On generalized Borgen plots. I: From convex to affine combinations and applications to spectral dataSpectra

In 1985, Borgen and Kowalski (Anal. Chim. Acta 1985; 174 : 1‐26) published their landmark paper on the geometric construction of feasible regions for nonnegative factorizations of spectral data matrices for three‐component systems. These geometric constructions are called Borgen plots. Borgen plots are principally restricted to nonnegative data and are sometimes considered as analytical tool. Major contributions to this theory have been given by Rajkó. In contrast to these geometric constructions, numerical methods to compute the so‐called area of feasible solutions (AFS) have been studied by Golshan et al. (Anal. Chem. 2011; 83 (3): 836‐841) and by Sawall et al. (J. Chemom. 2013; 27 : 106‐116). These numerical methods can even treat spectral data, which include slightly negative components. In this work, the concept of generalized Borgen plots is introduced for spectral data, which are polluted by small negative entries. The analysis is not restricted to three‐component systems but can be applied to general s‐component systems. Generalized Borgen plots are identical to the classical Borgen plots for nonnegative data. The analysis in this work also bridges the gap between the different scalings (Borgen norms) used for AFS computations. The algorithmic procedure of generalized Borgen plots for three‐component systems and its implementation in the FAC‐PACK software are described in the second part of this paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Component recognition with three‐dimensional fluorescence spectra based on non‐negative matrix factorization

Non‐negative matrix factorization (NMF) is a widely used approach in signal processing. In this work, we apply it to the component recognition of mixtures with multicomponent three‐dimensional fluorescence spectra. Compared with the popular PARAFAC for component recognition, NMF has the following advantages: on one hand, the decomposed spectra are three dimensional, and thus, more information can be obtained, which is beneficial for component recognition; on the other hand, the decomposed spectra are non‐negative and thus have a certain physical significance. More importantly, we propose a type of integrated similarity indices for the three‐dimensional fluorescence spectra, which, by construction, is good at component recognition from overlapping fluorescence spectra. Experiment results demonstrate that NMF combined with integrated similarity index provides an effective method for component recognition of multicomponent three‐dimensional overlapping fluorescence spectra. Copyright © 2011 John Wiley & Sons, Ltd.     

On the determination of partial molar polarizations and dipole moments of solutes from multicomponent solutions alone: experimental and model development using deutero-labeled organic compounds

A general inverse problem methodology is introduced to determine the partial molar polarizations and the dipole moments of individual solutes from multicomponent solutions alone. A model quaternary system consisting of three deuterated solutes, for example, acetone-d6, acetonitrile-d3, and dimethylformamide-d7 in cyclohexane at 298.15 K and 0.1013 MPa, was studied. Following an experimental design protocol, multicomponent solutions in the range of concentration 0.0006 < x(solute i) < 0.0085 were prepared using a semi-batch procedure by injecting one solute at a time. In situ FTIR spectroscopic measurements of these quaternary solutions were performed together with simultaneous condensed-phase bulk measurements of density, refractive index, and relative permittivity. Three different numerical approaches were used to determine the individual limiting solute molar polarizations from the multicomponent solutions. These limiting molar polarizations were then used to calculate the individual solute dipole moments using the Debye formula. In addition, direct dipole moment calculations were performed using the Guggenheim-Smith formula where individual solute parameters were obtained from multivariate analysis of the multicomponent solution data. Response surface models played a central role in many of the inverse problems. The results of the various methods are compared. In general, the dipole moments of all solutes from multicomponent solutions were in good agreement with those determined from independent binary experiments. Additionally, numerical sensitivity analysis was performed in order to identify the significant contributions to dipole moment uncertainty. The general approach introduced in the present contribution can be applied to a wide range of systems.     

Multivariate Composition Distribution in Free‐Radical Multicomponent Polymerization, 1

Statistical multicomponent polymerization is a typical example of a Markovian process for which the generating function approach can be applied. Up to the present, generating functions have been used mainly to obtain analytical solutions. However, recent advances of computer software capable of handling symbolic calculations can throw new light on the old mathematical technique. After formulating the equations representing the instantaneous composition distribution of polymers for a given chain length, r, the illustrative numerical calculations are conducted by using the symbolic calculator. For a multicomponent polymerization consisting of more than two components, the second component distribution is dependent on the composition of the first component (F₁), which is represented by the conditional probability given r and F₁, . It is found that is well approximated by the Gaussian distribution with the variance following the relationship, , as in the case of the first component distribution , where A and B are the constants. With the knowledge of chain length distribution, it is now possible to conduct the full analysis of multivariate distribution of chain length and compositions for multicomponent free‐radical polymerization.

Bivariate distribution of composition F₁ and F₂ for chain length r = 100 in a three‐component system.     

Adaptive multicomponent analysis by genetic algorithms

The applicability of genetic algorithms for solving multicomponent analyses is systematically examined. As a genetic algorithm (GA), the basic proposal of Goldberg is implemented in a straightforward manner to simulate multicomponent analyses in analogy to the well-established UV-vis or IR methods, especially multicomponent regression. The main focus of the study is to investigate the behavior of the genetic algorithm in order to compare it with the well-known behavior of multicomponent regression. A remarkable difference between the two methods is that the genetic algorithm method does not need any calibration procedure because of its pure searching characteristic. As important features of multicomponent systems, the degree of signal overlap (selectivity), the behavior of systems with known and unknown component numbers and qualities, and linear as well as nonlinear relationships between the analytical signal and concentration are varied within the simulations. According to multicomponent regression, recovering concentrations by a genetic algorithm is of limited applicability with the exception of systems at a low degree of signal overlap. On the other hand, the recovery of a probe spectrum in the analytical process always gives satisfactory results independent of the features of the probe system. The genetic algorithm obviously shows autoadaptive behavior in probe spectrum recovery. The quality and quantity of the resulting components may dramatically differ from the given probe, although the resulting spectrum is nearly the same. In such cases, the resulting component mixture can be interpreted as an imitation of the probe. As well probe spectra, theoretically designed spectra can also be autoadapted by genetic algorithms. The only limitation is that the desired spectrum must, of course, be incorporated into the search space defined by the involved components. Furthermore, a spectral signal is only one single property of a chemical compound or mixture. Because of the nonlinear search characteristic of genetic algorithms, any other chemical or physical property can also be treated as a desired property. Therefore, the conclusion of the study is well-founded that an old challenge of applied chemistry, namely, the development of new chemical products with desired properties, seems to be reachable under the control of genetic algorithms.     

Micro‐/Nanostructured Multicomponent Molecular Materials: Design,Assembly, and Functionality

Molecule‐based micro‐/nanomaterials have attracted considerable attention because their properties can vary greatly from the corresponding macro‐sized bulk systems. Recently, the construction of multicomponent molecular solids based on crystal engineering principles has emerged as a promising alternative way to develop micro‐/nanomaterials. Unlike single‐component materials, the resulting multicomponent systems offer the advantages of tunable composition, and adjustable molecular arrangement, and intermolecular interactions within their solid states. The study of these materials also supplies insight into how the crystal structure, molecular components, and micro‐/nanoscale effects can influence the performance of molecular materials. In this review, we describe recent advances and current directions in the assembly and applications of crystalline multicomponent micro‐/nanostructures. Firstly, the design strategies for multicomponent systems based on molecular recognition and crystal engineering principles are introduced. Attention is then focused on the methods of fabrication of low‐dimensional multicomponent micro‐/nanostructures. Their new applications are also outlined. Finally, we briefly discuss perspectives for the further development of these molecular crystalline micro‐/nanomaterials.     

Low‐bandwidth space/frequency component separation for quantitative imaging

Quantitative MRI is often used to analyse multicomponent systems. The analysis requires the contributions from different species to be isolated. Species with distinct chemical shifts can be separated by using a low acquisition bandwidth, which is easy to achieve in common quantitative imaging protocols. The bandwidth reduction leads to separation of NMR contributions from different species in the image space. This new method was implemented and tested on two multicomponent systems containing several spectrally and spatially unresolved components with both distinctly different and similar diffusion coefficients and relaxation times. Separation was achieved with routine MRI diffusion and relaxation measurement pulse sequences in a microimaging environment for water/polyethylene glycol solution and for chloroform/TMS/polyethylene glycol solution. Conventional monoexponential fitting was used to determine diffusion coefficients and relaxation times from the spectrally separated data, whereas biexponential or triexponential fitting was required in the unseparated reference experiments. In the two‐component sample, the variation in the determined fast diffusing components was on the same order of magnitude for all experiments, while the variation in the slow diffusing polyethylene glycol was larger when no separation was present. The separation technique provided lower variability for all the determined diffusion coefficients and relaxation times in the three‐component sample. The low‐bandwidth separation method can provide separation of multicomponent systems based on the chemical shift difference between the species. The accuracy of the technique is comparable with the commonly used methods for bicomponent system analysis and surpasses those when there are more than two components in the sample. Copyright © 2016 John Wiley & Sons, Ltd.     

Multicomponent Supramolecular Systems: Self‐Organization in Coordination‐Driven Self‐Assembly

The self‐organization of multicomponent supramolecular systems involving a variety of two‐dimensional (2 D) polygons and three‐dimensional (3 D) cages is presented. Nine self‐organizing systems, SS₁ – SS₉ , have been studied. Each involves the simultaneous mixing of organoplatinum acceptors and pyridyl donors of varying geometry and their selective self‐assembly into three to four specific 2 D (rectangular, triangular, and rhomboid) and/or 3 D (triangular prism and distorted and nondistorted trigonal bipyramidal) supramolecules. The formation of these discrete structures is characterized using NMR spectroscopy and electrospray ionization mass spectrometry (ESI‐MS). In all cases, the self‐organization process is directed by: 1) the geometric information encoded within the molecular subunits and 2) a thermodynamically driven dynamic self‐correction process. The result is the selective self‐assembly of multiple discrete products from a randomly formed complex. The influence of key experimental variables ‐ temperature and solvent ‐ on the self‐correction process and the fidelity of the resulting self‐organization systems is also described.     

多组分体系单级萃取平衡的Newton-Raphson算法

提出了一种多组分体系串级萃取动态仿真中的单级萃取平衡和物料计算的新同了有机相萃取量,水相洗涤量和混合萃取比等限制条件下两相组成关系的２λ元非线性方程组,构造以水相中某一组分的平衡含量为变量的目标函数,采用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ迭代求解,并以萃取平衡和物料平衡得到该级其它所有组分在两相的含量。     

Small‐Peptide‐Based Organogel Kit: Towards the Development of Multicomponent Self‐Sorting Organogels

The results presented here highlight the extremely useful nature of ultra‐short peptides as building blocks in the development of smart multicomponent supramolecular devices. A facile bottom‐up strategy for the synthesis of a small library of stimuli‐responsive smart organogelators has been proposed based on the predictive self‐assembly of ultra‐short peptides. More importantly, the narcissistic self‐sorting of the gelators has been evaluated as a simple method for the efficient co‐assembly of a donor–acceptor dual‐component gel, allowing the investigation of possible future applications of similar systems in the development of a supramolecular photo‐conversion device. Interestingly, it was observed that the self‐organization of the components can lead to highly ordered systems in which discrimination between compatible and non‐compatible building blocks directs the effective organization of the chromophores and gives rise to the formation of an excited‐state complex with exciplex‐like emission. The current report may prove important in the development of organogel‐based multicomponent smart devices.     

Self-recognition in the coordination driven self-assembly of 2-D polygons

Self-recognition in the transition-metal-mediated self-assembly of some 2-D polygons is presented. Prolonged heating of two or three organoplatinum reagents with 4,4'-dipyridyl in aqueous acetone results in the predominant formation of a rectangle, triangle, and/or square. All mixtures are characterized with NMR and electrospray ionization mass spectrometry (ESIMS). Despite the potential for ill-defined oligomeric products, these mixed ligand systems prefer to self-assemble into discrete species.     

Combinatorial Crystal Synthesis: Structural Landscape of Phloroglucinol:1,2‐bis(4‐pyridyl)ethylene and Phloroglucinol:Phenazine

A large number of crystal forms, polymorphs and pseudopolymorphs, have been isolated in the phloroglucinol‐dipyridylethylene (PGL:DPE) and phloroglucinol‐phenazine (PGL:PHE) systems. An understanding of the intermolecular interactions and synthon preferences in these binary systems enables one to design a ternary molecular solid that consists of PGL, PHE, and DPE, and also others where DPE is replaced by other heterocycles. Clean isolation of these ternary cocrystals demonstrates synthon amplification during crystallization. These results point to the lesser likelihood of polymorphism in multicomponent crystals compared to single‐component crystals. The appearance of several crystal forms during crystallization of a multicomponent system can be viewed as combinatorial crystal synthesis with synthon selection from a solution library. The resulting polymorphs and pseudopolymorphs that are obtained constitute a crystal structure landscape.     

Simple Fabrication of Multicomponent Heterogeneous Fibers for Cell Co‐Culture via Microfluidic Spinning

Microfluidic spinning, as a combination of wet spinning and microfluidic technology, has been used to develop microfibers with special structures to facilitate cell 3D culture/co‐culture and microtissue formation in vitro. In this study, a simple microchip‐based microfluidic spinning strategy is presented for the fabrication of multicomponent heterogeneous calcium alginate microfibers. The use of two kinds of microchip enables the one‐step preparation of multicomponent heterogeneous microfibers with various arrangement patterns, including the preparation of one‐, two‐, and three‐component microfibers by a two‐layer microchip and preparation of four component microfibers with different arrangement by a membrane‐sandwiched three‐layer microchip. The obtained microfibers could be used to encapsulate various kinds of cells, such as the human non‐small cell lung cancer cell NCI‐H1650, the human fetal lung fibroblast HFL1, the normal pulmonary bronchial epithelial cell 16HBE, and human umbilical vein endothelial cells. By adding chitosan to the medium to keep the fibers stable, 3D long‐term in vitro cell co‐culture has been carried out up to 21 days. This method is very simple and easy to operate, continuously produces spatially well‐defined heterogeneous microfibers, has important applications for composite functional biomaterials, and shows great potential in organs‐on‐a‐chip and biomimetic systems.     

Empirical Multicomponent Equilibrium and Film-Pore Model for the Sorption of Copper,Cadmium and Zinc onto Bone Char

The adsorption of three metal ions onto bone char has been studied in both equilibrium and kinetic systems. An empirical Langmuir-type equation has been proposed to correlate the experimental equilibrium data for multicomponent systems. The sorption equilibrium of three metal ions, namely, cadmium (II) ion, zinc (II) ion and copper (II) ion in the three binary and one ternary systems is well correlated by the Langmuir-type equation. For the batch kinetic studies, a multicomponent film-pore diffusion model was developed by incorporating this empirical Langmuir-type equation into a single component film-pore diffusion model and was used to correlate the multicomponent batch kinetic data. The multicomponent film-pore diffusion model shows some deviation from the experimental data for the sorption of cadmium ions in Cd-Cu, Cd-Zn and Cd-Cu-Zn systems. However, overall this model gives a good correlation of the experimental data for three binary and one ternary systems.     

Implementation and performance of the artificial force induced reaction method in the GRRM17 program

This article reports implementation and performance of the artificial force induced reaction (AFIR) method in the upcoming 2017 version of GRRM program (GRRM17). The AFIR method, which is one of automated reaction path search methods, induces geometrical deformations in a system by pushing or pulling fragments defined in the system by an artificial force. In GRRM17, three different algorithms, that is, multicomponent algorithm (MC‐AFIR), single‐component algorithm (SC‐AFIR), and double‐sphere algorithm (DS‐AFIR), are available, where the MC‐AFIR was the only algorithm which has been available in the previous 2014 version. The MC‐AFIR does automated sampling of reaction pathways between two or more reactant molecules. The SC‐AFIR performs automated generation of global or semiglobal reaction path network. The DS‐AFIR finds a single path between given two structures. Exploration of minimum energy structures within the hypersurface in which two different electronic states degenerate, and an interface with the quantum mechanics/molecular mechanics method, are also described. A code termed SAFIRE will also be available, as a visualization software for complicated reaction path networks. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

完全未知混合体系的纯物种光谱辨析

基于因子分析的迭代目标转换算法,本文提出一种从完全未知混合物体系中获取纯物种光谱的解析方法。该法简单明了,不增加任何困难即可拓广至含n组份的混合体系,对光谱峰形状亦无任何附加限制要求。先采用计算机模拟技术对该法进行了校验,继用于紫外可见与荧光光谱的实际混合体系的解析,均获满意结果。     

Radiation of multicomponent aqueous salt solutions in the millimeter-wave spectral region

The low-intensity radiation and radiobrightness contrasts of multicomponent aqueous solutions of alkali metal chlorides have been studied at a frequency of 61.2 GHz. An additive character of changes in radiobrightness contrasts relative to initial binary systems (component ratio, 1: 1) is shown. The concentration dependence for solutions of potassium and lithium chlorides shows that initial different-sign radiation effects are eliminated. The radiation of mixed solutions proves to be close to the radiation of pure water (up to 4 m solutions).     

Two-component protein adsorption kinetics in porous ion exchange media

This work provides a theoretical analysis of multicomponent adsorption kinetics for conditions typical of protein adsorption in porous ion exchangers as well as experimental results for the adsorption of lysozyme/cytochrome c mixtures in the cation exchanger SP-Sepharose-FF. The theory predicts the formation of overshoots in the intraparticle concentration profiles and in the total amount adsorbed for the more weakly adsorbed component. An analytical solution valid for the case where the isotherms are rectangular is developed and found to be in good agreement with the limiting behavior of the general numerical solution of the model equations. The experimental results show that the two proteins are competitively adsorbed and that an overshoot of adsorbed cytochrome c occurs during simultaneous adsorption. Model predictions based on the assumption that the adsorption isotherms are rectangular and that lysozyme completely displaces cytochrome c are in qualitative and quantitative agreement with the experimental kinetics suggesting that the overshoot phenomena observed with multicomponent systems in these resins can be explained with a diffusion model without the need to account for flux coupling or electrophoretic contributions to transport.     

Some selected problems of nonaqueous microemulsions — phase diagrams and variation of the composition in the quaternary and ternary systems

A variety of quaternary and ternary systems of the type of dodecane/aliphatic alcohols/Na-dodecyl sulphate/water or a water-replacing component (formamide, ethylene glycol, propylene glycol, propylene carbonate, dimethylsulfoxide, acetonitrile) were subjected to a comparative analysis of microemulsification. The compositions of the systems of the type of oil/surfactant/cosurfactant/water or nonaqueous liquid were changed with respect to surfactant (Na-dodecyl sulfate and triton X 114) concentration, cosurfactant (homologous aliphatic alcohols) concentration and mixing ratio of water and water-replacing component. The appertaining phase diagrams were plotted and compared with those of aqueous systems.The experimental results suggest that the phase regions, which are designated as nonaqueous microemulsions, probably represent, not only microemulsions in the usual sense, but a separate kind of mixed phase whose microstructure is examined by special studies. Analogously to aqueous microemulsion systems, transparency and spontaneous formation of homogeneous multicomponent systems cannot serve as the sole criteria for waterless microemulsion formation. But they are important guiding properties of microemulsion formation in multicomponent systems.The variety of components involved in the chemical composition and the current insufficient knowledge do not permit to generally decide whether nonaqueous systems can be assigned to microemulsions or to molecular solutions. For clarifying this problem a detailed examination of the miscibility behavior, especially that of binary systems as a function of temperature, and the role that surfactant and cosurfactant play in the formation of homogeneous systems will be necessary.     

Excitation-emission-lifetime analysis of multicomponent systems—II. Synthetic model data

To determine the efficacy of three-dimensional principal component factor analysis (PCFA) for extracting non-exponential decay parameters from multicomponent data, we have constructed synthetic data matrices which mimic the possible outcomes of experiments in the nanosecond time domain with copper porphyrins. Our results demonstrate that PCFA is capable of determining non-exponential time decay in systems with two and three emitting species. The accuracy of the rate constants determined by this method is limited by the accuracy of the non-linear Marquardt algorithm that we have used for the final fits. Although extremely overlapped components have been resolved using this method, degeneracy in one of the dimensions is problematic.