Simulation of heterogeneous end-coupling reactions in polydisperse polymer blends

The influence of polydispersity on the interfacial kinetics of end-coupling and microstructure formation in the melt of immiscible polymers was studied using dissipative particle dynamics simulations. The irreversible reaction started at a flat interface between two layers, each of which contained polymer chains of two different lengths with functionalized or unreactive end groups. As in the case of fully functionalized monodisperse reactants [A. V. Berezkin and Y. V. Kudryavtsev, Macromolecules 44, 112 (2011)], four kinetic regimes were observed: linear (mean field coupling at the initial interface), saturation (decreasing the reaction rate due to the copolymer brush formation or reactant depletion near the interface), autocatalytic (loss of the initial interface stability and formation of a lamellar microstructure), and terminal (microstructure ripening under diffusion control). The interfacial instability is caused by overcrowding the interface with the reaction product, and it can be kinetically suppressed by increasing chain length of the reactants. Main effects of polydispersity are as follows: (i) the overall end-coupling rate is dominated by the shortest reactive chains; (ii) the copolymer concentration at the interface causing its instability can be not the same as in the lamellas formed afterwards; (iii) mean length of the copolymer product considerably changes with conversion passing through a minimum when a microstructure is just formed.     

Na[Li(NH2BH3)2]--the first mixed-cation amidoborane with unusual crystal structure

We describe the successful synthesis of the first mixed-cation (pseudoternary) amidoborane, Na[Li(NH(2)BH(3))(2)], with theoretical hydrogen capacity of 11.1 wt%. Na[Li(NH(2)BH(3))(2)] crystallizes triclinic (P1) with a = 5.0197(4) ?, b = 7.1203(7) ?, c = 8.9198(9) ?, α = 103.003(6)°, β = 102.200(5)°, γ = 103.575(5)°, and V = 289.98(5) ?(3) (Z = 2), as additionally confirmed by Density Functional Theory calculations. Its crystal structure is topologically different from those of its orthorhombic LiNH(2)BH(3) and NaNH(2)BH(3) constituents, with distinctly different coordination spheres of Li (3 N atoms and 1 hydride anion) and Na (6 hydride anions). Na[Li(NH(2)BH(3))(2)], which may be viewed as a product of a Lewis acid (LiNH(2)BH(3))/Lewis base (NaNH(2)BH(3)) reaction, is an important candidate for a novel lightweight hydrogen storage material. The title material decomposes at low temperature (with onset at 75 °C, 6.0% mass loss up to 110 °C, and an additional 3.0% up to 200 °C) while evolving hydrogen contaminated with ammonia.     

Inequalities for Gondran-Minoux rank and idempotent semirings

The rank-sum, rank-product, and rank-union inequalities for Gondran-Minoux rank of matrices over idempotent semirings are considered. We prove these inequalities for matrices over quasi-selective semirings without zero divisors, which include matrices over the max-plus semiring. Moreover, it is shown that the inequalities provide the linear algebraic characterization for the class of quasi-selective semirings. Namely, it is proven that the inequalities hold for matrices over an idempotent semiring S without zero divisors if and only if S is quasi-selective. For any idempotent semiring which is not quasi-selective it is shown that the rank-sum, rank-product, and rank-union inequalities do not hold in general. Also, we provide an example of a selective semiring with zero divisors such that the rank-sum, rank-product, and rank-union inequalities do not hold in general.     

How linker's modification controls swelling properties of highly flexible iron(III) dicarboxylates MIL-88

A series of organically modified iron(III) terephthalate MIL-88B and iron(III) 4,4'-biphenyl dicarboxylate MIL-88D flexible solids have been synthesized and characterized through a combination of X-ray diffraction, IR spectroscopy, and thermal analysis (MIL stands for Material from Institut Lavoisier). The swelling amplitude of the highly flexible MOFs tuned by introducing functional groups onto the phenyl rings shows a clear dependence on the steric hindrance and on the number of groups per aromatic ring. For instance, while the introduction of four methyl groups per spacer in dried MIL-88B results in a large permanent porosity, introducing two or four methyl groups in MIL-88D allows an easier pore opening in the presence of liquids without drastically decreasing the swelling magnitude. The influence of the degree of saturation of the metal center and the nature of the solvent on the swelling is also discussed. Finally, a computationally assisted structure determination has led to a proposal of plausible structures for the closed (dried) and open forms of modified MIL-88B and MIL-88D and to evaluation of their framework energies subject to the nature of the functional groups.     

Simplified monoharmonic approach to investigation of forced vibrations of thin wall multilayer inelastic elements with piezoactive layers under cyclic loading

A coupled dynamic problem of electromechanics for thin wall multilayer elements is formulated based on the Kirchhoff–Love hypotheses. In the case of harmonic loading, a simplified formulation is given using the monoharmonic approach and the concept of complex moduli to characterize the cyclic properties of the material. The problem of forced vibrations of three-layer beam, whose outer layers are made of a viscoelastic piezoactive material, and, the inner layer of a passive physically nonlinear material, is considered as an example to demonstrate the possibility of the technique elaborated. The possibility of damping the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is studied. Results obtained for the transient response of the beam using the complete model are compared with data found using the simplified model. Limitations on the simplified model application are specified.     

Hilbert-style axiomatization of first-degree entailment and a family of its extensions

This paper presents a Hilbert-style system for the logic of first-degree entailment defined in a Fmla-Fmla framework. The effective use of this formulation as a basis for a whole family of systems extending the logic of first-degree entailment in various directions is shown. By systematizing this family, some new systems are uncovered, and some other well-established logics (such as the first-degree entailment fragment of Priest's Logic of Paradox) obtain new axiomatization. Semantics for the key systems from the family is formulated.     

Tl2Te and its relationship with Tl5Te3

The crystal structure of Tl₂Te, dithallium telluride, has been determined by single‐crystal X‐ray diffraction. The analysis of the structure shows that this compound is the first known representative of a new crystal structure type. The structural relationship with the related Tl₅Te₃ phase is discussed.     

GOSH: derivative-free global optimization using multi-dimensional space-filling curves

Global optimization is a field of mathematical programming dealing with finding global (absolute) minima of multi-dimensional multiextremal functions. Problems of this kind where the objective function is non-differentiable, satisfies the Lipschitz condition with an unknown Lipschitz constant, and is given as a “black-box” are very often encountered in engineering optimization applications. Due to the presence of multiple local minima and the absence of differentiability, traditional optimization techniques using gradients and working with problems having only one minimum cannot be applied in this case. These real-life applied problems are attacked here by employing one of the mostly abstract mathematical objects—space-filling curves. A practical derivative-free deterministic method reducing the dimensionality of the problem by using space-filling curves and working simultaneously with all possible estimates of Lipschitz and Hölder constants is proposed. A smart adaptive balancing of local and global information collected during the search is performed at each iteration. Conditions ensuring convergence of the new method to the global minima are established. Results of numerical experiments on 1000 randomly generated test functions show a clear superiority of the new method w.r.t. the popular method DIRECT and other competitors.     

Generalized Correspondence Analysis for Three-Valued Logics

Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP (which is built in the \( \{\vee ,\wedge ,\lnot \} \)-language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete analogue of LP, strong Kleene logic \( \mathbf K_3 \). In this paper, we generalize these results for the negative fragments of LP and \( \mathbf K_3 \), respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or \( \mathbf K_3 \), but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of \( \mathbf K_3 \) and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic \( \mathbf G_3 \) and its dual \( \mathbf DG_3 \) (which have different interpretations of negation than \( \mathbf K_3 \) and LP).