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Multivariate Curve Resolution (MCR)

Multivariate Curve Resolution is defined as a group of techniques which help resolve mixtures by determining the number of constituents, their response profiles (spectra, pH profiles, time profiles, elution profiles) and their estimated concentrations, when no prior information is available about the nature and composition of these mixtures.

It is a well-established technique for evaluating and soft-modeling evolving systems and 2 Dimensional Correlation Spectroscopy (2DCoS), a method that is spreading the modulated spectra over a second spectral dimension, thus enhancing spectral resolution.

A very flexible 2 way data analysis method based on the assumption of Lambert-Beer’s Law, MCR decomposes the experimental data matrix D into the product of two smaller matrices C and ST, with C being a matrix of concentration profiles for each modeled component in the system and S being the matrix of the corresponding pure spectra:

D = C ST + E

The number of components (chemical species) contributing to D and to be modeled by MCR has to be determined and initial estimates for C or ST have to be provided. Then C and ST are optimized iteratively in an Alternating Least Squares (ALS) algorithm until convergence is reached. Diverse constraints (non-negativity, unimodality, selectivity, closure…) can be applied during the iterations in order to obtain a physically and/or chemically meaningful solution.

Multivariate Curve Resolution (MCR) methods can be extended to the analysis of many types of experimental data including multi-way data and non-evolutionary processes.

The Unscrambler® X provides the most flexible and adaptable approach to Multivariate Data Analysis (MVA) and Design of Experiments (DoE) available.
Multivariate Curve Resolution (MCR): Resolve time evolving data such as chemical reaction or chromatographic data into pure constituent profiles and pure spectra.