PulsedFieldGradientNMR

Pulsed field gradient NMR (PFG NMR) is a set of nuclear magnetic resonance methods that use short, spatially varying magnetic field gradients to encode position into spin phase. This enables quantitative measurements of molecular self-diffusion, flow, and microstructure. PFG NMR has been a core technique in diffusion studies since the work of Stejskal and Tanner in the 1960s.

Principle: In a pulsed-gradient spin-echo sequence, two gradient pulses of duration δ are applied, separated by diffusion time Δ. Spins acquire a position-dependent phase during the pulses; diffusion during Δ causes incomplete rephasing, attenuating the signal. The simplest relation, known as the Stejskal–Tanner equation, is S = S0 exp(-D γ^2 g^2 δ^2 (Δ - δ/3)), with γ the gyromagnetic ratio, g the gradient strength, and D the self-diffusion coefficient.

Typical implementations include PGSE and PGSTE sequences. PGSTE extends diffusion times via stimulated echoes, permitting slower diffusion measurements and more viscous samples. Experiments vary gradient strength to produce an attenuation curve from which D is extracted.

Applications: DOSY NMR uses diffusion contrast to separate signals by diffusion coefficients, aiding the analysis of mixtures or aggregates. PFG NMR also informs studies of pore sizes, confinement, binding interactions, and flow in microfluidic or porous systems.

Limitations: Convection and temperature control, gradient-induced heating, and artifacts from anisotropic diffusion or complex exchange. Accurate interpretation requires well-calibrated gradient pulses and careful experimental design.