## 3 Key Time-Domain NMR Methods  
### Nuclear Magnetic Resonance Relaxation (NMRR) for Material Science  
NMRR is an extremely useful quantitative technique for material science, particularly applicable to polymers and porous materials. A powerful RF pulse (a \(\pi\)/2 pulse) at the NMR resonant frequency may be used to tip the equilibrium nuclear magnetization of certain nuclei such as hydrogen into the transverse plane. There it precesses at the resonant RF frequency, generating an exceedingly small RF signal that may be amplified and detected. The initial amplitude of the NMR signal--the Free Induction Decay (FID)--gives a robust quantitative measure of the amount of material in the sample; to obtain a mass calibrated measurement, it is necessary to also make measurements on one or more calibration samples of known weight that ideally should be similar to the expected liquid, polymer or hydrocarbon. The amplitude of the FID decays at a rate at least partly determined by the dipole-dipole interactions between the nuclei--dipolar broadening--the adjacent nuclei alter the local magnetic field at a given nucleus, resulting in a short, often Gaussian-like T\({}_{2}\) decay. A short transverse or dipolar decay time of around 10 us is characteristic for a very rigid material like ice. If there is motion of the nuclei, this can cause an averaging of this effect, so that the decay can become slower, and can then tend to be approximately an exponential. This is typical for say a tar, with T\({}_{2}\)s perhaps between 20 us to 100 us. However, as T\({}_{2}\) gets longer due to motional narrowing, the FID decay time is then often limited by local field variation such as the homogeneity of the magnet, or sometimes by inhomogeneities in the sample (which may beporous), and the FID decays at a rate characterised as T\({}_{2}\)*. This is then typical of a soft material such as a polymer or say a candle wax. This is not the end of the story, however, as the dephased magnetisation can often then be re-focussed by applying a chain of re-focussing NMR pulses, such as the Car-Purcell-Meiboom-Gill (CPMG) sequence, to obtain a chain of NMR echoes, whose peak amplitudes then trace out the true T\({}_{2}\) decay. These longer true T\({}_{2}\) times are then typical of the above polymers or candle wax, and are often around a few milli-seconds, or can be as long as seconds, typical of a mobile liquid. Organic molecules frequently exhibit reptation, which often result in a non- or multi- exponential signal decay. The decays may also be multi-component when both crystalline and amorphous components are present in a polymer. Finally, we need to consider the time for the magnetisation to re-equilibrate with the \"lattice\" (the longitudinal decay time T\({}_{1}\)). T\({}_{1}\) is often long (many seconds) for rigid materials but reduces and becomes equal to the true T\({}_{2}\) time for a mobile liquid like water. It can thus be seen that the NMR FID, T\({}_{2}\)* and true T\({}_{2}\) may give information on the sample that for different applications is variously characterised as mobility, dynamics, stiffness, viscosity or rigidity. These are highly useful parameters, rapidly providing data on the physical state of the sample as a function of local condition and sample temperature [1; 2; 3]. NMRR for Determining Mass and Mobility of Hydrocarbons in Porous Materials  
Many porous materials, such as recovered porous rocks, or fired carbons such as biochar, contain hydrocarbons in the pores. As well as the hydrocarbon mass, the dynamical information may also be obtained as above from the NMR decay. For hydrocarbons that are fairly rigid, like tars or some polymers, the FID decays rapidly, and information on the mobility may be obtained directly from the T\({}_{2}\) of the FID, which may be multi-component [27], and also see Section 4.