Instrumental broadening, correction methods

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... 

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

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. 

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

When MWD is used as an instrument for analyzing a kinetic scheme, very stringent requirements must be imposed upon the accuracy of its measurement. In117 a method is proposed to determine the instrumental broadening function in GPC based on the obtained relationship between the corrected gel chromatograms of the initial polymer sample and its i-th fraction collected within the range of elution volumes ( i j,... 

Prougenes, P. Berek, D. Meira, G. Size exclusion chromatography of polymers with molar mass detection. Computer simulation study on instrumental broadening biases and proposed correction method. Polymer 1998, 40, 117-124. 

The X-ray diffraction patterns have been recorded with a Philips diffractometer equipped with a proportional counter by using a Nl-flltered CuKa radiation. The samples have been examined without any previous pretreatment. The crystallinity degree has been determined by a procedure developed in our laboratory (ref. 8). The method is based on a comparison of the integrated intensities of two different spectral ranges affected respectively by the crystalline and amorphous fractions of the solid. In this manner the use of standards with a known crystallinity can be avoided. The crystallite size has been determined from the half height width using the Scherrer equation (ref. 8) after the corrections for the Kal,a2 doublet and the instrumental broadening. 

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). 

The peak position and universal calibration methods rely on peak position calibration with known polymers of narrow molecular weight distribution. Several other calibration procedures requiring only a single broad moleculau weight standard have been proposed [77,439]. These procedures are quite c< plex and have a major drawback in that, unlike the peak position methods, instrumental peak broadening must be accounted for correctly if accurate results are to be obtained. 

Firstly, the main source of instrumental distortion of the signal is quite different in the two domains. In the CW method, the signal is broadened due to the modulation of the applied RF, and corrections must be made for the effects of this broadening on the different components [30]. In the pulse method, the main distortion of the signal is due to the dead-time. Efforts may be made to minimise the dead-time by optimisation of instrumental characteristics, or in the case of rigid solids, some of the problem may be overcome by the application of suitable echo sequences [18, 37], but it cannot be totally eliminated. 

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