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Nuclei With Spin Align in Magnetic Fields

Efficiency factor- nucleus. H o. Alignment. Energy. parallel. D E = h g H o. Constants. Strength of magnet. anti-parallel. Nuclei With Spin Align in Magnetic Fields. Resonance: energy match causes transitions. p. 1. equilibrium. D E. Efficiency factor- nucleus. H o. ap. H 1.

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Nuclei With Spin Align in Magnetic Fields

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  1. Efficiency factor- nucleus Ho Alignment Energy parallel DE = h g Ho Constants Strength of magnet anti-parallel Nuclei With Spin Align in Magnetic Fields Resonance: energy match causes transitions

  2. p 1. equilibrium DE Efficiency factor- nucleus Ho ap H1 DE = h g Ho hn = DE 2. pump in energy Constants Strength of magnet p 3. non-equilibrium ap Resonance: Perturb Equilibrium

  3. p DE 3. Non-equilibrium ap hn = DE 4. release energy (detect) p 5. equilibrium ap Return to Equilibrium (Relax): Read Out Signals

  4. Sensitivity f (population difference) Efficiency factor- nucleus Np Nap -DE/kT = e S ~ DN = DE = h g Ho Constants Strength of magnet Magnetic Resonance Sensitivity DE is small At room temp., DN ~ 1:105 Intrinsically low sensitivity! Increase sensitivity by increasing magnetic field strength

  5. Intrinsic Sensitivity Nucleusg % Natural Relative Abundance Sensitivity 1H 2.7 x 108 99.98 1.0 13C 6.7 x 107 1.11 0.004 15N -2.7 x 107 0.36 0.0004 31P 1.1 x 108 100. 0.5 e- 1.8 x 1011 100. >600

  6. Two spins All spins  Sum Ho parallel anti-parallel Bulk Magnetization excess facing down The Classical Treatment:Nuclear Spin Angular Momentum • Torque + int. motion = precession • Precession around Z axis • Larmor frequency:  =  H0

  7. Effect Of An RF Pulse RFy RFy t =  =  H0 Only the excess spins phase coherence Ax t Fourier Transform f  Variation of signal at X axis vs. time NMR frequency

  8. The Power of Fourier Transform t 90ºx RF pulse + 1 =  H0 2 =  H0 A t Fourier Transform f 2 1 • NMR frequency domain • Spectrum of frequencies • NMR time domain • Variation in amplitude vs time

  9. Relaxation- Return to Equilibrium t t x,y plane z axis 0 0 Longitudinal Transverse 1 1 t t 2 2 E-t/T2 1-e-t/T1 8 8 Transverse always faster!

  10. dMz/dt = Meq – Mz/T1 Mz(t) = Meq (1-e-t/T1) t Mz(t)  Meq Longitudinal (T1) Relaxation • MECHANISM • Molecular motions cause the nuclear magnets to fluctuate relative to a fixed point in space • Fluctuating magnetic fields promote spins to flip between states • Over time, spin flips cause a return to equilibrium

  11. Transverse (T2) Relaxation • MECHANISM • Magnetic field is not homogenous to an infinite degree • Each spin comprising the bulk magnetization will feel a slightly different field • Over time, the spin fan out (lose coherence) t dMx,y/dt = Mx,y/T2 Linewidth time

  12. Fourier Transform Data Analysis Time domain (t) The Pulse FT NMR Experiment 90º pulse Experiment (t) equilibration detection of signals

  13. NMR SpectrumChemical Shift & Linewidth Chemical shift: intrinsic frequency Linewidth: relaxation (MW)

  14. Preparation of MagnetizationBuilding Towards 2D NMR E t1 If E is sufficiently long, full peak intensity Equilib. Detect 90º pulse If E is too short, intensity is reduced E-d t1 Detect 90º pulse What if we caused the peak intensity to vary at a rate equal to the precession freqeuncy?

  15. Frequency LabelingSystematically Alter The Equilibrium I 0 t1 t t1 D D 3D 5D 0 FT t1 2D t1 3D FT the variation in intensity and get Larmor frequency!

  16. 1) Add pulse to frequency label during t1 2) Introduce mixing period before t2 mix t1 t2 Indirect Detection 2D NMR F2 t1 t2 F1

  17. The Mixing Process- Uses Coupling Through Space Through Bonds

  18. t1 t2 t1 t2 2D NMR: Coupling is the Key 2D detect signals twice (before/after coupling) 90º pulse Mixing causes an exchange between spins that are coupled Same as 1D experiment 2D NMR Pulse Sequence

  19. The 2D NMR Spectrum Pulse Sequence t1 t2 Spectrum Before mixing Coupled spins give rise to crosspeaks After mixing

  20. t2 t1 t3 Multi-Dimensional NMR:Built on the 2D Principle 3D- detect signals 3 times 90º pulse (t3) Same as 1D experiment 3D NMR Pulse Sequence • Experiments are composites

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