PARAFAC under non-negativity constraint is adapted to recover the underlying Beer-Lambert law of the excitation-emission fluorescence matrix measurements acquired from analyte-triggered semiconductor QDs photoluminescence modulation. When and why?

Background: Analyte-triggered semiconductor quantum dots (QDs) modulation in the presence of non-consistently responsive fluorescent species represents a challenging analytical issue in concrete multi-way data handling. QDs with heterogeneous sizes and/or uneven distribution of functional moieties on their surfaces exhibit significant fluctuations in the fluorescent response components, known as chemical rank, across different excitation/emission modes. This phenomenon may lead to a substantial deviation from the proportionality prescribed by Beer-Lambert law. Nonetheless, even in the presence of such deviation, a multi-way model may be successfully selected after determining a proper chemical rank in a QDs system.

Results: We show that in a valid PARAllel FACtor (PARAFAC) model under properly determined chemical rank, meaningfully resolved pure spectral profiles can be reached for each fluorescent responsive constituent in the original excitation-emission fluorescence matrix (EEFM) measurements. This was thoroughly illustrated by applying PARAFAC trilinear decomposition of a three-way data array of two distinct datasets acquired from semiconductor QDs sensing systems with low-rank trilinear assumption. The first dataset, presented here for the first time, comprises EEFM measurements of the ligand-driven quenching of thiomalic acid (TMA)-capped AgInS₂ (AIS) QDs by vomitoxin. The second dataset, employed for illustrative purposes, comprises EEFM measurements of the quenching, via cation bridging, of glutathione (GSH)-capped CdTe QDs by Pb(II). The results of this study enabled the determination of vomitoxin at a ppb level in real samples of fish feeds, showcasing the efficacy of the PARAFAC model in resolving spectral signatures (loadings) and pure concentration profiles (scores).

Significance: PARAFAC under a properly examined chemical rank can be easily adapted for retrieval the underlying Beer-Lambert law of the original EEFM measurements with a low-rank trilinear structure through the chemically meaningful information either when (i) no deviation of Beer-Lambert law was observed as deeply discussed in connection with the dataset acquired from vomitoxin-driven molecular sensing through TMA-capped AIS QDs, or when (ii) substantial deviations of the Beer-Lambert law are evident, as discussed in connection with the dataset collected from sensing ionic species through Pb(II) bridging of GSH-capped CdTe QDs.