Rh(III)-Catalyzed One-Step Synthesis of ortho-Alkynylated Perylene Imide Dyes: Optical and Electrochemical Properties of New Derivatives

A one-step Rh-catalyzed site-selective ortho-C−H alkynylation of perylene as well as naphthalene mono- and diimides is reported. A single step regioselective access to ortho-C−H alkynylated derivatives of these ryleneimides not only increases the step economy of the ortho-functionalization on these dyes but also provides a quick access route towards highly functionalized dyes that have potential optoelectronic applications. Increased solubility of tetra(triisopropylsilyl)acetylenyl PDIs in organic solvents greatly enhances their utility for further derivatization.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Can a Procedure for the Growth of Single-layer Graphene on Copper be used in Different Chemical Vapor Deposition Reactors?

In the last decade, catalytic chemical vapor deposition (CVD) has been intensively explored for the growth of single-layer graphene (SLG). Despite the scattering of guidelines and procedures, variables such as the surface texture/chemistry of catalyst metal foils, carbon feedstock, and growth process parameters have been well-scrutinized. Still, questions remain on how best to standardize the growth procedure. The possible correlation of procedures between different CVD setups is an example. Here, two thermal CVD reactors were explored to grow graphene on Cu foil. The design of these setups was entirely distinct, one being a “showerhead” cold-wall type, whereas the other represented the popular “tubular” hot-wall type. Upon standardizing the Cu foil surface, it was possible to develop a procedure for cm²-scale SLG growth that differed only by the carrier gas flow rate used in the two reactors.     

13C NMR investigations of molecular order of rod-like,bent-core,and thiophene mesogens

In this review, methods to obtain the orientational order of topologically variant molecular mesogens using by one- and two-dimensional (2D) solid-state ¹³C nuclear magnetic resonance (NMR) spectroscopy are described. Besides ¹³C chemical shifts, the ¹³C─¹H dipolar couplings measured from 2D-separated local field (SLF) technique are used for computing the order parameters of a variety of mesogens. The investigated molecules are composed of a variable number of rings in the core, that is, core ranging from simply one ring to five rings. Among the mesogens investigated, a special focus has been placed on mesogens with thiophene rings, which are gaining popularity as liquid crystalline organic semiconductors. The replacement of a phenyl ring by thiophene in the core has a dramatic influence on molecular topology, as observed from the measured order parameters. The review highlights the advantages of the 2D SLF method for understanding the local dynamics and for mapping the topology of mesogens through the measured order parameters. SLF NMR studies of as many as 24 molecular mesogens that vary in terms of the molecular structure as well as topology are covered in the review. Order parameters of the rings have been estimated from the ¹³C─¹H dipolar couplings in the nematic, smectic A, smectic C, and tilted hexatic phases as well as in B₁ and B₂ mesophases of various mesogens. It is anticipated that, in the years to come, the 2D SLF method would provide advanced molecular information on structurally complex mesogens that are emerging in liquid crystal science through the incessant efforts of synthetic chemists. The mini review covers the orientational order of topologically variant molecular mesogens determined by 1D and 2D solid-state ¹³C NMR spectroscopy. Accordingly, rod-like, bent-core, and thiophene mesogens were subjected to 2D SLF measurements to get the order parameters from which the topology was established. The replacement of phenyl ring by thiophene and its influence on order parameters as well as on molecular topology is also discussed.