Correction for instrumental broadening

As previously stated, GPC is the method of choice for studying polymer degradation kinetics. The GPC trace, as given by the detector output, does not provide the true MWD due to various diffusion broadening processes inside the different parts of the equipment. The first step is to correct for instrument broadening if a precise evaluation of MWD is desired. Even with the best columns available, this correction may change the MWD significantly as can be visualized... 

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

In the first section, the mechanisms involved in size exclusion chromatography are discussed this is an area where additional understanding and clarification still are needed. Data treatment with respect to statistical reliability of the data along with corrections for instrumental broadening is still a valid concern. Instrumental advances in the automation of multiple detectors and the developm.ent of a pressure-programmed, controlled-flow supercritical fluid chromatograph are presented. 

Maximum extinction coefficients will not do, even for non-rigorous discussions, since band widths differ so widely. Quantitative discussions should include corrections for instrumental broadening the procedures available are described in (59). 

Tung (55) has shown that the normalized observed SEC chromatogram, F(v), at retention volume v is related to the normalized SEC chromatogram corrected for instrument broadening, W(y), by means of the shape function G(v,y) through the relation... 

Correction for Instrumental Broadening in Size Exclusion Chromatography Using a Stochastic Matrix Approach... 

Most methods of correction for instrumental broadening in SEC (or hydrodynamic chromatography) are based on the deterministic integral equation due to Tung ( ) ... 

Figure 14. Deconvolution correction for instrumental broadening—simulation. Profile b unfolded from Profile a to give Profile c.

Corrections for instrumental broadening (also called axial dispersion) are also sometimes applied [15]. This phenomenon arises because of eddy diffusion and molecular diffusion at the leading and trailing edges of the pulse of polymer solution [16]. Hie result is a symmetrical, Gaussian spreading of the GPC... 

L. M. Gugliotta, D. Alba, and G. R. Meira, Correction for instrumental broadening in SEC through a stochastic matrix approach based on Wiener filtering theory, ACSSymp. Ser. 352 287 (1987). 

R. O. Bielsa and G. R. Meira, Linear copolymer analysis with dual-detection size exclusion chromatography Correction for instrumental broadening, /. Appl. Polym. Sci. 46 835 (1992). 

In 1949, however, Warren pointed out that there was important information about the state of a cold-worked metal in the shape of its diffraction lines, and that to base conclusions only on line width was to use only part of the experimental evidence. If the observed line profiles, corrected for instrumental broadening, are expressed as Fourier series, then an analysis of the Fourier coefficients discloses both particle size and strain, without the necessity for any prior assumption as to the existence of either [9,3, G.30, G.39]. Warren and Averbach [9.4] made the first measurements of this kind, on brass filings, and many similar studies followed [9.5]. Somewhat later, Paterson [9.6] showed that the Fourier coefficients of the line profile could also disclose the presence of stacking faults caused by cold work. (In FCC metals and alloys, for example, slip on 111 planes can here and there alter the normal stacking sequence ABCABC... of these planes to the faulted... 

The correction for instrumental broadening is known as deconvolution. Deconvolution procedures that can be used with dispersive spectrometers have been described (see for instance [51]. In this book, unless otherwise specified, the FWHMs indicated are considered to be corrected for instrumental broadening. 

Thermogravimetric analyses (TGA) of catalyst precursors were carried out with a Shimazu DT-30 thermal analyzer by heating in a stream of hydrogen to 800°C at a rate of 10°C min. The mean crystallite size of Co (Dc) in the reduced catalyst was calculated from the half-maximum breadth of the (111) peak of f.c.c. Co metal in the powder X-ray diffraction (XRD) pattern after correction for instrumental broadening... 

X-ray diffraction patterns were measured using a powder diffractometer (Philips PW 1700) and CuKo-radiation. Mean crystallite sizes were estimated from the peak width at half maximum of the (HI) reflection of Cu or CuO, respectively, using the Scherrer equation. The measured peak width was corrected for instrumental broadening using the function proposed by Warren (ref. 17). 

Powder X-ray diffraction (XRD) patterns of the catalysts separated from the reaction mixture were measured using a Shimadzu VD-1 diffractometer with CuKa radiation. The mean crystallite size (D. ) of iron metal in a catalyst was calculated from the half-maximum breadth of the (110) peak of a-Fe after correction for instrumental broadening (ref. 10). The crystallite size distributions (CSD) of iron in some catalysts were obtained according to the Fourier transform method (Stokes method) for X-ray line profile analysis (ref. 11). 

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