 Orientation is a probe of in-plane force Sitz, Kummel, Zare, Tully, JCP 89, 2572 (1988) 62

62 Frictional Cube Model Sitz, Kummel, Zare, Tully, JCP 89, 2572 (1988) 63

63 Vibrational excitation 64

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65 Attempt to observe vibrational excitation in TOF data for CH 4 scattering from Pt(111) No sign of any additional peaks in the TOF spectrum corresponding to energy loss of 1 vibrational quantum Janda, Hurst, Cowin, Wharton, Auerbach, Surf. Sci (1983) 66

66 State Specific Detection: NH 3 / Au(111) 67

67 NH 3 / Au Vibrational Excitation Finger print of adiabatic T V energy transfer Clear E kin Threshold No effect of T s Kay et al., PRL, 59, (1987)

68 End of Lecture 9 Detailed Balance and Nonreactive Molecular Inelastic Scattering 69

69 Preview of Lecture 10 Nonadiabatic Electronic Effects: coupling of vibrational motion to electron hole pairs 70

70 Vibrational Excitation NO(v=0) + Ag(111) Probability Increases with E i no threshold E i Not T V Energy comes from the surface Strong effect of T s Arrhenius like dependence Rettner, Fabre, Kinman, Auerbach, PRL 55, 1904 (1985) 71

71 Vibrational excitation via Electron-Hole Pairs Thermally Excited EHP E vac conduction band E F v = 1 v = 0 Adsorbate Metal 72

72 Vibrational Excitation Mechanism Decay of a thermally excited electron-hole pair NO NO - NO E = E vib 74

73 EXTRA SLIDES 75

74 Stimulated Emission Pumping Field and Kinsey, JOURNAL OF CHEMICAL PHYSICS 75 (5):

75 Desorption Distributions Detailed balance: f desorption = f adsorption Adsorption distributions depends on sticking probability Therefore, the desorption distribution depends on sticking probability as a function of the incidence conditions, S( θ, v, V, J, T,...) i i i i S 77

76 Principle of Detailed Balance as applied to Ar on 2-H/W For adsorption f ads = β ( EI, ΘI ) = 78( cosθ ) e E I 1 I For Desorption mv f ( v, Θ, T ) = β ( v, Θ)cosΘ v 3 e 2kT desorb S Velocity distribution at a given desorption angle. 2 78

77 Experimental Results: Angular distributions broaden with increasing T S Chemical Dynamics at Surfaces Dalian - October 14, 2014 Lecture 9 79

78 REMPI Rempi Advantages State specific detection CO REMPI in a UHV chamber while turning ion gauges on and off Naturally also species specific detection High sensitivity: CO to at least 5 x Torr High time resolution, ns pulsed laser Fs pulsed lasers October 14, 2014 Chemical Dynamics at Surfaces Dalian - Lecture 9 80

79 Resonance Enhanced Multi-photon Ionization (REMPI) of HCl Energy HCl + + e ω ion ω 1 Automatic absorption of 3 rd photon to ionization continuum HCl (E 1 Σ + ) Tightly focussed Laser beam REMPI signal, arb. units ω 1 v=2 v=1 v=0 HCl (X 1 Σ + ) Q(8) E 1 Σ + (v'=0) - X 1 Σ + (v"=2) two-photon energy, cm -1 October 14, 2014 Chemical Dynamics at Surfaces Dalian - Lecture 9 81

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81 Optical Pumping and Detection of NO Capabilities Franck-Condon Pumping of low vibrational states Stimulated Emission Pumping of high vibrational states Laser induced fluorescence detection Resonance enhanced multiphoton Ionization detection October 14, 2014 Chemical Dynamics at Surfaces Dalian - Lecture 9 83