Análisis e interpretación de resultados prueba piloto

The concept of coherence order was introduced in the last section. Coherence is created as a direct result of an rf pulse. Pulse sequences are designed specifically to introduce certain desired coherences, based on the needs of the user. A significant problem therefore arises: how do we selectively create only specific coherences? An rf pulse will, if left to itself, create all manner of coherences, desired or otherwise.

Figure 3.2 Schematic representation of a DQ/SQ MAS pulse sequence, using one rotor period of BABA recoupling for the excitation and reconversion of DQ coherence, and the corresponding coherence transfer pathway diagram. The preparation (or excitation), evolution (t1), mixing and detection (t2) periods of a two-dimensional experiment are presented. The purpose

One method used in solution-state NMR to filter out the unwanted coherences is to use pulse field gradients, in which spatially homogeneous magnetic fields dephase and then rephase only desired coherences.(164) The idea being that the application of a magnetic field along the z axis forces a phase shift on all existing coherences, with the shift being proportional to the coherence order. However, a much more commonly executed method, especially in solid-state NMR, where it is technologically demanding to combine gradients with MAS, is the concept of phase cycling which, in modern NMR, is an integral part of any experiment.

Before any specific discussion of phase cycling, it is prudent to introduce the concept of coherence transfer pathways. Such pathways represent a convenient and visual method of observing the specific coherence order at any time of free precession during the experiment. As an example, Fig. 3.2 presents the coherence transfer pathway diagram and pulse sequence for the workhorse double-quantum/single- quantum (DQ/SQ) MAS NMR experiment that, as in this thesis, is often used in work concerning high

resolution 1_{H solid-state NMR. The purpose of the experiment is to excite DQ coherence which then}

evolves in t1 before being converted into in-phase SQ coherence. The generation of the desired

coherences is presented by the coherence transfer pathway diagram in Fig. 3.2.

The basic concept of phase cycling involves repeating the experiment many times where, for each FID, the phase of the rf pulses and the receiver are changed. The principles of phase cycling are enshrined in the two ‘Golden’ rules:

1. If the phase of a single or group of pulses is changed by 𝛥𝜙, then a coherence undergoing a

change in coherence order, 𝛥𝑝, experiences a phase shift equal to −𝛥𝜙𝛥𝑝.

The significance of the first rule is that pathways with different 𝛥𝑝 acquire a different phase, therefore it is possible to differentiate between them. Practically, this is achieved by repeating the experiment several times, each time using a different value of 𝛥𝜙 and combining the results in such a way as to amplify the signals from desired pathways whilst totally suppressing those signals from unwanted pathways. This is achieved by altering the receiver phase. Experimentally, it is important that the receiver phase follows the overall phase acquired by the desired coherence, so that the total signal due to this pathway is amplified over the duration of the phase cycle. All other signals will then cancel. Note that any phase acquired by a particular coherence is carried forward with that coherence until the end of the pulse sequence. This effectively means that any signal arising from that coherence will have the same phase shift.

2. If a phase cycle uses steps of 360°/N then, along with desired coherences, 𝛥𝑝, 𝛥𝑝 ± 𝑛𝑁 pathways are also selected, where 𝑛 = 1, 2, 3 … All other pathways are suppressed.

Phase cycling is therefore used to drive changes in coherence order via the use of rf pulses during the course of the experiment. Note that the coherences at the start (thermal equilibrium) and end of an

experiment are always fixed, at 𝑝 = 0 and 𝑝 = −1, respectively. In order for the phase cycle to achieve its purpose, i.e., the cancellation of signals due to unwanted coherences, the total number of FIDs collected must be equal to an integer multiple of the N steps of the phase cycle employed. Only in such a manner will these unwanted coherences cancel completely. Higher order coherences selected automatically as a result of the second rule are normally ignored because the efficiency of exciting a coherence decreases as the order increases and hence the chance of exciting 4, 5, 6Q, ... is negligible. For complex experiments in which multiple coherence changes occur over the sequence, it is necessary to employ nested phase cycles. In such a cycle, the phases of individual pulses are chosen according to the rules outlined above. Importantly, the overall receiver phase is calculated as the sum of all the individual receiver phases existing for each coherence change, defined by the second rule. Crucially, nested phase cycles allow for the selection of both positive and negative coherence pathways, therefore allowing the data to be acquired in an amplitude-modulated fashion.

3.3 Experimental techniques in solid-state NMR – dipolar decoupling