nuclear magnetic resonance spectrometry chap 19. absorption in cw experiments energy of precessing...

Nuclear Magnetic Resonance Nuclear Magnetic Resonance SpectrometrySpectrometry

Chap 19Chap 19

Absorption in CW ExperimentsAbsorption in CW Experiments

• Energy of precessing particle

E = -μz Bo = -μ Bo cos θ

• When an RF photon is absorbed by a nucleus,θ must change direction

∴ magnetic moment μz “flips”

• For μz to flip, a B field must be applied ⊥ Bo in acircular path in phase with precessing dipole

• B is applied ⊥ Bo using circularly-polarized RF field

Fig 19-3 Model for the Absorption of RadiationFig 19-3 Model for the Absorption of Radiationby a Precessing Particleby a Precessing Particle

μ’z

Fig 19-3 Model for the Absorption of RadiationFig 19-3 Model for the Absorption of Radiationby a Precessing Particleby a Precessing Particle

When νRF = vo absorptionand spin flip can occur

Fig 19-4 Equivalency of a Plane-polarized Beam toFig 19-4 Equivalency of a Plane-polarized Beam toTwo (d, l) Circularly-polarized BeamsTwo (d, l) Circularly-polarized Beams

• Result is vector sum that vibrates in a single plane

• In instrument, RF oscillator coil is 90° to fixed Bo field

• Only B rotating in precessional direction is absorbed

• Classical Description of NMRClassical Description of NMR

• Absorption ProcessAbsorption Process

• Relaxation Processes (to thermal equil.)Relaxation Processes (to thermal equil.)

• Spin-LatticeSpin-Lattice

• Spin-SpinSpin-Spin

Relaxation Processes (to thermal equilibrium)Relaxation Processes (to thermal equilibrium)

• When absorption causes N1/2 = N-1/2 system is “saturated”

• Fast decay is desirable

• Probability of radiative decay (fluorescence)

∝ v3

• Therefore in RF region, non-radiative decay predominates

BBoo field off: field off:

α = β at random angles

Magnetization is zero

BBoo field on: field on:

Spins precess around

their cones at νLarmor

α spins > β spins

Net magnetization, M

Circularly-polarizedCircularly-polarized

radio frequency mag.radio frequency mag.

field Bfield B11 is applied: is applied:

When applied rf frequencyWhen applied rf frequency

coincides with coincides with νLarmor

magnetic vector begins to

rotate around B1

Behavior of Magnetic Moments of NucleiBehavior of Magnetic Moments of Nuclei

Spin-Lattice (Longitudinal) RelaxationSpin-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

Spin-Spin (Transverse) RelaxationSpin-Spin (Transverse) Relaxation

• Occurs between 2 nuclei havingOccurs between 2 nuclei having same precessional frequencysame precessional frequency

• Loss of “phase coherence”Loss of “phase coherence”

• Orderly spins to disorderly spinsOrderly spins to disorderly spins

• TT22 ≡ spin-spin relaxation time≡ spin-spin relaxation time

• No net change in populationsNo net change in populations

• Result is broadening Result is broadening

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

Simple FID of a sample of spins with a single frequencySimple FID of a sample of spins with a single frequency

Fourier TransformNMR SpectrumNMR Spectrum

Simple FID of AX species with two frequenciesSimple FID of AX species with two frequencies

Vector Model of Angular MomentumVector Model of Angular Momentum

Fig. 19-2

55°