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