Cumulative spectra

A different procedure to process Py-GC/MS data is to generate a sum of all spectra of all the peaks in a chromatogram [45c]. Particular peak information is lost in this technique, but characteristic cumulative spectra can be generated for different polymers. Examples of cumulative spectra for cellulose, CMC, and hydroxypropylmethyl cellulose (10% substitution with hydroxypropyl and 30% substitution with methyl) are shown in Figures 5.3.13 to 5.3.15, respectively. 

These cumulative spectra provide fingerprint information, generate some structural hints such as the typical ions for furfural in the cumulative spectrum of cellulose, and seem to be quite independent of the chromatographic conditions utilized for the separation [45c]. However, they are similar to Py-MS spectra (see section 5.4) where the chromatography step is completely eliminated and the analysis time is much shorter. 

These spectra are in fact cumulative spectra from Py-GC/MS, but they are a close equivalent to Py-MS spectra. As seen in Figures 5.4.10 (A), (B), and (C), except for the intensities of the ions, the fragments seen in the pyrolysate are not too different. In fact, the El spectrum and Ar I PI spectrum of amylose are quite similar, and only the Kr 1 PI spectrum shows differences. 

These cumulative spectra provide information for polymer identification and can generate some structural hints. The search can be done on the special library or on regular mass spectra libraries (e.g. NIST 2002 or Wiley 7). For the cumulative spectrum of polyethylene pyrolysate, the regular mass spectra library indicates a long chain alkene and for poly(ethylene glycol) indicates bis(2-ethoxyethyl) ether, pointing to the dominant structure in the pyrolysate. However, the use of cumulative spectra is very limited in practice. 

The variable offset cumulative spectra (VOCS) method has been a major step forward for the acquisition of broad wideline and ultra-wideline SSNMR powder patterns, representing a time-efficient way to overcome the excitation limitations of rectangular rf pulses [51,53,54]. VOCS involves acquiring the broad overall SSNMR spectrum by collecting a series of individual subspectra at evenly spaced transmitter frequencies. The spacing between subspectra is typically set to be equal to or less than the pulse excitation bandwidth in order to ensure proper spectral excitation in each experiment. The resulting series of subspectra are then added together in the frequency domain to yield the overall broad powder pattern. In this marmer, even extremely broad powder patterns can be collected without any... 

Figure 4.1.5. Cumulative spectrum of poly(ethylene glycol) pyrolysate.

The Raman spectrum of carbon onions is rather simple, too. Essentially, there are two bands situated in the regions about 1350 and 1580cm . In principle, a Raman signal should be expected for every single shell. These signals are, however, presumed to lie in close proximity and thus a cumulative spectrum with broad signals is obtained. 

GINAA Cyclic instrumental neutron activation analysis is used to determine very short lived isotopes. The sample is irradiated for a short time, rapidly transferred to a detector for counting the entire process repeated for a number of cycles with the gamma-ray spectrum recorded from each cycle accumulated to yield a cumulative spectrum. 

In order to overcome the excitation bandwidth limitations associated with typical rf pulses used in NMR experiments, in addition to the low natural abundance and poor sensitivity associated with Zr experiments, the variable offset cumulative spectrum (VOCS) method incorporated with the QCPMG pulse sequence has been applied to collect Zr SSNMR spectra [45,46,63,64]. It should be noted that VOCS may also be used in... 

With the availability of computerized data acquisition and storage it is possible to build database libraries of standard reference spectra. When a spectrum of an unknown compound is obtained, its identity can often be determined by searching through a library of reference spectra. This process is known as spectral searching. Comparisons are made by an algorithm that calculates the cumulative difference between the absorbances of the sample and reference spectra. For example, one simple algorithm uses the following equation... 

Each cage contained six infrared photocell beams arranged around the base of a circular tract. Each interruption of a beam registered a count on a total-event counter and on a cumulative recorder. Cumulative IV doses at 30-minute intervals were administered over dose ranges that included the complete spectrum of effects on SLA. 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Unlike the density cumulant expansion, which can in principle be exact for certain states (such as Slater determinants), the operator cumulant expansion is never exact, in the sense that we cannot reproduce the full spectrum of a three-particle operator faithfully by an operator of reduced particle rank. However, if the density cumulant expansion is good for the state of interest, we expect the operator cumulant expansion to also be good for that state and also for states nearby. 

Electronic spectrum. The N3 group is a chromophore, and may be classified as a chromophore with two cumulated double bonds (Braude [16])... 

These studies demonstrated that DNA-binding can be a reliable probe of metabolic activation. In contrast to studies of metabolites per se, which usually involve large numbers of metabolite intermediates, DNA-binding monitors only chemically reactive metabolites. Also, if there is no selective repair of specific adducts, DNA-binding monitors the cumulative production of metabolites over time, while direct measurement of metabolites can show the metabolite spectrum only at the time observed. This can be particularly critical for studies of activation of complex chemicals such as polycyclic aromatic hydrocarbons whose primary metabolites are subject to secondary and tertiary metabolism (8). 

This being the case, the coherence among energy levels, hence the time dependence of the initial state, has no influence whatsoever on the product yield. This implies, for example, that in the weak-field regime, the product yield obtainable with a subfemtosecond laser pulse with frequency spectrum 1(a)) is exactly equal to the sum of a set of, for example, microsecond pulses with an appropriate set of frequen-cies and intensities that have the same cumulative I(co). Shorter pulses alter the. product probabilities only to the extent that they excite a larger number of states, as the frequency spectrum broadens with diminishing pulse duration. Clearly, am observation of increased yield of a particular product upon use of a shorter pulse is then due solely to the fact that the shorter pulse encountered some states with at preference for a particular product. ... 

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