Diabatization of the reactive F + H<Subscript>2</Subscript> system employing rigorous Berry phases

In this article are presented the first ever derived single-valued diabatic potentials for the reactive H₂ +  F system based on a rigorous study of the conical intersection (ci) and Born-Oppenheimer non-adiabatic coupling terms (BO NACTs). This study revealed the existence of a Jahn-Teller (1, 2) ci located at a point on the collinear axis and a Renner-Teller (2, 3) ci along this axis. The diabatic potentials were calculated employing the rigorous adiabatic-to-diabatic transformation (ADT) angles (also known as mixing angles) which possess integer Berry phases along any closed contour at the region of interest in configuration space. The ADT angles were calculated employing BO NACTs and line integrals.     

Axial instability of double-nanobeam-systems

This Letter considers the axial instability of double-nanobeam-systems. Eringen's nonlocal elasticity is utilized for modelling the double-nanobeam-systems. The nonlocal theory accounts for the small-scale effects arising at the nanoscale. The small-scale effects substantially influence the instability (or buckling) of double-nanobeam-systems. Results reveal that the small-scale effects are higher with increasing values of nonlocal parameter for the case of in-phase (synchronous) buckling modes than the out-of-phase (asynchronous) buckling modes. The increase of the stiffness of the coupling elastic medium in double-nanobeam-system reduces the small-scale effects during the out-of-phase (asynchronous) buckling modes. Analysis of the scale effects in higher buckling loads of double-nanobeam-system with synchronous and asynchronous modes is also discussed in this Letter. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the instability analysis of complex-nanobeam-system such as complex carbon nanotube system.     

A Galerkin-type state-space approach for transverse vibrations of slender double-beam systems with viscoelastic inner layer

A novel state-space form for studying transverse vibrations of double-beam systems, made of two outer elastic beams continuously joined by an inner viscoelastic layer, is presented and numerically validated. As opposite to other methods available in the literature, the proposed technique enables one to consider (i) inhomogeneous systems, (ii) any boundary conditions and (iii) rate-dependent constitutive law for the inner layer. The formulation is developed by means of Galerkin-type approximations for the fields of transverse displacements in the system. Numerical examples demonstrate that the proposed approach is accurate and versatile, and lends itself to be used for both frequency- and time-domain analyses.     

Pyrene-containing peptide-based fluorescent organogels: inclusion of graphene into the organogel

The N-terminally pyrene-conjugated oligopeptide, Py-Phe-Phe-Ala-OMe, (Py=pyrene 1-butyryl acyl) forms transparent, stable, supramolecular fluorescent organogels in various organic solvents. One of these organogels was thoroughly studied using various techniques including transmission electron microscopy (TEM), field-emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), Fourier-transform infrared (FTIR) spectroscopy, photoluminescence (PL) spectroscopy, and rheology. Unfunctionalized and non-oxidized graphene was successfully incorporated into this fluorescent organogel in o-dichlorobenzene (ODCB) to form a stable hybrid organogel. Graphene is well dispersed into the gel medium by using non-covalent π-π stacking interactions with the pyrene-conjugated gelator peptide. In the presence of graphene, the minimum gelation concentration (mgc) of the hybrid organogel was lowered significantly. This suggests that there is a favorable interaction between the graphene and the gelator peptide within the hybrid organogel system. This hybrid organogel was characterized using TEM, AFM, FTIR, PL, and rheological studies. The TEM study of graphene-containing hybrid organogel revealed the presence of both graphene sheets and entangled gel nanofibers. The AFM study indicated the presence of 3 to 4 layers in exfoliated graphene in ODCB and the presence of both graphene nanosheets and the network of gel nanofibers in the hybrid gel system. The rheological investigation suggested that the flow of the hybrid organogel had become more resistant towards the applied angular frequency upon the incorporation of graphene into the organogel. The hybrid gel is about seven times more rigid than that of the native gel.     

Comparison of P···D (D = P,N) with other noncovalent bonds in molecular aggregates

All the minima on the potential energy surfaces of homotrimers and tetramers of PH(3) are identified and analyzed as to the source of their stability. The same is done with mixed trimers in which one PH(3) molecule is replaced by either NH(3) or PFH(2). The primary noncovalent attraction in all global minima is the BP···D (D = N,P) bond which is characterized by the transfer of charge from a lone pair of the donor D to a σ? B-P antibond of the partner molecule which is turned away from D, the same force earlier identified in the pertinent dimers. Examination of secondary minima reveals the presence of other weaker forces, some of which do not occur within the dimers. Examples of the latter include PH···P, NH···P, and PH···F H-bonds, and "reverse" H-bonds in which the source of the electron density is the smaller tail lobe of the donor lone pair. The global minima are cyclic structures in all cases, and exhibit some cooperativity, albeit to a small degree. The energy spacing of the oligomers is much smaller than that in the corresponding strongly H-bonded complexes such as the water trimer.     

Structured eigenvalue condition numbers and linearizations for matrix polynomials

This work is concerned with eigenvalue problems for structured matrix polynomials, including complex symmetric, Hermitian, even, odd, palindromic, and anti-palindromic matrix polynomials. Most numerical approaches to solving such eigenvalue problems proceed by linearizing the matrix polynomial into a matrix pencil of larger size. Recently, linearizations have been classified for which the pencil reflects the structure of the original polynomial. A question of practical importance is whether this process of linearization significantly increases the eigenvalue sensitivity with respect to structured perturbations. For all structures under consideration, we show that this cannot happen if the matrix polynomial is well scaled: there is always a structured linearization for which the structured eigenvalue condition number does not differ much. This implies, for example, that a structure-preserving algorithm applied to the linearization fully benefits from a potentially low structured eigenvalue condition number of the original matrix polynomial.     

A new topological degree theory for perturbations of the sum of two maximal monotone operators

Let X be an infinite dimensional real reflexive Banach space with dual space X^∗ and G⊂X, open and bounded. Assume that X and X^∗ are locally uniformly convex. Let T:X⊃D(T)→2^X∗ be maximal monotone and strongly quasibounded, S:X⊃D(S)→X^∗ maximal monotone, and C:X⊃D(C)→X^∗ strongly quasibounded w.r.t. S and such that it satisfies a generalized (S₊)-condition w.r.t. S. Assume that D(S)=L⊂D(T)∩D(C), where L is a dense subspace of X, and 0∈T(0),S(0)=0. A new topological degree theory is introduced for the sum T+S+C, with degree mapping d(T+S+C,G,0). The reason for this development is the creation of a useful tool for the study of a class of time-dependent problems involving three operators. This degree theory is based on a degree theory that was recently developed by Kartsatos and Skrypnik just for the single-valued sum S+C, as above.     

Multiple proton ionizable calixarene derivatives with different ring sizes and complexation ability as efficient ionophores for complexation and solvent extraction of trivalent indium

The solvent extraction behavior of multiple proton ionizable p-tert-butylcalix[4]arene and [6]arene carboxylic acid derivatives towards indium has been investigated along with an acyclic monomeric analogue from weakly acidic media into chloroform. The extraction mechanism is ion exchange and carboxylic acid groups are adequate ligating sites for extraction. The cyclic structure of calixarene ligands to accommodate the potential guest species and the cooperativity effect of multifunctional groups significantly affect the complexation behavior and calixarene derivatives are found to be excellent extractants over the monomeric analogue. The composition of the extracted complex depends on the solution pH and attempts to determine the composition of the extracted complex for the extraction of indium have been stymied by complications arising from the formation of polynuclear species of indium and bridged polymeric species of calixarene carboxylic acid derivatives. One mole of calix[4]arene derivative extracts 2.5 moles of indium whereas the calix[6]arene derivative tends to extract 4.0 moles of indium. The loaded indium is back extracted with 1 mol dm(-3) hydrochloric acid solution. Though quantitative back extraction of indium was achieved from the fully loaded calix[6]arene derivative, it was only achieved up to 85% in the case of the calix[4]arene derivative.     

Synthesis, structures and membrane properties of siloxane-imide co-polymers produced by aqueous polymerization

We report for the first time, the synthesis of siloxane-imide co-polymers by the reaction of mixtures of 1,4-bis(aminobutyl)tetramethyldisiloxane (ABTMDS) and 1,3-bis(4-aminophenoxy)benzene (TPE-R) with bisphenol A diphthalic anhydride (BPADA) using water as the polymerization solvent. A series of co-polymers were prepared incorporating 10, 20, 40 and 100 mol% of ABTMDS with the aromatic diamine TPE-R as the co-monomer. The synthesized co-polymers showed number average molecular weights in the range of 25,000–60,000. As expected the glass transition temperatures (T_gs) and moduli of the polymers were found to decrease with increasing amounts of the siloxane monomer and the homo-polymer containing only the siloxane diamine showing the lowest T_g (60 °C). The resulting polymers could be solution cast into strong and flexible membranes which showed significant decreases in water absorption and moisture permeability compared to the control polymer without siloxane groups. The polymers were characterized by FTIR, ¹³C and ¹H NMR, GPC, DSC and mechanical properties and structural comparisons were made with similar polymers made by standard solvent synthesis methods. Also cross-linked polymers were prepared by the reaction of ABTMDS with the aromatic homo-polymer control and their membrane properties were compared to those of the water synthesized siloxane co-polymers with a similar siloxane content.