Curve resolution method

Multivariate curve resolution methods (MCR [17]) describe a family of chemometric procedures used to identify and solve the contributions existing in a data set. These procedures have been traditionally applied for the resolution of multiple chemical components in mixtures investigated by spectroscopic analysis techniques [18]. 

The field of curve resolution was bom in response to the need for a tool to analyze multivariate experimental data from multicomponent dynamic systems. The common goal of all curve-resolution methods is to mathematically decompose the global instrumental response into the pure-component profiles of each of the components in the system. The use of these methods has become a valuable aid for resolving complex systems, especially when obtaining selective signals for individual species is not experimentally possible, too complex, or too time consuming. 

Different approaches have been proposed during recent years to improve the solutions obtained by curve-resolution methods, and some of them are summarized in the next sections. The field is already mature and, as it has been recently pointed out [26], multivariate curve resolution can be considered as a sleeping giant of chemometrics, with a slow but persistent growth. 

In summary, using either principal component analysis or multivariate curve-resolution methods, the main contamination sources of semivolatile organic compounds present in the surface waters of Portugal were identified, and their geographical... 

Although many reports are available regarding constraints in curve resolution methods, the majority describe constraints linked to process profiles, such as unimodality (only one maximum per concentration profile) or closure (mass balance in reachon systems). These process-related constraints are not applicable to image concentrahon profiles, due to the above-mentioned lack of pattern in this direction of the data set. Instead, other types of informahon are used. One fairly intuitive possibility is to include knowledge of the identity (and pure spectrum) of certain image conshtuents, and when this is the case these spectral shapes are fixed in the matrix during the iterative resoluhon process. In doing so, the possible combinations for spectral shapes of unknown constituents decrease and the recovery of the correct distribuhon map for the known component is ensured. 

Curve resolution methods are focused on extracting information of the pure components in a mixture system through a suitable factorization of the experimental data matrix D into the product of two simpler matrices C and that refer to pure peak prohles and pure spectra of components, respectively (33). Mathematically, the equation of the resolution process can be written as follows ... 

Early visualization in chemical three-way analysis was used in curve resolution methods, and especially GRAM. The extraction and visualization of unknown spectra (curve resolution) was considered very important. Tucker and PARAFAC analysis were used much in the exploratory sense and PARAFAC also for curve resolution. The first publication of Ho et al. [1978] has figures of eigenvalues expressed as a function of a parameter /S, see Figure 8.1. The second publication of Ho et al. [1980] also contains contour plots for the excitation-emission spectra of polyaromatic compounds (see Figures 8.2 and 8.3). They also show excitation and emission spectra as line plots (see Figures 8.4 and 8.5). The plots are only used to show the raw data and show no results after analysis. An early publication of de Ligny et al. [1984] has all the results shown as numbers in tables. 

When the underlying model is low-rank bilinear, the data matrices produced are often close to this bilinear model, except for noise and nonlinearities. In such a case, a low-rank bilinear model can be fitted, for example, by curve resolution methods. When certain added conditions such as selective channels, nonnegative parameters etc. are fulfilled, unique models can sometimes be obtained [Gemperline 1999, Manne 1995],... 

Mas, S., Fonrodona, G., Tauler, R., and Barbosa, J., Determinahon of phenohc acids in strawberry samples by means of fast liquid chromatography and multivariate curve resolution methods. Talanta, 71,... 

Li, H., Hon, J., Wang, K., and Zhang, F., Resolution of multicomponent overlapped peaks. A comparison of several curve resolution methods, Talanta, 70, 336, 2006. 

Ivanisevic et al. (2009) applied pure curve resolution method (PCRM) and alternative least square (ALS) method to pXRD data of ASD for miscibility studies. The PCRM-based approach follows the analysis of the variance among the measured intensity points of pXRD patterns of ASD with varying drug loadings thus... 

V. del Rio, M.S. Larrechi, M.P. Callao, Determination of sulphate in water and biodiesel samples hy a sequential injection analysis-multivariate curve resolution method. Anal. Chim. Acta 676 (2010) 28-33. 

Two procedures have been adopted to resolve the preceding problem. Vitha et al. have used a modified curve resolution method [14,15]. This method is based on singular value decomposition (SVD) of a matrix of spectra recorded at several concentrations of surfactant. The method assumes that only two components, namely, the indicator in the aqueous and micellar phase, contribute to the observed spectra. A knowledge of the molar volume of the surfactant and the aggregation number is also required. The curve resolution method gives three parameters the distribution coefficient and the spectra of the indicator solute in the two phases. The value of the spectroscopic parameter of interest (e.g., the position of band maximum) was then determined from the spectrum in the micellar phase. 

It is well-known that the polymerisation of vinyl chloride proceeds under the control of the Bernoullian statistical model (selection between meso and racemo). Table 6.3 shows the comparison of the observed relative areas of methine pentad and methylene peaks with those calculated by Bernoullian propagation statistics. Relative areas of observed peaks are determined by the curve resolution method. The relative areas of observed pentad peaks agree well with calculated values, indicating the validity of their pentad assignments by the method of Dong and co-workers [61]. As for the methylene peaks, observed areas (except peak 6 ) agree well with calculated values. Assuming... 

The activation process of the ATRP of styrene catalyzed by the Cu(I)Br/2dHbipy (Figure 12) complex was studied by the GPC curve-resolution method at 110 Under the usual condi-... 

Multivariate Curve Resolution Methods for Food Chemistry... 

TABLE 1 Multivariate Curve Resolution Methods Applied to Qualitative and Quantitative Analysis of Compounds in Food Samples ... 

TABLE 2 Multivariate Curve Resolution Methods and Food Fingerprints—Cont d ... 

MCR multivariate curve resolution—Curve resolution method... 

SIMPLISMA simple-to-use interactive self-modelling mixture analysis— Curve resolution method... 

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