The Simple Deconvolution Procedure

If the results are to be expressed as heat capacities, then the average total heat flow is divided by the underlying heating rate fl. Thus, 

Having obtained the reversing heat capacity, then one can calculate the non-reversing heat capacity. Viz 

This is then subtracted irom the total heat flow to obtain the non-reversing heat flow. Viz 

Note that the simple deconvolution procedure makes no use of the phase lag signal. 

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FIGURE 4.2 Flowchart representing the simple deconvolution procedure for TA Instruments MTDSC signals. (From Jiang, Z., Imrie, C.T., and Hutchinson, J.M., Thermochim. 

The intensity of the mass spectral peaks in the mixture originates from two different polymers. Therefore, the simple summation procedure on which the composition estimates method is based (Eq. 2.45) may be affected by error, because it is not able to deconvolute the contributions of isobaric oligomers to the intensity of the single peaks. 

Figure 1.3. Results from simple deconvolution procedure for the data shown in Figure L2.

Deconvolution Analysis of DSC. Data analysis was carried out using the DECONV section of the DA-2 software package. This software, which is based on the deconvolution procedure of Freire and Biltonen (4), allows deconvolution of differential heat-capacity peaks either as the result of simple addition of multiple independent transitions or as the result of more complex mathematical processes representing the combination of transitions that interact in such a way that an obligatory reaction sequence is imposed (sequential transitions). 

Since the development of the Fourier-transform deconvolution procedure for OHD-RIKES data by McMorrow and Lotshaw (22), the intermolecular dynamics of a wide range of liquids have been studied with this technique (26,52,65-85). Figure 13 illustrates representative OKE reduced spectral densities we have recorded in symmetric-top liquids, including acetonitrile, benzene, benzene-d6, carbon disulfide, chloroform, hexafluorobenzene, mesitylene, and 1,3,5-trifluorobenzene. Although there are conspicuous differences among these spectra, they are all broad and relatively featureless. Indeed, with rare exceptions the reduced spectral densities of simple liquids are devoid of sharp features, which makes it difficult to find an unambiguous interpretation of these spectra. 

MTDSC was introduced by Reading et al. (1-4) and is an extension of conventional DSC. In essence, the technique involves the application of a perturbation to the heating program of a conventional DSC (a sinusoidal wave in most cases, but sawtooth and square waves are also used) combined with a mathematical procedure designed to separate different types of sample behavior. The separation (also called deconvolution) procedure can most easily be understood in terms of a simple equation (5,6), that is,... 

The basis of the separation or deconvolution procedure can be illustrated by a few simple equations. When used with a sinusoidal perturbation, the temperature program for an MTDSC experiment is given by ... 

For MTDSC, it is also essential to calibrate for the reversing heat capacity to allow quantification of the deconvoluted results. There are several approaches by which this may be achieved, with more accurate methods requiring greater sophistication and more time hence, a decision needs to be made with regard to how important accurate heat capacity data are to the objectives of the study. For most pharmaceutical applications, fairly simple calibration procedures such as those about to be outlined are usually sufficient. However, for more accurate work it is essential to use more detailed approaches such as that described in Reference 11. In this summary, we outline only the simple approaches, but readers should be aware of the availability of more complex methods that yield more reliable results. 

In conclusion, the deconvolution procedure seems to be a suitable method for the rapid and simple estimation of global phenolic compound concentration. Commercial built-in spectrophotometer software such as UVPro from Secomam or any multicomponent procedure can be used for this purpose. In this last case, samples have to be filtered in order to avoid interference due to the high TSS level in UV spectrophotometry measurement. Nevertheless, this method must be extended to other phenolic families such as aminophenols or polyphenols. 

The first scenario will produce the most accurate results in the first step of the dual-step procedure in determining the absorption rate. The second scenario will estimate the gastrointestinal release rate that more directly should fink to the in vitro release/dissolution rate than the absorption rate, but the evaluation is confounded by the first-pass PK and possible violation of the deconvolution assumptions. The advantage of the oral solution reference may be largely offset to a negative extent by a violation of the assumptions specific to GI deconvolution (e.g., multiple input site, nonlinear absorption, etc., discussed above). Use of an IR reference is problematic in making the quite strict assumption of a simple, first-order absorption rate,... 

Figure 1.6. Co-plot of reversing and non-reversing heat capacity arising from the simple and full deconvolution procedures apphed to the raw data from Figure 1.2.

In obtaining the binding energies of the CF2 and F carbon-ls levels a simple deconvolution is necessary. In any estimation of copolymer compositions, however, it is obviously desirable to avoid even such a minor complication. The procedure, therefore, is to measure the area of the CF3 peak, the total area of the ( F2 + F) peak and the area of the CH2 peak. The degree of incorporation of hexafluoro-propene (HFPT in the copolymers may then be calculated from the percentage of the total area due to Cis levels represented by each peak ... 

Intramolecular distances determined from steady state measurements are average distances. These are simple average quantities only when all molecules have exactly the same distance. A more quantitative analysis of excitation energy transfer in flexible molecules can be achieved by analyzing donor fluorescence decay kinetics and the deconvolution procedure described above. 

The above algorithm works well for pure compounds and simple mixtures, but it becomes increasingly difficult to assign all peaks properly when complex mixtures are to be addressed. Additional problems arise from the simultaneous presence of peaks due to protonation and alkali ion attachment etc. Therefore, numerous refined procedures have been developed to cope with these requirements. [102] Modem ESI instrumentation is normally equipped with elaborate software for charge deconvolution. 

The relative molecular mass determination of an unknown protein is generally performed automatically using various deconvolution algorithms, but the procedure is limited to relatively simple mixtures. 

The procedures described next were developed for the deconvolution of electronic absorption spectra (UV-visible spectra) but are equally applicable to the deconvolution of infrared, Raman or NMR spectra. UV-visible spectra differ from vibrational spectra in that the number of bands is much smaller and the bandwidths are much wider. Band shape may also be different. UV-visible spectra are also usually recorded under conditions of high resolution and high signal-to-noise ratio. Spectra from older instruments usually require manual digitization from a spectrum on chart paper, at e.g., 10 nm intervals. With the widespread use of computer-controlled instruments, it is a simple matter to obtain a file of spectral data at, e.g., 1 nm intervals. In fact, it may be necessary to reduce the size of the data set to speed up calculations. 

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