An Approximate Expression for the Degree of Counterion Binding of Dressed Micelles

A simple formula for calculating the degree of counterion binding of dressed micelles is presented. This approximate expression for the spherical micelle is derived from the extending Langmuir's method in the case of high surface potentials. It works quite well for the estimation of the degree of counterion binding of micelles. The simple form is very convenient for practical use.     

Electrical Properties of Cylindrical Reverse Micelle

In this article, accurate analytic expressions of the surface charge density/surface potential and adsorption excesses for cylindrical reverse micelle in a solution of symmetric electrolyte are derived from the nonlinear cylindrical Poisson–Boltzmann equation. These expressions are in good agreement with numerical values and Van Aken's results for cylindrical reverse micelle with high surface potentials and large κa.     

Novel mesophases in fluorine substituted banana-shaped mesogens

A new homologous series of achiral banana-shaped mesogens ('Dn') has been synthesized and studied by the classical techniques (optical microscopy, differential scanning calorimetry, X-ray diffraction, miscibility studies and electro-optic investigations). The short homologues (D6-D8) exhibit a two-dimensional phase 'B1_x' different from a B1 phase with a rectangular lattice. The longer homologues (D9-D14) present a mesophase which displays the defects of the B7 phase of the PIMB-NO₂ compounds. Nevertheless the D9-D14 mesophase is not miscible with the B7 phase, and contrary to B7, exhibits a bistable behaviour ('ferroelectric' type) suggesting at least a B7 variant.     

Heptametallic,Octupolar Nonlinear Optical Chromophores with Six Ferrocenyl Substituents

New complexes with six ferrocenyl (Fc) groups connected to Zn^II or Cd^II tris(2,2′‐bipyridyl) cores are described. A thorough characterisation of their BPh₄^? salts includes two single‐crystal X‐ray structures, highly unusual for such species with multiple, extended substituents. Intense, visible d(Fe^II)→π* metal‐to‐ligand charge‐transfer (MLCT) bands accompany the π→π* intraligand charge‐transfer absorptions in the near UV region. Each complex shows a single, fully reversible Fe^III/II wave when probed electrochemically. Molecular quadratic nonlinear optical (NLO) responses are determined by using hyper‐Rayleigh scattering and Stark spectroscopy. The latter gives static first hyperpolarisabilities β₀ reaching as high as approximately 10^?27 esu and generally increasing with π‐conjugation extension. Z‐scan cubic NLO measurements reveal high two‐photon absorption cross‐sections σ₂ of up to 5400 GM in one case. DFT calculations reproduce the π‐conjugation dependence of β₀, and TD‐DFT predicts three transitions close in energy contributing to the MLCT bands. The lowest energy transition has octupolar character, whereas the other two are degenerate and dipolar in nature.     

From Nitro‐ to Sulfonyl‐Based Chromophores: Improvement of the Comprehensive Performance of Nonlinear Optical Dendrimers

Through the combination of the divergent and convergent approaches, coupled with the utilization of the powerful Sharpless “click‐chemistry” reaction, two series of sulfonyl‐based high‐generation NLO dendrimers were conveniently prepared with high purity and in satisfactory yields. Thanks to the perfect three‐dimensional (3D) spatial isolation from the highly branched structure and the isolation effect of the exterior benzene moieties and the interior triazole rings, these dendrimers exhibited large second harmonic generation coefficient (d₃₃) values up to 181 pm V^?1, which, to the best of our knowledge, is the highest value so far for polymers containing sulfonyl‐based chromophore moieties. Meanwhile, compared with the nitro‐chromophore‐based analogues, their optical transparency and NLO stability were improved in a large degree, due to the lower dipole moment (μ) and the special main‐chain structure of sulfonyl‐based chromophore in these dendrimers.     

Theoretical Modelling of Photoswitching of Hyperpolarisabilities in Ruthenium Complexes

Static excited‐state polarisabilities and hyperpolarisabilities of three Ru^II ammine complexes are computed at the density functional theory (DFT) and several correlated ab initio levels. Most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals B3LYP, B3P86 or M06 for the complex [Ru^II(NH₃)₅(MeQ⁺)]³⁺ (MeQ⁺=N‐methyl‐4,4′‐bipyridinium, 3 ) in acetonitrile. The match with experimental data is less good for [Ru^II(NH₃)₅L]³⁺ (L=N‐methylpyrazinium, 2 ; N‐methyl‐4‐{E,E‐4‐(4‐pyridyl)buta‐1,3‐dienyl}pyridinium, 4 ). These calculations confirm that the first dipole‐ allowed excited state (FDAES) has metal‐to‐ligand charge‐transfer (MLCT) character. Both the solution and gas‐phase results obtained for 3 by using B3LYP, B3P86 or M06 are very similar to those from restricted active‐space SCF second‐order perturbation theory (RASPT2) with a very large basis set and large active space. However, the time‐dependent DFT λ_max predictions from the long‐range corrected functionals CAM‐B3LYP, LC‐ωPBE and wB97XB and also the fully ab initio resolution of identity approximate coupled‐cluster method (gas‐phase only) are less accurate for all three complexes. The ground state (GS) two‐state approximation first hyperpolarisability β_2SA for 3 from RASPT2 is very close to that derived experimentally via hyper‐Rayleigh scattering, whereas the corresponding DFT‐based values are considerably larger. The β responses calculated by using B3LYP, B3P86 or M06 increase markedly as the π‐conjugation extends on moving along the series 2 → 4 , for both the GS and FDAES species. All three functionals predict substantial FDAES β enhancements for each complex, increasing with the π‐conjugation, up to about sevenfold for 4 . Also, the computed second hyperpolarisabilities γ generally increase in the FDAES, but the results vary between the different functionals.     

A Combined Kinetic and Thermodynamic Approach for the Interpretation of Continuous‐Flow Heterogeneous Catalytic Processes

The heterogeneous proline‐catalyzed aldol reaction was investigated under continuous‐flow conditions by means of a packed‐bed microreactor. Reaction‐progress kinetic analysis (RPKA) was used in combination with nonlinear chromatography for the interpretation, under synthetically relevant conditions, of important mechanistic aspects of the heterogeneous catalytic process at a molecular level. The information gathered by RPKA and nonlinear chromatography proved to be highly complementary and allowed for the assessment of optimal operating variables. In particular, the determination of the rate‐determining step was pivotal for optimizing the feed composition. On the other hand, the competitive product inhibition was responsible for the unexpected decrease in the reaction yield following an apparently obvious variation in the feed composition. The study was facilitated by a suitable 2D instrumental arrangement for simultaneous flow reaction and online flow‐injection analysis.     

Nonlinear Schrödinger equation in a semi-strip: Evolution of the Weyl–Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions

Rectangular matrix solutions of the defocusing nonlinear Schrödinger equation (dNLS) are studied in quarter-plane and semi-strip. Evolution of the corresponding Weyl–Titchmarsh (Weyl) function is described in terms of the initial Weyl function and boundary conditions. In the next step, the initial Weyl function is recovered (for the quarter-plane case) from the long-time asymptotics of the wave function considered at the boundary. Thus, it is shown that the evolution of the Weyl function is uniquely defined by the boundary conditions. Moreover, a procedure to recover solutions of dNLS (uniquely defined by the boundary conditions) is given. In a somewhat different way, the same boundary value problem is also dealt with in a semi-strip (for the case of a quasi-analytic initial condition).     

Existence of pulses in excitable media with nonlocal coupling

We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with finite-range, non-local coupling. Our approach replaces methods from geometric singular perturbation theory, that had been crucial in previous existence proofs, by a PDE oriented approach, relying on exponential weights, Fredholm theory, and commutator estimates.