Matrix sample problems

The trends begun with the general introduction of FTIR technology will undoubtedly continue. It is safe to say that the quality of the data being produced far exceeds our ability to analyze it. In fact, for many current applications, the principle limitations are not with the equipment, but rather with the quality of the samples. Thus, the shift from qualitative to quantitative work will proceed, reaching high levels of sophistication to address the optical and matrix interference problems discussed above. 

Because of the lack of standards, variations in analyses made by other methods, and errors caused by coal sampling problems, it was difficult to evaluate the need for x-ray matrix corrections and to select the best method for applying them. However, corrections were necessary because some elements in whole coal such as iron, silicon, and sulfur may vary considerably. For these elements, corrections were applied indiscriminately to all samples, because it was impossible to determine the point at which matrix variations required a correction greater than the accuracy limits of the method. We elected to use the minimum number of corrections compatible with reasonably accurate results. Therefore,... 

In addition, reference measurements carried out by competent laboratories on customer samples are increasingly required to eliminate or, at least, reduce the matrix mismatch problem which is almost ubiquitous in chemical measurement and cannot be solved with off-the-shelf reference materials due to the great variety of different matrices occurring in practice. This is particularly important in dif ficult areas like clinical chemistry and food analysis. 

The diligent analyst would develop a robust method with rigorous matrix effect tests on multiple lots, including hemolyzed and lipidemic samples. An initial test would be a spike-recovery evaluation on at least six individual lots. Samples should be spiked at or near the LLOQ, and at a high level near the ULOQ. If matrix interference were indicated by unacceptable relative error (RE) percentage in certain lots, the spiked sample of the unacceptable lots should be diluted with the standard calibrator matrix to estimate the minimum dilution requirement (MDR) at and above which the spike-recovery is acceptable. The spike-recovery test should then be repeated with the test samples diluted at the MDR. Note that this approach will increase the LLOQ for a less sensitive assay. If sensitivity is an issue, then other venues will be required to address the matrix effect problem. For example, the method can be modified to include sample clean-up, antibodies and/or assay conditions may be changed, or the study purpose may be tolerable to acknowledge that the method may not be selective for a few patients (whose data may require special interpretation). 

Once the procedure is decided the next step is calibration, which will require suitable standards and determination of the effect of the matrix and reagents on the measurements made. The precision and accuracy of the procedure should then be assessed by-the analysis of either synthetic or spiked samples. In the latter method, the recovery of a known amount of analyte added to an actual sample matrix is checked. Finally, the procedure selected should he compared with other procedures available. The following examples will serve to illustrate some aspects of sampling problems, method selection and procedures. 

Applying this algorithm to our sample problem is revealing. The permutation matrix is found to be... 

The extent of mixed-ci-ystal contamination is governed by the law of mass action and increases as the ratio of contaminant to analyte concentration increases. Mixed-crystal fomiation is a particularly troublesome type of coprecipitation because little can be done about it when certain combinations of ions are present in a sample matrix. This problem is encountered with both colloidal suspensions and crystalline precipitates. When mixed-crystal formation occurs, the interfering ion may have to be separated before the final precipitation step. Alternatively, a different precipitating reagent that does not give mixed crystals with the ions in question may be used. 

Microwave digestion has been proven to help speed up and improve the productivity and quality of the sample preparation in our laboratory. It has become the method of choice for many unknown and/or complicated matrix samples. Obtaining a representative sample can be a problem when smaller quantities (<0.2 g) are used for microwave digestion. Other applications, such as speciation, organic extraction, and sample preparation for wet chemistry are some areas to which we can apply this powerful tool in order to further improve our laboratory practice. 

TABLE 7 Regret Matrix for Sample Problem (Cell values are multiples of 1,000,000)... 

For an efficient dissolution of the ash of samples with silicate compounds in the matrix, such problems highlight the absolute necessity of utilizing an HF step followed by evaporation to dryness if the objective is the determination of total element content. However, this problem, typically associated with plant samples, is similar when applying a wet digestion procedure if an insoluble residue remains, an additional HF step, followed by evaporation to dryness, must also be performed. 

Electrochemical detection in LC provides a sensitive assay method for certain vitamins, such as AA, folates, and flavins. AA may be easily detected with femtomolar sensitivity. Sample preparation and matrix interference problems limit the routine applicability of electrochemistry in the analysis of water-soluble vitamins currently to AA. 

However, solid samples are often highly inhomogeneous (e.g., contaminated soils), leading to a sampling problem (Section 8.5) before any kind of analytical procedure is even started. This problem refers to selection of aliquots of matrix plus analyte (e.g. soil samples plus contaminant) that are of suitable size for the analytical... 

We conclude that the QCL description represents a promising approach to the treatment of multidimensional curve-crossing problems. The density-matrix formulation yields a consistent treatment of electronic populations and coherences, and the momentum changes associated with an electronic transition can be directly derived from the formalism without the need of ad hoc assumptions. Employing a Monte-Carlo sampling scheme of local classical trajectories, however, we have to face two major complications, that is, the representation of nonlocal phase-space operators and the sampling problem caused by rapidly varying phases. At the present time, the... 

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