Faster, simpler, and more precise calibration curves: Expanding the scope of continuous calibration

Accurate calibration curves are essential for quantitative analysis but are often neglected due to their time, cost, and labour demands. Traditional calibration involves measuring solutions of known concentrations to construct a calibration curve relating analyte concentration to instrument response. While these relationships rarely follow simple closed-form equations, linear approximations are commonly used for simplicity, often being fitted with too few data points for high-accuracy calibration. Continuous calibration addresses these challenges by continuously infusing concentrated calibrant into a clean matrix solution while monitoring the response online. This approach significantly reduces time and labour while generating extensive data, improving calibration precision and accuracy. Despite its advantages, method limitations and technical complexities have hindered widespread adoption.

Here, continuous calibration is expanded and simplified with modern accessible equipment, open-source code, and a user-friendly web tool that together streamline experiments and data processing. The software generates smoothed and equation-fitted calibration curves complete with statistical-validity, quality-of-fit, and dynamic-range estimates. The method was demonstrated over a broad range of systems and analytical techniques, including external, standard addition, and internal standardization calibrations, and mass spectrometry, and infrared and ultraviolet-visible spectroscopies. The technique was also demonstrated to be more efficient and precise than discrete calibration. In ultraviolet-visible applications, molar absorption coefficients (ε) were obtained from a single experiment, with values for multiple analytes matching literature. For example, KMnO₄/H₂O analysis yielded ε = 2450 ± 40 M^-1 cm^-1 compared to the reported 2250-3340 M^-1 cm^-1. The approach was further extended to calibrate instrument response across pH ranges, yielding the literature pK_a of a weak acid from a single experiment.

These advancements substantially improve the precision, efficiency, and accessibility of calibration, with the potential to enhance experimental quality and efficiency across many fields. We hope that these improvements encourage scientists to conduct high-quality calibration more frequently.