Coupling factor measurement

Equations (12) and (13) give a link between the coupling factor measured from a DNP experiment and the translational correlation time rt. This relationship is shown by the solid line in Figure 3, where the coupling factor is plotted as a function of the product of the electron Larmor frequency and the translational correlation time. 

The contribution to the stress from electromechanical coupling is readily estimated from the constitutive relation [Eq. (4.2)]. Under conditions of uniaxial strain and field, and for an open circuit, we find that the elastic stiffness is increased by the multiplying factor (1 -i- K ) where the square of the electromechanical coupling factor for uniaxial strain, is a measure of the stiffening effect of the electric field. Values of for various materials are for x-cut quartz, 0.0008, for z-cut lithium niobate, 0.055 for y-cut lithium niobate, 0.074 for barium titanate ceramic, 0.5 and for PZT-5H ceramic, 0.75. These examples show that electromechanical coupling effects can be expected to vary from barely detectable to quite substantial. 

The isolation of the coupling factor is very important to gaining the desired information from an experiment. The first step towards isolating the coupling factor is to measure signal enhancement as a function of ESR saturation power and extrapolate to infinite power.26 50 This determines the maximum enhancement, Emax, where... 

Since the leakage factor can be easily calculated from Ti relaxation data, and ys/y is constant, that only leaves the determination of smax before the coupling factor can be directly accessed. For solutions of radicals where Heisenberg exchange is prominent, Emax must be measured as a function of concentration and extrapolated to infinite concentration where smax 26,50 pQr jmmobilized or tethered radicals, nitrogen nuclear spin relaxation effectively mixes the hyperfine states in virtually all cases (small peptides may be an exception) and smax 1 can safely be assumed. 56 Alternately, the determination of smax can be avoided... 

To reach this conclusion, Turke et al. investigated the experimental parameters that should affect the evaluation of DNP enhancement and found a condition where they believed complete saturation of the ESR line occurred with no sample heating for 15N,16D-4-oxo- TEMPO.71 From there, they measured actual enhancements of E = —170 at 0.35 T, yielding a coupling factor of p < 0.34 at 27 °C. This experimental DNP data more closely approaches the NMRD data in the accompanying paper by Ben-nati et al., where a coupling factor of p = 0.35 was determined at 25 °C, which corresponds to a maximum predicted DNP signal enhancement of Emax = 218.76 Electron-electron double resonance (ELDOR) experi-... 

As the discussion in this section shows, there remains somewhat conflicting reports on the proper way to measure the coupling factor and maximum saturation factor for nitroxide radicals. While this is not a concern for radicals (such as trityl) with only one hyperfine line, nitroxide radicals have been shown to give generally better DNP signal enhancements for solution-state systems than water-soluble trityl radicals at both 0.34 and 3.3 T.41 Because of the importance of nitroxide radicals, further work needs to be done to resolve all discrepancies. However, the most recent results show that theory and various experimental reports are closer in agreement than ever before. 

Much of the recent development of theory and methods for measuring the coupling factor has been performed with X-band DNP.26,29,41,50 71 7 Since these studies were discussed earlier in Section 3.1, they are not included here and instead this section covers recent applications for DNP carried out at this field. 

A remedy obviously should be available using polarization tricks. In conventional Raman spectroscopy, the isotropic and anisotropic components are deduced from linear combinations of the polarized and depolarized spectra, while a nonresonant part is not clearly recognized (41). In frequency-domain CARS it is known how to suppress the nonresonant contribution and solely measure resonant scattering (isotropic plus anisotropic part) (42). In time-domain CARS, polarization interference can do an even better job with three magic cases (derived in Refs. 35,39). These authors derived explicit expressions for the coupling factors F in Equations (2)-(4) ... 

Furthermore, for the face detected emission (as usually is the case), the light output coupling factor (287) reduces the measured Oel to OgE, so that we deal with the external quantum EL efficiency... 

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