The Physical Methods in Inorganic Chemistry (Fall Term, 2004) (Fall Term, 2005) Department of Chemistry National Sun Yat-sen University 無機物理方法（核磁共振部分） Chapter 4

90 o pulse width T 1 measurement T 2 measurement Chemical exchange

π/2 π

Any degree (n)-pulse = t π *n/ o pulse width= t π /2 Fine Tuning until t π

Spin Relaxation Any system that is prepared to off-equilibrium “state” tends to restore to its equilibrium state. Random forces are the origin of relaxation. Nuclear spin relaxation is driven by random magnetic fields. The transverse component of the random magnetic field causes longitudinal relaxation (T1) and the longitudinal component of the random magnetic field causes transverse relaxation (T2). Random magnetic field being generated by the molecular motions, relaxation measurement offers information on dynamics.

Inversion-Recovery π π_2π_2 τ τ FT MyMy

τ

When magnetic field inhomogeneity Δν is not negligible, it Introduces observable contributions to signal decay:

T 2 Effect

τ1τ1τ2τ2 π/2π τ1 = τ 2 τ1 = T 2 τ1τ1

τ1 = τ 2 τ2 τ2

τ τ 2τ2τ 2τ=T 2

CPMG Sequence for T 2 Measurement δ δ π xy π/2 xy n

δ δ π xy π/2 xy n 2nδ Mx 2nδ 2nδ=T 2

T 1, T 2 and Dynamics… Just A Little Example S I r IS How far between two nuclei How fast the molecule tumbles.

Example of relaxation: dipolar relaxation

How does the magnetization relax back to equilibrium after applying a radiofrequency pulse?

Thus, to bring the bulk magnetization back to the z axis, an oscillating field (oscillating at the Larmor frequency of the transition) that is orthogonal to the Zeeman field is required. The source of these additional fields is easy to see, the other nuclei which have magnetic moments nearby. Thus, the dipole-dipole interaction can actually provide a mechanism for relaxation.

How does the spectra density J depend on the correlation time?

The following gives the relaxation rate when it is dominated by dipolar interaction. It should be noted that relaxation can be afforded by other mechanisms such as chemical shift anisotropy, scalar relaxation, spin-rotation and quadrupolar interaction. For protons, in solution free of molecular oxygen, the dipolar mechanism usually dominates. In the extreme narrowing limit (very fast motion and very short correlation time), the following holds.

Can one use one correlation time for all the sites in a molecule? That depends. This is true only if the motion is isotropic and NOT segmental. Below are examples where the motion is segmental (first example). Listed are the T1 values for each of the carbons in this long- chain alcohol. Clearly, motion is restricted near the -OH end of the molecule (presumably due to hydrogen bonding). As a result, these protons have relatively shorter relaxation times (or faster relaxation rates) as the motions get slower and approach the Larmor frequency. The second example illustrates anisotropy. Listed are the T1 values for some of the carbons in phenol. The relaxation time of the C directly attached to the -OH group illustrates the importance of nearby protons in the relaxation of C spins. Since this C is not directly attached to any proton, its relaxation time is appreciable long. The anisotropic motion of the ring (it prefers rotation about the axis that contains -OH) leads to appreciably longer relaxation times for the C's that do not lie on this rotational axis.

Listed are the T1 values for each of the carbons in this long-chain alcohol. Clearly, motion is restricted near the -OH end of the molecule (presumably due to hydrogen bonding). As a result, these protons have relatively shorter relaxation times (or faster relaxation rates) as the motions get slower and approach the Larmor frequency.

This example illustrates anisotropy. Listed are the T1 values for some of the carbons in phenol. The relaxation time of the C directly attached to the -OH group illustrates the importance of nearby protons in the relaxation of C spins. Since this C is not directly attached to any proton, its relaxation time is appreciable long. The anisotropic motion of the ring (it prefers rotation about the axis that contains -OH) leads to appreciably longer relaxation times for the C's that do not lie on this rotational axis.

The effect of T 1 on the setting of recycle delay (d1) Pulse sequence d1 M0 M0’ M0 (If d1 is long enough) (If d1 is not long enough) d1

Saturation: Bad! Pulse sequence d1 Pulse sequence d1 Pulse sequence d1 …… M0 M0’ M0’’ ’ ’ No more signal added to the total signal after a few scans.

Steady State: Not Bad, Maybe. Signal for each scan is lower than single 90 degree pulse but the transients can be added up. Pulse sequence d1 Pulse sequence d1 Pulse sequence d1 …… M0 M0’ M0’’ M0 M0’’

Ernst Angle d 1 /T 1

Many More Relaxation Rates… T 1, T 2 and K are just a small tip of the iceberg of relaxation/exchange rates.

Chemical Exchange dimethylamino-7-methyl-1,2,4-benzotriazine.

Chemical Exchange General Cases:

Modified Bloch Equations

Example of Chemical Exchange dimethylamino-7-methyl-1,2,4-benzotriazine. When exchange rate is larger than chemical shift difference, coalescence between two signals occurs. 116 Hz

Another Example

Simulation

Lab: Phase Cycling