Sweep frequencies

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

CW Continuous wave or frequency sweep, the older, less sensitive, more time consuming basic technique of NMR detection... 

It was suggested above that the field Hq is held constant while the Hi frequency is swept this mode is called frequency sweep. An equivalent result is obtained by holding the rf field at a constant frequency and sweeping the field Ho- NMR spectra obtained by field-sweep measurements are displayed with the field increasing from left to right spectra obtained by frequency sweep are displayed with the frequency increasing from right to left, so that the two presentations are comparable. 

All P.M.R. spectra were measured with a Varian HA 100 spectrometer operating in the frequency-sweep mode with tetramethylsilane as the reference for the internal lock. The double and triple resonance experiments were performed using a Hewlett Packard 200 CD audio-oscillator and a modified Hewlett Packard 200 AB audio-oscillator (vide infra). Spectra were measured using whichever sweep width was required to ensure adequate resolution of the multiplets under investigation, generally 250 or 100 Hz, and sweep rates were selected as necessary. Extensive use was made of the Difference 1 and Difference 2 calibration modes of the instrument, both for the decoupling experiments and for the calibration of normal spectra. 

A preferable experimental arrangement, which eliminates both of the above disadvantages, is the so-called frequency-sweep N.M.D.R. experiment. Here H0 is kept constant at all times, o>2 is located on the center of the resonance to be irradiated and then the spectrum is observed by slowly sweeping o>i through the spectrum. Since a>2 remains at all times on the center of the resonance to be decoupled, this experiment enables one to remove simultaneously all of the couplings caused by that particular resonance. All of the experiments discussed below were performed under these conditions. 

Figure 2. Partial 100 MHz P.M.R. Spectrum of 3,4,6-tri-O-acetyl-v-glucal (1) measured for a chloroform -d solution (A normal spectrum of the Hi and H2 resonances respectively (B) frequency sweep spin-decoupled spectrum of the Hi and H2 resonances, with a strong decoupling field centred on the Hs resonance (C), as in (B) above, but with an additional weak radiofrequency field centred on the high field transition of the H2 resonance (D), as in (B) above, but with a weak radiofreauency field centred on the low field transition...

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

Figure. 9 Visco-elastic range of pectin gels Strain frequency sweep...

Figure 10. Graphical illustration of frequency sweep meas-urements taken from four different substances.

The exceptionally strong influence of calcium-ions on pectin solutions especially made with HM citrus pectins can be shown by a frequency sweep. The addition of calcium leads to an increase of the complex viscosity. Additionally we can observe a stable trapping of air bubbles in the solution. This effect can not be caused by the increase of viscosity. The frequency sweeps of the solutions give the answer. The storage modulus curves show the significant increase of the elastic shares caused by the addition of calcium-ions. 

The dynamic Weissenberg number W can be calculated from data obtained by the strain frequency sweep measurement. It s the ratio of the elastic to the viscous shares in the measured gel and leads to an objective description of the sensoric properties, representing the basis for the standardization of pectins. 

Adiabatic pulse A type of pulse employing a frequency sweep during the pulse. This type of pulse is particularly efficient for broadband decoupling over large sweep widths. 

Significant progress in signal enhancement methods for the central transition has been achieved by the implementation of double frequency sweeps (DFS) [62]. The basic idea of DFS, applicable for both static and MAS experiments, is to invert simultaneously the STs so that the populations of the outer spin levels are transferred to the CT energy levels before they are selectively excited (Fig. 4). 

Siegel et al. showed that enhancement of the CT can also be obtained using hyperbolic secant (HS) pulses to invert selectively the STs [74], Unlike the DFS waveform, whose frequency sweep is generated by a constant rf-pulse phase while modulating the amplitude, the HS pulse utilizes both amplitude and phase modulation, yielding an enhancement exceeding that obtained by DFS or RAPT [61, 74, 75]. Most recently, the pulse sequence called wideband uniform-rate smooth truncation (WURST) [76] was introduced to achieve selective adiabatic inversion using a lower power of the rf-field than that required for the HS pulses [77,78]. One of its applications involved more efficient detection of insensitive nuclei, such as 33S [79]. 

Fig. 15. Adiabatic decoupling of 13CO from 13C with a compensating pulse applied on the other side of the peaks. The compensating and decoupling pulses have the same shape but opposite frequency sweep. Due to the Bloch-Siegert effects, both the left and the right peaks are pushed towards the center while the centre peak is balanced and remains in its position. Reprinted from Ref. 47 with permission from Elsevier.

Fig. 11.5 Schematic comparison of (a) sudden and (b) adiabatic inversion of the z-component of the polarization vector. In the sudden case a n-pulse is applied while in the adiabatic case a frequency sweep is shown. The time evolution of the z-polarization as a function of the pulse duration...

---