Fi-increment

A Vcc 55 Hz optimized 1,1-ADEQUATE spectrum was recorded over 2 days 13 h as a 2K x 256 data file with 352 transients accumulated/fi increment. The observed 1,1-ADEQUATE correlations are shown on the structure. The expected correlation (double-tailed arrow) was observed from the 8-benzyl to the 9-aromatic carbon resonance. The corresponding absence of a correlation from C8 to C3 (dashed arrow) confirmed that... 

ACCORD-ADEQUATE spectrum using a 500-MHz spectrometer equipped with a 5-mm cryoprobe. The data were acquired as 180 hypercomplex points in the second frequency domain using 256 transients/fi increment. The broad 14-vinyl methylene resonance was located in the structure based on correlations in the ACCORD-ADEQUATE spectrum from H14 to C13 and from H12 to both Cll and C13. The C18 aromatic methine resonance afforded ADEQUATE correlations to the flanking C17 and C19 non-protonated carbons and, finally, the C23 methine provided a correlation to the C22 non-protonated carbon. 

Fig. 4. Two-dimensional (2D) spectra of cyclo(Pro-Gly), 10 mM in 70/30 volume/volume DMSO/H2O mixture at CLio/27r = 500 MHz and T = 263 K. (A) TCX SY, t = 55 ms. (B) NOESY, Tm = 300 ms. (C) ROESY, = 300 ms, B, = 5 kHz. (D) T-ROESY, Tin = 300 ms, Bi = 10 kHz. Contours are plotted in the exponential mode with the increment of 1.41. Thus, a peak doubles its intensity every two contours. All spectra are recorded with 1024 data points, 8 scans per ti increment, 512 fi increments repetition time was 1.3 s and 90 = 8 ps 512x512 time domain data set was zero filled up to 1024 x 1024 data points, filtered by Lorentz to Gauss transformation in u>2 domain (GB = 0.03 LB = -3) and 80° skewed sin" in u), yielding a 2D Fourier transformation 1024 x 1024 data points real spectrum. (Continued on subsequent pages)...

Fig. 2.—Multiple quantum spectrum of benzene (15 mol %) in />-ethoxybenzylidene-n-butylaniline (EBBA) at 20 C. The three pulse sequence was PI = n/2, P2 = 7t/2, P3 = k/2. The magnitude spectra obtained for 11 values of t spaced at 0.1 ms intervals from 9.6 to 10.7 ms were added. The value of /i ranged from 0 to 13.824 ms in 13.5 fis increments for each t. A single sample point was taken at 2 = r after Pj, One half of a symmetrical spectrum is shown.

Radiation effects and a need to achieve Fi frequency discrimination can lead to reduced water suppression in jump-and-retum NOESY experiments especially at short mixing times. Stonehouse et therefore modified the original sequence to include gradient pulses to achieve a constant water suppression for all phases and fi increments. 

As for ID data,/i quadrature detection requires two data sets that differ in phase by 90° to be collected, thus providing the necessary sine and cosine amphtude-modulated data. Since the fi dimension is generated artificially, there is strictly no reference rf to define signal phases, so it is the phase of the pulses that bracket fi that dictate the phase of the detected signal. Thus,/3r each fi increment, two data sets are collected, one with a 90 preparation pulse (fi sine modulation) and the other with 90y (fi cosine modulation), both stored separately (Fig. 5.17). These two sets are then equivalent to the two channel data collected with simultaneous acquisition, which produces the desired fi quency discrimination when subject to a complex FT (also referred to as a hypercomplex transform in relation to 2D data). The rate of sampling in fi or, in other words, the size of the fi time increment, is dictated by the/i spectral width and is subject to the same rules as for the simultaneous samphng of one-dimensional data. This... 

Figure 7.5. A region of the selective heteronuclear /-resolved spectrum of 7.2. Long-range heteronuclear couplings to the selected proton appear as splittings in/i, the values of which are shown. The vertical trace is taken through the resonance at 199 ppm. 4K 2 data points were collected for 32 fi-increments over spectral widths of 100 ppm and MHz, respectively. A 100ms Gaussian 180° pulse was used to select the proton resonance. The final /i resolution after zero-filling was 0.1 Hz/pt.

The pulse sequence illustrated in Fig. 20.11 is appropriate for observation of a chemical shift correlated or COSY spectrum, where the correlating influence between nuclear spins is their scalar /-coupling. In a typical experiment we might utilize 1 k, or 1,024, fi-increments, with t = 0.5—500 ms. The FID following each t is different because the interacting spins modulate each other s respmise. 

Figure 11 (A) / and S enantiomers of 2-ethyloxirane. (B) A H Q-COSY Fz spectrum of 2-ethyloxirane obtained from 268 uniformly fi-incremented data array by the FT method. (C)-(K) Comparison of spectra obtained by FT with uniform sampling, covariance with uniform sampling, and covariance with nonuniform sampling. Reprinted with...

Experimental spectrum of the methylene region of glassy atactic poly(propylene) (b) recorded atT 240 K on a BRUKER MSL-300 with a DAS probehead. The two angles for evolution and detection, respectively, were =81.7° and = S m = 54.7°. The rotation frequency was 3000 Hz, and 128 fi-increments were recorded. The theoretical values (o) are superimposed on the experimental contour plot. The absolute positions were adjusted like in the ID spectrum. A qualitative agreement of theory and experiment is seen... 

Consider the particular case as corresponding to low frequency. Assuming b 0, (j) 0 and Fi aj, we arrive at the following equation for increment of oscillations... 

A number of parameters have to be chosen when recording 2D NMR spectra (a) the pulse sequence to be used, which depends on the experiment required to be conducted, (b) the pulse lengths and the delays in the pulse sequence, (c) the spectral widths SW, and SW2 to be used for Fj and Fi, (d) the number of data points or time increments that define t, and t-i, (e) the number of transients for each value of t, (f) the relaxation delay between each set of pulses that allows an equilibrium state to be reached, and (g) the number of preparatory dummy transients (DS) per FID required for the establishment of the steady state for each FID. Table 3.1 summarizes some important acquisition parameters for 2D NMR experiments. 

The compositions of the monomer feed and of the polymer formed may be expressed as mole fractions instead of the mole ratios used above. To this end we let Fi represent the fraction of monomer Mi in the increment of copolymer formed at a given stage in the polymerization. Then... 

The composition of the increment of polymer formed at a monomer composition specified by /i(= 1 —/2) is readily calculated from Eq. (8) if the monomer reactivity ratios ri and V2 are known. Again it is apparent that the mole fraction Fi in general will not equal /i hence both /i and Fi will change as the polymerization progresses. The polymer obtained over a finite range of conversion will consist of the summation of increments of polymer differing progressively in their mole fractions F. ... 

Fig. 24.—Incremental polymer composition (mole fraction Fi) plotted against the monomer composition (mole fraction/i) for ideal copolymerizations (ri — X/r F). Values of r are indicated.

Fig. 25.—Incremental polymer compositions Fi as functions of the monomer composition fi for the values of the reactivity ratios indicated ri/r ). The broken straight line represents Fi—fi (i.e., ri=r2 = l).

Table 2. The frequencies f , phases 6 , scaling factors Xn of the effective RF fields and the amplitudes A of the excitation bands created by a Gaussian shaped PIP10 (0°, 144°, 40ps, fi(k), 125) with /i(fc) = 0.1577 exp[ — 0.002 x (k —63)2] kHz and a total phase increment 2nA/r = 2mn...

It proved helpful for the purpose of noise reduction to perform relaxation experiments in an interleaved fashion, as one pseudo-3D experiment, where the 2D planes in the F2 dimension correspond to various relaxation delays. The acquisition order (3-2-1) is selected so that cycling through various relaxation delays (in R1 or R2 experiments) or through NOE/NONOE 2D planes is performed prior to incrementing the evolution period in the indirect dimension (FI) (see e.g. Ref. [16]). The resulting pseudo-3D spectrum can be processed as a set of 2D spectra in tl and t3 dimensions, and then analyzed in the usual way. This procedure reduces the noise arising from switching from one 2D experiment to the other and helps minimize temperature variations between the spectra acquired... 

The results of this analysis are shown in Figures 10 and 11 for the extract and O-methylated extract. Note that a substantial portion of each curve is linear or nearly linear at long times, indicating a first-order process. This is particularly evident for the incremental sorptions where linearity is observed over a 50 to 60 hour period. At short times, the curves clearly deviate fi om linearity, suggesting that other processes are dominating. 

Quadrature images in the Fi dimension can be suppressed by expanding the 8-step phase cycle to 32 steps or 16 steps, respectively, using CYCLOPS [20] or 2-step CYCLOPS [21]. In the CYCLOPS scheme, the phases of all pulses are simultaneously incremented by 90°, 180° and 270°. In the 2-step CYCLOPS scheme, the incrementation of the pulse phases is limited to the 90° step. 

The absolute configuration of a chair cyclohexanone substituted in the a or fi position (I) can be determined with the aid of increments calculated from experimental data (Table 1). 

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