Calibration by Proxy

Abstract

Calibration by Proxy (CbPx) is a matrix-matched calibration method that utilizes multiple internal standard species to build a calibration curve. The technique requires only two solutions: solution 1 containing a sample solution and a suite of internal standards at known concentrations, and solution 2 identical to solution 1, plus an aliquot of a standard containing all analytes and the internal standards at the same concentration. The calibration curve is prepared by plotting the signal measured for each internal standard in solution 1 divided by the signal arising due to the aliquot of internal standard added to solution 2 on the y-axis. In this ratio, the sensitivity for each element cancels, because the sample matrix is equal between the solutions. Therefore, the y-axis value measured for a specific internal standard is identical to the value that would be measured for any other element present at the same concentrations in the two solutions. Hence, each internal standard serves as a proxy for analyte values. The concentrations of internal standards in solution 1 are plotted on the x-axis, and these correspond to any analytes present in solution 1 at the same concentration. CbPx is applied to the analysis of five certified reference materials by inductively coupled plasma optical emission spectrometry (ICP-OES). Percent recoveries for analytes range from 89 to 106%, with relative standard deviations on the order of 1%. A recommended working range for the method is developed through both theoretical simulation and experimental results and then exhibited through the analysis of off-the-shelf vitamin tablets.

Figure 1

Solution preparation required for Calibration by Proxy.

Figure 2

Representative CbPx plots obtained for several analytes in certified reference materials using added concentrations for all species of 1 mg L^–1 (A) and 200 μg L^–1 (B).

Figure 3

Raw intensities (blue diamonds) vs intensity ratio (red circles) comparison obtained for three Cr emission lines when changing sample matrix (A), plasma power (B), and nebulizer flow rate (C). Intensities are relative to DDI for the matrix comparison, and relative to default instrument conditions for both plasma power and nebulizer flow rate, represented by the dashed black line.

Figure 4

Recovery values using both simulated signals (A) and real signals for Cd measured using different samples and standard concentrations (B). The blue, red, and black points for the real data correspond to sample concentrations of 1 mg L^–1, 500 μg L^–1, and 200 μg L^–1, respectively. Dashed horizontal lines correspond to the recovery range of 90–110%.