Surface area | EPFL Graph Search

The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration. A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski cont

Chemical and electrochemical promotion of supported rhodium catalyst

Olena Baranova

The chemical and electrochemical promotion of highly dispersed nanofilm Rh catalysts (dispersion: about 10 %, film thickness: 40 nm) has been investigated for the first time. To this end Rh metal was sputter-deposited, either on a purely ionic conductor (8 % Y2O3-stabilized ZrO2) or on a mixed ionic-electronic conductor (TiO2), the latter being a highly dispersed layer of TiO2 (4 µm) deposited on YSZ. These catalysts are designated as Rh/YSZ and Rh/TiO2/YSZ, respectively. It was established analytically that both in the Rh/YSZ and in the Rh/TiO2/YSZ system, the catalyst films have a nanoparticle-size grain structure. The Rh supported on titania is rather porous, exhibiting a higher dispersion and surface area than Rh on YSZ. Both after reduction (H2, T=400 °C) and after oxidation (O2, T=400 °C), Rh supported on TiO2 was found to be in a more highly reduced state than Rh on YSZ. After reducing treatment, the Rh/TiO2/YSZ samples contain a larger amount of weakly bonded oxygen, which can be attributed to oxygen "backspillover" from the TiO2. A major feature of this research was the electrochemical characterization of the oxygen/Rh/solid electrolyte three-phase boundary by steady-state polarization measurements and by impedance spectroscopy. These are powerful techniques for extracting experimental trends and details that are useful for an understanding of the electrochemical promotion principles. It was shown that the exchange current densities at the Rh/solid electrolyte interface are lower on account of the TiO2 layer. The exchange current densities are more than twice lower at Rh/TiO2(4 µm)/YSZ than at Rh/YSZ, demonstrating that the former interface is much more polarizable. The mechanism of oxygen exchange occurring close to equilibrium (O2/O2- couple) was investigated for the first time at Rh catalyst electrodes interfaced with solid electrolyte. The processes of cathodic oxygen reduction and anodic oxygen evolution are not symmetric, but they are similar in the two systems, Rh/YSZ and Rh/TiO2(4 µm)/YSZ. The cathodic process consists of three steps: dissociative adsorption of oxygen at the gas-exposed Rh surface, atomic oxygen diffusion to the electrochemical reaction sites (ERS), and a two-electron transfer to this oxygen on the ERS. The cathodic process is limited by interfacial diffusion of oxygen atoms from the gas-exposed metal surface to the ERS. The anodic process includes two steps: two-electron transfer reaction, which is the rate-determining step, and oxygen desorption to the gas phase. With data obtained from impedance spectroscopy at the equilibrium potential, it was possible to confirm the reaction scheme proposed. It was demonstrated that Rh nanofilm catalysts interfaced with YSZ or TiO2/YSZ can be electrochemically promoted for the reaction of ethylene oxidation. Small anodic currents cause periodic oscillations in catalytic rate and potential of the Rh/YSZ catalyst, while at Rh/TiO2/YSZ they give rise to a stable and reversible rate enhancement by up to a factor 80. The increase in ethylene oxidation rate is up to 2000 times larger than the electrochemical rate, I/2F, of O2- oxidation. The pronounced electrochemical promotion behavior that has been observed is due to the anodically controlled migration of O2- species from the electrolyte to the Rh/gas interface. At the Rh surface, these species destabilize the formation of rhodium surface oxide (Rh2O3). The existence of backspillover oxygen species has been confirmed by impedance measurements under positive applied potential. Another significant result for heterogeneous catalysis is the finding that thick as well as thin films of Rh/TiO2/YSZ catalyst are open to chemical promotion of ethylene oxidation and partial methane oxidation, ie, they offer a higher catalytic activity and stability than the Rh/YSZ catalysts. The modification of catalytic activity observed for Rh/TiO2/YSZ was attributed to either a "long-range" electronic-type SMSI mechanism or to a self-driven electrochemical promotion mechanism. In both cases, the ultimate cause of promotion are different work functions of catalyst and support. Equilibration of the work functions of two solids in contact induces surface charging, a migration of O2- ions to the catalyst/gas interface, and a weakening of the Rh-O chemisorptive bonds. It facilitates reduction of oxidized surface sites. Another important achievement of the present work was that of exploring and confirming the possibilities of current-assisted activation of Rh/TiO2/YSZ catalysts. In partial methane oxidation using close to stoichiometric gas compositions (CH4 : O2 = 2 : 1) at 550 °C, the inactive (oxidized) Rh/TiO2/YSZ catalyst was successfully activated by applied currents, either positive or negative. This phenomenon is an example of "permanent" electrochemical promotion furnishing a permanent rate enhancement ratio of γ = 11. The activation by negative currents is explained in terms of an electrochemical reduction of rhodium surface oxide, while the activation by positive currents can be explained by the mechanism of electrochemical promotion.

EPFL2005

Heterogeneous kinetics of some atmospherically relevant reactions

A low pressure reactor (Knudsen cell) coupled to molecular beam modulated mass spectrometry was used to study the heterogeneous kinetics of the following three systems: (1) NO2 on amorphous carbon, (2) H2O vapor on ice and (3) gaseous HCl on ice. The first system was investigated at ambient temperature while the two last ones were investigated at temperatures typical of the stratosphere, that is roughly between 160 and 220K. The solid phase samples correspond to model surfaces whose physicochemical properties come very close to the ones of atmospheric particulates. Firstly, we studied the interaction of gaseous NO2 with three different commercial samples of amorphous carbon having widely differing physicochemical properties. Using in situ laser-induced fluorescence, the only major product was unambiguously determined to be NO with the oxidation product of carbon apparently remaining on the surface. Probing the gas phase with mass spectrometry (MS), both pulsed valve dosing and steady state experiments were performed and revealed a complex reaction mechanism for both the uptake as well as product formation. The initial uptake coefficient γo for NO2 was (6.4±2.0)·10-2 and proved to be identical within experimental uncertainty for all three types of amorphous carbon. The initial NO2 uptake rate was independent of the mass of the carbon sample and scaled with its external geometrical surface. Applying a simple chemical kinetic model to both pulsed dosing and steady state experiments resulted in an effective surface for uptake on amorphous carbon ranging between a factor of 2.8 to 8.4 larger than the geometrical surface area, but inversely proportional to the measured BET surface area of the three types of amorphous carbon. This means that the amorphous carbon with the highest BET surface (FW2) had the lowest external surface for NO2 adsorption. The chemical kinetic model included competing processes between Langmuir-type adsorption and inhibition controlling the adsorption kinetics of NO2 and revealed that the NO generation rate differed greatly between the three carbon samples examined. All samples showed saturation effects of differing degree that were partially reversible through prolonged pumping at 10-4 Torr and/or heating. Virgin amorphous carbon samples did not take up H2O vapor at 20 mTorr, and no HONO and/or HNO3 was detected in simultaneous NO2/H2O exposure experiments. CO and CO2 were detected when a sample previously exposed to NO2 was heated by an incandescent lamp. Moreover, upon heating such a sample, a MS signal m/e 62 originating from NO3 and/or N2O5 was detected. In addition to the experiments conducted on the three commercial carbon samples, we carried out uptake experiments of NO2 on acetylene soot. Originating from the flame of an acetylene burner, this soot was freshly deposited on glass dishes before each experiment. The initial uptake coefficient γo for NO2 was measured to be (3.0±1.1)·10-2 is smaller by a factor of two compared to γo observed in the uptake on commercial samples whose mass was a factor of 10 higher. In addition to NO, a net formation of HONO (m/e 47) was observed. This HONO formation is strongly dependent on the instantaneous water desorption from the sample as well as on the NO2 partial pressure in the reactor. On the other hand, it is not enhanced by an external water flow which did not show any interaction with the carbon sample. Upon heating the sample using an incandescent lamp, significant amounts of water desorbed, suggesting that the water vapor had condensed into the micropores of the soot during combustion. No quantitative results are presented yet. However, as no correlation between HONO formation and NO partial pressure has been observed so far, we suggest a reaction mechanism that only involves NO2 and H2O but no NO: 2 NO2 (g) + H2O HONO + HNO3 In a second study, the kinetics of condensation and evaporation of water on ice was determined in the temperature range of 170 to 220K. The rate of evaporation Fev corresponds to the evaporation of 70±10 monolayers of H2O per second at 200K. The condensation rate constant kc has a negative activation energy of -3.l±1.5kcal/mol which is significantly larger than the one recently measured by Haynes et al. We report the first real time kinetic measurements of water condensation on ice at stratospherically relevant temperatures. At temperatures above 160K, pulsed dosing experiments show a dose dependence of the condensation rate coefficient. For example, the condensation rate coefficient increases by a factor of five with a 1000 fold increase of the H2O dose from 1·1015 to 1·1018 molecules per pulse at 180K. This pressure dependence of the condensation rate constant may be explained by an autocatalytic mechanism involving the competition of two condensation channels. These two channels feed two different surface species, one of which leads to autocatalytic condensation. This mechanism gives insight into the manner in which a gas phase molecule is stepwise incorporated into tetrahedrally coordinated bulk ice. In a third and ongoing study, the uptake kinetics of HCl on ice has been investigated by pulsed valve experiments in the temperature range of 180 to 210K and are discussed as a function of the state of the surface. In fact, some of the pulsed valve experiments present a relaxation to a steady state level. It is shown that this level originates from the evaporation of a liquid solution corresponding to a temperature specific HCl concentration. The threshold of the injected dose leading to this solution layer is estimated to be 8·1014 molecules. This threshold corresponding to a fraction of a monolayer may be explained by the formation of small domains along grain boundaries or other lattice imperfections. Within detection limit, no difference in keff has been observed for pulses on the solution or on a previously exposed sample without formation of the solution. In the case of pulses forming a solution layer, a fraction of 20±20% of the injected molecules remains permanently adsorbed on the surface. In the temperature range from 210 to 180K, the pulsed valve experiments yield values of keff roughly between 5 and 25s-1 and an activation energy of -1.6±0.7kcal/mol which are consistent with the values observed by Flueckiger in steady state experiments using the 15mm escape aperture (kuni varying from 12 to 23s-1 and an activation energy of -1.9±0.25 kcal/mol).

EPFL1996

Preparation and Characterization of High-Surface-Area Bi(1-x)/3V1-xMoxO4 Catalysts

Lioubov Kiwi, Alexandre Nell

We report the successful application of a templating approach employing ordered mesoporous carbon to the synthesis of BiVO4, Bi2Mo3O12, and Bi0.85V0.55Mo0.45O4 and the performance of these materials as catalysts for the oxidation of propene to acrolein. Ordered mesoporous carbon templates were used to control the nucleation and growth of the mixed metal oxide crystals, allowing higher final surface areas to be obtained. The resulting materials were characterized by X-ray diffraction, Raman spectroscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, and BET surface area analysis. The surface area of the mixed metal oxide catalysts was found to depend on the type of mesoporous silica used to prepare the carbon template and on the conditions under which the carbon template was formed. Through an appropriate choice of template, the surface areas of the mixed metal oxides exceeded 15 m(2)/g. Catalytic testing revealed that materials produced via templating in ordered mesoporous carbon had per-gram activities that were up to 85 times higher than those produced by a conventional hydrothermal synthesis and exhibited stable catalytic activities over 24 h.

American Chemical Society2014

Chemical and electrochemical promotion of supported rhodium catalyst

Olena Baranova

EPFL2005

Heterogeneous kinetics of some atmospherically relevant reactions

EPFL1996