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In the experiments presented in this work, third-order, time-resolved spectroscopy was applied to the disentanglement of nuclear and electronic degrees of freedom in polyatomic molecules. The motivation for approaching this problem was given by the decisive role that the coupling of nuclear and electronic dynamics plays in the mechanism of photochemical reactions and photobiological processes. In order to approach this complex problem, different strategies within the framework of time-resolved, four-wave mixing spectroscopy were developed that allowed for the dynamic as well as the energetic aspects of vibronic coupling in non-radiative transitions of polyatomic molecules to be addressed. This was achieved by utilizing the influence of optical as well as Raman resonances on four-wave mixing processes. These resonance effects on third-order, optical processes allow for a high selectivity to be attained with respect to the interrogation of specific aspects of molecular dynamics. The development of different strategies within the framework of time-resolved, four-wave mixing spectroscopy for addressing the problem of vibronic coupling began with the experiments on gaseous iodine. This simple, well investigated molecular system was chosen in order to unambiguously characterize the effect of Raman resonances on four-wave mixing processes. A time-resolved degenerative four-wave mixing (DFWM) experiment was carried out on gaseous iodine that allowed for the dynamics of coherent Stokes Raman scattering (CSRS) as well as a coherent anti-Stokes Raman scattering (CARS) to be observed parallel to the dynamics of a DFWM process at different spectral positions of the FWM signal. Here, the state-selectivity of these different FWM processes manifests itself in the vibrational wave packet dynamics on different electronic potentials of iodine. It could be shown that Raman resonances determine the selectivity with which these FWM processes prepare and interrogate nuclear dynamics in different electronic states. With the insight gained into the relevance of Raman resonant processes in FWM spectroscopy, an experimental scheme was devised that utilizes this effect to selectively interrogate the dynamics of a specific vibrational mode within a polyatomic molecule during a radiationless electronic transition. Here, a CARS process was employed to selectively probe specific vibrational modes of a molecular system by variably tuning the energy difference between the lasers involved in the CARS process to be in Raman resonance with the vibrational energy spacing of a particular vibrational mode. Using this aspect of a tunable resonance enhancement within a CARS scheme, this optical process was incorporated in a time-resolved pump-probe experiment as a mode-selective probe mechanism. This type of experimental configuration, that employs four pulsed laser fields, was classified as a pump-CARS scheme. Here, a laser pulse independent of the CARS process initiates the molecular dynamics that are interrogated selectively with respect to the vibrational mode of the system through the simultaneous interaction of the three pulsed fields involved in the CARS process. Time-resolution on a femtosecond timescale is achieved by introducing a time delay between the independent pump laser and the laser pulses of the CARS process. The experimental configuration of a pump-CARS scheme was applied to the study of the nuclear dynamics involved in the radiationless electronic transition between the first excited singlet state (S1) and the electronic ground state (S0) of all-trans-b-carotene. The mode-selective CARS probe allowed for the characteristic timescale with which specific vibrational modes are repopulated in the S0 state to be determined. From the varying repopulation times of specific vibrational modes, a mechanism with which the full set of vibrational states of the S0 potential are repopulated subsequent to the internal conversion process could be postulated. Most importantly, the form of nuclear motion that primarily funnels the population between the two electronic states could be identified as the C=C symmetric symmetric stretch mode in the polyene backbone of b-carotene. With this, the reaction coordinate of this radiationless electronic transition could be identified. The experiment shows, that the CARS probe is capable of determining the nuclear motion coupled to a radiationless electronic transition in complex polyatomic systems. The S1/S0 internal conversion process in b-carotene was further investigated with time-resolved transient gratings. Here, the energetic aspects of a non-adiabatic transition was addressed by determining the influence of the vibrational energy on the rate of this internal conversion. In order to compare the rate of internal conversion taking place out of vibrational ground state modes versus this transition initiating out of vibrationally hot modes, the strategy of shifting the probe mechanism in the transient grating scheme to spectral positions within and out of the red flank of the S1 absorption profile was pursued. The interrogation of different vibrational states was verified by determining the degree of vibrational cooling, taking place parallel to the internal conversion process. With this strategy, it could be shown that vibrationally hot states contribute to the internal conversion with a higher rate than vibrational ground state modes. In summary, different third-order, optical processes in the framework of time-resolved FWM were applied to the study of non-adiabatic dynamics in polyatomic molecules. By utilizing the effect of optical as well as Raman resonances on different FWM processes, it could be shown that third-order, time-resolved spectroscopy is a powerful tool for gaining insight into complex molecular dynamics such as vibronic coupling. The experiments presented in this work showed that the CARS process, as a mode-selective probe in time-resolved experiments, is capable of disentangling nuclear and electronic dynamics.
The present thesis considers the modelling of gas mixtures via a kinetic description. Fundamentals about the Boltzmann equation for gas mixtures and the BGK approximation are presented. Especially, issues in extending these models to gas mixtures are discussed. A non-reactive two component gas mixture is considered. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the two species. The model presented here contains several models from physicists and engineers as special cases. Consistency of this model is proven: conservation properties, positivity of all temperatures and the H-theorem. The form in global equilibrium as Maxwell distributions is specified. Moreover, the usual macroscopic conservation laws can be derived.
In the literature, there is another type of BGK model for gas mixtures developed by Andries, Aoki and Perthame, which contains only one interaction term. In this thesis, the advantages of these two types of models are discussed and the usefulness of the model presented here is shown by using this model to determine an unknown function in the energy exchange of the macroscopic equations for gas mixtures described in the literature by Dellacherie. In addition, for each of the two models existence and uniqueness of mild solutions is shown. Moreover, positivity of classical solutions is proven.
Then, the model presented here is applied to three physical applications: a plasma consisting of ions and electrons, a gas mixture which deviates from equilibrium and a gas mixture consisting of polyatomic molecules.
First, the model is extended to a model for charged particles. Then, the equations of magnetohydrodynamics are derived from this model. Next, we want to apply this extended model to a mixture of ions and electrons in a special physical constellation which can be found for example in a Tokamak. The mixture is partly in equilibrium in some regions, in some regions it deviates from equilibrium. The model presented in this thesis is taken for this purpose, since it has the advantage to separate the intra and interspecies interactions. Then, a new model based on a micro-macro decomposition is proposed in order to capture the physical regime of being partly in equilibrium, partly not. Theoretical results are presented, convergence rates to equilibrium in the space-homogeneous case and the Landau damping for mixtures, in order to compare it with numerical results.
Second, the model presented here is applied to a gas mixture which deviates from equilibrium such that it is described by Navier-Stokes equations on the macroscopic level. In this macroscopic description it is expected that four physical coefficients will show up, characterizing the physical behaviour of the gases, namely the diffusion coefficient, the viscosity coefficient, the heat conductivity and the thermal diffusion parameter. A Chapman-Enskog expansion of the model presented here is performed in order to capture three of these four physical coefficients. In addition, several possible extensions to an ellipsoidal statistical model for gas mixtures are proposed in order to capture the fourth coefficient. Three extensions are proposed: An extension which is as simple as possible, an intuitive extension copying the one species case and an extension which takes into account the physical motivation of the physicist Holway who invented the ellipsoidal statistical model for one species. Consistency of the extended models like conservation properties, positivity of all temperatures and the H-theorem are proven. The shape of global Maxwell distributions in equilibrium are specified.
Third, the model presented here is applied to polyatomic molecules. A multi component gas mixture with translational and internal energy degrees of freedom is considered. The two species are allowed to have different degrees of freedom in internal energy and are modelled by a system of kinetic ellipsoidal statistical equations. Consistency of this model is shown: conservation properties, positivity of the temperature, H-theorem and the form of Maxwell distributions in equilibrium. For numerical purposes the Chu reduction is applied to the developed model for polyatomic gases to reduce the complexity of the model and an application for a gas consisting of a mono-atomic and a diatomic gas is given.
Last, the limit from the model presented here to the dissipative Euler equations for gas mixtures is proven.