Analysis of the aggregation-fragmentation population balance equation with application to coagulation

Coagulation of small particles in agitated suspensions is governed by aggregation and breakage. These two processes control the time evolution of the cluster mass distribution (CMD) which is described through a population balance equation (PBE). In this work, a PBE model that includes an aggregation rate function, which is a superposition of Brownian and flow induced aggregation, and a power law breakage rate function is investigated. Both rate functions are formulated assuming the clusters are fractals. Further, two modes of breakage are considered: in the fragmentation mode a particles splits into w2 fragments of equal size, and in the erosion mode a particle splits into two fragments of different size. The scaling theory of the aggregation-breakage PBE is revised which leads to the result that under the negligence of Brownian aggregation the steady state CMD is self-similar with respect to a non-dimensional breakage coefficient theta. The self-similarity is confirmed by solving the PBE numerically. The self-similar CMD is found to deviate significantly from a log-normal distribution, and in the case of erosion it exhibits traces of multimodality. The model is compared to experimental data for the coagulation of a polystyrene latex. It is revealed that the model is not flexible enough to describe coagulation over an extended range of operation conditions with a unique set of parameters. In particular, it cannot predict the correct behavior for both a variation in the solid volume fraction of the suspension and in the agitation rate (shear rate).     

A kinetic study of the electron-transfer reaction of the phthalimide-N-oxyl radical (PINO) with ferrocenes

A kinetic study of the one-electron oxidation of a series of ferrocenes (FcX: X = H, CO2Et, CONH2, CH2CN, CH2OH, Et, and Me2) by PINO generated in CH3CN by reaction of N-hydroxyphthalimide (NHPI) with the cumyloxyl radical produced by 355 nm laser flash photolysis of dicumyl peroxide has been carried out. Ferrocenium cations were formed, and the reaction rate was determined by following the decay of PINO radical at 380 nm as a function of the FcX concentration. Rate constants were very sensitive to the oxidation potential of the substrates and exhibited a good fit with the Marcus equation, from which a lambda value of 38.3 kcal mol(-1) was calculated for the reorganization energy required in the PINO/ferrocenes electron-transfer process. Knowing the ferrocene/ferrocenium self-exchange reorganization energy it was possible to calculate a value of 49.1 kcal mol(-1) for the PINO/PINO- self-exchange reaction in CH3CN. Moreover, from the Marcus cross relation and the self-exchange rates of ferrocene and dimethylferrocene, the intrinsic reactivity of PINO in electron-transfer reactions has been calculated as 7.6 x 10(2) M(-1) s(-1). The implications of these values and the comparison with the electron-transfer self-exchange reorganization energies of peroxyl radicals are briefly discussed.     

Self-assembled metallacycles with pyrazine edges: a new example in which the unexpected molecular triangle prevails over the expected molecular square

The combination of cis-protected metal fragments with linear linkers is expected to yield molecular squares. We found instead that treatment of the 90 degrees angular precursor trans-[RuCl2(dmso-S)4] (1) with an equivalent amount of the linear and rigid pyrazine (pyz) linker unexpectedly yields, in a number of different experimental conditions, the molecular triangle [{trans,cis-RuCl2(dmso-S)2(mu-pyz)}3] (3), together with polymeric material. Very similar results were also obtained from the reaction between 1 and the preformed corner fragment trans,cis,cis-[RuCl2(dmso-S)2(pyz)2] (6). In both cases, the expected molecular square [{trans,cis-RuCl2(dmso-S)2(mu-pyz)}4] (4) was observed only as a transient species. These results suggest that 3, which is the first example of a neutral molecular triangle with octahedral metal corners and pyrazine edges, is both the thermodynamic and the kinetic product of the reactions described above. The X-ray structure of 3 shows that the main distortions from ideal coordination geometry concern the N-Ru-N angles, which are narrower than 90 degrees , and the coordination bonds of pyz. The pyrazine molecules, which are basically planar, are significantly tilted from linearity. Calculations performed on 6 indicated that the N-Ru-N angle is ca. six times more rigid than the tilt angle of pyrazine. The structural and theoretical findings on 3 and 6, together with the previous examples of molecular triangles and squares with cis-protected metal corners and linear pyz edges, suggest that the entropically favored molecular triangles might be preferred over the expected molecular squares with metal corner fragments that spontaneously favor Npyz-M-Npyz angles narrower than 90 degrees because of the presence of ancillary ligands with significant steric demand on the coordination plane. The rather-flexible coordination geometry of pyrazine can accommodate the moderate distortions from linearity required to close the small metallacycle with modest additional strain.     

Sequential multiphoton absorption enhancement induced by zinc complexation in functionalized distyrylbenzene analogs

Functionalized distyrylbenzene analogs and , bearing a tris-(2-pyridylmethyl)amine-based receptor for Zn(2+), were synthesized by a Horner-Emmons-Wittig coupling reaction. It has been found that Zn(2+) complexation induces changes in the linear absorption spectrum that enhance a nonlinear sequential two-photon absorption of nanosecond pulses at 532 nm. This absorption was also found to depend on the nature of the substituent at the side benzene ring of the styrylbenzene structure.     

Synthesis of benzo[1,2-d;3,4-d']diimidazole and 1H-pyrazolo[4,3-b]pyridine as putative A2A receptor antagonists

The synthesis and the binding affinity for the putative adenosine receptor antagonist 6-methyl-7-[1,2,3]triazol-2-yl-1,6-dihydrobenzo[1,2-d;3,4-d']diimidazole (10) and 5-oxazol-2-yl-1H-pyrazolo[4,3-b]pyridin-3-ylamine (16) are reported. The title compounds were prepared from commercially available 1-chloro-2,4-dinitrobenzene (1) and 2-chloro-6-methoxy-3nitropyridine (11), respectively, but proved devoid of affinity for the adenosine A1 and A2A receptors.     

Polycondensation Kinetics of Lactic Acid

The direct polycondensation of D ,L ‐lactic acid in the absence and presence of different catalysts at various temperatures has been studied experimentally. Two types of reactions were carried out, one under closed conditions to estimate the equilibrium constant and the other under flow of nitrogen to estimate the polymerization rate constant. A mathematical model was developed based on a suitable kinetic scheme for polycondensation reaction accounting for the rate of water removal. The effects of different operating conditions (temperature and pressure) on the average molecular weight of the polymer have been explored through experiments and model simulations.

     

Solution and solid-state preparation of 18-crown[6] complexes with M[HSO4]n salts (M = NH4+, K+, Sr2+ and n = 1, 2) and an investigation of solvation/desolvation processes and crystal polymorphism

18-Crown[6] ether has been used to prepare a new class of organic-inorganic complexes of general formula 18-crown[6]M[HSO(4)](n) (where M = NH(4) (+), K(+), Sr(2+) and n = 1, 2) by reacting directly in solution or in the solid state the crown ether 18-crown[6] with inorganic salts such as [NH(4)][HSO(4)], K[HSO(4)], and Sr[HSO(4)](2). The structures of 18-crown[6][NH(4)][HSO(4)]2 H(2)O (12 H(2)O), 18-crown[6][NH(4)][HSO(4)] (1), 18-crown[6]K[HSO(4)]2 H(2)O (22 H(2)O), 18-crown[6]K[HSO(4)] (2), and 18-crown[6]Sr[HSO(4)](2) (3) have been characterized by single-crystal X-ray diffraction. The reversible water loss in compounds 12 H(2)O and 22 H(2)O leads to formation of the corresponding anhydrous phases 18-crown[6][NH(4)][HSO(4)] (1), and 18-crown[6]K[HSO(4)] (2), which undergo, on further heating, enantiotropic solid-solid transitions very likely associated with the on-set of a solid state dynamical process. Similar high-temperature behavior is shown by 18-crown[6]Sr[HSO(4)](2) (3). The dehydration and phase-transition processes have been investigated by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and variable temperature X-ray powder diffraction.     

Mechanism of quinol oxidation by ferricenium produced by light excitation in reaction centers of photosynthetic bacteria

The kinetics and thermodynamics of cyclic electron transfer through the isolated reaction center protein of photosynthetic bacterium Rhodobacter sphaeroides were determined in detergent (Triton X-100) solution. The redox reactions between the reducing (ubiquinol-0 or ubiquinol-10) and oxidizing species (ferricenium, ferricytochrome, or ferricyanide) produced chemically or by light excitation of the protein were monitored by absorption changes of the reactants and by acidification of the solution accompanied with the disappearance of the quinol. The bimolecular rate constants of reactions of anionic ubiquinol-0 with different oxidizing agents showed large variation: 5 x 10(8) M(-1) s(-1) for ferricenium, 3.5 x 10(5) M(-1) s(-1) for ferricyanide, and 1.5 x 10(5) M(-1) s(-1) for ferricytochrome. Although the redox partners were created in pairs by the same protein promptly after light excitation, their bimolecular redox reaction was not observed even in the case of the fastest reacting partners of ferricenium and ubiquinol-0. Instead, they equilibrate with the corresponding (donor and acceptor) pools before the electron is transferred. The (logarithms of the) observed rate constants of quinol oxidation showed steep pH-dependence for water soluble ubiquinol-0 (slope +1) and mild pH-dependence for hydrophobic ubiquinol-10 (slope approximately 0.25). Combined with studies of the ionic strength dependence of the rate, it was concluded that the electron-transfer pathways of ubiquinol-0 and ubiquinol-10 oxidation started from their anionic and neutral forms, respectively. The mild pH-dependence of the rate of ubiquinol-10 oxidation came from the electrostatic interactions between ferricenium and the pH-dependent surface charges of the reaction center. The results help to understand, monitor, and design (cyclic) electron flow in bioenergetic proteins.     

Examining the Research on Business Information-Entropy Correlation in the Accounting Process of Organizations

Open business organizations, where information flows, is shared, and exchanged, are more prepared to adapt and survive chaos, uncertainty, and entropy, so they will be more predisposed to change management. The aim of this study is to analyze research trends at the international level on business information–entropy correlation in the accounting process of organizations. Mathematical and statistical techniques were applied to 980 articles during the period 1974–2020, obtaining results on the scientific productivity of the driving agents of this topic: authors, research institutions, countries/territories, and journals. Five lines of research were identified during the period analyzed, which mainly study information theory, maximum entropy, information entropy, decision-making, and enthalpy. Future research should focus on analyzing the evolution of this topic, which forms new thematic axes related to bitcoin market efficiency, business hierarchy information, business model evaluation systems, catastrophic economic collapse, corporate diversification, CSR reports affecting accounting conservatism, economic income accounting, and information loss. Currently, the research presents an upward trend, which allows a growing interest in the subject to be deduced in the academic and scientific community worldwide.