Resolution of multicomponent systems

In specialized studies, chemical measurements achieve particular importance by their temporal and spatial resolution. In process control, the momentary value is interesting only in such exceptional situations in which a warning or control limit is passed. Much more information is contained in the time function of an analytical system, y = f(t), or y = f(z, t), in case of multicomponent systems as shown in Fig. 3.11. 

In the resolution of any multicomponent system, the main goal is to transform the raw experimental measurements into useful information. By doing so, we aim to obtain a clear description of the contribution of each of the components present in the mixture or the process from the overall measured variation in our chemical data. Despite the diverse nature of multicomponent systems, the variation in then-related experimental measurements can, in many cases, be expressed as a simple composition-weighted linear additive model of pure responses, with a single term per component contribution. Although such a model is often known to be followed because of the nature of the instrumental responses measured (e.g., in the case of spectroscopic measurements), the information related to the individual contributions involved cannot be derived in a straightforward way from the raw measurements. The common purpose of all multivariate resolution methods is to fill in this gap and provide a linear model of individual component contributions using solely the raw experimental measurements. Resolution methods are powerful approaches that do not require a lot of prior information because neither the number nor the nature of the pure components in a system need to be known beforehand. Any information available about the system may be used, but it is not required. Actually, the only mandatory prerequisite is the inner linear structure of the data set. The mild requirements needed have promoted the use of resolution methods to tackle many chemical problems that could not be solved otherwise. 

Factor analysis methods allow resolution of multicomponent mixtures when individual contribution of each component is unknown. In broad terms, this methodology yields a solution set for each component whose width depends on the data supplied. Nevertheless, the complexity of the mathematical treatment has actually prevented the resolution of chemical systems with more than three components. 

A practical method for enhancing the peak capacity, and thus the resolution of analytes in multicomponent complex mixtures, can be achieved by changing the mode of the separation during the chromatographic analysis, employing a column switching system in order to optimize a separation. 

The resolution of a multicomponent system involves the description of the variation of measurements as an additive model of the contributions of their pure constituents [1-10]. To do so, relevant and sufficiently informative experimental data are needed. These data can be obtained by analyzing a sample with a hyphenated technique (e.g., HPLC-DAD [diode array detection], high-performance liquid chromatography-DAD) or by monitoring a process in a multivariate fashion. In these and similar examples, all of the measurements performed can be organized in a table or data matrix where one direction (the elution or the process direction) is related to the compositional variation of the system, and the other direction refers to the variation in the response collected. The existence of these two directions of variation helps to differentiate among components (Figure 11.1). 

The correct performance of any curve-resolution (CR) method depends strongly on the complexity of the multicomponent system. In particular, the ability to correctly recover dyads of pure profiles and spectra for each of the components in the system depends on the degree of overlap among the pure profiles of the different components and the specific way in which the regions of existence of these profiles (the so-called concentration or spectral windows) are distributed along the row and column directions of the data set. Manne stated the necessary conditions for correct resolution of the concentration profile and spectrum of a component in the 2 following theorems [22] ... 

Another AFM-based technique is chemical force microscopy (CFM) (Friedsam et al. 2004 Noy et al. 2003 Ortiz and Hadziioaimou 1999), where the AFM tip is functionalized with specific chemicals of interest, such as proteins or other food biopolymers, and can be used to probe the intermolecular interactions between food components. CFM combines chemical discrimination with the high spatial resolution of AFM by exploiting the forces between chemically derivatized AFM tips and the surface. The key interactions involved in food components include fundamental interactions such as van der Waals force, hydrogen bonding, electrostatic force, and elastic force arising from conformation entropy, and so on. (Dther interactions such as chemical bonding, depletion potential, capillary force, hydration force, hydrophobic/ hydrophobic force and osmotic pressure will also participate to affect the physical properties and phase behaviors of multicomponent food systems. Direct measurements of these inter- and intramolecular forces are of great interest because such forces dominate the behavior of different food systems. 

The publication in 1984 of the resolution of the X-ray crystal structure of the reaction center (RC) of the photosynthetic bacterium Rhodopseudomonas viridis [73] inspired many research groups, and thus initiated the design and synthesis of multifarious multicomponent systems expected both to display structural analogy with the RC and to fulfill some of its photochemical and electron transfer functions [74]. 

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