Synchrotron X-ray Electron Density Analysis of Chemical Bonding in the Graphitic Carbon Nitride Precursor Melamine

Melamine is a precursor and building block for graphitic carbon nitride (g-CN) materials, a group of layered materials showing great promise for catalytic applications. The synthetic pathway to g-CN includes a polycondensation reaction of melamine by evaporation of ammonia. Melamine molecules in the crystal organize into wave-like planes with an interlayer distance of 3.3 Å similar to that of g-CN. Here we present an extensive investigation of the experimental electron density of melamine obtained from modelling of synchrotron radiation X-ray single-crystal diffraction data measured at 25 K with special focus on the molecular geometry and intermolecular interactions. Both intra- and interlayer structures are dominated by hydrogen bonding and π-interactions. Theoretical gas-phase optimizations of the experimental molecular geometry show that bond lengths and angles for atoms in the same chemical environment (C−N bonds in the ring, amine groups) differ significantly more for the experimental geometry than for the gas-phase-optimized geometries, indicating that intermolecular interactions in the crystal affects the molecular geometry. In the experimental crystal geometry, one amine group has significantly more sp³-like character than the others, hinting at a possible formation mechanism of g-CN. Topological analysis and energy frameworks show that the nitrogen atom in this amine group participates in weak intralayer hydrogen bonding. We hypothesize that melamine condenses to g-CN within the layers and that the unique amine group plays a key role in the condensation process.     

Holographic thermalization in a quark confining background

Journal of Experimental and Theoretical Physics - We study holographic thermalization of a strongly coupled theory inspired by two colliding shock waves in a vacuum confining background....     

Spectra of some block operator matrices and application to transport operators

In this paper a new concept for a 3×3 block operator matrix is studied on a Banach space. It is shown that, under certain conditions, it defines a closable operator and its essential spectra are determined. Application to transport operators in L₁-space is given.     

Symmetric family of Fredholm operators of indices zero, stability of essential spectra and application to transport operators

In this paper, we prove that, if the product A=A₁?An is a Fredholm operator where the ascent and descent of A are finite, then Aj is a Fredholm operator of index zero for all j, 1?j?n, where A₁,…,An be a symmetric family of bounded operators. Next, we investigate a useful stability result for the Rako?evi?/Schmoeger essential spectra. Moreover, we show that some components of the Fredholm domains of bounded linear operators on a Banach space remain invariant under additive perturbations belonging to broad classes of operators A such as γ(Am)<1 where γ(⋅) is a measure of noncompactness. We also discuss the impact of these results on the behavior of the Rako?evi?/Schmoeger essential spectra. Further, we apply these latter results to investigate the Rako?evi?/Schmoeger essential spectra for singular neutron transport equations in bounded geometries.     

Essential Spectra of a 3 × 3 Operator Matrix and an Application to Three-Group Transport Equations

In this paper we study spectral properties of a 3 × 3 block operator matrix with unbounded entries and with domain consisting of vectors which satisfy certain relations between their components. It is shown that, under certain conditions, this block operator matrix defines a closed operator, and the essential spectra of this operator are determined. These results are applied to a three-group transport equation.     

Perturbation of unbounded linear operators by $$\gamma $$-relative boundedness

Diagana (Handbook on operator theory. Springer, Basel, pp 875–880, 2015) studied some sufficient conditions such that if S,  T and K are three unbounded linear operators with S being a closed operator, then their algebraic sum \(S+T+K\) is also a closed operator. The main focus of this paper is to extend these results to the closable operator by adding a new concept of the gap and the \(\gamma \)-relative boundedness inspired by the work of Jeribi et al. (Linear Multilinear Algebra 64:1654–1668, 2015). After that, we apply the obtained results to study the specific properties of some block operator matrices.     

Catalysis of black holes/wormholes formation in high energy collisions

The current paradigm suggests that BH/WH formation in particles collisions will happen when a center-mass energy of colliding particles is sufficiently above the Planck scale (the transplanckian region). We confirm the classical geometrical cross section of the BH production reconsidering the process of two transplanckian particles collision in the rest frame of one of incident particles. This consideration permits to use the standard Thorne’s hoop conjecture for a matter compressed into a region to prove a variant of the conjecture dealing with a total amount of compressed energy in the case of colliding particles. We briefly mention that the process of BH formation is catalyzed by the negative cosmological constant and by a particular scalar matter, namely dilaton, while it is relaxed by the positive cosmological constant and at a critical value just turns off.     

A theoretical study on the chirality detection of serine amino acid based on carbon nanotubes with and without Stone-Wales defects

In the present study, the interaction of serine (SER) amino acid (AA) with the pristine and defected carbon nanotubes (CNTs) has been investigated by employing the molecular dynamics (MD) and the density functional theory (DFT) approaches. Furthermore, the potential application of CNTs with and without the Stone-Wales (SW) defects in sensing of SER chirality has been studied. Our results confirm that introducing the chiral l and d SERs (LSER and DSER) exerts a significant effect on the electronic and optical properties of the CNTs with and without the SW defect. According to the MD results, it is observed that for all the structures, the obtained minimum distance is among the SER aliphatic segments and the tube atoms. The calculated structural and electronic properties of pristine and defected CNT are in good agreement with the reported research studies. The results indicate that pyramidalization angles (θ_p) at C atoms are altered in the presence of the SW defects. The overall increment of θ_p suggests that the reactivity has increased at the defective regions. In the case of CNT with one SW defect (CNTSW1), the central C–C bond of the SW defect is the most chemically reactive site. Our results establish that pristine CNT is a semiconductor when the LSER and DSER are adsorbed (with the band gap of 0.30 eV and 0.32 eV, respectively). The LSER-adsorbing CNT with two SW defects (CNTSW2) is a semiconductor with a reduced band gap (0.41 eV), while the DSER-adsorbing CNTSW2 is an n-type semiconductor (with a band gap of 0.70 eV). The optical properties are inferred from the dielectric functions of the CNTs. The most remarkable result belongs to the CNTSW2; the imaginary part of the CNTSW2 dielectric function can sensitively distinguish the chirality of the SER amino acid.

     

On a characterization of the essential spectra of the sum and the product of two operators

In this paper, we consider the sum and the product of two operators acting on a Banach space and we present some new and quite general conditions to investigate their Wolf, Schechter and Browder essential spectra.