Hamiltonian Formulation of FRW Equations of Cosmology

We give a general Hamiltonian formulation of the Friedmann-Robertson-Walker (FRW) fundamental equations of a homogeneous and isotropic universe in the Standard Cosmological model. It gives some interesting insight on the 3-curvature of the universe, which is found to be obtained in terms of the scale factor (also termed radius of the universe) and its first derivative. It also leads to an easy determination of the Schrödinger equation for the (R) wave function of the universe, in the radiative era.     

Impact of potassium on the heats of adsorption of adsorbed CO species on supported Pt particles by using the AEIR method

The heats of adsorption at several coverages of the linear and bridged CO species (denoted L and B, respectively) adsorbed on the Pt⁰ sites of the 2.9 wt% Pt/10% K/Al₂O₃ catalyst are determined using the Adsorption Equilibrium Infrared spectroscopy method. The addition of K on 2.9% Pt/Al₂O₃ modifies significantly the adsorption of CO on the Pt particles: (a) the ratio L/B is decreased from 8.4 to 1, (b) a new adsorbed CO species is detected with an IR band at 1763 cm⁻¹, (c) the heats of adsorption of L and B CO species are significantly altered and the positions of their IR bands are shifted. The heats of adsorption of L CO species are decreased: i.e. 206 and 105 kJ/mol at low coverages on Pt/Al₂O₃ and Pt/K/Al₂O₃ respectively. Two B CO species denoted B1 and B2, with different heats of adsorption are observed on Pt/K/Al₂O₃. The heats of adsorption of B2 CO species (major B CO species) are significantly larger than those measured in the absence of K: i.e. 94 and 160 kJ/mol at low coverages on Pt/Al₂O₃ and Pt/K/Al₂O₃ respectively, whereas those of B1 CO species (minor species) are similar: 90 kJ/mol at low coverages. These values are consistent with the qualitative High Resolution Electron Energy Loss Spectrometry literature data on Pt(1 1 1) modified by potassium.     

A study on densities of sets of points and lines

In this paper, firstly, our purpose is to give the relationship among the densities of the sets of collinear points, the relationship among the densities of the sets of noncollinear points, and the relationship among the densities of the sets of the intersecting lines in Euclidean plane, respectively. In addition to that, we define the density formulas for the sets of points and lines under the two‐parameter planar Euclidean motion. By means of these results, we obtain essential properties that explain the connection among the densities of the sets of points and among the densities of the sets of intersecting lines under the two‐parameter planar Euclidean motion.     

‘All‐supramolecular’ Nanocapsules from Low‐Molecular Weight Ureas Through Interfacial Addition Reaction in Miniemulsion

This contribution presents a new strategy for preparing nanocapsules with a shell made of a supramolecular polymer which repeating units are held together by reversible interactions rather than covalent bonds. These nanocapsules were prepared in classical miniemulsion through interfacial addition reaction of a diisocyanate (IPDI) and a monoamine (iBA), forming low‐molecular weight bis‐ureas moieties which are strong self‐complementary interacting molecules through hydrogen‐bonding. The nanocapsules present a diameter around 100 nm, and MALDI‐TOF MS and ¹H NMR analyses confirm the expected molecular characteristics for the shell. This strategy opens the scope of a new type of nanomaterials exhibiting stimuli‐responsiveness due to the reversible interaction linking the repeating units.

     

Heats of adsorption using temperature programmed adsorption equilibrium: application to the adsorption of CO on Cu/A12O3 and H2 on Pt/Al2O3

A new simple analytical procedure is described that allows the determination of the heats of adsorption (denoted E(theta)) of adsorbed species at several coverages (theta's) using a single experiment. This procedure is an extension of an original method previously developed (denoted AEIR: adsorption equilibrium infrared spectroscopy). A mass spectrometer is used to determine the amounts of gas (in the present study, CO and H2) either desorbed from or adsorbed on a metal supported catalyst (4.7% Cu/Al2O3 and 2.9% Pt/Al2O3) during the perturbation of the adsorption equilibrium due to a controlled change of the adsorption temperature (Ta) at a quasi-constant adsorption pressure (Pa). These amounts allow us to follow the evolution of the adsorption equilibrium coverage (theta(e)) with Ta at the quasi-constant partial pressure (Pa). Then, the curve theta(e) = f(Ta) provides Etheta = f(theta) with the support of an adsorption model. This procedure presents several advantages as compared to the TPD methods, in particular, considering the theoretical supports linked to the exploitation of the experimental data. As compared to AEIR, the TPAE procedure allows one to study the heats of adsorption of adsorbed species that are not detectable by IR. However, it is not adapted if surface reactions occur in parallel to adsorption/desorption processes.     

Three‐dimensional framework structures: isomorphous bis(2,6‐diamino‐3,5‐dibromopyridinium) tetrabromidometallate(II) salts with CdII and MnII

In the structural motifs of two isomorphous triclinic salts, (C₅H₆Br₂N₃)₂[MBr₄] (M = Cd^II and Mn^II), each [MBr₄]²⁻ anion interacts with eight surrounding 2,6‐diamino‐3,5‐dibromopyridinium cations through intermolecular C/N—H...Br and Br...Br interactions, leading to a three‐dimensional framework structure. The cations show a minor degree of π–π stacking, adding extra stability to the three‐dimensional architecture.     

Three isomorphous 2,6‐dibromopyridinium tetrabromidometallates: (C5H4Br2N)2[MBr4]·2H2O (M = Cu,Cd and Hg)

The structures of three isomorphous compounds, namely bis(2,6‐dibromopyridinium) tetrabromidocuprate(II) dihydrate, (C₅H₄Br₂N)₂[CuBr₄]·2H₂O, bis(2,6‐dibromopyridinium) tetrabromidocadmate(II) dihydrate, (C₅H₄Br₂N)₂[CdBr₄]·2H₂O, and bis(2,6‐dibromopyridinium) tetrabromidomercurate(II) dihydrate, (C₅H₄Br₂N)₂[HgBr₄]·2H₂O, show a crystal supramolecularity represented by M—Br...H—O—H...Br—M intermolecular interactions along with (π)N—H...OH₂ hydrogen‐bonding interactions forming layers connected via aryl–aryl face‐to‐face stacking of cations, leading to a three‐dimensional network. The anions have significantly distorted tetrahedral geometry and crystallographic C₂ symmetry. The stability of this crystal lattice is evidenced by the crystallization of a whole series of isomorphous compounds.     

New cytotoxic isoprenoid derivatives from the Red Sea soft coral Sarcophyton glaucum

Chemical investigation of the soft coral Sarcophyton glaucum collected from the Red Sea led to isolation of 11 isoprenoidal metabolites (1–11). A new sesquiterpenoid, 6-oxo-germacra-4(15),8,11-triene (1), a new natural cembranoid, sarcophinediol, along with two known sesquiterpenoids (2 and 3) and seven known cembranoids (5–11) was obtained. The structures of the compounds were established based on their NMR, MS, IR and UV spectral data. All compounds were evaluated for their cytotoxicity employing three cancer cell lines (HepG2, MCF-7 and HCT116). Compounds 4 and 6 showed significant cytotoxicity towards HepG2 with IC₅₀ values of 18.8 ± 0.07 and 19.9 ± 0.02 μM; respectively. Compounds 5–7 exhibited potent cytotoxicity against MCF-7 cells with IC₅₀ values of 9.9 ± 0.03, 2.4 ± 0.04 and 3.2 ± 0.02 μM, respectively. Compounds 1, 4 and 5 showed significant activities towards HCT116 cells with IC₅₀ values of 29.4 ± 0.03, 19.4 ± 0.02 and 25.8 ± 0.03 μM, respectively.