Stochastic Utility of Internal Standard Method in Liquid Chromatography

Abstract

A probability theory is presented to judge the utility of the internal standard method in high-performance liquid chromatography (HPLC). The relative standard deviation (RSD) of experimental results in the internal standard method is theoretically predicted based on the recently proposed uncertainty theory for sample dilution and HPLC measurement. The experiments comprise the taking of sample solution, addition of internal standard, dilution, measurement on HPLC and signal processing. Two kinds of correlation between concentrations of analyte and internal standard are formulated distinctively in the sample preparation process and in the HPLC measurement. The RSD values for the total experimental process are calculated from the volume error of pipette, signal shape of analytes and some probabilistic properties of baseline drift in chromatograms and are shown to be in good agreement with the observed ones over a wide range of dilution degree. The external calibration is also examined. KeywordsLiquid chromatography, internal standard method , chemometrics, statistics Internal standard (IS) methodology has been widely used in HPLC quantitative analysis. Instead of the absolute value of the measured quantity such as peak area or height in chromatograms, the ratio of the quantity for an analyte to that for internal standard added to the sample solution during sample preparation is used in the internal standard method. The usefulness of this method is ensured by the high possibility that the error of the analyte concentration is compensated by an equivalent amount of error of the internal standard concentration.Precision which is usually expressed as the standard deviation (SD) or relative standard deviation of measured quantities) has been the criterion of the statistical studies to evaluate the utility of the internal standard method in HPLC quantitative analysis.2-6As demonstrated by Haefelfinger4, however, the internal standard method is not always preferable to the external calibration. In some instances, the latter yields more precise results.4 The aims of this paper are to comprehend the uncertainty structure (i.e., stochastic properties) of the internal standard method and to predict the total precision or RSD of experimental results from the sample preparation, measurement and signal processing. The common but often elusive question concerning which is more precise, the internal standard method or external calibration, is answered mathematically for some typical examples.The studies on the internal standard method carried out so far2~6 are helpful to understand the statistical or practical aspects of the method, but little attention has been paid toward the subject of this paper: (1) the actual RSD of measurements in the internal standard method is predicted without repeated experiments; (2) the correlation between the concentrations of analyte and internal standard is mathematically discriminated between the sample preparation and the HPLC measurement; (3) the precision of the IS methods depends on the concen...

On-column internal standardisation as an alternative calibration strategy for speciation analysis: feasibility demonstration through analysis of inorganic As in rice

“…within each sample as a surrogate standard or post-column). Details on the different types of internal standardisation approaches readily available in the literature 11,12,13,14 . In summary, the post-column set-up includes a switching valve, positioned online the sample flow, after the separation module (e.g.…”