Cosmological evolution of general scalar fields in a brane-world cosmology

We study the cosmology of a general scalar field and barotropic fluid during the early stage of a brane-world where the Friedmann constraint is dominated by the square of the energy density. Assuming both the scalar field and fluid are confined to the brane, we find a range of behaviour depending on the form of the potential. Generalising an approach developed for a standard Friedmann cosmology, in \cite{delaMacorra:1999ff}, we show that the potential dependence $V(\phi)$ can be described through a parameter $\lambda \equiv -\sqrt{2} m_5^{3/2} V'/(\sqrt{H}V)$, where $m_5$ is the 5-dimensional Planck mass, $H$ is the Hubble parameter and $V' \equiv \frac{dV}{d\phi}$. For the case where $\lambda$ asymptotes to zero, we show that the solution exhibits stable inflationary behaviour. On the other hand if it approaches a finite constant, then $V(\phi) \propto \frac{1}{\phi^2}$. For $\lambda \to \infty$ asymptotically, we find examples where it does so both with and without oscillating. In the latter case, the barotropic fluid dominates the scalar filed asymptotically. Finally we point out an interesting duality which leads to identical evolution equations in the high energy $\rho^2$ dominated regime and the low energy $\rho$ dominated regime.Comment: 10 pages, 3 figure

Attractive fluorine···fluorine interactions between perfluorinated alkyl chains: A case of perfluorinated Cu(II) diiminate Cu[C2F5-C(NH)-CF=C(NH)-CF3]2

A synthesis of the perfluorinated copper diiminate complex Cu[C2F5-C(NH)-CF=C(NH)-CF3]2 (3) and its self-assembly into infinite 1D chains in the crystal via Type II C(sp3)-F···F-C(sp3) contacts between perfluoroethyl substituents is reported. Rare Type II F···F interactions were studied by DFT calculations and topological analysis of the electron density distribution within the formalism of Bader's theory (QTAIM method). This is the first report which discusses Type II contacts between perfuoroalkyl chains. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021

Attractive fluorine···fluorine interactions between perfluorinated alkyl chains: A case of perfluorinated Cu(II) diiminate Cu[C₂F₅-C(NH)-CF=C(NH)-CF₃]₂

A synthesis of the perfluorinated copper diiminate complex Cu[C2F5-C(NH)-CF=C(NH)-CF3]2 (3) and its self-assembly into infinite 1D chains in the crystal via Type II C(sp3)-F···F-C(sp3) contacts between perfluoroethyl substituents is reported. Rare Type II F···F interactions were studied by DFT calculations and topological analysis of the electron density distribution within the formalism of Bader's theory (QTAIM method). This is the first report which discusses Type II contacts between perfuoroalkyl chains

Эффективность использования гетерополисоединений типа (NH4)2[Co(H2O)4]2[Mo8O27]∙6H2O в качестве катализаторов для получения этилена

Carrying out heterogeneous acid catalysis with the use of heteropoly compounds has received considerable attention due to the great economic and environmental benefits. In spite of this, its industrial application is limited as there are difficulties in catalyst regeneration (settling) caused by its relatively low thermal stability. The aim of present work was to search and select catalysts related to the class of heteropoly compounds for propane cracking, to test the selectivity of the prosses as well as to discuss possible approaches for solving the problem of catalyst deactivation, that can contribute to achieve stable characteristics of solid heteropoly catalysts. Among these approaches are: the development of new catalysts with high thermal stability, the modification of catalysts to promote coke combustion, the inhibition of coke formation on heteropoly compound catalysts during the process, carrying out the reactions in supercritical media and also the cascade reactions using a multifunctional heteropoly catalyst. The obtained catalyst was also studied by physicochemical methods to get deep knowledge about which features of these compounds influence on the catalytic activity. A highly active and selective catalyst for ammonium octomolybdenocobaltate(II) ammonium (NH4)2[Co(H2O)4]2[Mo8O27]∙6H2O was synthesized for cracking associated petroleum gases. The qualitative, quantitative, and structural composition as well as the specific surface area of the obtained catalyst was established by the methods of X-ray diffraction, X-ray phase and fluorescence analysis. It was revealed that ammonium octomolybdenocobaltate(II) crystallizes in a triclinic syngony with cell parameters: а = 8.6292(9) Å b = 9.4795(10) Å c = 12.2071(13) Å α = 104.326(2)° β = 109.910(2)° γ = 100.820(2)°.Гетерогенный кислотный катализ с помощью гетерополисоединений обладает большой экономической выгодой и экологическими преимуществами. Его применение, однако, было ограничено в некоторой степени из-за относительно низкой термостабильности гетерополисоединений, следовательно, из-за сложности регенерации катализатора (отстаивания). Целью данной работы является поиск и подбор катализаторов из класса гетерополисоединений для крекинга пропана, обсуждение подходов к проблеме дезактивации катализатора, которые могут способствовать достижению устойчивых характеристик твердых катализаторов гетерополисоединений, а так же проверка на селективность в крекинге пропана. Эти подходы включают в себя: разработку новых катализаторов, обладающих высокой термической стабильностью, модификацию катализаторов для улучшения сгорания кокса, ингибирование образования кокса на катализаторах гетерополисоединений во время работы, реакции в сверхкритических средах и каскадные реакции с использованием многофункционального катализатора из гетоерополисоединений. Полученный катализатор так же был исследован физико-химическими методами для более полного понимания какие именно особенности данного класса соединений влияют на каталитическую активность. Был синтезирован высокоактивный и селективный катализатор октомолибденокобальтат(II) аммония (NH4)2[Co(H2O)4]2[Mo8O27]∙6H2O для крекинга попутных нефтяных газов. Установлен качественный, количественный и структурный состав полученного катализатора методами рентгено-структурного, рентгенофазового, рентгенофлюорисцентного анализа, определенна удельная поверхность катализатора, а так же выявлена высокая каталитическая активность. Октомолибденокобальтат(II) аммония кристаллизуется в триклинной сингонии с параметрами ячейки: а = 8.6292(9) Å b = 9.4795(10) Å c = 12.2071(13) Å α = 104.326(2)° β = 109.910(2)° γ = 100.820(2)°