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

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1 , 2017 Uwe Burghaus, Fargo, ND, USA

HCl/DCl IR data from NDSU Pchem lab class 2008 IR spectroscopy rotations & vibrations Vibration-rotation EXAMPLE HCl/DCl 90 80 inensity (a.u.

2 HCl/DCl IR data from NDSU Pchem lab class 2008 IR spectroscopy rotations & vibrations Vibration-rotation EXAMPLE HCl/DCl inensity (a.u.) 70 P branch R branch isotope splitting wave number in 1/cm inensity (a.u.) wave number in 1/cm v = 1 v = 0 j = 3 j = 2 j = 1 j = 0 j = 3 j = 2 j = 1 j = 0

4 Raman and nanoscience Dresselhaus, Jorios, Saito, Annu.Rev.Condens.Matter Phys. 1 (2010) 89 M.S. Dresselhaus, G. Dresselhaus, R. Saito, A. Jorio, Physics Reports 409 (2005) Raman Spectroscopy in Graphene Related Systsems, ISBN Rather didactic outline. Way too expensive, however, as a textbook for students. The basics E. Smith, G. Dent, Modern Raman Spectroscopy, A practical approach, Wiley, ISBN 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, Oxford University Press, Chapter 8 Physics of Atoms and Molecules, B.H. Bransden, C.J. Joachain, Wiley, Chapter 9, 10 Molecular Spectroscopy, J.M. Brown, Oxford Chemistry Primers, Vol. 55, Chapter 6

5 Application of to nano materials I made this PowerPoint originally for a different class Raman scattering is the inelastic scattering of a photon. LASER sample Detector Characterization 1 U. Burghaus, 2014

6 sample LASER LASER sample Detector transmission Detector scattering Detector LASER sample reflection / scattering Characterization 1

7 1917 Professor of Physics at the University of Calcutta 1928 Raman effect discovered together with K. S. Krishnan 1930 Nobel Prize for Physics He was the first Asian and first non-white to receive any Nobel Prize in the sciences discovered photon spin -) Apparently one of his cousins also won the Nobel price (Subrahmanyan Chandrasekhar) Sir Chandrasekhara Venkata Raman ( ) Indian physicist It was discovered by C. V. Raman and K. S. Krishnan (who was a student of C.V. Raman) in liquids, [1] and independently by Grigory Landsberg and Leonid Mandelstam in crystals. [2] The effect had been predicted theoretically by Adolf Smekal in [3] Characterization 2

9 Raman effect is a three step process.. 2) Electron scatters, emitting phonon q, k 1) Photon ω 1, k 1 excites 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

10 Virtual states are.. Virtual states ω 1, k 1 sample ω 2, k sample 2 q, k In layman's terms: The photon polarizes (distorts) the electron distribution of the target. ω 1, k 1 sample A short lived photon-electron complex is formed. The scattering is fast such that the nuclear coordinates of the target are not affected, but only the charge distribution. That complex is unstable, i.e., a photon is released. ω 2, k 2 7

11 Virtual states are.. Virtual states ω 1, k 1 sample ω 2, k sample 2 q, k In layman's terms: The photon polarizes (distorts) the electron distribution of the target. A short lived photon-electron complex is formed. The scattering is fast such that the nuclear coordinates of the target are not affected, but only the charge distribution. That complex is unstable, i.e., a photon is released. Summary: In Raman scattering, the light distorts (polarizes) the electron distribution of the scatterer forming a short lived state. A photon is re-emitted and phonon excited. 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 mixing a ground and excited state. 7

12 Polarization is key Intensity of Raman signal I 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. x α xx µ y = α yx µ z α zx α zy α zz E E E µ α xy α xz x In order to take the polarization of the photon and structure of the target α yy α yz y into account a tensor description is used. z µ = α E + α E + α x xx x xy y xz E z µ: dipole moment E: electrical field 8

13 Preventing that you fall asleep.. Q1) What is the difference between absorption spectroscopy and? Q2) Why is the sky blue? Q3) Who is Smekal? What did he do in 1923? Q4) Name at least three absorption spectroscopy techniques. Q5) Why is often a wavenumber used rather than the frequency? 5

14 Preventing that you fall asleep.. answers Q1) What is the difference between absorption spectroscopy and? One major difference is the required resonance condition for absorption spectroscopy which is not required for a scattering process. Q2) Why is the sky blue? Q3) Who is Smekal? What did he do in 1923? Q4) Name at least three absorption spectroscopy techniques. 6 There are more or less sophisticated answers to that question. Density fluctuations of the atmosphere can cause Rayleigh scattering, Briefly, blue (short wavelength) scatters more than red (long wavelength), i.e., the sky is blue. Similarly, at sunset the light travels a longer way through the atmosphere and red light scattered less efficiently. X-ray absorption, NMR, EPR, IR, FTIR Q5) Why is often a wavenumber used rather than the frequency? We deal with processes proportional to an energy. The wavenumber is linear with energy. Wavelength could be measured more precisely than speed of light.

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

17 Raman effect involves at least three states Virtual states I vibronic state of an excited electronic state Vibrational states F vibronic ground state (final state) G vibronic ground state (initial state)

Kramer Heisenberg Dirac Expression / photon-electron scattering µ = αe vibronic ground state (final state)

vibronic ground state (initial state) ( α ρσ constant ) GF = k I ( F ω r ρ GI I I ω L r σ iγ I G + I r ω ρ

direction of the photons dipole operator I vibronic state of an excited electronic state F vibronic ground

18 Kramer Heisenberg Dirac Expression / photon-electron scattering µ = αe vibronic ground state (final state) Vibronic state of an excited electronic state µ: dipole moment E: electrical field α: polarizability vibronic ground state (initial state) ( α ρσ constant ) GF = k I ( F ω r ρ GI I I ω L r σ iγ I G + I r ω ρ IF G F + ω L r σ iγ I I ) molecular polarization 10 scattered incident all vibronic states polarization direction of the photons dipole operator I vibronic state of an excited electronic state F vibronic ground state (final state) G vibronic ground state (initial state) One can write this also as the probability for Raman scattering.

19 Kramer Heisenberg Dirac Expression / photon-electron scattering I vibronic state of an excited 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 I ( F ω r ρ GI I I ω L r σ iγ I G + I r ω ρ IF G F + ω L r σ iγ I I ) * I r G = ψ Irˆ ψ GdV ρ ρ Mixing the ground state and vibronic excited state I I I F rρ I I r G F r ρ σ I Mixing the final state and vibronic excited state I Similar but using the excited state. The creation of the virtual state is described by mixing electronic states. 11

20 Kramer Heisenberg Dirac Expression / photon-electron scattering I vibronic state of an excited 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 I ( F ω r ρ GI I I ω L r σ iγ I G + I r ω ρ IF G F + ω L r σ iγ I I ) Ground state to intermediate state Intermediate state to final state Excitation frequency (LASER input) Line width of the intermediate state At least we know what all the symbols are 12

21 Preventing that you fall asleep.. Q--) Again what is the difference between the absorption and scattering of a photon? Virtual states τ very small Electronic state τ larger ω 1, k 1 ω 1, k 1 Vibrational states Electronic state 13

22 14 Stokes and AntiStokes were not cusins but... SUMMARY Virtual states excitation Rayleigh classical scattering Stokes Raman scattering Anti-Stokes Raman scattering Vibrational states excitation excitation IR absorption

25 Classical model undergrad version Where are Stokes & anti-stokes coming from? µ x = αe E: external field Dipole moment depends on polarizability µ = αe 0 cos(2πνt) x x x x(t) = equilibriu m + bond length of vibrating molecule x( t) = xmax cos(2πν t) vib α dα α( xequi ) + x( ) x x. dx =. = equi +... Taylor expansion of polarizability µ = α( x ) + x cos(2πν dα t)( )] E dx cos(2πν ) [ equi. xmax vib 0 t 1 cos( x )*cos( y) = [cos( x y) + cos( x + y)] 2 α E 14a

26 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 ) ( max 0 0. max max 0 0. vib vib vib vib equi vib equi vib equi x t t dx d x E t E x t t dx d x E t E x t E dx d t x E t E x ν ν ν ν ν πν πν πν πν α πν α πν πν α πν α πν α πν πν α µ + = = + = + = 0 ) ( = e x x dx dα selection rule Rayleigh Stokes Anti-stokes )] cos( ) [cos( 2 1 ) )*cos( cos( y x y x y x + + = ) cos(2 )] )( cos(2 ) ( [ 0 max. t E dx d t x x vib equi x πν α πν α µ + =

27 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

Preventing that you fall asleep.. Q6) What has greater intensity stokes or anti-stokes? -) Due to distribution of excited vibrational states, at room temperature, Stokes lines dominate.

28 Preventing that you fall asleep.. Q6) What has greater intensity stokes or anti-stokes? -) Due to distribution of excited vibrational states, at room temperature, Stokes lines dominate. -) For usually only Stokes lines are actually measured. Q7) Aehhh? Who is Stokes? Q8) What is that? Rayleigh scattering Virtual states Vibrational states

29 Remember PChem364 quantum mechanics SUMMARY /10-5 intensity ν scat < ν 0 Stokes lines ν 0 ν scat > ν 0 anti-stokes lines v = 0 1 v = 0 0 v = 1 0 frequency vibrations & rotations pure rotations vibrations & rotations Selection rule Vibrations: Polarizability must change with vibration. V = 1 Rotations: Polarizability must be anisotropic. J = 0, 2 Compare: IR dipole moment must change (resonant adsorption / desorption) Raman polarizability must change (scattering process) 17

30 Preventing that you fall asleep.. Q9) What causes the most intense Raman lines, symmetric or asymmetric vibrations? Q10) What has the highest vibrational frequencies? -) strong bonds & light atoms -) weak bonds & heavy atoms Q11) Again what is the difference between the absorption and scattering of a photon? 18

31 Preventing that you fall asleep.. Q9) What causes the most intense Raman lines, symmetric or asymmetric vibrations? For Raman active modes a change in polarization is required. Usually symmetric vibration cause the largest polarizability and most intense Raman lines. This is in contract to IR, here change in dipole moment is required, which is most efficient for asymmetric molecules. O C O Symmetric vibration Large polarization Raman active O C O Asymmetric vibration Large dipolmoment IR active O O One vibration 3N-5=3*2-5=1 N O One vibration 3N-5=3*2-5=1 Raman active Raman active No dipolmoment, IR inactive dipolmoment, IR active Q10) What has the highest vibrational frequencies? -) strong bonds & light atoms -) weak bonds & heavy atoms 1 ν = 2π k m 19

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

34 If I really want to take Raman spectra Dispersive Raman Microscope Raman LASER 532 nm excitation laser CCD detector sample diffraction gratings mirror LASER 532 nm excitation laser CCD Fourier transform Raman microscope diffraction gratings LASER 1 μm excitation laser sample sample beam splitter mirror IR detector moveable mirror 21 interferometer

36 22 A few more details.. getting more intensity Virtual states phonon excitation Deexcitation / e- recombination Non-resonant

37 22 A few more details.. getting more intensity Virtual states phonon excitation Deexcitation / e- recombination Electronic excitation Non-resonant

38 22 A few more details.. getting more intensity Virtual states phonon phonon phonon phonon excitation Deexcitation / e- recombination Electronic excitation Non-resonant Resonant Double resonant 1 st order 2 nd order 1000-times greater intensity (e.g. Raman from single layer graphene is possible)

39 Why??? At resonance ω GI = ω GF ω L Virtual states I vibronic state of an excited electronic state ωgi ωgf Vibrational states F vibronic ground state (final state) G vibronic ground state (initial state) ω = ω = ω L LASER excitation

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

41 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): x I P α 2 ω 4 Intensity of Raman signal LASER power SERS Surface enhanced Raman scattering SERRS Surface enhanced resonance Raman scattering CARS coherent anti-stokes Raman scattering Hyper Raman Stimulated Raman Pumping

42 Object prepare molecules in excited vibrational levels (for subsequent experiments) by inducing transition with E = E 1 E 0 (from v = 0 to 1) Example E: E 0 = H 2 (v=0, j= 1) E 1 = H 2 (v= 1, j= 1) How to do? 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 0 = E Practical efficacy apparently 35%

43 Virtual states ω S ω S LASER ω P Stokes Raman scattering ω P Stokes Raman scattering Vibrational states excitation excitation populate this state E = E 1 E 0 Spontaneous Raman scattering SRS Stimulated Raman scattering

44 Apparently similar to stimulated Raman scattering Input Two LASER beams Pump & probe LASER apparently the same anti-stokes signal detected 7/Chan_CARS%20lecturer.pdf for details Stokes_Raman_spectroscopy

45 There are a dozen more Raman versions ***

48 How to apply to carbon nanotubes? 26 Nanotube Modeler

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 (120-350/cm). ω = + RBM 223.5 d 12.

49 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 ( /cm). ω = + RBM d 12.5 G - mode G + mode G +/- -Band: G + mode: C atoms vibrate along the tube axis ~1590/cm G - mode: C atoms vibrate along the circumferential direction ~1570/cm Different for metallic and semiconducting CNTs. 27 See for example: R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon nanotubes Imperial College Press, 2005

Example - of carbon nanotubes SEM 30000 162 cm -1 Raman spectrum of metallic CNTs RBM Raman Intensity 20000 10000 150 200 250 300 Wavenumber (cm -1 ) G combination bands 1 µm 0 D D 500 1000 1500 2000

50 Example - of carbon nanotubes SEM cm -1 Raman spectrum of metallic CNTs RBM Raman Intensity Wavenumber (cm -1 ) G combination bands 1 µm 0 D D Wavenumber (cm -1 ) RBM: breathing mode D: defects (vacancies, impurities, etc.) G: along tube axis 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. 2009

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

52 Example - 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 ~1350/cm (for ev excitation) Disorder band Intensity ~ defect density Defect induced double resonant Raman Double resonance 2D-band, G, ~2685/cm (for ev excitation) Overtone of D band Shape depends on layer thickness Independent of defects Depends on excitation energy Double resonance No RBM mode for graphene. All features are resonant Raman. 30 Spectra reproduced with permission of A Chakradhar, U. Burghaus (NDSU)

53 More Examples - of graphene intensity (a.u.) graphene/silica G G' or 2D pristine Graphene/silica intensity (a.u.) Standard silicon bare silica support D 0 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 -1 ) wavenumber (cm -1 ) 30 Spectra reproduced with permission of Nilushni Sivapragasam, N.M.K.M. Tilan Abey, U. Burghaus (NDSU)

54 More Examples - of graphene intensity (a.u.) Blank Copper-Sample 5 Copper wavenumber (cm -1 ) Sample 6(2) graphene/cu Sample 6(2) graphene/cu (bc) Intensity (arb.units) Raw data Graphene/Copper Intensity (arb.units) Corrected data Graphene/Copper Raman shift (cm -1 ) Raman shift (cm -1 ) Sample 6(4) graphene/cu Sample 6(4) graphene/cu bc Intensity (arb.units) Raw data Graphene/Copper intensity (a.u.) Corrected data Graphene/Copper % (Raman shift (cm -1 ) wavenumber (cm -1 ) 30 Spectra reproduced with permission of Nilushni Sivapragasam, N.M.K.M. Tilan Abey, U. Burghaus (NDSU)

55 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. 2010, 10, ). Copyright (2010) American Chemical Society. 32

56 Tricky questions Why are all Raman modes in graphene resonant Raman? No band gap at Fermi level for sp 2 carbon. Go back to class 8 (nanostructure characterization) which includes an image of the electronic structure of CNTs. Why do some Raman modes shift with excitation energy? Side-effect of double resonance. This is tricky to explain in detail. I have to refer you to specialty literature. 33

57 Internet resources Very detailed roscopy_basics.pdf han_cars%20lecturer.pdf Lecture draft 35 The PowerPoints were developed over the years, i.e., not all links may work anymore.

58 Homework 1) In one sentence: what is? 2) What are the advantages of which made it recently a so popular technique? 3) Research one of the techniques that was not described here SERS Surface enhanced Raman scattering SERRS Surface enhanced resonance Raman scattering Hyper Raman 36

59 Figure acknowledgement All images shown in this power point presentation were made by the author except the following with are excluded for the copyright of the author: xxx No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means except as permitted by the United States Copyright Act, without prior written permission of the author. Trademarks and copyrights are property of their respective owners., 2016 Publisher and author: Uwe Burghaus, Fargo, ND, USA

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

Raman spectroscopy., 2017 Uwe Burghaus, Fargo, ND, USA , 217 Uwe Burghaus, Fargo, ND, USA 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 1 1 6 4 3