Evaluation of the Optimal Dilution Sequence for the Minimization of the Concentration Uncertainty in Total Reflection X-Ray Fluorescence (TXRF)

The effect of different dilution series on the obtained concentration uncertainty was investigated in order to identify the optimal dilution sequence which produces the smallest confidence interval on the sought concentration. A theoretical model was developed to describe this uncertainty, and a simple rule was obtained which was used to further reduce the inherent uncertainty caused by dilution procedures. The experimental analytical technique used to validate the theoretical model was total reflection x-ray fluorescence (TXRF) due to its simplicity and its simultaneous multielemental evaluations. To carry out the study two steps were made (1) model the theoretical uncertainties in the final concentration after a given dilution sequence through the developed mathematical formulation and (2) validate the results predicted by the obtained formulation by performing numerical evaluations on TXRF experimental spectra. Two sets of ad hoc samples were generated according to two different dilution series in order to experimentally assess the influence of the dilution sequences on the measured concentration uncertainties. In order to avoid systematic errors, the procedures and measurements were repeated in three independent laboratories. The proposed method identifies the optimal dilution sequence that minimizes the computed uncertainty of the final concentration which is particularly useful in techniques with high sensitivity (10−7 g/g or less). Since the formulation allows to reduce the inherent uncertainty component of the dilution procedure, our conclusions provide useful guidance for dilution procedures, regardless of the analytical technique used and the analytes.