Methodological considerations and spectral interpretation

The two approaches z-filtered MQMAS and shifted-echo MQMAS both produce MQMAS spectra with pure-absorption mode lineshapes, but the practical differences between these methods have been investigated in the literature.[134,237,238] Even though the z-filtered approach combines the contribution of the two CTPs, while the shifted-echo only uses one, paradoxically, it is complicated to establish which of the method is, overall, the most sensitive. On one hand, with the shifted-echo approach, there is no imaginary signal after FT and phasing, and this component contains only noise. The whole echo contains the equivalent of ×2 the signal of a regular FID, for only ×√2 more noise, giving a SNR increased by approximately ×√2≃1.41.[134,223] On the other hand, the shifted-echo requires the whole echo to be recorded, requiring a sufficiently long echo period during which the signal may experience T2 relaxation, decreasing sensitivity. Furthermore, relaxation may cause a distortion on the echo (see Appendix G, Figure G.3), re-introducing an imaginary part and causing some phase problems with the spectral lineshapes.

Sheared and split-t₁ MQMAS spectra should, in principle, be identical (see Appendix E), but the split-t₁ possess several advantages.

−35 −60 −70 δ1 (ppm) −30 δ2 (ppm) Rb 1 Rb 3 Rb 2 −65 −35 −30 Experimental lineshapes Simulated lineshapes −35 −30 CQ = 1.63 MHz ηQ = 0.45 ẟiso = −33.0 ppm CQ = 1.94 MHz ηQ = 1 ẟiso = −30.2 ppm CQ = 1.63 MHz ηQ = 0.33 ẟiso = −28.8 ppm

a

b

Figure 3.17: (a): Cross-sections of the individual quadrupolar lineshapes from a87Rb st₁ shifted-echo MQ-

MAS spectrum of RbNO3recorded atB0= 20.0 T (ν0= 278.6 kHz).(b): Lineshape and corre-

sponding quadrupolar parameters obtained from fitting those extraction with the module SOLA.

Literature values are report in Appendix C.2 from Baltisbergeret al.[239] for comparison. The

MQMAS spectrum is reported from Figure 5.11e.

• As investigated by Brown and Wimperis,[134] shearing a spectrum is not free from artefacts, as it leads to small distortions in the sheared ridges in the anisotropic dimensionδ1, which have been shown to arise solely from the processing method. • The quadrupolar echo for a non-split-t₁ experiment would result in an echo that appears at a different point in t2 ast1 is incremented, requiring the duration of the direct acquisition to be much longer to be recorded for much longer than the visible than for split-t₁ approaches, where the echo appears at a fixed time. In the latter case, the acquisition period can be minimised, limiting the amount of noise processed by the FT and increasing the sensitivity.

In summary, split-t₁ experiments do not intrinsically present any disadvantages com- pared to a shearing transformation. Setting a shifted-echo experiment to be split-t₁ does not present any difficulty, so is almost systematically applied. Implementing this into z-filtered experiment is not as straightforward as there is not a convenient 1Q evolution period in the pulse sequence apart from acquisition, and the quadrupolar echo occurs just after the final 90° pulse. To introduce a 1Q evolution period, the alternative pulse sequence presented in Figure 3.13b can be employed, but the additional pulse results

in a longer phase cycling and potentially a lower sensitivity. The pulse sequence and CTP for the split-t₁ shifted-echo MQMAS experiment, used throughout this work, is presented in Figure 3.16.

As presented in Section 3.3.2, a sheared or split-t₁ MQMAS spectrum resolves the differ- ent components of the signal according to their isotropic shifts and the QIS. An analysis of the MQMAS spectrum gives the following informations:

1. The maximum23 _{number of distinct species contained in the sample for the el-} ement considered. This can be directly obtained from counting the number of resonances present, either directly on the spectrum or on a projection of the indirect dimension.

2. The quadrupolar productPQ(Equation (2.3.36)). This quantity is directly related

to the QIS shiftδQIS, that can be obtained from the barycentre of the ridges on MQ- MAS spectra (either sheared or unsheared) as expressed by in Equation (2.3.37), that can be rewritten into a more practical form

PQ=ω0

2I(2I−1) 3π

√

δQ.10−3 . (3.3.23)

The position of the barycentre of the lineshape in an MQMAS spectra (denotedδI

and δD for the indirect and direct dimension, respectively) provides information

on the QISδQIS, and the isotropic chemical shiftδiso, as shown in Appendix E.2.

3. If several sites are sufficiently well resolved in an MQMAS spectrum, and appear as well separated ridges, it may then be possible to separate the two quadrupolar parameters CQ and ηQ by fitting the cross-sections taken parallel to δ2 of the quadrupolar MAS lineshape as illustrated in Figure 3.17.[240, 241] In order for this fit to be successful, the observed quadrupolar lineshape must not deviate24 too much from the idealised quadrupolar lineshape.[126, 222] Programs such as DMFit,[242] or the SOLA25_{) module integrated in Topspin,[243] can be used to} perform those fittings.

23_{Sometimes, ridges overlap because of very similarδ}

isoandδQIS, giving a misleading number of resonances. 24_{As discussed in Section 2.3.3, distortions of the lineshapes can occur on 3QF spectra.}

b

DAS