Equilibrium spectrum

Contrary to earlier expectations (see Dorfman, 1965), Hentz and Kenney-Wallace (1972, 1974) failed to find any correlation between s and Emax. Actually, there is a better correlation of matrix polarity with the spectral shift from e(to e upon solvation and the time required to reach the equilibrium spectrum (Kevan, 1974). Furthermore, Hentz and Kenney-Wallace point out that emax is smaller f°r alcohols with branched alkyl groups, the spectrum being sensitive to the number, structure, and position of these groups relative to OH. Clearly, a steric effect is called for, and the authors claim that a successful theory must not rely too heavily on continuum interaction as appeared in the earlier theories ofjortner (1959,1964). Instead, the dominant interaction must be of short range, and probably the spectrum is determined by optimum configuration of dipoles within the first solvation shell. 

Fig. 7. The equilibrium spectrum (top) and the spectrum immediately after a selective inversion (bottom) of the molecule in fig. 6.

Fig. 19. Line shape analysis of the equilibrium spectrum of P420. The large dotted Lorentzians centered at 32.4 and 30.5 ppm and rather wide dotted Lorentzian centered at 32 ppm represent the orthorhombic crystalline and noncrystalline amorphous phases and crystalline-amorphous interphase, respectively. The dotted curve that is almost completely superimposed on the experimental spectrum indicates the composite curve of the component Lorentzians. dashed Weakly Lorentzians at 39, 34, 28, and 26 ppm represent the contributions from the methine and methylene carbons (a and p to the methine and methylene in the ethyl side group), respectively...

Fig. 20. Equilibrium spectrum and line shape analysis in the IB2 carbon range for the sample PI6. The spectrum was obtained by a single pulse sequence with a repetition time of 50 s...

The resonance lines at 72.9 and 28.3 ppm are assigned to the crystalline components of a- and 3-methylene carbons because of their longer Tic values. These crystalline resonance lines are associated with two T1C values of ca. 209 and 9-10 s. This shows that both methylene carbons possess two components with different Tic >s> but this will not be discussed further, since the existence of plural TiC s is a normal finding for crystalline polymers as discussed in previous sections. On the other hand, the resonance lines at 70.9 and 27.0 ppm recognized for a-and (3-methylene carbons are assignable to the noncrystalline component, because these chemical shifts are very close to those in the solution. These lines are associated with only one Tic of 0.15 or 0-14 s and two T2c values of 7.95 s and 0.099 ms, or 8.22 s and 0.099 ms, respectively for the a- and (3 -methylene carbons. This suggests that the noncrystalline component involves two components, both associated with a same Tic and different T2c Js. The noncrystalline component with a T2c of 7.95 or 8.22 ms is thought to form an amorphous phase and that with a T2C of 0.099 ms comprises a crystalline-amorphous interphase. In order to confirm this, we examined the elementary line shapes of each component and performed the line shape decomposition analysis of the equilibrium spectrum. 

Figure 22-(a) shows the DD/MAS spectrum in the resonance range of a-methyl-ene carbon at 0 °C. This spectrum represents the thermal equilibrium state of this sample, because it was obtained by a single pulse sequence with the repetition time of 600 s longer than 5 times the longest Tic in the system. The spectrum (b) is that of the crystalline component, which was obtained with use of Torchia s pulse sequence [53]. In the equilibrium spectrum, the noncrystalline contribution (amorphous plus interfacial) can be seen upfield to the crystalline component. Figure 23 shows the elementary line shapes of the amorphous and crystalline-amorphous interphases that comprise the noncrystalline resonance. 

Fig. 22. (a) Equilibrium spectrum of poly(tetramethylene oxide) at 0 °C in the range of the a-methylene carbon and (b) its crystalline component... 

The line-decomposition analysis of the equilibrium spectrum of the a-meth-ylene carbon was carried out using the elementary line shapes thus obtained for the three phases. The result is shown in Fig. 24. The composite curve of the decomposed components reproduces well the experimentally observed spectrum. The mass fraction of the crystalline component was estimated as 0.60 that is described in the figure. Based on the heat of fusion of 8.13 KJ/mol of this sample and the value of 14.2 KJ/mol for the crystalline material of this polymer the crystalline fraction was estimated to be 0.57. Here the heat of fusion for the crystalline material was obtained from the effect of diluent on the melting temperature with use of the relationship developed by Flory [91 ]. The crystalline fraction estimated from the NMR analysis is in good accord with the value estimated from the heat of fusion, supporting the rationality of the NMR analysis. 

Fig. 24. Line shape analysis of the equilibrium spectrum of the a-methylene carbon shown in Fig. 22-(a). A, By and C represent the crystalline, crystalline-amorphous interfacial, and amorphous components, respectively...

Fig. 27. Equilibrium DD/MAS 13C NMR spectrum of sPP/o-dichlorobenzene gel (13.6 wt%), obtained by a n/2 single pulse sequence with a repetition time of 300 s. In the lower part the equilibrium spectrum of the bulk sPP crystal in ttgg form is shown for reference. The arrows indicate the resonance of the amorphous component of each carbon...

Fig. 1.17. Simulated (solid line) and experimental (dotted line) spectra of radical pairs in colloidal Ti02 modified with ascorbic acid. The g-tensors were taken as an axially simmetric with g(R,+)=(2.004, 2.004, 2.000), g(R ) = (1.988,1.988,1.958) according to the data experimentally determined earlier [57]. Anisotropic line width was obtained from the simmulation of the equilibrium spectrum AH(R +) = (4.3 Gs, 4.3 Gs, 5.6 Gs), AH(R ) = (2.5 Gs, 2.5 Gs, 7.0 Gs). The best fit of the polarized spectrum was simulated without any contribution of the equilibrium spectrum and with the dipole (HD) contribution dominating over the exchange (Hj) one ...

Figure 1.10 UV-VIS absorbance of the H404A mutant of VCPO and the effect of H2O2 at pH 8.3. (a) Spectrum a 200 /xM apo-H404A spectrum b mixture of holo- and apo-enzyme after addition of 200 fxM vanadate spectrum c the effect of addition of 200 (xM H2 O2. (b) Spectrum a titration of 200 fxM apo-H404A with 0-800 /xM vanadate the line shown is a fit to the data points for a simple dissociation equilibrium spectrum b absorbance of 0-200 fxM free vanadate. Source Renirie, R., Hemrika, W. and Wever, R. (2000). Journal of Biological Chemistry, 275, 11650-11657. Reprinted with permission from The American Society for Biochemistry and Molecular Biology.

Instead of a 90° pulse, a 45° pulse is sometimes used to save time for the measurement. In this case, the equilibrium spectrum is obtainable by settingas 3 times Tic. For one pulse sequence only I/V2 times signal is obtainable bnt 5/3 times pulse seqnences can be repeated for the same time as used for the measurement by the 90° pulse sequence. Since (I/V2) X (5/3) times signal is obtainable and the noise decreases by V3/5 times (the noise is thought to decrease proportionally to the reciprocal square root of the repetition number of the measurements), a spectrum with larger signal/noise ratios is obtainable in the same measuring time. 

A model that calculates the actual local ocean surface wave spectrum, based on relaxation towards the equilibrium spectrum and... 

In what follows, the above elements will successively be discussed. In section 2, the VIERS-1 equilibrium spectrum will be briefly described, followed by a discussion of the extensions that have been implemented in order to be able to better use it for the present purpose of slick modelling. In section 3, an attempt is made to derive relaxation rates from this spectrum, and the form of the net restoring source term when out of equilibrium is established. In section 4, the radar image modelling will be discussed. Section 5, finally, discusses and summarises the results. 

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