Decoupled

If the problem in the absence of significant constraints can be decoupled in this way, there must be some mechanism which allows this, and that mechanism should be explored. 

Having established that there is apparently a mechanism whereby the problems of sequencing and heat integration can be decoupled for simple columns on the basis of energy costs, it is interesting to consider whether there is any conflict with capital cost. A column sequence that handles a large amount of heat must have a high capital cost for two reasons ... 

In free space (p = 0, J= 0, <[) = constant), the equations for the potentials decouple and take the following simple fonn ... 

Once again, these fluxes are not all independent and some care must be taken to rewrite everything so that syimnetry is preserved [12]. Wlien this is done, the Curie principle decouples the vectorial forces from the scalar fluxes and vice versa [9]. Nevertheless, the reaction temis lead to additional reciprocal relations because... 

Out of the five hydrodynamic modes, the polarized inelastic light scattering experiment can probe only the tliree modes represented by equation (A3.3.18), equation (A3.3.19) and equation (A3.3.20). The other two modes, which are in equation (A3.3.17), decouple from the density fluctuations diese are due to transverse... 

For model A, the interfaces decouple from the bulk dynamics and their motion is driven entirely by the local curvature, and the surface tension plays only a background, but still an important, role. From this model A... 

The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

It is evident from the figure that impurities can complicate the use of NMR integrals for quantitation. Further complications arise if the relevant spins are not at Boltzmaim equilibrium before the FID is acquired. This may occur either because the pulses are repeated too rapidly, or because some other energy input is present, such as decoupling. Both of these problems can be eliminated by careful timing of the energy inputs, if strictly accurate integrals are required. 

Their effects are illustrated in figure B1.11.4 which is a H-decoupled C NMR spectrum of the same sample of paracetamol, obtained without such precautions. The main peak integrals are displayed both as steps and... 

Figure Bl.11.4. Hydrogen-decoupled 100.6 MHz C NMR spectrum of paracetamol. Both graphical and numerical peak integrals are shown.

NOEs between nuclei are often exploited to demonstrate their spatial proximity, as described in the final section. It is possible to obtain decoupled NMR spectra without the complications of the NOE, by confining the decoupling irradiation to the period of the FID alone, and then waiting for 10 x before... 

Single-frequency decoupling is easy and rapidly carried out. However, it may be limited by the closeness of different multiplets. Also, it will not nonnally be possible to apply more than one frequency of decoupling irradiation at a time. Fortunately, these disadvantages do not apply to the equivalent multidimensional methods. 

It is also usually possible to remove all the couplings from a particular isotope, e.g. H, provided that one only wishes to observe the spectrum from another isotope, e.g. Either the decoupling frequency is noise-modulated to cover the relevant range of chemical shifts, or else the same decoupling is achieved more efficiently, and with less heating of the sample, by using a carefiilly designed, continuous sequence of... 

In the absence of decoupling, the resonances would each be split by at least four short- and long-range... 

Aue W P, Kharan J and Ernst R R 1976 Homonuclear broadband decoupling and two-dimensional J-resolved NMR spectroscopy J. Chem. Phys. 64 4226-7... 

The simplifying approximation of a linear response is now made, by which it is assumed that rotations about different axes may be decoupled. This is only strictly valid for small rotations, but is surprisingly good for larger rotations too. This means that Mo(r)constant. Accordingly, at the end of the pulse the... 

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