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NMR Spectroscopy. Relaxation Time Phenomenon & Application. Relaxation- Return to Equilibrium. t. t. x,y plane. z axis. Longitudinal. Transverse. 0. 0. 1. 1. t. t. 2. 2. E -t/ T 2. 1- e -t/ T 1. 8. 8. Transverse always faster!. Relaxation.

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nmr spectroscopy

NMR Spectroscopy

Relaxation Time

Phenomenon & Application

relaxation return to equilibrium
Relaxation- Return to Equilibrium

t

t

x,y plane

z axis

Longitudinal

Transverse

0

0

1

1

t

t

2

2

E-t/T2

1-e-t/T1

8

8

Transverse always faster!

relaxation
Relaxation

magnetization vector's trajectory

The initial vector, Mo, evolves under the effects of T1 & T2 relaxation and from the influence of an applied rf-field. Here, the magnetization vector M(t) precesses about an effective field axis at a frequency determined by its offset. It's ends up at a "steady state" position as depicted in the lower plot of x- and y- magnetizations.

http://gamma.magnet.fsu.edu/info/tour/bloch/index.html

relaxation4
Relaxation

The T2 relaxation causes the horizontal (xy) magnetisation to decay. T1 relaxation re-establishes the z-magnetisation. Note that T1 relaxation is often slower than T2 relaxation.

spin lattice relaxation time longitudinal t 1
Spin-lattice Relaxation time (Longitudinal) T1

Relaxation mechanisms:

1. Dipole-Dipole interaction "through space"

2. Electric Quadrupolar Relaxation

3. Paramagnetic Relaxation

4. Scalar Relaxation

5. Chemical Shift Anisotropy Relaxation

6. Spin Rotation

relaxation8
Relaxation
  • Spin-lattice relaxation converts the excess energy into translational, rotational, and vibrational energy of the surrounding atoms and molecules (the lattice).
  • Spin-spin relaxation transfers the excess energy to other magnetic nuclei in the sample.
longitudinal relaxation time t 1
Longitudinal Relaxation time T1

Inversion-Recovery Experiment

180y (or x)

90y

tD

slide12

Interaction

Range of interaction (Hz)

relevant parameters

Dipolar coupling

104 - 105

- abundance of magnetically active nuclei- size of the magnetogyric ratio

Quadrupolar coupling

106 - 109

- size of quadrupolar coupling constant- electric field gradient at the nucleus

Paramagnetic

107 -108

concentration of paramagnetic impurities

Scalar coupling

10 - 103

size of the scalar coupling constants

Chemical Shift Anisotropy (CSA)

10 - 104

- size of the chemical shift anisotropy- symmetry at the nuclear site

6- Spin rotation

spin spin relaxation transverse t 2
Spin-spin relaxation (Transverse) T2
  • T2represents the lifetime of the signal in the transverse plane (XY plane)
  • T2 is the relaxation time that is responsible for the line width.

line width at half-height=1/T2

spin spin relaxation transverse t 214
Spin-spin relaxation (Transverse) T2

Two factors contribute to the decay of transverse magnetization.

  • molecular interactions

( lead to a pure pure T2 molecular effect)

  • variations in Bo

( lead to an inhomogeneous T2 effect)

spin spin relaxation transverse t 215
Spin-spin relaxation (Transverse) T2
  • signal width at half-height (line-width )= (pi * T2)-1

90y

180y (or x)

tD

tD

t 1 and t 2
T1 and T2
  • In non-viscous liquids, usually T2= T1.
  • But some process like scalar coupling with quadrupolar nuclei, chemical exchange, interaction with a paramagnetic center, can accelerate the T2relaxation such that T2becomes shorter than T1.
relaxation and correlation time
Relaxation and correlation time

For peptides in aqueous solutions the dipole-dipole spin-lattice and spin-spin relaxation process are mainly mediated by other nearby protons

why the interest in dynamics
Why The Interest In Dynamics?
  • Function requires motion/kinetic energy
  • Entropic contributions to binding events
  • Protein Folding/Unfolding
  • Uncertainty in NMR and crystal structures
  • Effect on NMR experiments-spin relaxation is dependent on rate of motions  know dynamics to predict outcomes and design new experiments
  • Quantum mechanics/prediction (masochism)
nmr parameters that report on dynamics of molecules
NMR Parameters That Report On Dynamics of Molecules
  • Number of signals per atom: multiple signals for slow exchange between conformational states
  • Linewidths: narrow = faster motion, wide = slower; dependent on MW and conformational states
  • Exchange of NH with solvent:requires local and/or global unfolding events  slow timescales
  • Heteronuclear relaxation measurements
    • R1 (1/T1) spin-lattice- reports on fast motions
    • R2 (1/T2) spin-spin- reports on fast & slow
    • Heteronuclear NOE- reports on fast & some slow
linewidth is dependent on mw

B

A

B

A

Big

(Slow)

Small

(Fast)

15N

15N

15N

1H

1H

1H

Linewidth is Dependent on MW
  • Linewidth determined by size of particle
  • Fragments have narrower linewidths