Decomposition analysis

Zergliederung, /. decomposition, analysis dis section dismimberment. Zergllederungs-kunde, -kunst, /. anatomy, zerhackezt, v.t. cut to pieces, chop up, mince. Zerhacker, m. chopper (Elec.) vibrator. 

Park, S.-H. Dissniann, B. and Nam, K.-Y. (1993). A Cross-Country Decomposition Analysis of Manufacturing Energy Consumption. Energy 18 843-858. 

Secondly, although stable solutions covering the entire temporal range of interest are attainable, the spectra may not be well resolved that is, for a given dataset and noise, a limit exists on the smallest resolvable structure (or separation of structures) in the Laplace inversion spectrum [54]. Estimates can be made on this resolution parameter based on a singular-value decomposition analysis of K and the signal-to-noise ratio of the data [56], It is important to keep in mind the concept of the spectral resolution in order to interpret the LI results, such as DDIF, properly. 

Glendening, E. D., Streitwieser, A., 1994, Natural Energy Decomposition Analysis An Energy Partitioning Procedure for Molecular Interactions With Apphcation to Weak Hydrogen Bonding, Strong Ionic, and Moderate Donor-Acceptor Interactions , J. Chem. Phys., 100, 2900. 

Reinhardt P, Piquemal J-P, Savin A (2008) Fragment-localized Kohn-Sham orbitals via a Singles-CI procedure and application to local properties and intermolecular energy decomposition analysis. J Chem Theory Comput 4 2020... 

For best yields, the entire series of reactions should be completed within 1 or 2 days. Distillation at higher pressures tends to cause some decomposition. Analysis of the product showed % Cl, 60.40, 60.64 (calculated % Cl, 60.63). 

In accord with the Dewar-Chatt-Duncanson model, we find that the dominant interaction is donation from the C C n bond into the rhodium LUMO. This interaction is enhanced when the double bond lies in the rhodium-diphosphine plane and with electron donating substituents which raise the energy of 7ito more closey match the LUMO Charge Decomposition Analysis (CDA) [81] shows that the amount of donation is... 

In physical terms the site inhomogeneous component may be conceived of either as slightly different protein binding sites for chromophores or as a distribution of protein conformational substates [127] at any one site. In operational terms the spectral forms are represented by the sub-bands of a gaussian or lorentzian decomposition analysis of absorption or fluorescence spectra. 

The result of an energy decomposition analysis performed for this complex was also unusual. In contrast to numerous dihydrogen-bonded systems with significant predominance of the electrostatic interaction, the dihydrogen-bonded dimer (LiH H20)2 has shown the charge transfer contribution to exceed the electrostatic energy —125.30 versus —81.40 kcal/mol, respectively. 

Romo, T.D., Clarage, J.B., Sorensen, D.C., Phillips, G.N. Automatic identification of discrete substates in proteins-singular-value decomposition analysis of time-averaged crystallographic refinements. Proteins 1995, 22, 311-21. 

Attempts to purify the material further met with little success because of its extreme sensitivity toward oxygen. Recrystallization from ether, for instance, in a modified Schlenk tube (25), with exclusion of air, invariably led to an off-colored product. An attempt to sublime the product in a high vacuum resulted in complete decomposition. Analysis even on the crude product, however, confirmed its identity as a disubstituted derivative of nickel carbonyl. 

Fig. 6.9. A Spontaneous Raman spectrum of d62-DPPC lipids and its decomposition into Lorentzian line profiles. B Normalized multiplex CARS spectra (dots) of a planar-supported bilayer and monolayer formed by d62-DPPC on a glass-water interface for parallel-polarized input beams, together with the fit using the center frequency and line width parameters extracted from the decomposition analysis in (A) (solid line). The spectrum exposure time was 0.64 s. Error bars indicate the shot-noise standard deviation (Copyright American Chemical Society [70])...

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. 

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. 

Similar line shape analyses for the equilibrium spectra at different temperatures were performed. At room temperature, where the amorphous phase is in a glassy state, the determination of the elementary line shape of the amorphous component was a little difficult. However, excellent line-decomposition analysis was obtained by introducing a broader Lorentzian centered at the same chemical shift as at higher temperatures. The result at room temperature is shown in Fig. 26-(b). Here the nature of the component line shapes A and B of the crystalline and crystalline-amorphous interphases is similar to that in the spectrum at 87 °C. However, the component line shape for the amorphous component is quite different from that at 87 °C that is distributed over a very wide chemical shift range centered at the same chemical shift to that at higher temperatures. This reflects the glassy state of the amorphous phase. In the glassy state, the molecular conformation in the amorphous phase will be distributed over all permitted conformations stationary in time and randomly in space. The wide component line shape of the amorphous component obtained here at room temperature well represents this molecular nature of the amorphous phase. 

Phase structure. It was confirmed in the previous section that the bulk iPP crystal consists of three phases the crystalline, noncrystalline amorphous phase and crystalline-amorphous interphase. Hence, it is also assumed that the bulk sPP crystal forms a three-phase structure in a similar manner. The question here is whether the sPP crystal involves such a phase structure in forming a gel or not In order to study this problem, we have analyzed 13C NMR spectra of the sPP gel. The noncrystalline contributions to each resonance of CH2, CH and CH3 carbons in the DD/MAS 13C NMR spectrum of the gel can be seen, as indicated by the arrows in Fig. 27, where their assignment as noncrystalline resonances was confirmed by the spin-lattice and spin-spin relaxation times as described above with relation to the results in Table 13. We carried out the line-decomposition analysis of the resonance lines of the methine and methyl carbons, since these resonances are most pertinent for the present purpose because of the simplicity of the spectral shape. 

Phase Structure as Revealed from the Mobility of the Solvent. The phase structure of the sPP crystal in the gel form, which was elucidated by the line-decomposition analysis of the DD/MAS 13C NMR spectrum, will reflect on the mobility of the solvent in the gel. The mobility of the solvent can be examined by the longitudinal relaxation of resonance lines assigned to the carbons of the solvent. Figure 31 shows the longitudinal relaxation for the line at 130 ppm of the o-dichlorobenzene. The open circles indicate the data of the pure solvent and the closed ones those of the solvent in the gel. As can be seen, the relaxation of the pure solvent evolves exponentially with a Tic of 3.0 s, whereas that of the solvent in the gel evolves nonexponentially. This indicates that there are some solvent molecules in the gel that differ in their mobility. We assume here that the longitudinal relaxation of each component of the solvent evolves exponentially. Then the longitudinal relaxation of the total solvent follows the relationship ... 

On the other hand, in the solid-state high resolution 13C NMR, elementary line shape of each phase could be plausibly determined using magnetic relaxation phenomenon generally for crystalline polymers. When the amorphous phase is in a glassy state, such as isotactic or syndiotactic polypropylene at room temperature, the determination of the elementary line shapes of the amorphous and crystalline-amorphous interphases was not so easy because of the very broad line width of both the elementary line shapes. However, the line-decomposition analysis could plausibly be carried out referring to that at higher temperatures where the amorphous phase is in the rubbery state. Thus, the component analysis of the spectrum could be performed and the information about each phase structure such as the mass fraction, molecular conformation and mobility could be obtained for various polymers, whose character differs widely. 

This is acceptable provided that the assumption is stated up front. The melt curves in the lower part of Fig. 17.3 were fit this way. Alternatively, the full model can be used, with additional steps taken to ensure the validity of the results. An example is shown in the upper part of Fig. 17.3. Here, the experiments were repeated multiple times (minimizing the measurement error), the data were fit simultaneously (using a global fitting algorithm), and the results were corroborated using a separate singular value decomposition analysis. 

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