Nutation Behaviour

The Refocused DIVAM nutation array of the 19F MAS NMR spectra of PVDF is shown in figure 58. The amorphous signal is seen to nutate at a faster rate than the crystalline signal, and passes through a null condition at ~ θ = 22.5 ο, where positive intensity of the crystalline signal remains. Also, the crystalline signal passes through a null condition at ~ θ = 62.5 ο, where the amorphous signal has returned to a positive intensity. Furthermore, the defect signals now nutate at a rate similar to that of the amorphous signal; this will be discussed further later. It is important to point out that these selection angles are approximate. To achieve complete selection of either the crystalline or amorphous domain one would have to increment the excitation angle in steps much smaller than 2.5ο.

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Figure 58 The Refocused DIVAM nutation array of the 19F MAS NMR spectra of PVDF over a series of excitation angles with an inter-pulse delay of 2.5 µ, a 90ο pulse width of 2.5 µs, a 180ο pulse width of 5 µs (TF = 150 µs), and a pulse offset of 1 kHz. The nutation array

ranges over excitation angles of 0o-90o in steps of 2.50 and was acquired with a spinning speed of 20 kHz. Enlargements of the 19F MAS NMR spectra of PVDF for selected excitation angles are shown above the array.

When comparing the nutation behaviour in Refocused DIVAM (figure 58) with Direct DIVAM (figure 43), a few observation can be made. First, note that the phase distortions in the Direct DIVAM array have been reduced in the Refocused DIVAM experiment. Second, the signal from all three chemical environments nutate for all excitation angles indicating that the offset dependence of Direct DIVAM has been reduced. Lastly, Refocused and Direct DIVAM show differences in their overall rate of nutation, which can be attributed to three factors: 1) the inter-pulse delays used in Direct DIVAM differ from the Refocused DIVAM sequence; 2) the Refocused DIVAM sequence has 24 inter-pulse delay periods due to the addition of refocusing pulses; 3) the selection mechanisms of Direct and Refocused DIVAM are different. As a result of the first two factors, the total filtering time of the sequence is changed and the net evolution in the transverse plain is different; therefore differences in their nutation rates are to be

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expected. The selection mechanism in Direct DIVAM, when off-resonance, becomes dominated by its offset dependence, while in Refocused DIVAM it appears to be driven primarily by the CSA term. This is further supported by SIMPSON simulations on Refocused DIVAM, which is discussed in Section 3.4.1.

Although, the offset dependence of Direct DIVAM has been greatly reduced, it can still be seen to a minor degree when comparing nutation rates of the amorphous and defect signals in Refocused DIVAM (Figure 58). These signals are known to be from similar environments and should have similar nutation rates; however, upon closer examination nutation of the defect signals lags slightly behind the amorphous signal. The extent of this remaining offset dependence will be examined further using Nafion 117.

The 19F MAS NMR spectra of Nafion 117 and its structural assignment can be seen in Figure 59.49, 124 Nafion provides an ideal case for testing the experimental extent over which the offset dependence of Direct DIVAM has been removed. The sidechain (SC) CF3 and OCF2 signals of Nafion (signal E and F, respectively, in figure 59b) have an isotropic chemical shift of ~40 ppm, or ~20 kHz, from the main backbone (BB) CF2 signal (signal B in figure 59b). In addition, these signals are far enough removed from each other that simple nutation behaviour is expected for each signal, so long as Direct DIVAM is applied on-resonance with respect to the signal of interest. Figures 60a and 60b show the nutation profile of the backbone (BB) signal (B in figure 59) at –122 ppm, and side-chain (SC) signals (E and F in figure 59) at –82 ppm, with the RF resonance frequency centered on the backbone (BB) signals. Similarly, Figures 60c and 60d show analogous nutation profiles but with the RF resonance centered on the SC signal.

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Figure 59 a) The polymer structure of Nafion 117 and b) the 19F MAS NMR spectra and structural assignment of Nafion 117 under ambient conditions, with the RF resonance set on the backbone CF2 peak, and a MAS rate of 24 kHz where: A = SCF2, B = (CF2) n,

C = CF (Backbone), D = CF (Side-chain), E = CF3, F = OCF2, SB = Spinning side band.

Figure 60 The 19F Direct DIVAM nutation arrays of various peaks in Nafion with an MAS frequency of 24 kHz and ranging over excitation angles of 0o-90o in steps of 2.50.Each Direct DIVAM array used an inter-pulse delay of 1.67 µs and a pulse width of 4.44 µs (TF = 83.3 µs). Array of the backbone CF2 peak (a, c) and side-chain CF3 and OCF2

peaks (b, d), with the RF resonance centered on either the backbone CF2 peak (a, b) or

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It is clear that nutation of each signal occurs only when the RF resonance is centered directly on the peak of interest (figures 60a and 60d) and that once the RF resonance is moved nutation is lost (figures 60b and 60c). This is a direct result of the aforementioned offset dependence of Direct DIVAM and will be further confirmed in section 3.4.1. Figure 61 illustrates the nutation profiles of the BB and SC signals in Nafion acquired using the Refocused DIVAM sequence and with the RF frequency centered at –100 ppm.

Figure 61 The 19F Refocused DIVAM nutation array, at an MAS rate of 24 kHz and ranging over excitation angles of 0o-90o in steps of 2.50, of the a) backbone CF2 peak and the b) side-

chain CF3 and OCF2 peaks in Nafion with the RF resonance centered at –100 ppm for

both arrays. An inter-pulse delay of 1.46 µs, a 90ο pulse width of 2.5 µs, a 180ο pulse width of 5 µs (TF = 125 µs), and a pulse offset of 1 kHz were used.

Refocused DIVAM recovers nutation of both the SC and BB signals and has removed the frequency offset dependence over a range of at least ~±20 ppm (~±10 kHz). Figure

61 illustrates the increase in the effective frequency range of the Direct DIVAM sequence by the introduction of refocusing pulses. Earlier it was stated that the selection mechanism of Refocused DIVAM appears to be driven by the CSA term. This term has

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an orientational dependence with respect to the static magnetic field and transient behaviour is expected on the rotor-time scale. This was investigated by carrying out a series of experimental measurements in which the inter-pulse delay was varied while both the pulse offset and excitation angle were fixed.