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A Pulse EPR Primer

A Pulse EPR Primer. FIDs and Echoes . ESEEM Relaxation Time Measurement 2 + 1, DEER, ELDOR EXSY. Structural Elucidation Dynamics, Distances Measurement of Long Distances Measurement of Slow Inter & Intra-molecular Chemical Exchange and Molecular Motions. Applications. Topics.

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A Pulse EPR Primer

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  1. A Pulse EPR Primer FIDs and Echoes

  2. ESEEM Relaxation Time Measurement 2 + 1, DEER, ELDOR EXSY Structural Elucidation Dynamics, Distances Measurement of Long Distances Measurement of Slow Inter & Intra-molecular Chemical Exchange and Molecular Motions Applications

  3. Topics • The Rotating Frame • The Effect of B1 • FIDs (Free Induction Decays) • FT (Fourier Transform) Theory • Spin Echoes • Relaxation Times

  4. Rotating Frame The Axis System

  5. Rotating Frame The Larmor Frequency wL = -g B0

  6. Rotating Frame Linearly and Circularly Polarized Light

  7. Rotating Frame The Rotating Frame

  8. Rotating Frame B1 in both Frames

  9. Rotating Frame Tip Angles a = -g |B1| tp

  10. Rotating Frame Pulse Phases

  11. Rotating Frame Transverse Magnetization in Both Frames

  12. Rotating Frame Generation of Microwaves

  13. Rotating Frame Off-resonance Effects

  14. Rotating Frame The Effective Field

  15. Rotating Frame Sin(x)/x Behavior

  16. Rotating Frame Excitation Bandwidth

  17. Relaxation Times Spin Temperature and Populations

  18. Relaxation Times Longitudinal Magnetization Recovery

  19. Relaxation Times Effect of Excessive Repetition Times

  20. Relaxation Times Homogeneous & Inhomogeneous Broadening Homogeneous Broadening The lineshape is determined by the relaxation time. The spectrum is the sum of a large number of lines each having the same Larmor frequency and linewidth. Lorentzian Lineshapes Inhomogeneous Broadening The lineshape is determined by the unresolved couplings. The spectrum is the sum of a large number of narrower homogeneously broadened lines each having the different Larmor frequencies. Gaussian Lineshapes

  21. Relaxation Times A FID (Free Induction Decay)

  22. Fourier Theory Fourier transforms convert time domain signals into frequency domain signals and vice versa.

  23. Fourier Theory Time Behavior of Magnetization

  24. Fourier Theory The Complex Axis System

  25. Fourier Theory The Fourier Transform

  26. Fourier Theory Some Fourier Facts • Even functions (f(-t) = f(t) or symmetric) have purely real Fourier transforms. • Odd functions (f(-t) = -f(t) or anti-symmetric) have purely imaginary Fourier transforms.

  27. Fourier Theory Some Fourier Facts • An exponential decay in the time domain is a lorentzian in the frequency domain. • A gaussian decay in the time domain is a gaussian in the frequency domain.

  28. Fourier Theory Some Fourier Facts • Quickly decaying signals in the time domain are broad in the frequency domain. • Slowly decaying signals in the time domain are narrow in the frequency domain.

  29. Fourier Theory A Simple Fourier Transform

  30. Fourier Theory

  31. Fourier Theory

  32. Fourier Theory Addition Properties

  33. Fourier Theory Shift Properties

  34. Fourier Theory Convolution Properties

  35. Fourier Theory Convolution Theorem

  36. Fourier Theory A Practical Example

  37. Fourier Theory A Practical Example Use Convolution

  38. Fourier Theory A Practical Example Use Addition

  39. Fourier Theory A Practical Example Use the Convolution Theorem

  40. Fourier Theory Linewidth Effects

  41. Fourier Theory Splitting Effects

  42. Fourier Theory Field Effects

  43. Fourier Theory Field vs Frequency

  44. Fourier Theory Field vs Frequency

  45. Echoes Spin Echoes

  46. Echoes Spin Echoes

  47. Echoes Spin Echoes with Inhomogeneous Broadening

  48. Echoes Phase Memory Time, TM

  49. Echoes Spectral Diffusion

  50. Echoes Spin Lattice Relaxation

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