13/02/2017. Overview. Magnetism. Electron paramagnetic resonance (EPR) Electron Paramagnetic Resonance and Dynamic Nuclear Polarisation CH916

Transcription

1 Electron Paramagnetic Resonance and Dynamic Nuclear Polarisation CH916 Overview What it is Why it s useful Gavin W Morley, Department of Physics, University of Warwick Dynamic nuclear polarization Why it s useful What it is (EPR) Magnetism Paramagnetism: Diamagnetism: Ferromagnetism: Electron s tend to: follow oppose ignore or electron resonance (ESR) or electron magnetic resonance (EMR) or ferromagnetic resonance (FMR) an applied magnetic field EPR is NMR for electrons 1

2 Magnetic resonance From Steven Brown s NMR lecture: n isolated I = ½ has m = ±½ ½ m = -½ m = +½ Photon energy Isidor Isaac Rabi ( ) Magnetic field Magnetic resonance Magnetic resonance condition gap ΔE = g μ B B z Pieter Zeeman ( ) g is the EPR equivalent of chemical shielding in NMR, µ B is the Bohr magneton gap ΔE = g μ B B z = hf res = ħω res 2

3 m s = ±½ J van Tol, L-C Brunel & RJ Wylde, Rev Sci Instrum 76, (2005) f res = 240 GHz Bruker f res = 10 GHz gap ΔE = g μ B B z I = ½ m I = ±½ (= m) m I = ½ m I = -½ m s = ±½ I = ½ m I = ±½ (= m) gap ΔE = g μ B B z ± /2 m I = ½ m I = -½ Stable free radicals: BDP Nitroxides DPPH TEMPO J van Tol, L-C Brunel & RJ Wylde, Rev Sci Instrum 76, (2005) 20/g from ldrich 3

4 absorbed m I = 1 m I = 0 m I = -1 Differential absorption m I = 1 m I = 0 m I = -1 Magnetic field modulation (~10 to 100 khz) dvantage: noise only at modulation frequency Magnetic field, B TEMPO Differential absorption Magnetic field, B J van Tol, L-C Brunel & RJ Wylde, Rev Sci Instrum 76, (2005) 20/g from ldrich Differential absorption m I = 1 m I = 0 m I = -1 spectrometer Magnetic field, B TEMPO Microwave bridge S Console Computer J van Tol, L-C Brunel & RJ Wylde, Rev Sci Instrum 76, (2005) 20/g from ldrich Electromagnet (up to 1.5 T) or superconducting magnet for higher field 4

5 spectrometer spectrometer Bridge source detector Modulation coils CW EPR so far Pulsed EPR next S Microwave resonator Pulsed electron paramagnetic resonance spectrometer Pulsed electron paramagnetic resonance Bridge High power pulsed source Protected detector Modulation coils off S Microwave resonator 5

6 Pulsed electron paramagnetic resonance B res resonance condition g m B B res = h f Pulsed EPR J van Tol, L-C Brunel & RJ Wylde, Rev Sci Instrum 76, (2005) f Polarize (thermalise) on timescale T 1 f ~100 MHz width Pulse width < 500 MHz Resonator ringing deadtime Short T 2 and T 2* compared to NMR p / 2 Free induction decay (FID) on timescale T 2 * p / 2 Homogeneous (T 2 ) can be much longer than inhomogeneous (T 2* ) so most pulsed EPR uses echo Rotating frame Spin echo In rotating frame 6

7 Spin echo decay Pulsed EPR Double electron-electron resonance (DEER) allows distances between two electron s in the range 2 to 6 nm to be measured (cf < 1 nm by NMR for two nuclear s) Dipolar coupling α 1/r 3 Site directed labelling with one or more TEMPO Erwin L Hahn (born 1921) Photo: IP Emilio Segre Visual rchives, Stephen Jacobs Collection Electron nuclear double resonance (ENDOR) m I = ½ m I = -½ m s = ±½ I = ½ m I = ±½ (= m) gap ΔE = g μ B B z ± /2 Electron nuclear double resonance (ENDOR) Why do ENDOR instead of NMR? only need ~10 10 s instead of ~10 15 NMR may be difficult near the electron gap ΔE = g μ B B z ± /2 7

8 Electron nuclear double resonance (ENDOR) ENDOR for quantum computing B 0 is static magnetic field B 1 is EPR magnetic field B 2 is NMR magnetic field Classical computer Quantum computer gap ΔE = g μ B B 0 ± /2 Bits Qubits 0 or 1 α 0 + β 1 Magnetic field, B 0 Spin qubits in silicon Other EPR applications Quality control in beer, wine etc Radiation dose received by teeth Image by Manuel Vögtli (UCL) 8

9 Overview What it is Why it s useful Dynamic nuclear polarization Why it s useful What it is Dynamic nuclear polarization More signal Thermal (Boltzmann) equilibrium: = n 2 n 1 ΔE Define polarization as: = + Polarization E-3 1E-4 1E-5 Electrons Protons Magnetic field = 10 T Temperature (K) Boltzmann polarization: = So transfer electronic polarization to nuclei 9

10 m s = ±½ m I = ½ m I = -½ m s = ±½ gap ΔE = g μ B B z I = ½ m I = ±½ (= m) I = ½ m I = ±½ (= m) gap ΔE = g μ B B z ± /2 (EPR) Initial polarizations: Electrons > 95% Nuclei < 0.1% Forbidden transition For 8.6 T and 3 K 10

11 Magnetic resonance Breit-Rabi diagram m s = ±½ m I = ½ m I = -½ gap ΔE = g μ B B z I = ½ m I = ±½ (= m) Gregory Breit ( ) gap ΔE g μ B B z ± /2...in high enough magnetic fields For a coupled two- at low magnetic field, the states of the two s are not good quantum numbers. Instead: Breit-Rabi diagram (EPR) Triplet, F = 1: Singlet, F = 0: ( + )/ 2 ( - )/ 2 more Forbidden at high magnetic fields gap ΔE =...at zero magnetic field 11

12 Solid effect DNP Cross effect e- n e- Thermal Mixing e- e- n e- n n e- also gets weaker at high magnetic fields also get weaker at high magnetic fields Ray Dupree, Steven Brown, Mark Newton, Kevin Pike, ndrew Howes, Tom Kemp, Mark Smith at Warwick, see KJ Pike et al, J Mag Res 215, 1 (2012), also Griffin Group (MIT) Ray Dupree, Steven Brown, Mark Newton, Kevin Pike, ndrew Howes, Tom Kemp, Mark Smith at Warwick, see KJ Pike et al, J Mag Res 215, 1 (2012) 12

13 Dynamic nuclear polarization Temperature jump Dynamic nuclear polarization Temperature jump with dissolution Polarization E-3 1E-4 1E-5 T DNP plus T NMR Magnetic field = 10 T Temperature (K) gain x50 from DNP and x200 from temp x10,000 total See rdenkjaer- Larsen et al, PNS 100, (2003) plus rnaud Comment and Rolf Gruetter, Lausanne Conclusion What it is Why it s useful Dynamic nuclear polarization Why it s useful What it is 13