NMR Relaxation Like You’ve Never Seen it Before

Roy Hoffman, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

New processing techniques make interpretation and visualization of NMR relaxation measurement quick and easy.

Relaxation time is usually calculated by fitting an exponential function to each peak individually. Inversion of the Laplace transform (ILT) combined with peak modeling processes the whole spectrum at once, speeding processing by over an order of magnitude.

Discover little known facts: For small molecules in solution, conventional wisdom is that T₂ is similar to but never greater than T₁ and T_1ρ is the same as T₂. WRONG! In theory, T₂ can be up to twice T₁ under usual NMR conditions and T_1ρ is not the same as either T₁ or T₂ (figure).

Peaks in the same multiplet have different relaxation times, especially so for strong second order coupling.

Open the door to applications: Relaxation time is reduced by spin-spin coupling between nuclei. This can be used for spectral assignment, for example a ¹³C that is attached to a proton will relax faster and produce a broader signal than a ¹³C with no neighboring protons.

The correlation time or tumbling rate can be evaluated from the T₁ and T₂ relaxations. The correlation time is slower for larger molecules and is slower for rigid parts of large molecules than for flexible chains. It finds applications in the assignment of proteins and the study of complex liquids such as microemulsions.

Relaxation time is strongly affected by paramagnetism. Even oxygen from dissolved air has a very significant effect. The difference between relaxation under vacuum and under air can be used to measure the extent of molecular binding to oxygen.

Figure. Relaxation of the H1 multiplet of 9,10-diphenylanthracene showing variations up to 38% in relaxation time within the multiplet and T₂ up to 18% greater than T₁. T₁ in blue, T₂ in red T_1ρ in green.