Raman spectroscopy., 2017 Uwe Burghaus, Fargo, ND, USA

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1 , 217 Uwe Burghaus, Fargo, ND, USA

2 HCl/DCl R data from NDSU Pchem lab class 28 R spectroscopy rotations & vibrations Vibration-rotation EXAMPLE HCl/DCl 9 8 inensity (a.u. 7 P branch R branch isotope splitting wave number in 1/cm inensity (a.u wave number in 1/cm v = 1 v = j = 3 j = 2 j = 1 j = j = 3 j = 2 j = 1 j =

3 Raman and nanoscience Dresselhaus, Jorios, Saito, Annu.Rev.Condens.Matter Phys. 1 (21 89 M.S. Dresselhaus, G. Dresselhaus, R. Saito, A. Jorio, Physics Reports 49 ( Raman Spectroscopy in Graphene Related Systsems, SBN Rather didactic outline. Way too epensive, however, as a tetbook for students. The basics E. Smith, G. Dent, Modern Raman Spectroscopy, A practical approach, Wiley, SBN Undergraduate level description with many practical notes and an applied description of Raman scattering theory. A good starting book. Most undergrad books include a few pages long introduction. Spectra of Atoms and Molecules, 3 rd Ed., Peter F. Bernath, Oford University Press, Chapter 8 Physics of Atoms and Molecules, B.H. Bransden, C.J. Joachain, Wiley, Chapter 9, 1 Molecular Spectroscopy, J.M. Brown, Oford Chemistry Primers, Vol. 55, Chapter 6

4 Application of to nano materials made this PowerPoint originally for a different class Raman scattering is the inelastic scattering of a photon. LASER sample Detector Characterization 1 U. Burghaus, 214

5 1917 Professor of Physics at the University of Calcutta 1928 Raman effect discovered together with K. S. Krishnan 193 Nobel Prize for Physics He was the first Asian and first non-white to receive any Nobel Prize in the sciences discovered photon spin Sir Chandrasekhara Venkata Raman ( ndian physicist Characterization 2 U. Burghaus, 214

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7 Raman effect is a three step process.. 2 Electron scatters, emitting phonon q, k 1 Photon ω 1, k 1 ecites electron hole pair Electron/hole pair 3 electron-hole pair recombines, emits photon ω 2, k 2 Virtual states ω 1, k 1 ω 2, k 2 Vibrational states q, k 4 Top Feynman diagram of the Raman effect; Bottom: energy diagram

8 Virtual states are.. Virtual states ω 1, k 1 sample ω 2, k sample 2 q, k n layman's terms: The photon polarizes (distorts the electron distribution of the target. A short lived photon-electron comple is formed. The scattering is fast such that the nuclear coordinates of the target are not affected, but only the charge distribution. That comple is unstable, i.e., a photon is released. Summary: n Raman scattering, the light distorts (polarizes the electron distribution of the scatterer forming a short lived state. A photon is re-emitted and phonon ecited. Quantum mechanics A virtual state is not a real eigenstate with distinct observables. Lifetime is restricted to energy-time uncertainty principle. The scattering is described by miing a ground and ecited state. 7

9 Polarization is key ntensity of Raman signal Pα 2 ω 4 LASER power Polarization of target Frequency of LASER µ = αe When photon interact with matter, the charge distribution of the target will be distorted by an amount that can be quantified by its polarizability. µ µ y µ z = α α α y z α α α y yy zy α α α z yz zz E E E y z n order to take the polarization of the photon and structure of the target into account a tensor description is used. µ = α E + α E + α y y z E z µ: dipole moment E: electrical field 8

10 Quantum Primer Bra-Ket Notation in Quantum Mechanics is. Consider it as a shorthand notation for integrals apparently introduced by Dirac F * r ρ = ψ Frˆ ρ ψ dv Bracket notation 9

11 Kramer Heisenberg Dirac Epression / photon-electron scattering µ = αe vibronic ground state (final state Vibronic state of an ecited electronic state µ: dipole moment E: electrical field α: polarizability vibronic ground state (initial state ( α ρσ constant GF = k ( F ω r ρ G ω L r σ iγ G + r ω ρ F G F + ω L r σ iγ scattered incident all vibronic states polarization direction of the photons dipole operator molecular polarization One can write this also as the probability for Raman scattering. 1

12 Kramer Heisenberg Dirac Epression / photon-electron scattering vibronic state of an ecited electronic state F vibronic ground state (final state G vibronic ground state (initial state α molecular polarization ρ scattered polarization direction of the photons σ incident polarization direction of the photons Σ sum over all vibronic states ( α ρσ GF = k ( F ω r ρ G ω L r σ iγ G + r ω ρ F G F + ω L r σ iγ * r G = ψ rˆ ψ GdV ρ ρ Miing the ground state and vibronic ecited state F rρ r G F r ρ σ Miing the final state and vibronic ecited state Similar but using the ecited state. The creation of the virtual state is described by miing electronic states. 11

13 Kramer Heisenberg Dirac Epression / photon-electron scattering vibronic state of an ecited electronic state F vibronic ground state (final state G vibronic ground state (initial state α molecular polarization ρ scattered polarization direction of the photons σ incident polarization direction of the photons Σ sum over all vibronic states ( α ρσ GF = k ( F ω r ρ G ω L r σ iγ G + r ω ρ F G F + ω L r σ iγ Ground state to intermediate state ntermediate state to final state Ecitation frequency (LASER input Line width of the intermediate state 12

14 Stokes and AntiStokes were not cusins but Virtual states ecitation Rayleigh classical scattering Stokes Raman scattering Anti-Stokes Raman scattering Vibrational states ecitation ecitation R absorption

15 Classical model undergrad version Where are Stokes & anti-stokes coming from? µ = αe E: eternal field Dipole moment depends on polarizability µ = αe cos(2πνt (t = equilibriu m + bond length of vibrating molecule ( t = ma cos(2πν t vib α dα α( equi + (. d =. = equi + µ = αe µ = α( + cos(2πν... Taylor epansion of polarizability dα t( ] E d cos(2πν [ equi. ma vib t 1 cos( *cos( y = [cos( y + cos( + y] 2 (t E 14a

16 Classical model undergrad version 14b...(...(... ]} 2 cos[(2 ] 2 {cos[(2 ( cos(2 ( cos(2 cos(2 ( cos(2 ( cos(2 ( cos(2 cos(2 ( ma. ma. ma. vib vib vib vib equi vib equi vib equi t t d d E t E t t d d E t E t E d d t E t E ν ν ν ν ν πν πν πν πν α πν α πν πν α πν α πν α πν πν α µ + = = + = + = ( = e d dα selection rule Rayleigh Stokes Anti-stokes ] cos( [cos( 2 1 *cos( cos( y y y + + =

17 Preventing that you fall asleep.. Q6 What has greater intensity stokes or anti-stokes? Q7 Aehhh? Who is Stokes? Q8 What is that? Virtual states Vibrational states

18 Preventing that you fall asleep.. Q6 What has greater intensity stokes or anti-stokes? Due to distribution of ecited vibrational states, at room temperature, Stokes lines dominate and for usually only Stokes lines are actually measured. (+ Raman shift, low energy side Q7 Aehhh? Who is Stokes? Q8 What is that? Rayleigh scattering Virtual states Vibrational states

19 Remember PChem364 quantum mechanics /1-5 intensity ν scat < ν Stokes lines ν ν scat > ν anti-stokes lines v = 1 v = v = 1 frequency vibrations & rotations pure rotations vibrations & rotations Selection rule Vibrations: Polarizability must change with vibration. V = 1 Rotations: Polarizability must be anisotropic. J =, 2 Compare: R dipole moment must change (resonant adsorption / desorption Raman polarizability must change (scattering process 17

20 f really want to take Raman spectra What Raman should purchase? UV, visible, NR monochromator Notch filter CCD detector Raman & microscope Practical aspects Sample preparation Sample container Calibration Spectrometer test Etc. nterferometer vs. dispersive Raman The basics E. Smith, G. Dent, Modern Raman Spectroscopy, A practical approach, Wiley, SBN

21 f really want to take Raman spectra Dispersive Raman Microscope Raman LASER 532 nm ecitation laser CCD detector sample diffraction gratings mirror LASER 532 nm ecitation laser CCD Fourier transform Raman microscope diffraction gratings LASER 1 μm ecitation laser sample sample beam splitter mirror R detector moveable mirror 21 interferometer

22 22 A few more details.. getting more intensity Virtual states phonon phonon phonon phonon ecitation Deecitation / e- recombination Electronic ecitation Non-resonant Resonant Double resonant 1-times greater intensity Raman from single layer graphene 1 st order 2 nd order

23 Kramer Heisenberg Dirac Epression eplains intensity enhancement of resonant Raman ( α ρσ GF = F r ρ rσ G k ( +... ω ω iγ G L At resonance ω G = ω GF ω L F rρ rσ G ( α ρσ GF k ( +... iγ large 2 4 Pα ω large 23

24 24 Some less commonly used versions Possible processes: one photon emission, two photon emission, one photon & 2 phonon scattering, etc.. Multi photon Raman (nonelinear spectroscopy: P α 2 ω 4 ntensity of Raman signal LASER power SERS Surface enhance Raman scattering SERRS Surface enhanced resonance Raman scattering CARS coherent anti-stokes Raman scattering Hyper Raman

25 Object prepare molecules in ecited vibrational levels (for subsequent eperiments by inducing transition with E = E 1 E (from v = to 1 Eample E: E = H 2 (v=, j= 1 E 1 = H 2 (v= 1, j= 1 How Two LASER frequencies needed 1 A pump laser pulse ω P 2 Stokes laser pulse ω S Condition needed: (ω P ω S = E 1 E = E Practical efficacy apparently 35%

26 Virtual states ω S ω S ω P Stokes Raman scattering ω P Stokes Raman scattering Vibrational states ecitation ecitation E = E 1 E Spontaneous Raman scattering SRS Stimulated Raman scattering

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28 How to apply to carbon nanotubes? 26 Nanotube Modeler

29 of carbon nanotubes RBM mode Radial Breathing Mode (RBM: C atoms vibrate in radial direction (in/out of the tube. Frequency depends on CNT diameter (12-35/cm. ω = + RBM d 12.5 G - mode G + mode G +/- -Band: G + mode: C atoms vibrate along the tube ais ~159/cm G - mode: C atoms vibrate along the circumferential direction ~157/cm Different for metallic and semiconducting CNTs. 27 See for eample: R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon nanotubes mperial College Press, 25

30 Eample - of carbon nanotubes SEM cm -1 Raman spectrum of metallic CNTs RBM Raman ntensity Wavenumber (cm -1 G combination bands 1 µm D D Wavenumber (cm -1 RBM: breathing mode D: defects (vacancies, impurities, etc. G: along tube ais and circumference Figures reproduced with permission of Ya-Ping Sun (Clemson University 28 For details, see: Possible effect of carbon nanotube crystal structure on gas-surface interactions the case of benzene, water, and n-pentane adsorption on SWCNTs at ultra-high vacuum conditions by M Komarneni,, A. Sand, J. Goering, U. Burghaus, M. Lu, L. Monica Veca, Ya-Ping Sun, Chem. Phys. Lett. 29

31 What about graphene? 1-LG: one layer graphene M-LG: multi layer graphene, HOPG 29

32 Eample - of graphene intensity (a.u. intensity (a.u graphene/silica G' or 2D G D wavenumber (cm -1 Grapphene/Cu G D G' or 2D wavenumber (cm -1 G-band ~1582/cm C-C stretch Position depends on graphene thickness Longitudinal optical phonon mode First order D-band ~135/cm (for ev ecitation Disorder band ntensity ~ defect density Defect induced double resonant Raman Double resonance 2D-band, G, ~2685/cm (for ev ecitation Overtone of D band Shape depends on layer thickness ndependent of defects Depends on ecitation energy Double resonance No RBM mode for graphene. All features are resonant Raman. 3 Spectra reproduced with permission of A Chakradhar, U. Burghaus (NDSU

33 More Eamples - of graphene intensity (a.u. 1 5 graphene/silica G G' or 2D pristine Graphene/silica intensity (a.u. Standard silicon bare silica support D D wavenumber (cm -1 Sample 9-Graphene/Silica wavenumber (cm -1 intensity (a.u. G G' or 2D Damaged Graphene/silica Sample No 13 HOPG wavenumber (cm -1 intensity (a.u. G Sample 12- graphene/silica intensity (a.u. D G' or 2D Damaged Graphene/silica wavenumber (cm wavenumber (cm -1 3 Spectra reproduced with permission of Nilushni Sivapragasam, N.M.K.M. Tilan Abey, U. Burghaus (NDSU

34 More Eamples - of graphene intensity (a.u. Blank Copper-Sample 5 Copper wavenumber (cm -1 Sample 6(2 graphene/cu Sample 6(2 graphene/cu (bc ntensity (arb.units Raw data Graphene/Copper ntensity (arb.units Corrected data Graphene/Copper Raman shift (cm Raman shift (cm -1 Sample 6(4 graphene/cu Sample 6(4 graphene/cu bc ntensity (arb.units Raw data Graphene/Copper intensity (a.u. Corrected data Graphene/Copper % (Raman shift (cm wavenumber (cm -1 3 Spectra reproduced with permission of Nilushni Sivapragasam, N.M.K.M. Tilan Abey, U. Burghaus (NDSU

35 Defects in nanocarbon can be detected by Disorder: stacking disorder Atomic defects D-to-G intensity is a disorder parameter Figure on the right: Reprinted with permission from (Mildred S. Dresselhaus, Ado Jorio, Mario Hofmann, Gene Dresselhaus, and Riichiro Saito, Nano Lett. 21, 1, Copyright (21 American Chemical Society. 32

36 nternet resources Very detailed roscopy_basics.pdf

37 Homework 1 n one sentence: what is? 2 What are the advantages of which made it recently a so popular technique? 36