Communication: Transition State Theory for dissipative systems without a dividing surface

Transition state theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Communication, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact.

Modelización de reacciones químicas en presencia de un campo electromagnético variable

En esta tesis se aborda el estudio del proceso de isomerización del sistema molecular LiNC/LiCN tanto aislado como en presencia de un pulso láser aplicando la teoría del estado de transición (TST). Esta teoría tiene como pilar fundamental el hecho de que el conocimiento de la dinámica en las proximidades de un punto de silla de la superficie de energía potencial permite determinar los parámetros cinéticos de la reacción objeto de estudio. Históricamente, existen dos formulaciones de la teoría del estado de transición, la versión termodinámica de Eyring (Eyr38) y la visión dinámica de Wigner (Wig38). Ésta última ha sufrido recientemente un amplio desarrollo, paralelo a los avances en sistemas dinámicos que ha dado lugar a una formulación geométrica en el espacio de fases que sirve como base al trabajo desarrollado en esta tesis. Nos hemos centrado en abordar el problema desde una visión fundamentalmente práctica, ya que la teoría del estado de transición presenta una desventaja: su elevado coste computacional y de tiempo de cálculo. Dos han sido los principales objetivos de este trabajo. El primero de ellos ha sido sentar las bases teóricas y computacionales de un algoritmo eficiente que permita obtener las magnitudes fundamentales de la TST. Así, hemos adaptado con éxito un algoritmo computacional desarrollado en el ámbito de la mecánica celeste (Jor99), obteniendo un método rápido y eficiente para la obtención de los objetos geométricos que rigen la dinámica en el espacio de fases y que ha permitido calcular magnitudes cinéticas tales como el flujo reactivo, la densidad de estados de reactivos y productos y en última instancia la constante de velocidad. Dichos cálculos han sido comparados con resultados estadísticos (presentados en (Mül07)) lo cual nos ha permitido demostrar la eficacia del método empleado. El segundo objetivo de esta tesis, ha sido la evaluación de la influencia de los parámetros de un pulso electromagnético sobre la dinámica de reacción. Para ello se ha generalizado la metodología de obtención de la forma normal del hamiltoniano cuando el sistema químico es alterado mediante una perturbación temporal periódica. En este caso el punto fijo inestable en cuya vecindad se calculan los objetos geométricos de interés para la aplicación de la TST, se transforma en una órbita periódica del mismo periodo que la perturbación. Esto ha permitido la simulación de la reactividad en presencia de un pulso láser. Conocer el efecto de esta perturbación posibilita el control de la reactividad química. Además de obtener los objetos geométricos que rigen la dinámica en una cierta vecindad de la órbita periódica y que son la clave de la TST, se ha estudiado el efecto de los parámetros del pulso sobre la reactividad en el espacio de fases global así como sobre el flujo reactivo que atraviesa la superficie divisoria que separa reactivos de productos. Así, se ha puesto de manifiesto, que la amplitud del pulso es el parámetro más influyente sobre la reactividad química, pudiendo producir la aparición de flujos reactivos a energías inferiores a las de aparición del sistema aislado y el aumento del flujo reactivo a valores constantes de energía inicial. ABSTRACT We have studied the isomerization reaction LiNC/LiCN isolated and perturbed by a laser pulse. Transition State theory (TST) is the main tool we have used. The basis of this theory is knowing the dynamics close to a fixed point of the potential energy surface. It is possible to calculate kinetic magnitudes by knowing the dynamics in a neighbourhood of the fixed point. TST was first formulated in the 30's and there were 2 points of view, one thermodynamical by Eyring (Eyr38) and another dynamical one by Wigner (Wig38). The latter one has grown lately due to the growth of the dynamical systems leading to a geometrical view of the TST. This is the basis of the work shown in this thesis. As the TST has one main handicap: the high computational cost, one of the main goals of this work is to find an efficient method. We have adapted a methodology developed in the field of celestial mechanics (Jor99). The result: an efficient, fast and accurate algorithm that allows us to obtain the geometric objects that lead the dynamics close to the fixed point. Flux across the dividing surface, density of states and reaction rate coefficient have been calculated and compared with previous statistical results, (Mül07), leading to the conclusion that the method is accurate and good enough. We have widen the methodology to include a time dependent perturbation. If the perturbation is periodic in time, the fixed point becomes a periodic orbit whose period is the same as the period of the perturbation. This way we have been able to simulate the isomerization reaction when the system has been perturbed by a laser pulse. By knowing the effect of that perturbation we will be able to control the chemical reactivity. We have also studied the effect of the parameters on the global phase space dynamics and on the flux across the dividing surface. It has been prove that amplitude is the most influent parameter on the reaction dynamics. Increasing amplitude leads to greater fluxes and to some flux at energies it would not if the systems would not have been perturbed.

Role of the interfacial water structure on electrocatalysis: Oxygen reduction on Pt(1 1 1) in methanesulfonic acid

Most of electrocatalytic reactions occur in an aqueous environment. Understanding the influence of water structure on reaction dynamics is fundamental in electrocatalysis. In this work, the role of liquid water structure on the oxygen reduction at Pt(1 1 1) electrode is analyzed in methanesulfonic (MTSA) and perchloric acids. This is because these different anions can exert a different influence on liquid water structure. Results reveal a lower ORR electrode activity in MTSA than in HClO4 solutions and they are discussed in light of anion's influence on water structural ordering. From them, the existence of an outer-sphere, rate determining, step in the ORR mechanism is suggested.

Symmetry contaminations in reactive scattering through long-lived collision complexes

We extend our Lanczos subspace time-independent wave packet method [J. Chem. Phys. 116 (2002) 2354] to investigate the issue of symmetry contaminations for the challenging deep-well H + O-2 reaction. Our central objective is to address the issue of whether significant symmetry contamination can occur if a wavepacket initially possessing the correct O-O exchange symmetry is propagated over tens of thousands of recursive steps using a basis which does not explicitly enforce the correct symmetry, and if so how seriously this affects the results. We find that symmetry contamination does exist where the symmetry constraint is not explicitly enforced in the basis. While it affects individual resonances and the associated peak amplitudes, the overall shape of the more averaged quantities such as total reaction probabilities and vibrational branching ratios are not seriously affected. (C) 2004 Elsevier B.V. All rights reserved.

Transport of simple fluids in nanopores: Theory and simulation

A theory is discussed of single-component transport in nanopores, recently developed by Bhatia and coworkers. The theory considers the oscillatory motion of molecules between diffuse wall collisions, arising from the fluid-wall interaction, along with superimposed viscous flow due to fluid-fluid interaction. The theory is tested against molecular dynamics simulations for hydrogen, methane, and carbon tetrafluoride flow in cylindrical nanopores in silica. Although exact at low densities, the theory performs well even at high densities, with the density dependency of the transport coefficient arising from viscous effects. Such viscous effects are reduced at high densities because of the large increase in viscosity, which explains the maximum in the transport coefficient with increase in density. Further, it is seen that in narrow pore sizes of less than two molecular diameters, where a complete monolayer cannot form on the surface, the mutual interference of molecules on opposite sides of the cross section can reduce the transport coefficient, and lead to a maximum in the transport coefficient with increasing density. The theory is also tested for the case of partially diffuse reflection and shows the viscous contribution to be negligible when the reflection is nearly specular. (c) 2005 American Institute of Chemical Engineers AIChE J, 52: 29-38, 2006.

From point defects to plate tectonic faults

Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100 km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed ``hydrolytic weakening''. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.

Simulation process of biodiesel production over heterogeneous catalysts

Biodiesel production is a very promising area due to the relevance that it is an environmental-friendly diesel fuel alternative to fossil fuel derived diesel fuels. Nowadays, most industrial applications of biodiesel production are performed by the transesterification of renewable biological sources based on homogeneous acid catalysts, which requires downstream neutralization and separation leading to a series of technical and environmental problems. However, heterogeneous catalyst can solve these issues, and be used as a better alternative for biodiesel production. Thus, a heuristic diffusion-reaction kinetic model has been established to simulate the transesterification of alkyl ester with methanol over a series of heterogeneous Cs-doped heteropolyacid catalysts. The novelty of this framework lies in detailed modeling of surface reacting kinetic phenomena and integrating that with particle-level transport phenomena all the way through to process design and optimisation, which has been done for biodiesel production process for the first time. This multi-disciplinary research combining chemistry, chemical engineering and process integration offers better insights into catalyst design and process intensification for the industrial application of Cs-doped heteropolyacid catalysts for biodiesel production. A case study of the transesterification of tributyrin with methanol has been demonstrated to establish the effectiveness of this methodology.

Simulation process of biodiesel production over heterogeneous catalysts

Biodiesel production is a very promising area due to the relevance that it is an environmental-friendly diesel fuel alternative to fossil fuel derived diesel fuels. Nowadays, most industrial applications of biodiesel production are performed by the transesterification of renewable biological sources based on homogeneous acid catalysts, which requires downstream neutralization and separation leading to a series of technical and environmental problems. However, heterogeneous catalyst can solve these issues, and be used as a better alternative for biodiesel production. Thus, a heuristic diffusion-reaction kinetic model has been established to simulate the transesterification of alkyl ester with methanol over a series of heterogeneous Cs-doped heteropolyacid catalysts. The novelty of this framework lies in detailed modeling of surface reacting kinetic phenomena and integrating that with particle-level transport phenomena all the way through to process design and optimisation, which has been done for biodiesel production process for the first time. This multi-disciplinary research combining chemistry, chemical engineering and process integration offers better insights into catalyst design and process intensification for the industrial application of Cs-doped heteropolyacid catalysts for biodiesel production. A case study of the transesterification of tributyrin with methanol has been demonstrated to establish the effectiveness of this methodology.

Seawater carbonate chemistry, chlorophyll a and phosphate during experiments with Trichodesmium erythraeum IMS101 (CCMP1985), 2010

In this laboratory study, we monitored the buildup of biomass and concomitant shift in seawater carbonate chemistry over the course of a Trichodesmium bloom under different phosphorus (P) availability. During exponential growth, dissolved inorganic carbon (DIC) decreased, while pH increased until maximum cell densities were reached. Once P became depleted, DIC decreased even further and total alkalinity (TA) dropped, accompanied by precipitation of aragonite. Under P-replete conditions, DIC increased and TA remained constant in the postbloom phase. A diffusion-reaction model was employed to estimate changes in carbonate chemistry of the diffusive boundary layer. This study demonstrates that Trichodesmium can induce precipitation of aragonite from seawater and further provides possible explanations about underlying mechanisms.

DEVELOPMENT OF A CONDENSED PHASE VELOCITY MAP IMAGING APPARATUS: DISSOCIATION PHOTODYNAMICS OF NITROGEN DIOXIDE AT 355 NM

The photochemistry of the polar regions of Earth, as well as the interstellar medium, is driven by the effect of ultraviolet radiation on ice surfaces and on the materials trapped within them. While the area of ice photochemistry is vast and much research has been completed, it has only recently been possible to study the dynamics of these processes on a microscopic level. One of the leading techniques for studying photoreaction dynamics is Velocity Map Imaging (VMI). This technique has been used extensively to study several types of reaction dynamics processes. Although the majority of these studies have utilized molecular beams as the main medium for reactants, new studies showed the versatility of the technique when applied to molecular dynamics of molecules adsorbed on metal surfaces. Herein the development of a velocity map imaging apparatus capable of studying the photochemistry of condensed phase materials is described. The apparatus is used to study of the photo-reactivity of NO2 condensed within argon matrices to illustrate its capabilities. A doped ice surface is formed by condensing Ar and NO2 gas onto a sapphire rod which is cooled using a helium compressor to 20 K. The matrix is irradiated using an Nd:YAG laser at 355 nm, and the resulting NO fragment is state-selectively ionized using an excimer-pumped dye laser. In all, we are able to detect transient photochemically generated species and can collect information on their quantum state and kinetic energy distribution. It is found that the REMPI spectra changes as different sections of the dissociating cloud are probed. The rotational and translational energy populations are found to be bimodal with a low temperature component roughly at the temperature of the matrix, and a second component with much higher temperature, the rotational temperature showing a possible population inversion, and the translational temperature of 100-200 K. The low temperature translational component is found to dominate at long delay times between dissociation and ionization, while at short time delays the high temperature component plays a larger role. The velocity map imaging technique allows for the detection of both the axial and radial components of the translational energy. The distribution of excess energy over the rotational, electronic and translational states of the NO photofragments provides evidence for collisional quenching of the fragments in the Ar-matrix prior to their desorption.

Variationelle Zeitdiskretisierungen höherer Ordnung der Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängigen Gebieten

Wir betrachten zeitabhängige Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängi- gen Gebieten, wobei die Bewegung des Gebietsrandes bekannt ist. Die zeitliche Entwicklung des Gebietes wird durch die ALE-Formulierung behandelt, die die Nachteile der klassischen Euler- und Lagrange-Betrachtungsweisen behebt. Die Position des Randes und seine Geschwindigkeit werden dabei so in das Gebietsinnere fortgesetzt, dass starke Gitterdeformationen verhindert werden. Als Zeitdiskretisierungen höherer Ordnung werden stetige Galerkin-Petrov-Verfahren (cGP) und unstetige Galerkin-Verfahren (dG) auf Probleme in zeitabhängigen Gebieten angewendet. Weiterhin werden das C 1 -stetige Galerkin-Petrov-Verfahren und das C 0 -stetige Galerkin- Verfahren vorgestellt. Deren Lösungen lassen sich auch in zeitabhängigen Gebieten durch ein einfaches einheitliches Postprocessing aus der Lösung des cGP-Problems bzw. dG-Problems erhalten. Für Problemstellungen in festen Gebieten und mit zeitlich konstanten Konvektions- und Reaktionstermen werden Stabilitätsresultate sowie optimale Fehlerabschätzungen für die nachbereiteten Lösungen der cGP-Verfahren und der dG-Verfahren angegeben. Für zeitabhängige Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängigen Gebieten präsentieren wir konservative und nicht-konservative Formulierungen, wobei eine besondere Aufmerksamkeit der Behandlung der Zeitableitung und der Gittergeschwindigkeit gilt. Stabilität und optimale Fehlerschätzungen für die in der Zeit semi-diskretisierten konservativen und nicht-konservativen Formulierungen werden vorgestellt. Abschließend wird das volldiskretisierte Problem betrachtet, wobei eine Finite-Elemente-Methode zur Ortsdiskretisierung der Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängigen Gebieten im ALE-Rahmen einbezogen wurde. Darüber hinaus wird eine lokale Projektionsstabilisierung (LPS) eingesetzt, um der Konvektionsdominanz Rechnung zu tragen. Weiterhin wird numerisch untersucht, wie sich die Approximation der Gebietsgeschwindigkeit auf die Genauigkeit der Zeitdiskretisierungsverfahren auswirkt.

Using Surface Spectroscopy to Help Interpret STM Images of Chemisorbed Molecules: Application to the Study of the Hydrogenation of Ketones and a-Ketoesters on Pt

Depuis que la haute énantiopureté est nécessaire dans l’industrie pharmaceutique, les études visant à découvrir les mécanismes pour l’hydrogénation énantiosélective de cétones ou céto-esters sur les surfaces, et à rechercher de nouveaux et plus performants catalyseurs asymétriques, sont d’une grande importance. La microscopie à effet tunnel (STM), la spectroscopie infrarouge de réflexion-absorption, la spectroscopie de désorption à température programmée et la spectrométrie de photoélectrons induits par rayons X sont des méthodes performantes facilitant la compréhension des mécanismes de réaction. En plus de nous permettre de comprendre les mécanismes réactionnels, les études peuvent fournir des informations sur la dynamique des réactions en catalyse hétérogène ainsi que sur le développement de la théorie de la fonctionnelle de la densité (DFT) afin de calculer des interactions faibles dans les processus de surface. D’autres parts, les calculs DFT fournissent une aide essentielle à l’interprétation des données de STM et spectroscopie de surface. Dans cette thèse, certains cétones et céto-esters sur la surface de platine sont étudiées par les techniques sophistiquées mentionnées ci-dessus. Mes études démontrent que la combinaison de l’utilisation de la spectroscopie de routine, des nanotechnologies et de nombreux calculs élaborés, est une méthode efficace pour étudier les réactions à la surface car ces techniques explorent les différents aspects de la surface ainsi que s’entraident mutuellement lors de certaines interprétations.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

Local and nonlocal integro-differential reaction-diffusion models for protein dynamics in Alzheimer's disease

In this work, integro-differential reaction-diffusion models are presented for the description of the temporal and spatial evolution of the concentrations of Abeta and tau proteins involved in Alzheimer's disease. Initially, a local model is analysed: this is obtained by coupling with an interaction term two heterodimer models, modified by adding diffusion and Holling functional terms of the second type. We then move on to the presentation of three nonlocal models, which differ according to the type of the growth (exponential, logistic or Gompertzian) considered for healthy proteins. In these models integral terms are introduced to consider the interaction between proteins that are located at different spatial points possibly far apart. For each of the models introduced, the determination of equilibrium points with their stability and a study of the clearance inequalities are carried out. In addition, since the integrals introduced imply a spatial nonlocality in the models exhibited, some general features of nonlocal models are presented. Afterwards, with the aim of developing simulations, it is decided to transfer the nonlocal models to a brain graph called connectome. Therefore, after setting out the construction of such a graph, we move on to the description of Laplacian and convolution operations on a graph. Taking advantage of all these elements, we finally move on to the translation of the continuous models described above into discrete models on the connectome. To conclude, the results of some simulations concerning the discrete models just derived are presented.