Second-Order Standard Addition Method Based on Alternating Trilinear Decomposition

Abstract

The standard addition method (SAM) as a means of overcoming matrix or background effects is usually applied to zeroth-order instrumentation (instruments that return only a scaler quantity per sample analyzed). 1 For a successful calibration, SAM requires two assumptions be fulfilled: (1) there is a linear change in the instrument response with increasing analyte concentration; (2) for zero concentration of an analyte the instrument response must be zero. A plot of the instrument response (ordinate) against the amount of standard added (abscissa) estimates the analyte concentration in the sample by fitting a line to the data and finding the intercept of the line on the abscissa.The generalized standard addition method (GSAM) 2,3 is an extension of SAM to first-order instruments (instruments that return a vector of data per sample, e.g., a diode array spectrometer). GSAM requires that the response profiles of the sought-for analyte be different from each other and any spectroscopically interfering species. This relaxes the constraint that the analytical method must be fully selective to the analyte of interest. However, a reliable analysis requires the absence of any unaccountable source of instrumental signal beyond the calibration framework. That is, in the absence of all species included in the calibration model, the instrument response is zero at all channels. Therefore, Booksh et al. have extended SAM to second-order instrumentation (instruments that return a matrix of data per sample, e.g., HPLC-DAD). 4 As pointed out in ref. 5, ideally, a second-order calibration can be performed in the presence of interfering species unaccounted by the calibration model. However, if the interfering species change the instrument response of the analyte (in scale or shape), standard additions must be employed to ensure an accurate analyte concentration estimation. 4 Booksh et al. presented a secondorder standard addition method (SOSAM) using direct trilinear decomposition (DTLD). The present authors have developed a method called the alternating trilinear decomposition (ATLD). 6 In this study, the SOSAM based on the ATLD algorithm was applied to second-order HPLC-DAD data and compared with methods employing DTLD and PARAFAC. Theory Second order dataSecond-order tensor data are usually generated from hyphenated instruments, such as HPLC-DAD or an excitation-emission fluorescence spectroscope. They should obey the following trilinear model (see Fig. 1):where N denotes the number of factors, or the total number of existing species, including sought-for component(s) as well as unexpected interferant(s) usually accounted as a part of the analytical background; xijk is the element (i, j, k) of the threeway response array X _ of size I×J×K; ain is the element (i, n) of an I×N matrix A of relative concentrations of N species in I samples after the (i-1)th standard is added; bjn is the element (j, n) of a J×N matrix B of relative sensitivity coefficients of N species at J wavelengths; ckn is the element (k, n) of a K×N matrix C of el...

Determination of pesticides in honey using excitation–emission matrix fluorescence coupled with second-order calibration and second-order standard addition methods

“…In 1995, Booksh et al have extended SAM to second-order instrumentation (instruments that return a matrix of data per sample) and presented the second-order standard addition method (SOSAM) [39]. Wu et al develop a novel SOSAM method based on ATLD [40]. The method relaxes the constraint …”

Simultaneous determination of cortisol and prednisolone in body fluids by using HPLC–DAD coupled with second-order calibration based on alternating trilinear decomposition

“…It is based on an alternating least squares principle and an improved iterative procedure that utilizes the Moore-Penrose generalized inverse obtained by singular value decomposition. The ATLD-based second-order calibration exploited the secondorder advantage making the calibration possible even in the presence of interferences that are not present in the calibration samples, so it can provide satisfactory concentration estimates [41][42][43].…”

Fast Determination of Phenanthrene in Soil by Gas Chromatography‐Mass Spectrometry Using Chemometric Resolution and Standard Addition Method

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