The techniques described until now have been focussed upon the averaging or removal of dipolar interactions in the solid-state by MAS or CRAMPS in order to
obtain high-resolution spectra. As the magnitude of the dipolar coupling between a pair of nuclei, (given by d, see Eq. 2.18) is related to the internuclear separation of the two spins, a controlled reintroduction of the dipolar interaction under MAS NMR (dipolar recoupling [182, 183]) can provide spectra containing information about interatomic proximities in solids. As the dipolar coupling is completely averaged to zero over each period of MAS rotation, the application of r.f. pulses specifically synchronised with the rotor period, τr (and applied at intervals of less than τr)
reintroduce the effect into the spin system [183].
The 1H-1H proximities have been studied in this thesis in Chapter 6 for the
organic-inorganic hybrid systems by the generation of 1H-1H double-quantum
coherences (DQC) between coupled spin pairs [156].
Symmetry based recoupling CNνn sequences, introduced by Levitt et al. [183, 184] are an efficient set of schemes for spin-interaction recoupling, where N, n and ν, the symmetry numbers, are integers. The symbol CNνn refers to a set of rotor synchronized r.f. pulse cycles, with the following properties [184]:
• Each r.f. cycle has a duration τC=nτr/N, where τr=2π/ωr is the rotation period,
and ωr is the sample rotation frequency. This implies that N r.f. cycles are timed to coincide with n sample rotation periods.
• Each r.f. cycle is designed to provide no net evolution of the nuclear spin states, when only the r.f. field is taken into account.
• The r.f. phase of consecutive cycles differs by 2πν/N. The phase (φ) of the pth
cycle is therefore given by φp=φ0+2πνp/N, with p = 0, 1, 2,... . Here φ0 is the
initial phase of the whole block.
The duration of an entire CNνn sequence is denoted T = N·τC. The symmetry numbers n and ν represent the spatial sample rotation and the phase rotations of the r.f. fields, respectively. A complete sequence consists of n complete sample rotations and ν
complete r.f. phase rotations. The sample rotation is continuous, while the pulse phase rotations are performed in N discrete steps. In the general case, each element Cφ may itself consist of pulses with different phase [184]. TheC712 sequence recouples homonuclear dipole-dipole coupling terms. This symmetry generates a double-quantum recoupling sequence.
The Permutationally Offset Stabilized C7 (POST-C7) [185] sequence, is given in Figure 3.6, where the Cφ elements are divided into component pulses of flip angle, θ, and overall phase, φ, in degrees. In the POST-C7 method, the phase φ is incremented by (2π/7) radians between successive elements.
C0 C1 C2 C3 C4 C5 C6 π/2 2π 3π/2 θ (2π·3/7) (–2π·3/7) (2π·3/7) 2τr φ C0 C1 C2 C3 C4 C5 C6 C0 C1 C2 C3 C4 C5 C6 π/2 2π 3π/2 θ (2π·3/7) (–2π·3/7) (2π·3/7) 2τr φ
Figure 3.6. Pulse sequences for the symmetry-based POST-C7 sequence [185].
The POST-C7 dipolar recoupling sequence is used in this thesis in the two- dimensional DQ-SQ CRAMPS experiment shown in Figure 3.7.
t2 t1
θ1 –θ1 θ2 –θ2
·
acq
POST-C7 eDUMBO-122 POST-C7 w-DUMBO-1
n
π/2 +1 0 –1 –2 +2 t2 t1 θ1 –θ1 θ2 –θ2·
acqPOST-C7 eDUMBO-122 POST-C7 w-DUMBO-1
n
π/2 t2 t1 θ1 –θ1 θ2 –θ2·
acqPOST-C7 eDUMBO-122 POST-C7 w-DUMBO-1
n
π/2 +1 0 –1 –2 +2 +1 0 –1 –2 +2Figure 3.7. Pulse sequence and coherence transfer pathway diagram for the 1H DQ CRAMPS experiment [155]. eDUMBO-122 [142.] and windowed DUMBO-1 [140, 141] homonuclear decoupling are applied in t1 and t2, while DQ excitation and reconversion is achieved using the POST-
High-resolution 1H spectra are obtained by the use of two phase-modulated homonuclear decoupling schemes, the windowless eDUMBO-122 [141] and
windowed-DUMBO-1 [140, 141] (see section 3.3.4.), applied in the t1 and t2
dimensions, respectively. The length, together with the phases (relative to that of the eDUMBO scheme) of the prepulses θ1, was carefully calibrated to minimize the
artifact in f1. The pulse θ1 before t1 ensures that there is no magnetisation component
along the effective field of the eDUMBO-122 sequence [141]. A second pulse θ1 after t1 rotates the magnetisation back in preparation for the application of the DQ reconversion sequence. In addition, prepulses θ2 were inserted before and after each
detection window to minimize quadrature images in the direct dimension. POST-C7 was chosen for the excitation and reconversion of DQ coherences. The C7 and POSTC7 sequences have a phase dependence upon the rotor phase, resulting in increased DQ efficiency and negating the need for rotor-synchronised 2D experiments [184].
As a result of the 1 2 7
C symmetry condition, the nutation frequency of the DQ irradiation is given by ω1C7 = 7ωr. The r.f. amplitude applied is typically 100 kHz.
The experiments were performed at νr = 12.5 kHz, corresponding to a recoupling
amplitude of ν1 = 87.5 kHz. A Bruker 4 mm probe has been used in these
experiments.
The number of Cφ elements used for excitation and reconversion, optimised
in general to 3 elements (the recoupling time, τrec = 68.6 µs, corresponding to a
spinning speed of 12.5 kHz [155]) was found to give maximum DQ intensity.
It has been shown [156] that pairs of 1H-1H DQ peaks are generally observed
in such 2D spectra for internuclear 1H distances of approximately <3.5Å.