Nuclear Magnetic Resonance Spectrometry Chap 19

Absorption in CW Experiments Energy of precessing particle E = -μ z B o = -μ B o cos θ When an RF photon is absorbed by a nucleus, θ must change direction ∴ magnetic moment μ z “flips” For μ z to flip, a B field must be applied ⊥ B o in a circular path in phase with precessing dipole B is applied ⊥ B o using circularly-polarized RF field

Fig 19-3 Model for the Absorption of Radiation by a Precessing Particle μ’zμ’z

Fig 19-3 Model for the Absorption of Radiation by a Precessing Particle When ν RF = v o absorption and spin flip can occur

Fig 19-4 Equivalency of a Plane-polarized Beam to Two (d, l) Circularly-polarized Beams Result is vector sum that vibrates in a single plane In instrument, RF oscillator coil is 90° to fixed B o field Only B rotating in precessional direction is absorbed

Classical Description of NMR Classical Description of NMR Absorption Process Absorption Process Relaxation Processes (to thermal equil.) Relaxation Processes (to thermal equil.) Spin-Lattice Spin-Lattice Spin-Spin Spin-Spin

Relaxation Processes (to thermal equilibrium) When absorption causes N 1/2 = N -1/2 system is “saturated” Fast decay is desirable Probability of radiative decay (fluorescence) ∝ v 3 Therefore in RF region, non-radiative decay predominates

B o field off: α = β at random angles Magnetization is zero B o field on: Spins precess around their cones at ν Larmor α spins > β spins Net magnetization, M

Circularly-polarized radio frequency mag. field B 1 is applied: When applied rf frequency coincides with coincides with ν Larmor magnetic vector begins to rotate around B 1 Behavior of Magnetic Moments of Nuclei

Spin-Lattice (Longitudinal) Relaxation Precessional cones representing spin ½ angular momenta: spins number β spins > number α spins After time T 1 : Populations return to Boltzmann distribution Momenta become random T 1 ≡ spin-lattice relaxation time Tends to broaden NMR lines

Spin-Spin (Transverse) Relaxation Occurs between 2 nuclei having Occurs between 2 nuclei having same precessional frequency same precessional frequency Loss of “phase coherence” Loss of “phase coherence” Orderly spins to disorderly spins Orderly spins to disorderly spins T 2 ≡ spin-spin relaxation time T 2 ≡ spin-spin relaxation time No net change in populations No net change in populations Result is broadening Result is broadening

Fourier Transform NMR Nuclei placed in strong magnetic field, B o Nuclei precess around z-axis with momenta, M Intense brief rf pulse (with B 1 ) 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 frequency Fourier Transform NMR Spectrum

Simple FID of AX species with two frequencies

Vector Model of Angular Momentum Fig °