2.4. NMR Relaxation Times (T1 and T2)

NMR relaxation phenomena describe the processes by which excited nuclei return to their equilibrium (ground state) distribution. These exponential decay processes can be described and measured using the longitudinal or spin-lattice (T₁) and the transverse or spin–spin (T₂) relaxation times that refer to the recovery of magnetization parallel and decay to zero perpendicular to the direction of the external magnetic field B₀, respectively. The relaxation times of nuclear spins depend on dynamic properties of the corresponding molecules and their interaction with the immediate environment [66]. In longitudinal relaxation (T₁), energy can be transferred to the environment (“lattice”) of the corresponding nucleus by different relaxation mechanisms that can be of paramagnetic, dipolar, or chemical shift anisotropy (CSA) origin [64]. For example, the principle of MRI contrast agents including metalloporphyrins is based on the paramagnetic relaxation enhancement of nearby proton nuclei (shortening of T₁ relaxation time) in biological tissue [36]. T₂ relaxation concerns the loss of transverse magnetization or phase coherence of spins that can be caused through spin–spin interactions and fluctuating magnetic fields. These in turn depend on molecular size and tumbling (Brownian motion), which is characterized by the rotational correlation time τ_c. For macromolecules, molecular motion is slow and τ_c is large, leading to efficient spin–spin relaxation, i.e., short T₂ relaxation times (while the T₁ relaxation time goes through a minimum with increasing τ_c). On the other hand, small fast tumbling molecules with small τ_c have slow relaxation rates (both T₁ and T₂ relaxation times are similar and high) [64].

The relationship between T₂ and τ_c is of particular value for describing the interactions between small and large molecules. Thus, the interaction of porphyrins with biomolecules or the polymeric encapsulation of a porphyrin molecule will lead to a shortening of the spin–spin T₂ relaxation times and can be easily monitored. However, a serious drawback is associated with this interesting property of T₂ relaxation times: Since the observed linewidths of the resonances are directly proportional to the inverse of T₂ (linewidth at half-height ν_1/2 = 1/πT₂), porphyrins interacting with biomolecules exhibit very broad lines, which reduces sensitivity and can make it very difficult to observe resonances.