Data Interpretation and Calibration

Let us now consider how the elution volume axis of a chromatogram, such as shown in Fig. 4.19, can be translated into a molecular weight scale. This necessitates calibration of the particular GPC column using monodisperse polymer samples. The main problem encormtered in this task is 

A theoretical validity of the aforesaid experimental observation is obtained from a consideration of the hydrodynamic volume of the polymer, as shown below. As long ago as 1906, it was shown by Einstein (1906) that the viscosity of a dilute suspension relative to that of the suspending 

If all polymer molecules exist in solution as discrete entities, without overlap and each solvated molecule of a monodisperse polymer has an equivalent volume (or hydrodynamic volume) V and molecular weight M, then the volume fraction 0 of solvent-swollen polymer coils at a concentration c (mass/volume) is 

Implicit in this equation is the assumption that the contributions of the individual macromolecules to the viscosity increase are independent and additive, which is tme when the polymer solution is 

Multiplying both sides by M and taking logarithm gives 

When a narrow MWD polystyrene sample, as described above, is injected hito the GPC column, the resulting chromatogram, though narrow, is not a simple 

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Requirement for sophisticated and costly instrumentation can sometimes be replaced by quite inexpensive methods, the performance of which is enhanced with respect to data interpretation and calibration modeling by chemometrics. 

Controls for maintaining set-points Functions for alarms and alarm logs Functions for trending over short and long term Preventative maintenance including calibration Access controls for secnrity purposes Data interpretation and management... 

The results of environmental monitoring exercises will be influenced by a variety of variables including the objectives of the study, the sampling regime, the technical methods adopted, the calibre of staff involved, etc. Detailed advice about sampling protocols (e.g. where and when to sample, the volume and number of samples to collect, the use of replicates, controls, statistical interpretation of data, etc.) and of individual analytical techniques are beyond the scope of this book. Some basic considerations include the following, with examples of application for employee exposure and incident investigation. 

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

In the following, the stages of the analytical process will be dealt with in some detail, viz. sampling principles, sample preparation, principles of analytical measurement, and analytical evaluation. Because of their significance, the stages signal generation, calibration, statistical evaluation, and data interpretation will be treated in separate chapters. 

Another form of artificial intelligence is realized in artificial neural networks (ANN). The principle of ANNs has been presented in Sect. 6.5. Apart from calibration, data analysis and interpretation is one of the most important fields of application of ANNs in analytical chemistry (Tusar et al. [1991] Zupan and Gasteiger [1993]) where two branches claim particular interest ... 

Raman spectroscopy s sensitivity to the local molecular enviromnent means that it can be correlated to other material properties besides concentration, such as polymorph form, particle size, or polymer crystallinity. This is a powerful advantage, but it can complicate the development and interpretation of calibration models. For example, if a model is built to predict composition, it can appear to fail if the sample particle size distribution does not match what was used in the calibration set. Some models that appear to fail in the field may actually reflect a change in some aspect of the sample that was not sufficiently varied or represented in the calibration set. It is important to identify any differences between laboratory and plant conditions and perform a series of experiments to test the impact of those factors on the spectra and thus the field robustness of any models. This applies not only to physical parameters like flow rate, turbulence, particulates, temperature, crystal size and shape, and pressure, but also to the presence and concentration of minor constituents and expected contaminants. The significance of some of these parameters may be related to the volume of material probed, so factors that are significant in a microspectroscopy mode may not be when using a WAl probe or transmission mode. Regardless, the large calibration data sets required to address these variables can be burdensome. 

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. 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

Detailed review of reported data reduces laboratory risk of producing invalid data. Important features of internal data review are the spot checks of calculations the verification of the acceptability of calibrations and laboratory QC checks and the second opinion in data interpretation. Laboratories document internal review in appropriate checklist forms that are kept on file with the rest of the project documentation and sample data. The internal data review process is generally described in Laboratory QA Manual and detailed in appropriate SOPs. 

The interpretation and implementation of published methods invariably differ at different laboratories due to diversity of utilized instruments, their incidental elements and supplies, and the differences in method interpretation. Each analytical method must be validated at the laboratory before it is used for sample analysis in order to demonstrate the laboratory s ability to consistently produce data of known accuracy and precision. Method validation includes the construction of a calibration curve that meets the acceptance criteria the determination of the method s accuracy and precision and the MDL study. A method SOPs must be prepared and approved for use. Method validation documentation is kept on file and should be always available to the client upon request. 

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