Band-broadening correction

Ideally, a material with a unique molecular mass should elute from an SEC system at a single elution time. However, in all forms of chromatography, there are various effects which result in all species eluting over an elution time range. Hence in SEC a material with a unique molecular mass actually elutes as a peak with a definite width. A polymer, with a distinct molecular mass range, elutes from the SEC system with a peak width which is a function of its molecular mass distribution and the chromatographic band-broadening effects. 

It is possible to carry out mathematical corrections to the chromatographic peak to allow for the band-broadening effects and consequently be left with a peak which reflects only the molecular mass distribution of the polymer. 

The effects contributing to band-broadening in chromatography generally have been comprehensively studied [12], but when the species being separated is polymeric, these effects are more complicated [13] and most band- 

In practice, SEC is usually carried out using columns pre-packed by the manufacturers, and it can be assumed that they have optimized the columns, with band-broadening being taken into account. If the SEC operator takes the usual steps to maximize chromatographic efficiency (for example reducing extra-column connections to a minimum) and takes note of the column manufacturer s advice on operating conditions, it should not be necessary to apply band-broadening corrections. 

Normally in converting an SEC chromatogram to a molecular mass distribution, it is assumed that the concentration detector response is constant for the whole of the chroinatogram. While this is generally true, there are some situations where this does not apply and the apparent MMD could be very misleading. 

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The manual calculation is of course time- and labor-consuming. At present, it is done practically exclusively with help of computers. There are several software available for computer-assisted SEC data processing. Most of them include application of universal calibration dependence and few also comprise simple band broadening correction option. 

In general, band-broadening corrections are still required if a molecular weight-sensitive detector is added to SEC, especially if the molecular weight... 

Band broadening correction in SEC is still not a totally resolved issue, even when the MMD of a linear homopolymer is determined with a mass detector and a molar mass calibration. Fortunately, modem SEC columns are highly efficient, and the correction for BB is mainly limited to the case of narrowly distributed polymers. Even in the presence of BB, if an instantaneous quality variable is accurately measured, its corresponding global average will also be accurate. 

Injection time-. Most modern instruments have a control function of the injection pressure that automatically corrects for hydrodynamic injection variability through the injected time. An injection time of at least 3 s is needed for this to function properly. Too short injection times decrease precision and too long injection times induce band broadening. Rather increase pressure if possible. 

Instrumental band broadening or axial dispersion can cause calibration errors when employing polydisperse standards. Correction of the polydisperse standard calibration data for instrumental band broadening will minimize the effect on molecular weight analyses of polymer samples. However, as previously demonstrated in this report, when low dispersion SEC columns are employed instrumental band broadening is minimized and the effect on use of linear calibration methodology is negligible. 

A.31h / md ) and Fig. 6-5 to write F as 0.66h / md ), and then used Eq, (4-16) to write h / md ) as F2/2.I6. This result can be compared with that resulting from Eq. (6-19), which is written in the form 0 = 3.6OF2 — 4.44F, for the homopolar semiconductors. Neither is very accurate, but both correctly reflect a bondingantibonding splitting from the covalent energy, reduced by the band-broadening... 

The van Deemter equation is a useful approximation however, the experimental H u plots often show some downward curvature on the right-hand branch, unpredicted by Eq. (1.10). Giddings explained this behaviour by coupling the flow and the diffusion effects which demonstrates that it is not strictly correct to consider the simple additivity of their contributions to band broadening and he suggested more sophisticated equations to account for this phenomenon [3. For practical purpose, a simple empirical equation, which accounts for the experimental behaviour and is only slightly different from the van Deemter expression was introduced by Kennedy and Knox [4. ... 

Fig. 2 Thermal FFF elution profiles before (original) and after (corrected) removing the effects of band broadening. With the poly disperse sample (NBS 706), which was analyzed at a flow rate of 0.4 mL/min, the effect of band broadening on the elution profile is minimal. The polydispersity values listed were determined using thermal FFF.

In order to obtain the characteristics of the column the values of and must be first corrected for the extra-column band broadening contributions that... 

The classical shift-invariant convolution permits a simple calculation of the combined effects of multiple sources of band broadening when the column efficiency is not very low. This approach gives correct results in linear chromatography but is incorrect in nonlinear chromatography [1]. The simplest model that takes axial dispersion and mass transfer kinetics into account is the equilibrium-dispersive model. This model permits, with a good approximation, the accurate prediction of the importance of the self-sharpening and dispersive phenomena due to thermodynamics and kinetics of phase equilibria. This, in turn, results in correct prediction of the band profiles and the achievement of often excellent... 

Efficiency, N The column efficiency characterizes the combined effects of the sources of band broadening due to axial dispersion and mass transfer resistance. It is derived from the width of the elution peak observed as the response to the injection of a small, narrow pulse of a dilute solution of a compoimd. It is difficult to correct for the contribution of the extracolumn sources of band broadening which have to be kept small. In preparative and nonlinear chromatography, there is a correlation between the colmnn efficiency and both the steepness of the shock layer and the duration of the band beyond the retention time However, the column efficiency is essentially a concept of linear chromatography, and it is difficult to extend to and use in nonlinear chromatography, except through the shock layer thickness concept. 

Raman spectroscopy, compared to IR spectroscopy, is considered to be easy spectroscopy. Often, it is possible to identify spectral features that are unique to each chemical component in the sample, and to use them for univariate analysis. When the number of spectra in a Raman map is small and the chemical composition of the sample is simple, then a univariate analysis is usually sufficient. The typical analysis strategy would be to pretreat the spectra (baseline correction, nor-malizahon, etc.), explore to identify any unique spectral features, and to create intensity maps of those features as Raman images. When differences between spectral species are reflected in peak shifts or band broadenings, the peak positions or bandwidths can also be mapped to create Raman images. 

According to (7.46,47) the partial i pressure may be decomposed into a band-position term proportional to 6V/6ln(S) or SC/6ln(S), and a band-broadening term proportional to < ln(TS2)/Sln(S) or 6ln(yS2)/6ln(S). At large volumes in chromium V yxc < exc and t 1 for s and p states. The <5V term therefore provides an attractive pressure which is the correction due to exchange and correlation to the repulsive bandwidth or kinetic energy term proportional to 112... 

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