Evaluation of different approaches to applying the standard additions calibration method.

The extrapolation approach, traditionally used with standard additions (SA), is compared with the alternative strategies of interpolation, reversed-axis, and normalization. The interpolation approach is based on employing twice the analytical signal recorded for the sample (ysam) to determine an unknown analyte concentration. In the reversed-axis strategy, x- and y-axes are swapped when building the SA calibration plot to facilitate uncertainty estimation. A new strategy, based on signal normalization using ysam, is also described and compared to the other approaches. Results from 3 instrumental methods, 396 sample replicates, 16 analytes, and 2 certified reference materials are included in this study. For most applications, all four SA approaches provide statistically similar trueness and precision. However, extrapolation and reversed-axis provide more consistent values (within narrower ranges) than the other strategies when employing inductively coupled plasma optical emission spectrometry (ICP OES). On the other hand, normalization provides better trueness for the less robust method of microwave-induced plasma OES (MIP OES), as it is capable of minimizing systematic errors associated with different points of the calibration curve. Normalization is particularly useful for quickly processing data, without the need for inspecting each individual calibration plot to identify outlying points. Reversed-axis and normalization are the most adequate approaches for SA applications involving MIP OES and ICP-based methods. In addition to providing similar accuracies to the traditional extrapolation approach, these strategies present the advantage of a simple uncertainty estimation, which can be easily calculated using commonly available software such as Microsoft Excel and R.

Machine learning tools to estimate the severity of matrix effects and predict analyte recovery in inductively coupled plasma optical emission spectrometry.

Supervised and unsupervised machine learning methods are used to evaluate matrix effects caused by carbon and easily ionizable elements (EIEs) on analytical signals of inductively coupled plasma optical emission spectrometry (ICP OES). A simple experimental approach was used to produce a series of synthetic solutions with varying levels of matrix complexity. Analytical lines (n = 29), with total line energies (Esum) in the 5.0-15.5 eV range, and non-analyte signals (n = 24) were simultaneously monitored throughout the study. Labeled (supervised learning) and unlabeled (unsupervised learning) data on normalized non-analyte signals (from plasma species) were used to train machine learning models to characterize matrix effect severity and predict analyte recoveries. Dimension reduction techniques, including principal component analysis, uniform manifold approximation and projection and t-distributed stochastic neighborhood embedding, were able to provide visual and quantitative representations that correlated well with observed matrix effects on low-energy atomic and high-energy ionic emission lines. Predictive models, including partial least squares regression and generalized linear models fit with the elastic net penalty, were tuned to estimate analyte recovery error when using the external standard calibration method (EC). The best predictive results were found for high-energy ionic analytical lines, e.g. Zn II 202.548 nm (Esum = 15.5 eV), with accuracy and R2 of 0.970 and 0.856, respectively. Two certified reference materials (CRMs) were used for method validation. The strategy described here may be used for flagging compromising matrix effects, and complement method validation based on addition/recovery experiments and CRMs analyses. Because the data analysis workflows feature signals from plasma-based species, there is potential for developing instrument software capable of alerting users in real time (i.e. before data processing) of inaccurate results when using EC.