# Monitoring Electrochemical Reactions in Situ with Low Field NMR: A Mini-Review
## 2 TD NMR for the Quantification of Paramagnetic Ions  
In 1946, [PERSON], [PERSON] and Packard reported that \(T_{2}\) of the sample is dependent upon the concentration of the paramagnetic ions [14]. This was later elaborated on by several scientists who reported that \(T_{2}\) is inversely proportional to the concentration of paramagnetic ions in the solution [15; 16; 17]. The relaxation of the solvent due to the effect of the paramagnetic ions in the solution was first explained by [PERSON], [PERSON] and [PERSON] in 1948 [15]. They demonstrated that the longitudinal relaxation rate (\(1/T_{1}\)) is dependent on the gyromagnetic ratio of hydrogen (\(\gamma_{p}\)), effective magnetic moment (\(\mu_{eff}\)), ion density (N\({}_{ion}\)), viscosity (\(\eta\)), Boltzmann's constant(\(k\)) and absolute temperature (\(T\)), as shown in Equation (1).  
\[\frac{1}{T_{1}}=\frac{12\pi^{2}\gamma_{p}^{2}\eta N_{ion}\mu_{eff}^{2}}{5 kT} \tag{1}\]  
In the 1970s, [PERSON] and [PERSON] [18; 19; 20] indirectly quantified the concentration of paramagnetic ions in solution by measuring the relaxation rate (\(1/T_{1}\)) of the solution and taking advantage of the inverse correlation between both properties. Since measuring \(T_{1}\) using the conventional inversion-recovery pulse sequence is a long process, and since [PERSON], [PERSON] and [PERSON] reported that (\(1/T_{2}\)) is also proportional to the concentration of paramagnetic ions in solution it is possible to indirectly quantify the concentration of such ions using \(T_{2}\), which can be measured in a fast and simple way using the CPMG pulse sequence. Figure 1 shows how the transversal relaxation rate (\(1/T_{2}\)) varies linearly with the concentration of several paramagnetic ions [21].  
In 2016 [PERSON] et al. determined the limits of detection and quantification (LOD and LOQ, respectively) of two low-field NMR equipments. One based on a H-type magnet (0.23 T --9.8 MHz for \({}^{1}\)H) and the other using a unilateral magnet (0.33 T at 3 mm above the magnet surface--14.1 MHz for \({}^{1}\)H) using different paramagnetic ions (Ni\({}^{2+}\), Cu\({}^{2+}\), Cr\({}^{3+}\) and Mn\({}^{2+}\)). These values were compared to the LOD and LOQ of a Uv/Vis spectrometer for the same ions, with the exception of Mn\({}^{2+}\) which does not significantly absorb radiation in the Uv/Visible spectrum to be quantified. The authors concluded that the LOD and LOQ using the unilateral sensor was the highest, followed by those obtained by the Uv/Vis spectrometer, which also has the drawback of not being able to quantify ions that do not  
Figure 1: Variation of transverse relaxation rate (T\({}_{2}^{-1}\)) of the water versus the concentration of Co\({}^{2+}\), Cr\({}^{3+}\), Cu\({}^{2+}\), Fe\({}^{3+}\) and Mn\({}^{2+}\) in the solutions. Reprinted from Publication [21], Copyright (2018), with permission from Elsevier.  
absorb radiation in this region (as is the case with Mn\({}^{2+}\) ions). The NMR spectrometer with the H-type magnet showed the lowest LOD and LOQ. The average LOD and LOQ of all the paramagnetic ions tested and on each of the different magnets are summarized in Table 1[22].  
The linear relationship between the relaxation rate (\(1/T_{2}\)) and the concentration of paramagnetic ions has been exploited to quantify paramagnetic ions in solutions, to calculate K\({}_{\rm SP}\) values [23], to study coordination complexes with paramagnetic ions as ligands [24] and also to monitor electrochemical reactions in situ [8, 9].