954 resultados para Fuel Cell Engine
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In this paper we report the electrosynthesis of PVA-protected PtCo films (PVA = poly(vinylalcohol)) and their activities towards the oxygen reduction reaction (ORR). PtCo electrodeposits were potentiostatically obtained in the presence and absence of PVA at distinct potentials. The film morphology and composition were characterized by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX), which revealed that the use of PVA in the electrodeposition of PtCo films was decisive to achieve better film composition control. Cyclic voltammetry for PVA-protected PtCo films showed that the electrochemical surface area is dependent on the electrodeposition potentials and suggested different adsorption strengths of oxygen-containing species. Films produced in the presence of PVA presented the following activity order towards ORR as a function of the electrodeposition potential (vs. Ag/AgCl): -0.9 V> -0.8 V> -1.0 V> -0.7 V. In contrast, PtCo films electrodeposited in the absence of PVA displayed very similar activities regardless of the electrodeposition potential. The simplicity of the electrodeposition method combined with its effectiveness enabled the production of "model electrodes" for investigating the fundamental aspects of the reactions taking place in the fuel cell cathodes. (C) 2011 Elsevier B.V. All rights reserved.
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An interesting method to investigate the effect of fuel crossover in low temperature fuel cells consists of studying the open circuit interaction between the reducing fuel and an oxide-covered catalyst. Herein we report the experimental study of the open circuit interaction between borohydride and oxidized platinum surfaces in alkaline media. When compared to the case of hydrogen and other small organic molecules, two remarkable new features were observed. Firstly, the interaction with borohydride resulted in a very-fast reduction process with transient times about two to three orders of magnitude smaller. The second peculiarity was that the decrease of the open circuit potential was found to occur in two-stages and this, previously unseen, feature was correlated with the two-hump profile found in the backward sweep in the cyclic voltammogram The consequences of our findings are discussed in connection with fundamental and applied aspects. (C) 2011 Elsevier B.V All rights reserved.
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The oxygen reduction reaction (ORR) was studied in KOH electrolyte on carbon supported epsilon-manganese dioxide (epsilon-MnO2/C). The epsilon-MnO2/C catalyst was prepared via thermal decomposition of manganese nitrate and carbon powder (Vulcan XC-72) mixtures. X-ray powder diffraction (XRD) measurements were performed in order to determine the crystalline structure of the resulting composite, while energy dispersive X-ray analysis (EDX) was used to evaluate the chemical composition of the synthesized material. The electrochemical studies were conducted using cyclic voltammetry (CV) and quasi-steady state polarization measurements carried out with an ultra thin layer rotating ring/disk electrode (RRDE) configuration. The electrocatalytic results obtained for 20% (w/w) Pt/C (E-TEK Inc., USA) and alpha-MnO2/C for the ORR, considered as one of the most active manganese oxide based catalyst for the ORR in alkaline media, were included for comparison. The RRDE results revealed that the ORR on the MnO2 catalysts proceeds preferentially through the complete 4e(-) reduction pathway via a 2 plus 2e(-) reduction process involving hydrogen peroxide as an intermediate. A benchmark close to the performance of 20% (w/w) Pt/C (E-TEK Inc., USA) was observed for the epsilon-MnO2/C material in the kinetic control region, superior to the performance of alpha-MnO2/C, but a higher amount of HO2- was obtained when epsilon-MnO2/C was used as catalyst. The higher production of hydrogen peroxide on epsilon-MnO2/C was related to the presence of structural defects, typical of this oxide, while the better catalytic performance in the kinetic control region compared to alpha-MnO2/C was related with the higher electrochemical activity for the proton insertion kinetics, which is a structure sensitive process. (C) 2012 Elsevier Ltd. All rights reserved.
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EFFECTS OF ADDING LANTHANUM TO Ni/ZrO2 CATALYSTS ON ETHANOL STEAM REFORMING. The catalytic performance of Ni/ZrO2 catalysts loaded with different lanthanum content for steam reforming of ethanol was investigated. Catalysts were characterized by BET surface area, X-ray diffraction, UV-vis spectroscopy, temperature programmed reduction, and X-ray absorption fine structure techniques. Results showed that lanthanum addition led to an increase in the degree of reduction of both NiO and nickel surface species interacting; with the support, due to the higher dispersion effect. The best catalytic performance at 450 degrees C was found for the Ni/2LZ catalyst, which exhibited an effluent gaseous mixture with the highest H-2 yield.
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Since electrode electroactivity and stability depend directly on the nature, morphology, and structure of the material, we have investigated how modifications to the Pechini method during the synthesis of Pt-RuOx/C electrocatalysts affected catalyst activity. The structure and stability of the resulting materials were investigated after their submission to a large number of potential scans and to constant potential for a prolonged time period in sulfuric acid 0.5 mol L-1 and methanol 0.1 mol L-1 solution. DMFC tests were accomplished using membrane electrode assemblies (MEAs) prepared by hot-pressing a pretreated Nafion 117 membrane together with the prepared Pt-RuOx anodes and a Pt cathode (from E-TEK), in order to compare the catalytic activity of the materials prepared by different methods. The stability studies demonstrated that the catalyst whose resin/carbon support mixture was agitated in a balls mill before undergoing heat-treatment was more stable than the other prepared catalysts. The catalysts synthesized with the single resin consisting of Pt and Ru and subjected to ultrasound before heat-treatment furnished the highest power density in the single fuel cell. (C) 2012 The Electrochemical Society. [DOI: 10.1149/2.011208jes]
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Carbon supported Pt-Sn catalysts were prepared by reduction of Pt and Sn precursors with formic acid and characterized in terms of structure, morphology and surface properties. The electrocatalytic activity for ethanol oxidation was studied in a direct ethanol fuel cell (DEFC) at 70 degrees C and 90 degrees C. Electrochemical and physico-chemical data indicated that a proper balance of Pt and Sn species in the near surface region was necessary to maximize the reaction rate. The best atomic surface composition, in terms of electrochemical performance, was Pt:Sn 65:35 corresponding to a bulk composition 75:25 namely Pt3Sn1/C. The reaction products of ethanol electro-oxidation in single cell and their distribution as a function of the nature of catalyst were determined. Essentially, acetaldehyde and acetic acid were detected as the main reaction products; whereas, a lower content of CO2 was formed. The selectivity toward acetic acid vs. acetaldehyde increased with the increase of the Sn content and decreased by decreasing the concentration of the reducing agent used in the catalyst preparation. According to the recent literature, these results have been interpreted on the basis of ethanol adsorption characteristics and ligand effects occurring for Sn-rich electrocatalysts. (C) 2012 Elsevier Ltd. All rights reserved.
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Direct borohydride fuel cells (DBFCs) are attractive energy generators for powering portable electronic devices, mainly due to their high energy density and number of electrons per borohydride ion. However, the lack of a highly efficient electrocatalyst for the borohydride oxidation reaction limits the performance of these devices. The most commonly studied electrocatalysts for this reaction are composed of gold and platinum. Nevertheless, for these metals, the borohydride electrooxidation reaction mechanism (BOR) is not completely understood, and the total oxidation reaction, involving eight electrons per BH4- species, competes with parallel reactions, with a lower number of exchanged electrons and/or with heterogeneous chemical hydrolysis. Considering the above-mentioned issues, this work presents recent advances in the knowledge of the BOR pathways on polycrystalline (bulk) Au and Pt electrocatalysts. It presents the studies of the BOR reaction on Au and Pt electrodes using in situ Fourier Transform Infrared Spectroscopy (FUR), and on-line Differential Electrochemical Mass Spectrometry (DEMS). The spectroscopic and spectrometric data provided physical evidence of intermediate species and the formation of H-2 in the course of the BOR as a function of the electrode potential. These results enabled to advance in the knowledge about the BOR pathways on Au and Pt electrocatalysts. (C) 2012 Elsevier Ltd. All rights reserved.
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A comparative study using different proportions of CeO2/C (4%, 9% and 13% CeO2) was performed to produce H2O2, a reagent used in the oxidation of organic pollutants and in electro-Fenton reactions for the production of the hydroxyl radical (OH center dot), a strong oxidant agent used in the electrochemical treatment of aqueous wastewater. The CeO2/C materials were prepared by a modified polymeric precursor method (PPM). X-ray diffraction analysis of the CeO2/C prepared by the PPM identified two phases. CeO2 and CeO2. The average size of the crystallites in these materials was close to 7 nm. The kinetics of the oxygen reduction reaction (ORR) were evaluated by the rotating ring-disk electrode technique. The results showed that the 4% CeO2/C prepared by the PPM was the best composite for the production of H2O2 in a 1 mol L-1 NaOH electrolyte solution. For this material, the number of electrons transferred and the H2O2 percentage efficiency were 3.1 and 44%, respectively. The ring-current of the 4% CeO2/C was higher than that of Vulcan carbon, the reference material for H2O2 production, which produced 41% H2O2 and transferred 3.1 electrons per molecule of oxygen. The overpotential for this reaction on the ceria-based catalyst was substantially lower (approximately 200 mV), demonstrating the higher catalytic performance of this material. Gas diffusion electrodes (GDE) containing the catalyst were used to evaluate the real amount of H2O2 produced during exhaustive electrolysis. The 4% CeO2/C GDE produced 871 mg L-1 of H2O2, whereas the Vulcan carbon GDE produced a maximum amount of only 407 mg L-1. Thus, the 4% CeO2/C electrocatalyst prepared by the PPM is a promising material for H2O2 electrogeneration in alkaline media. (C) 2011 Elsevier B.V. All rights reserved.
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A tank experiment was conducted to check if self-potential (SP) signals can be generated when buried organic matter is wire-connected to a near-surface, oxygen-rich, sediment layer. This experiment demonstrated that once wired, there was a flux of electrons (hence an electric current) between the lower and upper layers of the sandbox with the system responding as a large-scale microbial fuel cell (a type of bioelectrochemical system). An electric current was generated by this process in the wire and the SP method was used to monitor the associated electric potential distribution at the top of the tank.. The electric field was controlled by the flux of electrons through the wire, the oxidation of the organic matter, the reduction of oxygen used as a terminal electron acceptor, and the distribution of the DC resistivity in the tank. The current density through the wire was limited by the availability of oxygen and not by the oxidation of the organic matter. This laboratory experiment incorporated key elements of the biogeobattery observed in some organic-rich contaminant plumes. This analogy includes the generation of SP signals associated with a flux of electrons, the capacity of buried organic matter in sustaining anodic reactions, network resistance connecting terminal redox reactions spatially separated in space, and the existence of anodic secondary coupled reactions. A resistivity tomogram of the tank, after almost a year in operation, suggests that oxidative processes triggered by this geobattery can be imaged with this method to determine the radius of influence of the bioelectrochemical system.
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Hybrid materials with enhanced properties can now be obtained by combining nanomaterials such as carbon nanotubes and metallic nanoparticles, where the main challenge is to control fabrication conditions. In this study, we demonstrate that platinum nanoparticles (PtNps) can be electrogenerated within layer-by-layer (LbL) films of polyamidoamine (PAMAM) dendrimers and single-walled carbon nanotubes (SWCNTs), which serve as stabilizing matrices. The advantages of the possible control through electrogeneration were demonstrated with a homogeneous distribution of PtNps over the entire surface of the PAMAM/SWCNT LbL films, whose electroactive sites could be mapped using magnetic force microscopy. The Pt-containing films were used as catalysts for hydrogen peroxide reduction, with a decrease in the reduction potential of 60 mV compared to a Pt film deposited onto bare ITO. By analyzing the mechanisms responsible for hydrogen peroxide reduction, we ascribed the enhanced catalytic activity to synergistic effects between platinum and carbon in the LbL films, which are promising for sensing and fuel cell applications.
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The work of this thesis has been focused on the characterization of metallic membranes for the hydrogen purification from steam reforming process and also of perfluorosulphonic acid ionomeric (PFSI) membranes suitable as electrolytes in fuel cell applications. The experimental study of metallic membranes was divided in three sections: synthesis of palladium and silver palladium coatings on porous ceramic support via electroless deposition (ELD), solubility and diffusivity analysis of hydrogen in palladium based alloys (temperature range between 200 and 400 °C up to 12 bar of pressure) and permeation experiments of pure hydrogen and mixtures containing, besides hydrogen, also nitrogen and methane at high temperatures (up to 600 °C) and pressures (up to 10 bar). Sequential deposition of palladium and silver on to porous alumina tubes by ELD technique was carried out using two different procedures: a stirred batch and a continuous flux method. Pure palladium as well as Pd-Ag membranes were produced: the Pd-Ag membranes’ composition is calculated to be close to 77% Pd and 23% Ag by weight which was the target value that correspond to the best performance of the palladium-based alloys. One of the membranes produced showed an infinite selectivity through hydrogen and relatively high permeability value and is suitable for the potential use as a hydrogen separator. The hydrogen sorption in silver palladium alloys was carried out in a gravimetric system on films produced by ELD technique. In the temperature range inspected, up to 400°C, there is still a lack in literature. The experimental data were analyzed with rigorous equations allowing to calculate the enthalpy and entropy values of the Sieverts’ constant; the results were in very good agreement with the extrapolation made with literature data obtained a lower temperature (up to 150 °C). The information obtained in this study would be directly usable in the modeling of hydrogen permeation in Pd-based systems. Pure and mixed gas permeation tests were performed on Pd-based hydrogen selective membranes at operative conditions close to steam-reforming ones. Two membranes (one produced in this work and another produced by NGK Insulators Japan) showed a virtually infinite selectivity and good permeability. Mixture data revealed the existence of non negligible resistances to hydrogen transport in the gas phase. Even if the decrease of the driving force due to polarization concentration phenomena occurs, in principle, in all membrane-based separation systems endowed with high perm-selectivity, an extensive experimental analysis lack, at the moment, in the palladium-based membrane process in literature. Moreover a new procedure has been introduced for the proper comparison of the mass transport resistance in the gas phase and in the membrane. Another object of study was the water vapor sorption and permeation in PFSI membranes with short and long side chains was also studied; moreover the permeation of gases (i.e. He, N2 and O2) in dry and humid conditions was considered. The water vapor sorption showed strong interactions between the hydrophilic groups and the water as revealed from the hysteresis in the sorption-desorption isotherms and thermo gravimetric analysis. The data obtained were used in the modeling of water vapor permeation, that was described as diffusion-reaction of water molecules, and in the humid gases permeation experiments. In the dry gas experiments the permeability and diffusivity was found to increase with temperature and with the equivalent weight (EW) of the membrane. A linear correlation was drawn between the dry gas permeability and the opposite of the equivalent weight of PFSI membranes, based on which the permeability of pure PTFE is retrieved in the limit of high EW. In the other hand O2 ,N2 and He permeability values was found to increase significantly, and in a similar fashion, with water activity. A model that considers the PFSI membrane as a composite matrix with a hydrophilic and a hydrophobic phase was considered allowing to estimate the variation of gas permeability with relative humidity on the basis of the permeability in the dry PFSI membrane and in pure liquid water.
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L’attuale condizione che caratterizza il settore energetico richiede un necessario processo di riconversione che, oltre a favorire il risparmio energetico, riduca la dipendenza dai combustibili fossili ed accresca l’impiego di fonti energetiche rinnovabili, dando un contributo fondamentale alla riduzione delle emissioni di gas serra come diversi accordi internazionali richiedono. Si rende pertanto necessario accelerare i processi che da alcuni anni stanno favorendo l’utilizzo di energia da fonti rinnovabili. Tra queste, le fonti legate ai processi di trattamento biologico dei reflui stanno avendo un interessante sviluppo. Esistono numerosi processi biologici che consentono la produzione di energia in maniera indiretta, quali ad esempio i processi di digestione anaerobica finalizzati alla produzione di biogas e/o produzione biologica di idrogeno. In tale contesto si inserisce la tecnologia delle Microbial Fuel Cell, che consente la produzione diretta di energia elettrica, finalizzata al recupero energetico inteso al miglioramento dell’efficienza energetica e alla riduzione dei costi d’esercizio di impianti di trattamento biologico dei reflui. Il presente lavoro di Tesi di Dottorato sperimentale, svoltosi in collaborazione al laboratorio PROT.-IDR. della sede ENEA di Bologna, riporta i risultati dell’attività di ricerca condotta su una MFC (Microbial Fuel Cell) a doppio stadio biologico per il trattamento di reflui ad elevato carico organico e produzione continua di energia elettrica. E’ stata provata l’applicabilità della MFC con entrambi i comparti biotici utilizzando elettrodi di grafite non trattata ottenendo, con un carico organico in ingresso di circa 9 gd-1, valori di potenza massima prodotta che si attestano su 74 mWm-2, corrente elettrica massima generata di 175 mAm-2 ad una tensione di 421 mV, ed una conversione di COD in elettricità pari a 1,2 gCODm-2d-1. I risultati sono stati molto positivi per quanto riguarda le prestazioni depurative ottenute dalla MFC. L’efficienza di depurazione misurata ha raggiunto un valore massimo del 98% di rimozione del COD in ingresso, mentre e la concentrazione di azoto ammoniacale nell’effluente raccolto all’uscita del sedimentatore è sempre stata inferiore a 1 mgN-NH4+l-1. Tra gli obiettivi posti all’inizio della sperimentazione si è rivelata di notevole interesse la valutazione del possibile utilizzo della MFC come sistema per il monitoraggio on-line del COD e degli acidi grassi volatili (VFA) prodotti all’interno di un digestore anaerobico, attraverso la definizione di una correlazione tra i dati elettrici registrati in continuo e le concentrazioni di CODanaer e VFA misurate in diversi periodi della sperimentazione. L’analisi DGGE della biomassa catodica ha fornito uno strumento analitico utile allo studio della diversità della comunità microbica sospesa ed adesa al catodo e ha confermato la forte similarità delle specie batteriche riconosciute nei campioni analizzati. In particolare, le bande di sequenziamento ottenute sono affiliate ai gruppi batterici Firmicutes, -Proteobacteria, -Proteobacteria, -Proteobacteria e Bacteroidetes. Da quanto emerso dalla sperimentazione condotta si può pertanto concludere che ad oggi le MFC sono in fase di evoluzione rispetto ai primi prototipi utilizzati per lo studio delle comunità microbiali e per la comprensione dei meccanismi di trasferimento elettronico. Sfruttarne la potenza prodotta in maniera commerciale diviene una grande sfida per il futuro, ed è opinione comune che le prime applicazioni pratiche delle MFC saranno come fonte di recupero energetico per i dispositivi utilizzati per il monitoraggio dell’ambiente e per il trattamento delle acque reflue.
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Es werden neuartige, polymere Protonenleiter vorgestellt die nach dem 'Konzept des polymergebunden Protonensolvens' realisiert wurden. Sie zeigen protonische Leitfähigkeit als intrinsische Eigenschaft, sodass keine zweite, flüssige Phase zur Protonenleitung nötig ist. Verwirklicht wurde das Konzept anhand von kammartigen Siloxanoligomeren und -polymeren, wobei Imidazol als Protonensolvens durch flexible Spacer kovalent an das Rückgrat gebunden ist. Durch Pfropfung mit imidazoltragenden Spacereinheiten wurden ferner Kieselgelnanopartikel oberflächenmodifiziert. Um die Auswirkungen der Immobilisierung von Imidazol auf die Leitfähigkeit zu untersuchen, wurden neben unterschiedlichen Molekulargewichten, die Verbindungen auch jeweils mit verschiedenen Spacerlängen synthetisiert. Die Materialien wurden umfassend charakterisiert und auf ihr thermisches Verhalten, Stabilität, Leitfähigkeit, Diffusion und dielektrisches Verhalten sowie auch nach Dotierung mit Säure untersucht. Thermisch stabil sind die Materialien bis ca. 200°C. Die Leitfähigkeiten betragen bis zu 1,5E-3 S/cm bei 160°C, welche aufgrund der Immobilisierung des Imidazols ausschließlich auf Strukturdiffusion zurückzuführen sind. Die Strukturdiffusion ist vergleichbar mit dem Grotthus-Mechanismus in Wasser und wird durch die lokale Mobilität der Imidazolmoleküle, d.h. durch die Glasübergangstemperatur des Systems bestimmt. Entsprechend wird das für Glasbildner typische Vogel-Tamman-Fulcher-Verhalten für alle untersuchten Transportprozesse gefunden. Die mit abnehmender Glasübergangstemperatur abnehmende mechanische Stabilität der Materialien kann, wie gezeigt ist, durch Compoundierung mit Kieselgelnanopartikeln entscheidend verbessert werden, was eine kostengünstige und aussichtsreiche Möglichkeit zur Herstellung von Membranen für Brennstoffzellen darstellt.
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Mit Hilfe von Brennstoffzellen wird eine effiziente Energieumwandlung von chemischer in elektrische Energie möglich. Die kommerziellen PEM-Brennstoffzellen benutzen Membra-nen, die zum Erreichen hoher Leitfähigkeiten eine wässrige Phase erfordern, in der der Proto-nentransport stattfindet. Somit wird die Betriebstemperatur durch den Siedepunkt des Wassers limitiert. Die verwendeten Pt-Katalysatoren zeigen bei niedrigen Temperaturen eine höhere Empfindlichkeit gegenüber CO, dass im Reformierungsprozess bei der Erzeugung von Was-serstoff entsteht. Austausch der wässrigen Phase gegen Heterozyklen, die ein zu Wasser ver-gleichbares Wasserstoffbrückennetzwerk aufbauen, in dem der Protonentransport stattfinden kann, ermöglicht eine höhere Betriebstemperatur. Durch das im Laufe des Brennstoffzellen-betriebs gebildete Wasser, können die Heterozyklen verdünnt bzw. komplett aus der Memb-ran ausgewaschen werden. Daher ist es erforderlich, die Ladungsträger an ein Polymerrück-grat zu binden, so dass sie eine hohe Beweglichkeit und Konzentration, die denen in der flüs-sigen Phase einer konventionellen Membran entsprechen, aufweisen. Diese Arbeit beschreibt die Synthese und Charakterisierung von Protonenleitern, die ohne eine flüssige Phase auskommen, da sie bereits protonische Leitfähigkeit als intrinsische Ei-genschaft zeigen. Es wurden verschiedene imidazol- bzw. benzimidazolhaltige Dimere und Polythiophene, in denen Benzimidazol in der Seitenkette über verschieden flexible Spacer mit dem Polymerrückgrat verbunden ist, synthetisiert. Die Materialien wurden in undotierten Zu-stand und nach Dotierung mit geringen Mengen Phosphorsäure umfassend charakterisiert und auf thermisches Verhalten, Stabilität und Leitfähigkeit untersucht. Die benzimidazolhaltigen Dimere weisen mit 250 °C die höchsten Zersetzungstemperaturen auf. Mit zunehmender Temperatur kann in allen Fällen eine Erhöhung der Leitfähigkeit beobachtet werden, die sich in der Arrhenius-Auftragung durch eine Gerade anpassen lässt, somit kann der Protonentrans-port durch einen Protonen-hüpfmechanismus beschrieben werden. Die höchste beobachtete Leitfähigkeit liegt im Bereich von 10-6 S/cm bei 160 °C. Durch Zusatz von Phosphorsäure kann die Leitfähigkeit z.T. um einige Größenordnungen gesteigert werden. Eine Ausnahme bilden die Polythiophene, die sowohl protonische als auch elektronische Leitfähigkeit besit-zen. Hier führt die Säure zu einer Lokalisierung der Ladungsträger, so dass die elektronische Leitfähigkeit eingeschränkt wird.
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In dieser Arbeit werden drei wasserstoffverbrückte Systeme in der kondensierten Phase mit Hilfe von first-principles-Elektronenstruktur-Rechnungen untersucht, die auf der Dichtefunktionaltheorie (DFT) unter periodischen Randbedingungen basieren. Ihre lokalen Konformationen und Wasserstoffbrückenbindungen werden mittels ab-initio Molekulardynamiksimulationen berechnet und weiterhin durch die Bestimmung ihrer spektroskopischen Parameter charakterisiert. Der Schwerpunkt liegt dabei auf lokalen Strukturen und auf schnellen Fluktuationen der Wasserstoffbrückenbindungen, welche von zentraler Bedeutung für die physikalischen und chemischen Eigenschaften der betrachteten Systeme sind. Die für die lokalen, instantanen Konformationen berechneten Spektren werden verwendet, um die physikalischen Prozesse, die hinter den untersuchten Phänomenen stehen, zu erklären: die Wasseradsorption auf metallischen Oberflächen, die Ionensolvatisierung in wässrigen Lösungen und der Protonentransport in protonleitenden Polymeren, welche Prototypen von Membranen für Brennstoffzellen sind. Die Möglichkeit der Vorhersage spektroskopischer Parameter eröffnet vielfältige Möglichkeiten des Dialogs zwischen Experimenten und numerischen Simulationen. Die in dieser Arbeit vorgestellten Ergebnisse zeigen, dass die Zuverlässigkeit dieser theoretischen Berechnungen inzwischen für viele experimentell relevante Systeme ein quantitatives Niveau erreicht hat.