Frequency Transmitter

Band-pass filter A filter used for selecting the desired coherence order, p. Carrier frequency The transmitter frequency that consists of high-frequency pulses. 

A double HS pulse with symmetrically placed offsets about the transmitter frequency (Acoo = 0) can be created by cosine modulation of the pulse amplitude ... 

An alternative method of running an nmr spectrometer is to hold the magnetic field constant and to sweep the transmitter frequency through the resonances. This mode of operation is more like other forms of spectroscopy and gives the same line shapes as sweeping the field (Figure 9-25). 

Exercise 9-21 Use Figure 9-24 to map the nmr spectrum you would expect for 13CCI31H in a field-sweep spectrometer in which the transmitter frequency is kept constant at 30 MHz and the magnetic field is swept from 0 to 30,000 gauss. Do the same for a frequency-sweep spectrometer when the magnetic field is kept constant at 10,000 gauss and the frequency is swept from 0 to 100 MHz. (For various reasons, practical spectrometers do not sweep over such wide ranges of field or frequency.)... 

Figure 9-27 Comparison of the proton nmr spectra of 2-methyl-2-butanol at rf transmitter frequencies of 60, 100, and 220 MHz. The line at 165 Hz in the 60-MHz spectrum is due to the OH protons, and this is off-scale to the left in the 220-MHz spectrum. The large single line in the center of the spectra arises from the resonances of the six methyl hydrogens. The line at 0 Hz is TMS in each case.

To reiterate, chemical shifts are strictly proportional to spectrometer frequency, thus lines 100 Hz apart at 60 MHz will be 167 Hz apart at 100 MHz. This might seem to make comparisons of nmr spectra on different spectrometers hopelessly complex but, because of the proportionality of shifts to frequency (or field), if we divide the measured shifts in Hz, (relative to the same standard) for any spectrometer by the transmitter frequency in MHz, we get a set of frequency-independent shifts in parts per million (ppm), which are useful for all nmr spectrometers. Nmr shifts reported in ppm relative to TMS as zero, as shown in Figure 9-23, are called 8 (delta) values ... 

Second, the chemical shift can be recognized by the fact that it is directly proportional to the transmitter frequency, v. If we double v, the chemical shifts double. In contrast, the first-order spin-spin splittings remain the same. By this we mean that the magnitude (in Hz) of the spacing between the lines of a split resonance is independent of the transmitter frequency, v. This spacing corresponds to what is called the spin-spin-coupling constant, or simply the coupling constant, and is symbolized by J. 

CH2 and 8CH are directly proportional to the transmitter frequency of the spectrometer, but the internal spacings of the split resonances,. /, are not (see Figure 9-27). 

Third, the second-order splitting tends to disappear with increasing transmitter frequency. For ethyl iodide (Figure 9-32), the second-order splitting at 60 MHz is barely discernible at 100 MHz and disappears at 200 MHz. This also can be seen to occur for the three-four splitting pattern of 2-methyl-2-butanol as a function of v (Figure 9-27). 

At the center of the echo all resonance offsets from interactions linear in the spin quantum number are canceled as long as these interactions operate for the full duration ofTE. Linear spin interactions include chemical shifts, heteronu-clear dipolar couplings, field inhomogeneity, field gradients, and transmitter frequency offsets but do not include quadru-polar and homonuclear dipolar couplings. There will however be a net phase evolution induced by an interaction to the extent its duration or intensity is not balanced with respect to the two halves of TE (that is, the balance with respect to amount of phase evolution on either side of the 180° pulse). 

Observe the H/ F, set on resonance by shifting the transmitter frequency and set the power to produce the desired 90° pulse. 

In the former case, an internal lock is established at the deuterium frequency of the solvent by adjusting the frequency of the lock transmitter until it matches that frequency. The operator typically observes a decreasing number of interference-pattern sine waves as the lock transmitter frequency approaches that of the deuterium nuclei in the solvent. A null appears when the two frequencies are identical the operator then turns the lock control to On. On most modem spectrometers, autolocking procedures are also available that search for the deuterium resonance and automatically lock the spectrometer when the signal is found. 

The transmitter offset describes the location of the observation frequency and is closely related to the spectral width. With quadrature phase detection of sample signals (Section 5-8), the frequency of the transmitter is positioned in the middle of the spectral width. In so doing, the operator has the best chance of irradiating, with equal intensity, those nuclei whose resonances are both close to and far from the transmitter frequency. Irradiation is not a problem for protons, with their small chemical shift range, but it can be for nuclei with large chemical shift ranges (Chapter 3). 

The period t is used to encode the double quantum frequency domain. The resulting 2D display contains a horizontal axis in V2 (the normal frequencies) and a vertical axis that is a double quantum domain represented by the sum of the frequencies of coupled nuclei ( U2 )- The latter frequencies are referenced to a transmitter frequency at zero. 

The multiple-quantum (MQ)/MAS NMR is one of the 2D NMR methods, which is capable of averaging out the second-order quadrupolar interaction in nuclei with spin > 1/2 such as H, "B, O, etc. The "B MQ/ MAS NMR measurements on boron as contained in silyl-carborane hybrid Si-based polymer networks considered here. The molded samples are cut into small pieces to insert them into a 4-mm NMR rotor and spun at 12 kHz in a MAS probe. The observation frequency of the "B nucleus (spin number I = 3/2 and isotope natural abundance = 80.42%) is 96.3 MHz. Excitation of both the echo (—3Q) and anti echo (+3Q) coherences is achieved by using a three-pulse sequence with a zero quantum filter (z-filter). The widths of the first, second, and third pulses are 3.0 4.1 ps, 1.1-1.6 ps, and 19-28 ps, respectively. The z-filter is 20 ps. The recycle delay time is 6-15 s and the data point of FI (vertical) axis is 64 and for each the number of scans is 144. Then, the total measurement time is 15-38 h. The phase cycling used in this experiment consists of 12 phases. Boron phosphate (BPO4 3 = 0 ppm) is used as an external standard for "B. The chemical shift value of BPO4 is —3.60 ppm from BF3 O(C2H5)2 which is used as a standard reference in " B NMR in the liquid state. The transmitter frequency of " B is set on peak of BPO4 for a trustworthy chemical shift after Fourier transform." " ... 

Symmetrically shifted pulses have been proposed as a means of solvent suppression. Symmetrically shifted pulses are symmetrically shifted laminar pulses that contain equal numbers of rectangular pulse components of the same phase at an offset frequency. The basis of the symmetrically shifted pulse family is the SS pulse which is conceptually equivalent to applying simultaneous ir/2 rectangular pulses with two separate, but in-phase, transmitters at offset frequency from the water. On a practical basis an SS pulse is obtained by a complete Itt cosine modulation of a single transmitter (see Fig. 15). An S pulse is half of an SS pulse (i.e. a half-cycle tt pulse) which results in a narrower null and a 180° phase inversion at the transmitter frequency. They are also the soft, continuous equivalent of binomial sequences. The SS and S pulses have broader excitation maxima than the sinusoidal profile of the JR sequence. The method has maximal excitation at an offeet frequency of second-order U-shaped water suppression. The exdtation profile is related to the maximum amplitude modulation and can be determined by numerical evaluation of the Bloch equations. Hence a new pulse shape must be used for each excitation window. The SS pulses give better water suppression than the JR sequence, but at the expense of poorer excitation of resonances closer to the water. Also, there is no phase inversion at zero frequency. The S pulse gives better excitation near the water frequency but with less water suppression. 

Figure 2.12. Chemical shifts in the rotating frame. Vectors evolve according to their offsets from the reference (transmitter) frequency vq. Here this is on-resonance for spins A (vo = va) whilst spins X move ahead at a rate of -l-v Hz (=vx - Vo).

In praetice, modem NMR instruments are designed to deliver high-power 90 pulses closer to 10 jls, rather than the hundreds predicted from the above arguments. This is to suppress the undesirable effects that arise when the pulse rf frequency is off-resonance, that is, when the transmitter frequency does not exactly match the nuelear Larmor frequency, a situation of considerable practical significance that has been ignored thus far. 

An alternative to adding additional reference materials is to use a so-called external reference. Here the spectrum of a separate reference substance is acquired before and/or after the sample of interest and the spectrum reference value carried over. Identical field settings should be used for both which, on some older instruments, requires the same lock solvent, or an additional correction to the spectrum reference frequency must be used to compensate any differences. This restriction does not arise on instruments that use shifting of the lock transmitter frequency to establish the lock condition. 

The first procedure for locking is to establish the resonance condition for the deuterium signal, which involves altering either the field or the frequency of the lock transmitter. Of these two options the latter is preferred since it avoids the need for changing transmitter frequencies and is now standard on modem instruments. Beyond this, there are three fundamental probe-dependent parameters that need to be considered for optimal lock performance. The first of these is the lock transmitter power used to excite the deuterium resonance. This needs to be set to the highest usable level to maximise the signal-to-noise ratio but must not be set so high that it leads to lock saturation. This is the... 

The third complicating factor specific to ROESY is the attenuation of cross-peak intensities as a function of resonance offset from the transmitter frequency [69]. Off-resonance spins experience a spin-lock axis that is tipped out of the x-y plane (Section 3.2.1) resulting in a reduction in observable transverse signal in addition to a reduction in cross-relaxation rates. This is more of a problem for quantitative measurements, although fortunately mid-sized molecules show the weakest dependence of ROE cross-relaxation rates on offset. The so-called compensated ROESY sequence [69] eliminates these frequency-dependent losses should quantitative data be required. 

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