Instrumental broadening, correction

Gugliotta, L. M., Vega, J. R., and Meira, G. R., Instrumental broadening correction in size exclusion chromatography. Comparison of several deconvolution techniques, /. Liq. Chromatogr., 13,1671, 1990. 

In this work, using ultrastyragel columns, it was found that instrumental broadening corrections were unnecessary. 

Figure 2.19. High-resolution Guinier scans over several reflections of a-iron of a sample of fully activated catalyst 2 which was 4 weeks on stream prior to analysis. The numbers report the d spacings (d) and linewidths (b) as FWHM without instrumental broadening correction. The natural linewidth of the instrument measured with silicon is 0.08 2-theta at the position of Fe(l 10). The x-axis is the same for all profiles the intensities were normalized to the respective maxima.

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 ... 

This approach also allows an easy correction of the diffraction peaks from the instrumental broadening that can be obtained by fitting the peak profile of a standard... 

Baldwin, M.A. Derrick, P.J. Morgan, R.P. Correction of Metastable Peak Shapes to Allow for Instrumental Broadening and the Translational Energy Spread of the Parent Ion. Org. Mass Spectrom. 1976,11, 440-442. 

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... 

The correction for non-uniform instrumental broadening in SEC is solved through a non-recursive matrix stochastic technique. To this effect, Tung s equation ( ) must be reformulated in matrix form, and the measurements assumed contaminated with zero-mean noise. 

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

The data that we acquire are usually in the form of U/U0. Only if there is no significant instrumental broadening present, or if it has already been corrected, may we remove the inherent broadening. In this case, we operate on the logarithm of the data or corrected data ... 

Four major computational steps are necessary to separate the individual peaks and the different profile-broadening components (i) correction and normalisation of the diffraction data, (ii) resolution of the total peak scattering from the so-called background scatter, and resolution of crystallographic, para-crystalline, and amorphous peaks from each other, (iii) correction of the resolved profiles for instrumental broadening, (iv) separation of the corrected profiles into size and distortion components. In this paper we will discuss these steps in turn, but most attention will be paid to the hitherto largely neglected step of profile resolution. 

The two most common methods used to correct resolved peak profiles for the broadening imposed by the finite width of the X-ray beam in the diffractometer, are due to Jones (15) and Stokes (16). Both are essentially unfolding or deconvolution methods, but the Jones method defines specific functions for both the uncorrected and the instrumental broadening profile. If the uncorrected profile is Gaussian, then... 

The Stokes method is essentially a Fourier transform method making use of the entire profile, and is a reasonably straightforward computation, although limits have to be applied to the profile in transform space to achieve correct results. The main peak from hexamethylene tetramine crystals compacted at 85°C (17) has been used as our standard for the instrumental broadening peak. 

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

Correction of 100 peak of PET 06 specimen for instrumental broadening by Stokes method and by Jones method... 

Two other technical issues must be discussed briefly. In deducing the viscoelastic parameters through the dispersion equation from the power spectrum of SLS, it must be corrected for the instrumental broadening. The other... 

In addition, diffraction line breadth contains information on lattice strain, lattice defects, and thermal vibrations of the crystal structure. The chief problem to determine crystallite size from line breadth is the determination of /3(20) from the diffraction profile, because broadening can also be caused by the instrument. To correct for the instrumental broadening on the pattern of the sample, it is convenient to run a standard peak from a sample in which the crystallite size is large enough to eliminate all crystallite size broadening. By use of a convolu-... 

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... 

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