# Time Domain NMR in Polymer Science: From the Laboratory to the Industry
## 2 Sequences
### Multiple-Quantum (MQ)  
MQ-NMR established itself as the most powerful and reliable method to measure the residual dipolar couplings (D\({}_{\text{res}}\)) in a material endowed with anisotropic motions as in the case of elastomers or liquid crystals. In crystalline solids or glassy systems proton-proton dipolar couplings are determined by the average distance among protons and by their relative position since molecular motions with large amplitudes are absent. On the other hand, in liquids and polymer melts isotropic motions average dipolar couplings to zero. In elastomers, cross-links (that represent fixed endpoints for polymer strands) prevent fully isotropic orientation fluctuations. Thus, finite residual dipolar couplings persist for strands in the polymer network [21] and are representative of the degree of motional constraint.  
The MQ-NMR sequence most applied at low-field is the Baum-Pines (BP) sequence [22], shown in Figure 4. It is composed of an excitation period, that produces the multiple quantum (dominated by the double-quantum) coherence, followed by a reconversion period, consisting of the same pulse sequence as the excitation period, but with different phase, that converts the multiple quantum coherences into observable one-quantum coherences. Finally, the converted coherence is detected as FID through a single \(\pi\)/2 pulse [7].  
One interesting feature of current implementations of the BP sequence is that, by simply changing the receiver phase during acquisition, one can selectively detect either the reconverted DQ coherence (I\({}_{\text{DQ}}\)) or a reference signal containing the magnetization that had not been evolved into DQ coherence (I\({}_{\text{ref}}\)). Thus, one can separate the build-up of the double-quantum (DQ) function (I\({}_{\text{DQ}}\)) from the relaxation phenomena that affect differently the various populations of \({}^{1}\)H nuclei (I\({}_{\text{ref}}\)). Normalization of the DQ curve respect to the total magnetization, calculated as the sum of I\({}_{\text{DQ}}\) and I\({}_{\text{ref}}\), yields pure structural information about the material with the appropriate fitting of the I\({}_{\text{nDQ}}\) curve [23].  
The excitation and reconversion blocks of the BP sequence are composed of eight \(\pi\)/2 pulses, and by four \(\pi\) pulses inserted in between to avoid the formation of artifacts. Considering the phase switching time, on most instruments, the minimum excitation time is then set at 0.1 ms. This timescale is not adequate to characterize strongly dipolar coupled systems, because the MQ coherences in  
Figure 4: Baum–Pines sequence to measure multiple-quantum (MQ) coherences. The two and three-pulses versions are indicated with dotted lines. All full boxes represent \(\pi\)/2 pulses and empty boxes denote \(\pi\) pulses.  
such systems are generated at much shorter times. Some alternative sequences have been proposed: two-pulse, three-pulse [23; 24] and five-pulse [25] sequences (Figure 4). They allow to access shorter times, that corresponds to strong dipolar couplings, but are less efficient in the long-time limit, because complete time reversal is not possible.