Rotational energy | EPFL Graph Search

Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed: E_\text{rotational} = \tfrac{1}{2} I \omega^2 where The mechanical work required for or applied during rotation is the torque times the rotation angle. The instantaneous power of an angularly accelerating body is the torque times the angular velocity. For free-floating (unattached) objects, the axis of rotation is commonly around its center of mass. Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion: E_\text{translational} = \tfrac{1}{2} m v^2 In the rotating system, the moment of inertia, I, takes the role of the mass, m, and the angular velocity, \omega ,

State-to-state surface scattering of methane studied by bolometric infrared laser tagging detection

Bo-Jung Chen

State-to-state molecule/surface scattering experiments prepare the incident molecules in a specific quantum state and measure the quantum state distribution of the scattered molecules. The comparison of state resolved experiments with theory can serve as stringent tests of the molecule/surface interaction potential and of the scattering dynamics. The overall motivation is to develop a predictive understanding of the molecule/surface interactions and reactions needed for the understanding and optimization of heterogeneous catalysis. In this thesis, I describe the design characterization, and first applications of a new apparatus, dedicated to performing state-to-state surfaces scattering using the bolometric infrared laser tagging detection (BILT). An important advantage of the BILT detection method over other state-resolved detection techniques such as resonant multi-photon ionization (REMPI), is its applicability to any molecule with an infrared active vibrational mode and a rotationally resolved vibrational gas phase spectrum. For example, BILT detection can be used to detect important molecules such as methane and carbon dioxide for which REMPI detection is not possible. Our new state-to-state scattering machine features a liquid helium-cooled bolometer detector installed on a rotatable lid allowing independent variation of the incident and the scattering angle. With this capability, one can study energy transfer such as the conversion of translational to rotational or vibrational energy as well as vibrational energy redistribution for molecules colliding with a well-defined single crystal surface at a wide variety of scattering geometry. To demonstrate the capabilities of the BILT machine, I studied the rotationally inelastic scattering of CH4 from Ni(111). The results show that rotational excitation depends not only on the kinetic energy along the surface normal but also on the parallel component although with lower efficiency. The extent of rotational excitation is found to increase with increasing surface temperature. The conversion efficiency appears to be higher for low velocity component normal to the surface. The observations indicate a mechanism of rotational excitation by phonon annihilation with the probability related to the relative velocity of the incoming molecules and surface atoms. Using the experimentally determined formula which takes into account the conversion efficiency of the normal, the parallel component of incident kinetic energy, and the surface thermal energy to the rotational energy, the mechanism of rotational excitation of CH4 scattering from Ni(111) is quantitatively unraveled. Besides rotational inelastic scattering, I report very distinct behavior of vibrationally inelastic scattering of CH4 from clean Ni(111) and Gr-Ni(111). Vibrational energy transfer to the surface dramatically changes when a clean Ni(111) surface is covered with a single layer of graphene. Theoretical calculations based upon reaction path Hamiltonian suggest that the probability of the vibrational energy transfer is related to the catalytic activity of the surface impact sites. Therefore, by monitoring the fate of the initially prepared vibrational energy, the state-to-state surface scattering technique can potentially serve as a probe of the catalytic activity of surfaces.

EPFL2022

Bond-selective and surface-site-specific dissociation of methane on platinum

Ana Gutiérrez González

I present a molecular beam study of methane dissociation on differ-ent surface sites of several platinum single crystal surfaces (Pt(111), Pt(211), Pt(210), Pt(110)-(2x1)). The experiments were performed in a molecular beam/surface-science apparatus that combines rovibrational state-selective excitation of reactants with detection of the reaction products by reflection absorption infrared spectroscopy (RAIRS), Auger electron spectroscopy (AES) and King and Wells (K&W) technique. First, I explore how the barrier for methane dissociation depends on the Pt surface site (terrace, step, kink, and ridge atoms). For that, I compare the average reaction probabilities of methane on the different crystals using K&W. Moreover, I used the site-specific detection of chemisorbed methyl species by RAIRS to obtain the site-specific reactivity on steps, ridges and terraces. The highest methane reactivity and therefore the lowest barrier was observed for the surface atoms with the lowest coordination. The trans-lational energy dependence of the reactivity shows clear evidence for a direct activated mechanism on all the surface sites studied. The decreasing catalyt-ic activity for Pt atoms with increasing coordination number agrees well with theoretical predictions using first principles quantum theory calculations. Second, I present the role of rovibrational excitation of the incident methane on the chemisorption on different surface sites. For CH4, excitation of one quantum of the antisymmetric C-H stretch vibration (Îœ3) was found to be less efficient than an equivalent amount of translational energy normal to the sur-face for promoting the dissociation on all the surface sites. The vibrational efficacy was seen to be lower for dissociation on the low coordinated sites, in accordance with calculations of transition state geometries. For CH3D, the excitation of the antisymmetric C-H stretch vibration (Îœ4) led to bond selec-tivity on the steps and terraces of the Pt(211) surface. These results show how careful control of the translational energy and rovibrational state of the incident CH3D can be used for site-specific and bond-selective dissociation of methane. As predicted previously by theory but not observed before experi-mentally, the C-H bond selectivity is shown to decrease with increasing translational energy. Third, I explore the effect of surface temperature on the methane dissocia-tion. The sticking coefficient for a direct chemisorption reaction such as CH4 on Pt, might be expected to be independent of surface temperature, because the reaction happens very fast leaving very little time for the molecule to equilibrate with the surface. However, I observed an increase in methane reactivity with increasing surface temperature at low incident CH4 energies. This observation is interpreted by a âloss of coordinationâ from the atoms displaced out of the plane due to their vibrational motion when the surface is heated. The surface-site and quantum-state-specific data presented in this thesis are ideally suitable for testing theoretical models that aim to describe the me-thane-surface reaction at the microscopic level. Moreover, the characteriza-tion of different catalytically active sites for methane dissociation contrib-utes to advancing the understanding of methane reactivity towards real cata-lytic conditions, where surfaces with several different atomic terminations are used.

EPFL2019

The inviscid, compressible and rotational, 2D isotropic Burgers and pressureless Euler-Coriolis fluids: Solvable models with illustrations

Philippe Choquard

The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics (Wu et al., 2006, pp. 3, 6) is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler Coriolis fluids respectively modeled by single vortices confined in compressible, local, inertial and global, rotating, environments. The field equations are established, inductively, starting from the equations of the characteristics solved with an initial Helmholtz decomposition of the velocity fields namely a vorticity free and a divergence free part (Wu et al., 2006, Sects. 2.3.2, 2.3.3) and, deductively, by means of a canonical Hamiltonian Clebsch like formalism (Clebsch, 1857, 1859), implying two pairs of conjugate variables. Two vector valued fields are constants of the motion: the velocity field in the Burgers case and the momentum field per unit mass in the Euler Coriolis one. Taking advantage of this property, a class of solutions for the mass densities of the fluids is given by the Jacobian of their sum with respect to the actual coordinates. Implementation of the isotropy hypothesis entails a radial dependence of the velocity potentials and of the stream functions associated to the compressible and to the rotational part of the fluids and results in the cancellation of the dilatation-rotational cross terms in the Jacobian. A simple expression is obtained for all the radially symmetric Jacobians occurring in the theory. Representative examples of regular and singular solutions are shown and the competition between dilatation and vorticity is illustrated. Inspired by thermodynamical, mean field theoretical analogies, a genuine variational formula is proposed which yields unique measure solutions for the radially symmetric fluid densities investigated. We stress that this variational formula, unlike the Hopf-Lax formula, enables us to treat systems which are both compressible and rotational. Moreover in the one-dimensional case, we show for an interesting application that both variational formulas are equivalent. (C) 2014 Elsevier B.V. All rights reserved.

Elsevier Science Bv2014