Modulation, amplitude

In an MTDSC experiment, a repeated temperature modulation is superimposed on the normal linear temperature programme [1-5,74]. The modulation amplitude and frequency, and the underlying heating rate can be chosen independently. 

For non-isothermal experiments, heating only conditions, with the modulation amplitude chosen so that no cooling occurs over one complete cycle, are of no use in cure studies. On the contrary, for experiments with very low underlying heating rate, or when Cp should be measured as accurately as possible, it is advisable to use a larger modulation amplitude. Of course, the amplitude of the temperature modulation has to be limited, since its effect on the cure kinetics has to be negligible. Typical amplitudes are between 0.1 andl°C. 

Depending on what you want to optimize, here are some rules  

For optimum S/N ratio, but decreased resolution Modulation amplitude = 2 x line-width. 

For accurate line width measurements Modulation amplitude = line-width/10. For most practical work Modulation amplitude = line-width/3. 

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More sophisticated pulse sequences have been developed to detect nuclear modulation effects. With a five-pulse sequence it is theoretically possible to obtain modulation amplitudes up to eight times greater than in a tlnee-pulse experunent, while at the same time the umnodulated component of the echo is kept close to zero. A four-pulse ESEEM experiment has been devised to greatly improve the resolution of sum-peak spectra. 

Figure 3 (a) [001] HRTEM image of the distorted austenite of figure 4 after (a) 1 min. and (b) 5 min. irradiation with 400 keV electrons inside the microscope. The increase of the modulation amplitude is apparent. The line in (b) indicates an interface between two adjacent martensite variants. 

Fig. 4. X-band EPR spectra of [Fe3S4]+ clusters in wild type and mutant forms of P. furiosus Fd. All spectra were recorded at 4.2 K microwave power, 1 mW microwave frequency, 9.60 GHz modulation amplitude, 0.63 mT. All samples were in 100 mM Tris-HCl buffer, pH 7.8.

Fig. 12. EPR spectra of the Rieske fragment from the 6ci complex of Paracoccus denitrificans (ISFpd, top) and of the Rieske-type ferredoxin from benzene dioxygenase (FdBED, bottom). EPR conditions were as follows (ISF/FdBEn) microwave frequency, 9.021 GHz modulation amplitude, 1 mT/0.9 mT microwave power, 1 mW/9 mW temperature, 15 K/30 K.

Fig. 1. EPR spectrum of the dithionite-reduced Fepr protein fromD. vulgaris [from (7)]. The protein was 272 ftmol dm" in 25 mmol dm Hepes buffer, pH 7.5, and was reduced under argon with 10 mmol dm sodium dithionite for 3 min at ambient temperature. EPR conditions microwave frequency, 9331 3 MHz modulation frequency, 100 kHz modulation amplitude, 0.63 mT microwave power, 200 mW temperature (relative gain) 16 K (6.3X).

Fig. 4. EPR redox titration of ZJ. vulgaris Fepr protein at pH 7.5 of S = J components with dithionite and ferricyanide in the presence of mediators, [from (ZZ)]. ( , ) The Fepr protein-fingerprint signal (the 3+ state) monitored at g = 1.825 (O, ) signal with aU < 2 (the 5+ state) monitored atg = 1.898 ( , ) Titration in two directions starting from the isolated protein, which corresponds approximately to the top of the bell-shaped curve. ( , O) A titration starting from the fully preoxidized state. EPR conditions microwave frequency, 9.33 GHz microwave power, 13 mW modulation amplitude, 0.63 mT temperature, 15 K.

Fig. 5. Effective g assignment of the low-field S = IEPR signals in D. vulgaris Fepr protein [from 11)]. The spectrum was recorded at the optimEd temperature of 12 K, that is, at which the amplitude is maximal and lifetime broadening is not significEmt. EPR conditions microwave frequency, 9.33 GHz microwave power, 80 mW modulation amplitude, 0.8 mT.

Fig. 6. Representative EPR spectra displayed by trinuclear and tetranucleEir iron-sulfur centers, (a) and (b) [3Fe-4S] + center in the NarH subunit of Escherichia coli nitrate reductase and the Ni-Fe hydrogenase fromD. gigas, respectively, (c) [4Fe-4S] + center in D. desulfuricans Norway ferredoxin I. (d) [4Fe-4S] center in Thiobacillus ferrooxidans ferredoxin. Experimental conditions temperature, 15 K microwave frequency, 9.330 GHz microwave power, (a) 100 mW, (b) 0.04 mW, (c) smd (d) 0.5 mW modulation amplitude (a), (c), (d) 0.5 mT, (b) 0.1 mT.

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

The surface reactions were investigated by a combination of AES and TPR studies, with authentic samples of the expected products being used to calibrate the signals from the two techniques. The Auger spectra were obtained with a single pass cylindrical mirror analyzer operated with a modulation amplitude of 4 eV the surface heating rate in the TPR studies was 2 K/s. 

The decay of the coherence is traced with the modulation amplitude. This series of optical transitions shown in Figure 6.1b contains three incident electric fields (Ql, Q,s> and offers bulk-sensitive, time-domain detection of vibrational... 

FIGURE 9.9 220GHz EPR spectrum of Ni-MCM-41 activated at 260°C, degassed, and measured at 5K. Modulation frequency 81 kHz, modulation amplitude 30mV, and sweep rate 0.1 T/min. (From Konovalova, T.A., J. Phys. Chem. B, 105, 7549, 2001. With permission.)... 

Sweep time Field offset Modulation amplitude Filter time constant... 

FIGURE 2.7 Overmodulation. The single-line spectrum of the strong pitch calibration sample (g = 2.0028) is recorded at v = 9.77 GHz with modulation amplitudes of 2.5, 10, or 40 gauss and with accordingly adjusted electronic gain such that in the absence of modulation deformation the signal should have constant amplitude. 

For Equation 6.7 to be valid it is assumed that all other experimental conditions are equal for the two samples. If this is not true, additional corrections may be required for differences in modulation amplitude (M), microwave power attenuation in IdBI OP), magnetic field scan width (W) (or equivalently, the step width in gauss between two subsequent digitization points), electronic gain (G), sample diameter Of), and absolute temperature (I) ... 

FIGURE 10.4 Anisotropy averaging in the EPR of TEMPO as a function of temperature. The spectra are from a solution of 1 mM TEMPO in water/glycerol (10/90). The blow-up of the middle 14N (/ = 1) hyperfine line in the 90°C spectrum has been separately recorded on a more dilute sample (100 pM) to minimize dipolar broadening and, using a reduced modulation amplitude of 0.05 gauss, to minimize overmodulation. The multiline structure results from hyperfine interaction with several protons. 

Figure 2. Current-time and photon-time data for the electron injection process by t-stilbene into a Au sphere electrode. These data were obtained using electronic compensation for the residual IR drop in solution, with a modulation amplitude of 3.1V (ie. -2.6V to 0.5V).

Figure 4. Derivative 1H NMR spectra of the measured clinoptilolite samples at room temperature. The modulation amplitude was 0.22 G, phase detector time constant 0.1 s, speed of the field 6.9 mGs -1. The lines are averaged out of eight accumulated repetitions.

For maximum ENDOR enhancement, the Zeeman modulation amplitude has to be about one half of the width of the EPR line which is saturated at an extremum of its first derivative. However, in an EPR spectrum with line widths of typically 1 mT this Zeeman modulation contributes 20 kHz to the width of a proton ENDOR line. It turns out that in many cases a remarkably better resolution of the spectra may be obtained with a single coding in which only the rf field is modulated. 

In powder samples with broad EPR lines, large Zeeman modulation amplitudes have to be applied to improve the sensitivity. Such amplitudes often produce microphonic noise in the cavity and cause an uncertainty in the orientation selection in single crystal-like ENDOR spectra (Sect. 4.1). A modulation technique which avoids these problems in powder ENDOR studies has been proposed by Hyde et al.32). In this scheme the Zeeman modulation is replaced by a 180° modulation of the phase of the microwave signal. 

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