Phase Detection Experiments

Microwave Hall experiments have been performed in our laboratory.16 They have shown that the mobility of charge carriers in semiconductors can be measured quite reliably even if the semiconductors are only available in the form of a powder. The measurement technique itself is relatively complicated and involves, for example, rectangular waveguides, which can be rotated against each other on opposite sides of the sample to monitor the phase rotation. In the two-mode resonator, two modes of 

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Peters and Miethschen, and the hazards of HF generation, 524 Phase detection experiments, with microwaves, 451... 

Now we show you a sketch of what is happening in the frequency domain. The rf carrier frequency is at which is chosen so that the entire spectrum of interest is bracketed between and v +Av or v -Av (but not both) where 2Av is the digitizing rate. In a single phase detection experiment the folding problem is avoided by deliberately locating the carrier frequency to one side of all spectral features and ignoring the other side of There are a couple of fairly... 

Because the reference frequency for the detector cannot be set within the spectrum without aliasing real lines in a single phase detection experiment, it is difficult to perform selective saturation experiments wherein only a small part of the spectrum is irradiated. We will see that it will be trivial to irradiate anywhere in the spectrum with quadrature detection. For such selective irradiation experiments, usually to saturate an unwanted water line, the reader is referred to the papers by Redfield (1976) and Hoult (1976). 

The situation is different in an experiment where the acquisition dimension of the conventional, direct detection experiment itself measures only the magnitude of a signal, as opposed to its time evolution. This is the case for example in an MRI experiment with phase encoding in all three dimensions. Here, it is the ID sensitivity that has to be compared between remote and direct detection, because the direct FID is no longer sampled point-by-point. Also, by following the treatment of ID sensitivity in Ref. [20], this yields ... 

Figure 17. Contour plot of the 360MHz homonuclear spin correlation mpa of 10 (2 mg, CDCL, high-field expansion) with no delay inserted in the pulse sequence shown at the top of the figure. Assignments of cross peaks indicating coupled spins in the E-ring are shown with tljie dotted lines. The corresponding region of the one-dimensional H NMR spectra is provided on the abscissa. The 2-D correlation map is composed of 128 x 512 data point spectra, each composed of 16 transients. A 4-s delay was allowed between each pulse sequence (T ) and t was incremented by 554s. Data was acquired with quadrature phase detection in both dimensions, zero filled in the t dimension, and the final 256 x 256 data was symmetrized. Total time of the experiment was 2.31 h (17).

Fig. 1. Pulse sequences for determining spin-lattice relaxation time constants. Thin bars represent tt/2 pulses and thick bars represent tt pulses, (a) The inversion-recovery sequence, (b) the INEPT-enhanced inversion recovery, (c) a two-dimensional proton-detected INEPT-enhanced sequence and (d) the CREPE sequence. T is the waiting period between individual scans. In (b) and (c), A is set to (1 /4) Jm and A is set to (1 /4) Jm to maximize the intensity of IH heteronuclei and to (1/8) Jm to maximize the intensity of IH2 spins. The phase cycling in (c) is as follows 4>i = 8(j/),8(-j/) 3 = -y,y A = 2(x),2(-x) Acq = X, 2 —x), X, —X, 2(x), —x, —x, 2(x), —x, x, 2 —x),x. The one-dimensional version of the proton-detected experiment can be obtained by omitting the f delay. In sequence (d), the phase 4> is chosen as increments of 27r/16 in a series of 16 experiments.

FIGURE 1.9 Schematic representation of the excitation, prohe, signal, and reference beams used for heterodyne detection in transient phase grating experiments. 

A variety of sequences exist, which differ with respect to the detected interaction ( J, or Jx ) and the mode of detection ( C or H detected, magnitude or phased mode, phase cycling or gradients for coherence selection). In view of the reduced sensitivity of heteronudear experiments with respect to homonuclear COSY experiments and the steadily decreasing sample amounts submitted for NMR experiments, there is no doubt that the inverse ( H) detected, gradient enhanced experiments are currently the best methods to apply. However on older type spectrometers, not equipped for inverse detection the old-fashioned direct C detected experiments are still in use. 

In contrast to the basic "C detected experiment, and as a consequence of the final H detection, the 2D spectra obtained with HMQC or HSQC have a projection onto the F2 axis which corresponds to the normal H spectrum and includes all chemical shifts and all Jfi, couplings. The latter may give rise to rather broad cross peaks for extensively coupled protons. The projection onto the Fl axis corresponds to a normal C spectrum but with the quaternary carbons missing. With HMQC, but not with HSQC, cross peaks are additionally split in Fl by "J couplings. The HMQC and the HSQC experiment are usually performed in phase-sensitive mode, which, after proper phasing in both dimensions, allow peaks to be displayed in pure absorption. 

A plot of Eq. 3.8 in the complex plane is shown in Fig. 3.3. Because the frequency of the output (a) — 0) is just the frequency at which Mxy precesses in the rotating frame, Fig. 3.3 also provides a visual depiction of this precession as viewed along the z axis. Note that the quadrature phase detection configuration permits us to differentiate between the frequencies (w — w ) and (o)rf — ), whereas such frequencies are indistinguishable with a single phase detector. The phase angle (4> — cf)r,-) can be chosen to provide the pure absorption mode on resonance, and in more complex experiments it can be adjusted as needed, as we shall see in detail later. 

Most immunochemically based sensors to date have been developed for liquid-phase measurements thus, the TSM resonator has been the device of choice. Of course, other plate-mode devices (SH-APM, FPW) would be equally well suited for liquid-phase detection and may have advantages in terms of sensitivity. A low-frequency (20 MHz) SAW liquid-phase immunoassay device has been reported [27], but operation of SAWs of higher frequencies in liquids is not feasible due to excessive attenuation of the SAW by the liquid. An alternative to in-situ detection is to expose a protein-coated AW device to a liquid-phase sample for a period of time, then dry it [226] the observed frequency shift is proportional to analyte concentration. When using this technique, it is crucial that careful control experiments in the absence of analyte be performed to obtain an accurate idea of the reproducibility of the baseline oscillation frequency throughout the procedure. 

In order to minimize the overall time of a 2D experiment, one wishes to keep the number of scans per increment (ns//) at a value that is sufficient to observe the spectrum of that particular increment. For heteronucleus detection, this number usually is large, but for protons, adequate detection can often be accomplished in 1 to 4 scans. The minimum ns//, however, is determined by the phase cycle (Section 5-8) of the pulse sequence used and may be anywhere from 4 to 64 scans. As a general rule, 8 scans// is a minimum value for H-detected experiments. Longer experiments that require a large ns//, such as the study of dilute solutions (proton detection) or heteronucleus detection, can make good use of interleaved acquisition with a suitable block size (as described in the discussion of the DEPT experiment in Section 7-2b). 

It is also important that LP not be abused. A sufficient number of increments must be taken from which the FID s can confidently be extended. A total of 64 increments has, for example, been found to be insufficient, while LP s have successfully been carried out with 96 increments. A good practice is to acquire at least 128 increments for accurate prediction. A second concern is that LP not be extended too far (e.g., 128 points predicted to 4,096). W. F. Reynolds (2002) has found that, as a general rule, data presented in the phase-sensitive mode can be predicted fourfold (e.g., 256 data points can be predicted to 1,024), while absolute-value data can be extended twofold, 256 points to 512. A significant exception to the fourfold rule for phase-sensitive experiments concerns the H-detected, heteronuclear chemical-shift correlation experiments. In marked contrast to COSY and HMBC spectra, for which the interferograms are frequently composed of many signals, those of HMQC and HSQC spectra constitute only one (due to the directly attached C). LP s up to sixteen-fold can be performed in these experiments (Sections 7-8a and 7-8b). 

In solution-state NMR, many important experiments incorporate the creation and evolution of MQ coherence (MQC).5,6,84-86 Since MQC cannot be directly detected, experiments that follow the evolution of a MQC are inherently at least two-dimensional. This is the case with H- H DQ MAS spectroscopy. Figure 7 shows a corresponding pulse sequence and coherence transfer pathway diagram first, a DQC is excited, which subsequently evolves during an incremented time period q the DQC is then converted into observable single-quantum (SQ) coherence (SQC), which is detected in the acquisition period, q. To select the desired coherence transfer pathways, e.g., only DQC during q, a phase cycling scheme is employed.79,80 Pure absorption-mode two-dimensional line shapes are ensured by the selection of symmetric pathways such that the time-domain... 

Sensitivity When used for coherence selection, gradients are able to refocus only one of two p coherence orders. In some applications this means that only one-half of the available signal is detected in contrast to phase-cycled experiments in which both pathways may be retained. Experiments which use PFGs for coherence selection may therefore exhibit lower sensitivity than the phase-cycled equivalent by a factor of typically 2 or V2 depending on the precise experimental details [24,34]. Purging gradients, however, do not cause such a sensitivity loss. 

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