Spectroscopy 3:Spectroscopy 3:Magnetic ResonanceMagnetic Resonance

CHAPTER 15CHAPTER 15

Pulse Techniques in NMR

• The “new technique”

• Rather than search for and detect each individual resonance,the pulsed technique detects all resonances simultaneously

• Analogous to hitting a bell with a hammer and recording allfrequencies, then separating each individual frequency

• The resulting Fourier-transform NMR gives much greatersensitivity and freedom from noise

• Classical Description of NMR

• Absorption Process

• Relaxation Processes to thermal equilibirum

• Spin-Lattice

• Spin-Spin

Fig 15.27 Vector model of angular momentum for a

single spin-1/2 nucleus

Fig 15.28 Spin-½ nuclei in absence of a B0 field

B0 = 0B0 ≠ 0

Fig 15.29(a) Circularly-polarized mag field B1 (from rf

pulse) is applied perpendicular to z-axis

Bo

Component absorbed (d or l)

is same as direction of

precession

Counter

Clockwise

rotation

Fig 15.29(b) Circularly-polarized mag field B1 (from rf

pulse) is applied perpendicular to z-axis

When applied rf frequency

coincides with νLarmor

magnetic vector begins to

rotate around B1

Fig 15.30 A 90° pulse is applied to rotate M vector

into xy-plane

Spin-Lattice (Longitudinal) Relaxation

• Precessional cones representing

spin ½ angular momenta:

• number β spinsspins > number α spins

• After time T1 :

• Populations return to

Boltzmann distribution

• Momenta become random

• T1 ≡ spin-lattice relaxation time

• Tends to broaden NMR lines

Fig 15.34

Spin-Spin (Transverse) Relaxation

• Occurs between 2 nuclei having same precessional frequency

• Loss of “phase coherence”

• Orderly spins to disorderly spins

• T2 ≡ spin-spin relaxation time

• No net change in populations

• Result is broadening

Fig 15.36

Fig 15.35 Variation in the two relaxational processes

Fourier Transform NMRFourier Transform NMR

• Nuclei placed in strong magnetic field, Bo

• Nuclei precess around z-axis with momenta, M

• Intense brief rf pulse (with B1) applied at 90° to M

• Magnetic vector, M, rotates 90° into xy-plane

• M relaxes back to z-axis: called free-induction decay

• FID emits signal in time domain

Fourier TransformNMR Spectrum

Time domain Frequency domainFT

Fig 15.31 A free-induction decay (FID) signal of

a single resonance frequency

Fig 15.32 A simple free-induction decay (FID)signal of

a sample with two FID frequencies

Fourier Transform

13C FID Signal for Dioxane

νRF = νLarmor

Fourier transform of (a)

13C FID Signal for Dioxane

νRF ≠ νLarmor

Fourier transform of (a)

13C FID Signal for Cyclohexane

Fig 15.33 A free-induction decay (FID) signal of

a sample of ethanol

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