Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Structure and physical properties of [µ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘')iron(II)] Bis(hexafluorophosphate), a new Fe(II) spin-crossover compound with a three-dimensional threefold interlocked crystal lattice

[μ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘)iron(II)] bis(hexafluorophosphate), [Fe(btzb)3](PF6)2, crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T1/2 = 174 K and a hysteresis of about 4 K between T1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, 57Fe-Mössbauer spectroscopy, and variable temperature far and midrange FTIR spectroscopy. The title compound crystallizes in the trigonal space group P30¯(No. 147) with a unit cell content of one formula unit plus a small amount of disordered solvent. The lattice parameters were determined by X-ray diffraction at several temperatures between 100 and 300 K. Complete crystal structures were resolved for 9 of these temperatures between 100 (only low spin, LS) and 300 K (only high spin, HS), Z = 1 [Fe(btzb)3](PF  6)2:  300 K (HS), a = 11.258(6) Å, c = 8.948(6) Å, V = 982.2(10) Å3; 100 K (LS), a = 10.989(3) Å, c = 8.702(2) Å, V = 910.1(4) Å3. The molecular structure consists of octahedral coordinated iron(II) centers bridged by six N4,N4‘ coordinating bis(tetrazole) ligands to form three 3-dimensional networks. Each of these three networks is symmetry related and interpenetrates each other within a unit cell to form the interlocked structure. The Fe−N bond lengths change between 1.993(1) Å at 100 K in the LS state and 2.193(2) Å at 300 K in the HS state. The nearest Fe separation is along the c-axis and identical with the lattice parameter c.

Amine-functionalised hexagonal mesoporous silica as support for copper(II) acetylacetonate catalyst

Copper(II) acetylacetonate was anchored onto a hexagonal mesoporous silica (HMS) material using a two-step procedure: (i) functionalisation of the surface hydroxy groups with (3-aminopropyl)triethoxysilane (AMPTSi) and then (ii) anchoring of the copper(II) complex through Schiff condensation with free amine groups, using two different metal complex loadings. Upon the first step, nitrogen elemental analysis, XPS and DRIFT showed the presence of amine groups on the surface of the HMS material, and porosimetry indicated that the structure of the mesoporous material remained unchanged, although a slight decrease in surface area was observed. Atomic absorption, XPS and DRIFT showed that copper(II) acetylacetonate was anchored onto the amine-functionalised HMS by Schiff condensation between the free amine groups and the carbonyl groups of the copper(II) complex; using EPR an NO3 coordination sphere was proposed for the anchored copper(II) complex. The new [Cu(acac)2]-AMPTSi/HMS materials were tested in the aziridination of styrene at room temperature, using PhI=NTs as nitrogen source and acetonitrile as solvent. The styrene conversion and total TON of the heterogeneous phase reaction are higher than those of the same reaction catalysed in homogeneous phase by [Cu(acac)2]; nevertheless, the initial activity decreases and the reaction time increases due to substrate and product diffusion limitations. The heterogeneous catalyst showed a successive slight decrease in catalytic activity when reused for two more times. © Wiley-VCH Verlag GmbH & Co. KGaA, 2006.

Covalent attachment of chiral manganese(III) salen complexes onto functionalised hexagonal mesoporous silica and application to the asymmetric epoxidation of alkenes

Two modified Jacobsen-type catalysts were anchored onto an amine functionalised hexagonal mesoporous silica (HMS) using two distinct anchoring procedures: (i) one was anchored directly through the carboxylic acid functionalised diimine bridge fragment of the complex (CAT1) and (ii) the other through the hydroxyl group on the aldehyde fragment of the complex (CAT2), mediated by cyanuric chloride. The new heterogeneous catalyst, as well as the precedent materials, were characterised by elemental analyses, DRIFT, UV-vis, porosimetry and XPS which showed that the complexes were successfully anchored onto the hexagonal mesoporous silica. These materials acted as active heterogeneous catalysts in the epoxidation of styrene, using m-CPBA as oxidant, and α-methylstyrene, using NaOCl as oxidant. Under the latter conditions they acted also as enantioselective heterogeneous catalysts. Furthermore, when compared to the reaction run in homogeneous phase under similar experimental conditions, an increase in asymmetric induction was observed for the heterogenised CAT1, while the opposite effect was observed for the heterogenised CAT2, despite of CAT2 being more enantioselective than CAT1 in homogeneous phase. These results indicate that the covalent attachment of the Jacobsen catalyst through the diimine bridge leads to improved enantiomeric excess (%ee), whereas covalent attachment through one of the aldehyde fragments results in a negative effect in the %ee. Using α-methylstyrene and NaOCl as oxidant, heterogeneous catalyst reuse led to no significant loss of catalytic activity and enantioselectivity. © 2005 Elsevier Inc. All rights reserved.

Asymmetric epoxidation of alkenes by a chiral manganese(III) salen complex anchored onto a functionalised hexagonal mesoporous silica

A Jacobsen-type catalyst was anchored onto an amine functionalised hexagonal mesoporous silica (HMS) through the diimine bridge fragment of the complex. The new heterogeneous catalyst, as well as the precedent materials, were characterised by elemental analyses, FTIR-DRIFT, UV-vis, porosimetry and XPS which showed that the complex was successfully anchored. This material was active in the epoxidation of styrene and α-methylstyrene in dichloromethane at 0°C using, respectively, m-CPBA/NMO and NaOCl. With the former substrate no asymmetric induction was found in the epoxide, whereas with the latter substrate higher %ee was found than in homogeneous phase. Using the latter experimental conditions, catalyst reuse led to no significant loss of catalytic activity and enantioselectivity. © 2005 Elsevier B.V. All rights reserved.

Lattice approach to the dynamics of the DPSK-encoded soliton trains

We study the dynamical properties of the RZ-DPSK encoded sequences, focusing on the instabilities in the soliton train leading to the distortions of the information transmitted. The problem is reformulated within the framework of complex Toda chain model which allows one to carry out the simplified description of the optical soliton dynamics. We elucidate how the bit composition of the pattern affects the initial (linear) stage of the train dynamics and explain the general mechanisms of the appearance of unstable collective soliton modes. Then we discuss the nonlinear regime using asymptotic properties of the pulse stream at large propagation distances and analyze the dynamical behavior of the train classifying different scenarios for the pattern instabilities. Both approaches are based on the machinery of Hermitian and non-Hermitian lattice analysis. © 2010 IEEE.