Our group has recently described a new form of kinetic isotope effect that arises from dynamic selectivity in the bifurcation of a reaction pathway on the slope of an energy surface. Since the selection between products does not occur at a potential energy saddle point, we proposed that the isotope effect is decided by dynamic factors that are not necessarily related to zero point energy effects on the surface. As an alternative explanation, it has recently been suggested that variational transition state theory can account for these isotope effects. The dynamic explanation and variational transition state theory explanation make distinct predictions as to the temperature dependence of these isotope effects. I describe here my studies of the temperature dependence of the intramolecular isotope effects for the reaction of singlet oxygen with gemtetramethylethylene- d6. The selectivity observed for this reaction across a broad temperature range is clearly a non-Eyring distribution and thus the mechanism cannot be adequately described solely using transition state theory or even some variation of it. After using these results to evaluate competing theories it was concluded that this mechanism could only be properly understood using a dynamic explanation.

Yes / Sheet specimens of a PLLA-based polymer have been extended at a temperature near to the glass transition in both uniaxial and planar tension, with stress relaxation observed for some time after reaching the final strain. Both axial and transverse stresses were recorded in the planar experiments. In all cases during loading, yielding at small strain was followed by a drop in true stress and then strain hardening. This was followed by stress relaxation at constant strain, during which stress dropped to reach an effectively constant level. Stresses were modelled as steady state and transient components. Steady-state components were identified with the long-term stress in stress relaxation and associated with an elastic component of the model. Transient stresses were modelled using Eyring mechanisms. The greater part of the stress during strain hardening was associated with dissipative Eyring processes. The model was successful in predicting stresses in both uniaxial and planar extension over a limited range of strain rate.

Companies providing products have many requirements, both from standards and customers, that they need to comply with in order to be able to sell their product. Veoneer AB is a leading automotive machine vision supplier, providing mono, stereo, night vision and driver monitoring systems consisting of both electronic, mechanical and optical components. These systems have to withstand certain environmental tests in order to assure the lifetime of the totalsystems. Since the life time is usually several years accelerated tests are used that correspond to a few weeks ormonths. The tests used at Veoneer are specified for electronic equipment and what Veoneer does not know today is ifthe accelerated environmental tests stated for electronic equipment are relevant for the optical component of the visionsystem. In this master thesis project two different accelerated environmental tests, dry and damp heat, have been chosen inorder to investigate the effect of temperature and relative humidity on the adhesive in the optical component connecting the sensor and lens. The optical components where characterized by measurement of focus position and mechanicalstrength. Different combinations of temperature and relative humidity where chosen in order to compare the effect of different stress levels but also for the purpose of deriving parameters needed for accelerated testing models such as theArrhenius, Eyring, Lawson and Peck model. Amongst the results from this thesis work is the focus shift measurement which follows the same trend as seen in previous research regarding the effect of temperature and relative humidity on adhesives. With an exponentialdistribution being seen in different directions for the respective stresses. Pull tests show a greater degradation withhigher stress levels, where one test case shows the greatest degradation. Calculations regarding activation energy and constants for models match previous research where one model, combining temperature and relative humidity, showssimilar values as found in literature. Calculations also show that standard accelerated life time tests overexpose adhesives due to calculations of test times with lower activation energies.

This article presents the derivation of the thermodynamic expressions for the activation free energy and reaction rate constant for cosolvent reaction systems. These expressions account for the factors that are specific to solution-phase reactions, which include isotropic electrostatic effects and close-range solvent−solute interactions. This article discusses the idea that electrostatic effects can be correlated with the isotropic relative permittivity, and solvent−solute interactions can be correlated with the cosolvent mole fraction. This article also shows that this type of thermodynamic analysis is necessary for understanding certain nuances of solution-phase reaction processes not tractable by other types of analyses.

The hydrolysis of acetic anhydride is a widely-studied liquid phase reaction studied since 1906. Different approaches have been used to study the kinetics of this reaction. Approaches used by researchers have involved the use of sophisticated experimental set-ups. In this work, the pH technique has been adopted which involves the use of a pH meter to monitor the hydrolysis reaction. Analysis of the hydrolysis reaction has been performed for water/acetone cosolvent systems over a range of temperatures and mole fractions. Eyring analysis was performed under isomole fraction conditions and activation enthalpy, entropy, and Gibbs free energy for hydrolysis of acetic anhydride have been determined. The isomole fraction Eyring plots are linear, because, activation enthalpy and entropy are independent of temperature under these conditions. Activation free Gibbs energy increases with increasing temperature at a constant water mole fraction, while it decreases with increasing water mole fraction at constant temperature.

Polymers are increasingly being used in engineering designs due to their favorable mechanical properties such as high specific strength, corrosive resistance, manufacturing flexibility. The understanding of the mechanical behavior of these polymers under both static and dynamic loading is critical for their optimal implementation in engineering applications. One such polymer utilized in a wide variety of applications from medical instrumentation to munitions is Polyetherimide, referred to as Ultem. This thesis characterizes both the static and dynamic mechanical behavior of Ultem 1000 through experimental methods and numerical simulations. Standard compression experiments were conducted on and MTS test frame to characterize the elastic-plastic behavior of Ultem 1000 under quasi-static conditions. The dynamic response of the material was investigated at very high strain rates using a custom built miniaturized Kolsky bar apparatus. The smaller Kolsky bar configuration was chosen over the conventional Kolsky device to increase the maximum capable strain rates and to reduce common experimental problems such as wave dispersion, friction, and stress equilibrium. Since a universal test standard for this apparatus is not available, the details of the design, construction, and experimental procedures of this device are provided. The results of the high strain rate testing revealed a bilinear relationship between the material yield stress and strain rate. This relationship was modeled using the Ree-Eyring two stage activation process equation.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.

This study determines the activation energy parameters for the hydrolysis of acetic anhydride in water/tetrahydrofuran solutions. These values are needed for studies to quantify the effect of the bulk electrostatic environment solvent-solute interactions on the hydrolysis reaction rate. Hydrolysis of an acetic anhydride with water or under basic conditions yields acetic acid. The current study is based on simple hydrolysis of acetic anhydride which produces acetic acid decreasing the pH over time. Simple hydrolysis is monitored by measuring pH versus time at temperatures ranging from 20.0 to 35.0 oC and mole fraction of water ranging from 0.75 to 1.00. Measuring pH over time has advantages over other methods such as conductivity, UV-vis spectroscopy, temperature scanning, FTIR, calorimeter as it is simple, inexpensive and reproducible. Experimental results were used to determine activation enthalpy and entropy for hydrolysis of acetic anhydride using tetrahydrofuran as the co-solvent. These values were determined using the Eyring rate equation under iso-mole fraction and isothermal conditions. Analysis was performed to determine if the activation enthalpy and entropy are temperature dependent. Eyring plots are expected to be linear for iso-mole fractions and isothermal conditions of tetrahydrofuran.

No / In tensile stretching, many polymers undergo strain localization. The geometrical form of the localization can take the form of either a shear band or an approximately symmetric neck. We present a constitutive model of the early stages of deformation that predicts which form the localization will take. The model consists of an Eyring process acting with a Gaussian network that is implemented numerically. A Levy-Mises flow rule associated with the Eyring process has a tendency to produce shear bands. A relatively stiff Gaussian network is used in a model of polycarbonate that ensures that most of the strain is taken up by the Eyring process, resulting in shear banding. In contrast, a relatively soft Gaussian network is used in a model of polyethylene, which takes up the greater part of the strain, resulting in a neck. The predictions are compared with experiments. For polyethylene, a two-Eyring-process model is introduced for better accuracy.

Dans cette thèse, nous étudions le comportement asymptotique précis à basse température de l’événement de sortie d'un domaine métastable $Omegasubset mathbb R^d$ (point de sortie et temps de sortie) pour le processus de Langevin sur amorti. En pratique, le processus de Langevin sur amorti peut par exemple simuler l'évolution des positions des atomes d'une molécule ou la diffusion d'impuretés interstitielles dans un cristal. Nos résultats principaux concernent le comportement asymptotique précis de la distribution de la loi du point de sortie de $Omega$. Dans la limite d'une petite température, ces résultats permettent de justifier l'utilisation de la formule d'Eyring-Kramers pour modéliser les événements de sortie de $Omega$. La loi d'Eyring-Kramers est par exemple utilisée pour calculer les taux de transition entre les états d'un système dans un algorithme de Monte-Carlo cinétique afin de simuler efficacement les différents états visités par le système. L'analyse repose de manière essentielle sur la distribution quasi stationnaire associée au processus de Langevin sur amorti dans $Omega$. Nos preuves utilisent des outils d'analyse semi-classique. La thèse se décompose en trois chapitres indépendants. Le premier chapitre (rédigé en français) est une introduction aux résultats obtenus. Les deux autres chapitres (rédigées en anglais) sont consacrés aux énoncés mathématiques / This thesis is dedicated to the study of the sharp asymptotic behaviour in the low temperature regime of the exit event from a metastable domain $Omegasubset mathbb R^d$ (exit point and exit time) for the overdamped Langevin process. In practice, the overdamped Langevin dynamics can be used to describe for example the motion of the atoms of a molecule or the diffusion of interstitial impurities in a crystal. The obtention of sharp asymptotic approximations of the first exit point density in the small temperature regime is the main result of this thesis. These results justify the use of the Eyring-Kramers law to model the exit event. The Eyring-Kramers law is used for example to compute the transition rates between the states of a system in a kinetic Monte-Carlo algorithm in order to sample efficiently the state-to-state dynamics. The cornerstone of our analysis is the quasi stationary distribution associated with the overdamped Langevin dynamics in $Omega$. The proofs are based on tools from semi-classical analysis. This thesis is divided into three independent chapters. The first chapter (in French) is dedicated to an introduction to the mathematical results. The other two chapters (in English) are devoted to the precise statements and proofs