Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Polymers with advanced structural and supramolecular features synthesized through topochemical polymerization

Polymers are an integral part of our daily life. Hence, there are constant efforts towards synthesizing novel polymers with unique properties. As the composition and packing of polymer chains influence polymer''s properties, sophisticated control over the molecular and supramolecular structure of the polymer helps tailor its properties as desired. However, such precise control via conventional solution-state synthesis is challenging. Topochemical polymerization (TP), a solvent- and catalyst-free reaction that occurs under the confinement of a crystal lattice, offers profound control over the molecular structure and supramolecular architecture of a polymer and usually results in ordered polymers. In particular, single-crystal-to-single-crystal (SCSC) TP is advantageous as we can correlate the structure and packing of polymer chains with their properties. By designing molecules appended with suitable reactive moieties and utilizing the principles of supramolecular chemistry to align them in a reactive orientation, the synthesis of higher-dimensional polymers and divergent topologies has been achieved via TP. Though there are a few reviews on TP in the literature, an exclusive review showcasing the topochemical synthesis of polymers with advanced structural features is not available. In this perspective, we present selected examples of the topochemical synthesis of organic polymers with sophisticated structures like ladders, tubular polymers, alternating copolymers, polymer blends, and other interesting topologies. We also detail some strategies adopted for obtaining distinct polymers from the same monomer. Finally, we highlight the main challenges and prospects for developing advanced polymers via TP and inspire future directions in this area.

This perspective showcases the potential of topochemical polymerization as an effective tool for synthesizing polymers with advanced molecular and supramolecular structures.     

16‐(4‐Cyanobenzylidene)‐3β‐pyrrolidinoandrost‐5‐en‐17β‐ol monohydrate

In the title compound, C₃₁H₄₀N₂O·H₂O, the outer two six‐membered rings are in chair conformations, while the central ring is in an 8β,9α‐half‐chair conformation. The five‐membered ring adopts a 13β‐envelope conformation and the cyano­benzyl­idene moiety has an E configuration with respect to the hydroxyl group at position 17. The steroid nuclei are linked by intermolecular O—H?O and O—H?N hydrogen bonds to form a molecular network. The molecular packing has an interesting feature, with the steroids aligned parallel to the b axis, forming a closed loop through hydrogen bonds linked via water mol­ecules.     

Rapid identification of trimethyl and triethyl amines using sulphonic acidic ionic liquids: A time-of-flight secondary ion mass spectrometry study of fragmentation reactions

The time-of-flight secondary ion mass spectrometry (TOF-SIMS) has emerged as a powerful tool for the unswerving detection of biomolecules, in particular, proteins and peptides. To date, there is very little information available on the direct determination of trimethyl/triethyl amines using TOF-SIMS. One major hurdle in this regard is an ultrahigh vacuum system, usually needed in TOF-SIMS, which hampers its usability to trimethyl/triethyl amines owing to their high evaporation rate. We designed an efficient and sensitive protocol for rapid identification and sensitive determination of tertiaryalkyl amines using TOF-SIMS. The amines were derivatized by reaction with 1,4-butane sultone and sulphuric acid sequentially to afford the corresponding sulphonic acidic ionic liquids (ILs). The TOF-SIMS analysis of these task-specific ILs (TSILs) was carried out in both positive and negative polarity. The positive ion mass spectra of TSILs showed sharp fragmented peaks for tertiaryalkyl amines at typical level and up to 10 ppm. The possible mechanism for different fragmentation pathways in positive polarity was discussed.     

Common fixed point theorems under a new continuity condition

The aim of the present paper is to generalize the notion of reciprocal continuity and obtain common fixed point theorems in diverse settings as an application of the new notion. The new notion unifies the approaches of three well known notions- reciprocal continuity, subsequential continuity and conditional commutativity. Our results generalize and extend several fixed point theorems. We also demonstrate that the new notion is a necessary condition for the existence of common fixed points.     

A Hydrosilylation Approach to Silicon‐Bridged Functional Dipyrromethanes: Introducing Silicon to A New Arena

Two silylene‐spaced ((E)‐vinylsilyl)anthracene‐dipyrromethane dyads have been designed and synthesized by RhCl(PPh₃)₃‐catalyzed hydrosilylation reactions of 5‐methyl‐5′‐(ethynylaryl)dipyrromethanes with (9‐Anthryl)‐dimethylsilane. The complexation studies of dyads toward different anions have also been performed, which reveal that dyads exhibit a highly selective response towards fluoride anion attributable to both hydrogen‐bonding and pentacoordination phenomena. This dual‐mode fluoride recognition event is unprecedented and may pave the way for future developments in the areas of porphyrinoids, organosilicon, polymer, and supramolecular chemistry.     

REACTIONS OF TELLURIUM TETRAHALIDES WITH GLYCOLS

Abstract

Tellurium tetrahalides undergo reaction with glycols to yield three different products: O,O'-dioxotrihalotellurates; bis(alkoxy)dihalotellurium (IV) compounds and hexahalotellurates. The course of the reaction appears to be determined primarily by the nature of the glycol. The structure of dichlorobis(cis- 2-hydroxycyclohexyloxy)tellurium(IV) has been determined crystallographically     

Synthesis and anion binding of 2-arylazo-meso-octamethylcalix[4]pyrroles

2-Arylazo-5,5,10,10,15,15,20,20-octamethylcalix[4]pyrroles (azo-OMCPs) have been synthesised by the reaction of calix[4]pyrrole with aryldiazonium chloride in 15–45% yields. The solution-state binding studies of the synthesised hosts were investigated by absorption spectroscopy and ¹H NMR in DMSO and CDCl₃, respectively. These receptors, appended with electron-donating and electron-withdrawing groups, displayed enhanced affinity and selectivity for fluoride anion. Well-defined colour change in the visible region of the spectrum was observed upon addition of fluoride ion in DMSO solution of azo-OMCPs. Detailed NMR studies in CDCl₃ revealed that azo-OMCPs with nitro and chloro groups have higher binding affinity for fluoride ion.

     

Room temperature thermoelectric performance of Methyl Ammonium Lead Iodide Perovskite and their MWCNT-PANI composites

The excellent properties of Methyl Ammonium Lead Iodide (MAPI) have already created an extensive research interest in photovoltaic applications. However, their utility in thermoelectric application is still not realized thoroughly by researchers. By continuing this interest, we have explored the formation of low dimensional CH₃NH₃PbI₃ (MAPI) perovskite in presence of Polyaniline (PANI) and Multi-Walled Carbon Nanotubes (MWCNT) and its thermoelectric performance. For this purpose, a two stage, in-situ synthesis method was developed to prepare various composites such as MAPI-PANI, MWCNT-MAPI and MWCNT-PANI-MAPI. The as-formed MWCNT-PANI-MAPI composite revealed p-type conductivity with enhanced ZT (up to ~20,000 times) and power factor (3000 times) at room temperature as compared to pristine MAPI sample. Finally, we have demonstrated a proto-type thermoelectric power generator (TE device) fabricated using the best performing composite sample and measured its power output and efficiency at varied δT.