M:-M0 dM,/dt T due to the excited state ' s dissipation of energy into the " lattice", i.e., other degrees of freedom (molecular vibrations, rotations etc. ) until the BOLTZMANN equilibrium is reached again(Mi) In the BOLtzMann equilibrium, all transverse magnetization must have also disappeared: T2< TI TI=T2 for "small "molecules; however, TI can also be much longer than T2(important for relaxation delay"between scans)! Measuring TI To avoid T2 relaxation, the system must be brought out of BoLTZMANN equilibrium without creating Mxy magnetization: a 180 pulse converts Mz into M-z, then T1 relaxation can occur during a defined period t. For detection of the signal, the remaining Mz/M-z component is turned into the x,y plane by a 90 pulse and the signal intensity measured 180°-τ-90°- acquisition Inversion-recovery experiment From integration of eq, [2-141, one gets zero signal intensity at time to=T, In 2 =0.7TI M2=(1-2exp(t/T)·M M2=99%M t=5T t=3T 0.5 0.0 t/T M2=0 t=T. In2 0.5
12 dMz / dt = - M M T z - 0 1 [2-14] due to the excited state's dissipation of energy into the "lattice", i.e., other degrees of freedom (molecular vibrations, rotations etc.), until the BOLTZMANN equilibrium is reached again (Mz). In the BOLTZMANN equilibrium, all transverse magnetization must have also disappeared: T2 £ T1 ; T1 = T2 for "small" molecules; however, T1 can also be much longer than T2 (important for "relaxation delay" between scans) ! Measuring T1: To avoid T2 relaxation, the system must be brought out of BOLTZMANN equilibrium without creating Mx,y magnetization: a 180º pulse converts Mz into M-z , then T1 relaxation can occur during a defined period t. For detection of the signal, the remaining Mz / M-z component is turned into the x,y plane by a 90º pulse and the signal intensity measured: 180°-t-90°-acquisition inversion-recovery experiment From integration of eq, [2-14], one gets zero signal intensity at time t0 = T1 ln 2 » 0.7 T1
T22 and linewidth Due to the characteristics of FT, the linewidth depends on the decay rate of the FID (for the linewidth at half-height) The FId being a composed of exponentially decaying sine and cosine signals, eq [2-12] should read M-y(t=M-ycos(ot)+ Mxsin(ot))exp(t/T2) Chemical shift Resonance frequencies of the same isotopes in different molecular surroundings differ by several ppm(parts per million). For resonance fr 100 MHz range these differences can be up to a few 1000 Hz. After creating a Mx,y coherence, each spin rotates with its own specific resonance frequency o, slightly different from the Bi transmitter(and receiver) frequency (o. In the rotating coordinate system, this corresponds to a rotation with an offset frequency Q2=@-0o time domain frequency domain
13 T2 and linewidth Due to the characteristics of FT, the linewidth depends on the decay rate of the FID: lw1/2 = 1 pT2 [2-15] (for the linewidth at half-height) The FID being a composed of exponentially decaying sine and cosine signals, eq. [2-12] should read M-y(t) = {M-ycos(wt) + Mx sin(wt)}exp(-t/T2 ) [2-16] Chemical Shift Resonance freuquencies of the same isotopes in different molecular surroundings differ by several ppm (parts per million). For resonance frequencies in the 100 MHz range these differences can be up to a few 1000 Hz. After creating a Mx,y coherence, each spin rotates with its own specific resonance frequency w, slightly different from the B1 transmitter (and receiver) frequency w0. In the rotating coordinate system, this corresponds to a rotation with an offset frequency W = w - w0 . time domain frequency domain