A Pulse EPR Primer FIDs and Echoes Applications

A Pulse EPR Primer FIDs and Echoes

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

Topics The Rotating Frame The Effect of B 1 FIDs (Free Induction Decays) FT (Fourier Transform) Theory Spin Echoes Relaxation Times

Rotating Frame The Axis System

Rotating Frame The Larmor Frequency w. L = -g B 0

Rotating Frame Linearly and Circularly Polarized Light

Rotating Frame The Rotating Frame

Rotating Frame B 1 in both Frames

Rotating Frame Tip Angles a = -g |B 1| tp

Rotating Frame Pulse Phases

Rotating Frame Transverse Magnetization in Both Frames

Rotating Frame Generation of Microwaves

Rotating Frame Off-resonance Effects

Rotating Frame The Effective Field

Rotating Frame Sin(x)/x Behavior

Rotating Frame Excitation Bandwidth

Relaxation Times Spin Temperature and Populations

Relaxation Times Longitudinal Magnetization Recovery

Relaxation Times Effect of Excessive Repetition Times

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

Relaxation Times A FID (Free Induction Decay)

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

Fourier Theory Time Behavior of Magnetization

Fourier Theory The Complex Axis System

Fourier Theory The Fourier Transform

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.

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.

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.

Fourier Theory A Simple Fourier Transform

Fourier Theory

Fourier Theory

Fourier Theory Addition Properties

Fourier Theory Shift Properties

Fourier Theory Convolution Properties

Fourier Theory Convolution Theorem

Fourier Theory A Practical Example

Fourier Theory A Practical Example Use Convolution

Fourier Theory A Practical Example Use Addition

Fourier Theory A Practical Example Use the Convolution Theorem

Fourier Theory Linewidth Effects

Fourier Theory Splitting Effects

Fourier Theory Field Effects

Fourier Theory Field vs Frequency

Fourier Theory Field vs Frequency

Echoes Spin Echoes

Echoes Spin Echoes

Echoes Spin Echoes with Inhomogeneous Broadening

Echoes Phase Memory Time, TM

Echoes Spectral Diffusion

Echoes Spin Lattice Relaxation

Echoes ESEEM

Echoes Stimulated Echo

Echoes Effect of Pulse Lengths with Two Equal Pulses