Chromatography calibration problems

The calibration problem in chromatography and spectroscopy has been resolved over the years with varying success by a wide variety of methods. Calibration graphs have been drawn by hand, by instruments, and by commonly used statistical methods. Each method can be quite accurate when properly used. However, only a few papers, for example ( 1,2,15,16,26 ), show the sophisticated use of a chemometric method that contains high precision regression with total assessment of error. 

Quality control laboratories may be equipped with instruments which indicate MW or MWD directly. The most common technique used for this purpose is gel permeation chromatography (GPC). Infrequent analysis is the rule. Such off-line measurements are most often used to update inferential models, or to effect open loop control of the polymerization by manual process adjustments based on GPC results. On-line GPC is available its application is not yet common in industrial practice, but applications of on-line measurement of MWD by GPC have been reported [26]. The difficulties encountered with on-line GPC are the maintenance, sampling and calibration problems associated with any process chromatography application. In addition, a compromise must be made between resolution of the MWD and time of analysis. As a rule of thumb, it is possible to determine an accurate average molecular weight in under 10 minutes. Determination of the MWD can take considerably longer. 

The analytical data were obtained by means of high-performance liquid chromatography (HPLC). The original data did not obey the stoichiometry exacdy due to calibration problems typically connected to this analytical technique. This implies that systematic deviations remain in the estimation of kinetic parameters and the fit of the model parameters is not very good. At the next stage, the original data were exposed to the normahzation algorithm, and the parameter estimation was repeated with the data consistent with stoichiometry. The systematic deviations disappeared and a much better fit was obtained (Fig. 11.20). 

In principle, any type of sample can be analysed by SEC provided that it can be solubilised and that there are no enthalpic interactions between sample and packing material. By definition then, this technique cannot be carried out on vulcanisates and even unvulcanised fully compounded rubber samples can present problems due to filler-rubber interactions. The primary use of SEC is to determine the whole MWD of polymers and the various averages (number, viscosity, weight, z-average) based on a calibration curve and to allow qualitative comparisons of different samples. Many commercial polymers have a broad MWD leading to strong peak overlap in the chromatography of complex multicomponent systems. 

One of the major problems lies in the extent of interference from other constituents of a sample. This can often be obviated by a prior separation using chromatography or solvent extraction (p. 55) or by the use of masking agents (p. 40), pH control or changes in oxidation state. Standards should always be matched to the gross composition of the sample as closely as possible, and calibration curves frequently checked. The precision of absorption measurements has already been discussed (p. 361). 

Quality assurance measures such as pre-analytical checks on instrumental stability, wavelength calibration, balance calibration, tests on resolution of chromatography columns, and problem diagnostics are not included. For present purposes they are regarded as part of the analytical protocol, and IQC tests their effectiveness together with the other aspects of the methodology. 

Detection, and the GC calibration process for the pesticide Fenvalerate constitutes a major focus of this paper. Though relatively simple compared to possible higher dimensional cases, it is representative of a large and basic class of problems (calibration in one-dimensional chromatography and spectroscopy), and it exhibits already some of the difficulties with assumption validity. 

Errors in trace analyses are usually hidden to all except those intimately involved in the sample collection and, later, in the bench analysis. In chromatography, especially, it is too easy to hide behind uncertain work because published research does not concern itself with exactly how the chromatographer makes his quantitative decisions. Today, with the advent of the microprocessor and with the use of black box instruments, the chromatographer knows even less about his calibration graph or line, or the error associated with it. In these instruments, a single point and the origin may determine the calibration graph. Similar problems exist in other modern instrumental analysis techniques. 

Tn the previous papers of this series (1, 2, 3, 4) calibration and repro- ducibility of gel permeation chromatography (GPC) have been extensively examined. This paper describes the application of GPC to two selected samples of linear polyethylenes, one having a narrow molecular weight distribution (NMWD) and another a broad molecular weight distribution (BMWD). These samples were distributed by the Macro-molecular Division of IUPAC (5) for the molecular characterization of commercial polymers. The average molecular weights by GPC are compared with the data obtained from infrared spectroscopy, osmotic pressure, melt viscosity, and intrinsic viscosity. Problems associated with data interpretation are discussed. 

While polydisperse model systems can nicely be resolved, the reconstruction of a broad and skewed molar mass distribution is only possible within certain limits. At this point, experimental techniques in which only a nonexponential time signal or some other integral quantity is measured and the underlying distribution is obtained from e.g. an inverse Laplace transform are inferior to fractionating techniques, like size exclusion chromatography or the field-flow fractionation techniques. The latter suffer, however, from other problems, like calibration or column-solute interaction. 

Headspace-GC-MS analysis is useful for the determination of volatile compounds in samples that are difficult to analyze by conventional chromatographic means, e.g., when the matrix is too complex or contains substances that seriously interfere with the analysis or even damage the column. Peak area for equilibrium headspace gas chromatography depends on, e.g., sample volume and the partition coefficient of the compound of interest between the gas phase and matrix. The need to include the partition coefficient and thus the sample matrix into the calibration procedure causes serious problems with certain sample types, for which no calibration sample can be prepared. These problems can, however, be handled with multiple headspace extraction (MHE) [118]. Headspace-GC-MS has been used for studying the volatile organic compounds in polymers [119]. The degradation products of starch/polyethylene blends [120] and PHB [121] have also been identified. 

Most chemometricians prefer inverse methods, but most traditional analytical chemistry texts introduce the classical approach to calibration. It is important to recognise that there are substantial differences in terminology in the literature, the most common problem being the distinction between V and y variables. In many areas of analytical chemistry, concentration is denoted by V, the response (such as a spectroscopic peak height) by y However, most workers in the area of multivariate calibration have first been introduced to regression methods via spectroscopy or chromatography whereby the experimental data matrix is denoted as 6X , and the concentrations or predicted variables by y In this paper we indicate the experimentally observed responses by V such as spectroscopic absorbances of chromatographic peak areas, but do not use 6y in order to avoid confusion. 

There are a whole series of problems in chemistry for which multivariate calibration is appropriate, but each is very different in nature. Many of the most successful applications have been in the spectroscopy or chromatography of mixtures and we will illustrate this chapter with this example, although several diverse applications are presented in the problems at the end. 

This book relies heavily on numerical examples many in the body of the text come from my favourite research interests, which are primarily in analytical chromatography and spectroscopy to have expanded the text more would have produced a huge book of twice the size, so I ask the indulgence of readers whose area of application may differ. Certain chapters, such as that on calibration, could be approached from widely different viewpoints, but the methodological principles are the most important and if you understand how the ideas can be applied in one area you will be able to translate to your own favourite application. In the problems at the end of each chapter I cover a wider range of applications to illustrate the broad basis of these methods. The emphasis of this book is on understanding ideas, which can then be applied to a wide variety of problems in chemistry, chemical engineering and allied disciplines. 

Size exclusion chromatography is the premier polymer characterization method for determining molar mass distributions. In SEC, the separation mechanism is based on molecular hydrodynamic volume. For homopolymers, condensation polymers and strictly alternating copolymers, there is a correspondence between elution volume and molar mass. Thus, chemically similar polymer standards of known molar mass can be used for calibration. However, for SEC of random and block copolymers and branched polymers, no simple correspondence exists between elution volume and molar mass because of the possible compositional heterogeneity of these materials. As a result, molar mass calibration with polymer standards can introduce a considerable amount of error. To address this problem, selective detection techniques have to be combined with SEC separation. 

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