<p>In this doctoral project, a relatively new form of carbon material, with unique narrow pore size distribution around 7 Å and with uniform structure, has been electrochemically characterised using the single particle microelectrode technique. The carbon has been used as electrode material for supercapacitors. This type of capacitors is used as high power energy buffers in hybrid vehicles and for stationary power backup. The principle for the microelectrode technique consists of connecting a carbon particle with a carbon fibre by means of a micromanipulator. The single particle and carbon fibre together form a microelectrode. Combination of this technique with electroanalytical methods such as cyclic voltammetry and potential step measurements allows for the survey of electrochemical phenomena and for the determination of ion transport parameters inside the nanopores.</p><p>A mathematical model based on Fick’s second law, for diffusion of ions inside the nanopores at non steady state, was used for the determination of effective diffusion coefficients (Deff). The coefficients were calculated from an asymptotic solution of Fick’s equation, applied for a thin layer adjacent to the external surface of the carbon particles and valid for the current response in a short time region. Another asymptotic solution was obtained, using spherical geometry and valid for the current response in a long time region.</p><p>In this doctoral work, the carbon particles have been exposed to potential cycling, which mimics that of large electrodes during operation of a double layer capacitor. The potential-current response, E-I, for the nanoporous carbon, shows a pure capacitive behaviour between –0.5 V and 0.1 V vs. the Hg|HgO reference electrode. The detection of the faradaic processes beyond these potentials was possible by lowering of the voltammometric sweep rate. The electrochemical processes occurring at positive and at negative potential were investigated separately.</p><p>Cyclic voltammometric measurements showed that the chemisorption of hydroxyl groups, occurring between 0.1 and 0.3 V, leads to a mild oxidation of the carbon structure, resulting in surface groups containing an oxygen atom at a specific carbon site (e.g., phenolic or quinine type). These oxygen-containing surface groups caused an increase of the specific capacitance, which remained constant throughout a number of voltammometric cycles. The Deff decreased on the other hand with the number of cycles. The Deff decreases also with the positive potential. The evaluation of Deff indicates adsorption of hydroxyl groups and an increase of the effective tortuosity of the pore system.</p><p>The oxidation of the carbon particles, between 0 and 0.5 V, leads to more extensive oxidation and to surface groups containing two oxygen atoms at a single carbon site, followed by formation of carbonate ions. The oxygen-containing surface groups and carbonate ions formed at these potentials do not contribute to the specific capacitance and drastically retard or obstruct the ion transport inside the nanopores.</p><p>At negative potentials the carbon particles show a dominantly capacitive behaviour. The faradaic processes taking place below –0.5 V vs. Hg|HgO reference electrode are generation and adsorption of hydrogen. These processes do not perturb significantly the electrochemical and ion transport properties of the nanoporous carbon particles. It was found that hydrogen generation occurs at –0.5 V vs. Hg|HgO and that two hydrogen oxidation processes take place at positive potentials. The results indicate that the weakly adsorbed hydrogen undergoes oxidation between 0 and 0.1 V and that the strongly adsorbed hydrogen is oxidised at more positive potentials.</p><p>The single particle technique was adapted for the determination of diffusion coefficients of an organic electrolyte. The different size of the anions and cations caused different transport characteristics at negative and positive potentials. Slow cycling was found important for ion penetration inside the nanopores and for the evaluation of the effective diffusion coefficients.</p><p>The effective diffusion coefficients for the nanoporous carbon using aqueous 6M KOH and 0.1M TEABF4 in acetonitrile were estimated to 1.4 (±0.8).10-9 cm2 s-1 and 1.3 (±0.4) 10-8 cm2 s-1, respectively.</p>

In this doctoral thesis the two dimensional material graphene has been studied in depth with particular respect to Zener tunnelling devices. From the hexagonal structure the Hamiltonian at a Dirac point was derived with the option of including an energy gap. This Hamiltonian was then used to obtain the tunnelling properties of various graphene nano-devices; the devices studied include Zener tunnelling potential barriers such as single and double graphene potential steps. A form of the Landauer formalism was obtained for graphene devices. Combined with the scattering properties of potential barriers the current and conductance was found for a wide range of graphene nano-devices. These results were then compared to recently obtained experimental results for graphene nano-ribbons, showing many similarities between nano-ribbons and infinite sheet graphene. The methods studied were then applied to materials which have been shown to possess three dimensional Dirac cones known as topological insulators. In the case of Cd3As2 the Dirac cone is asymmetrical with respect to the z-direction, the effect of this asymmetry has been discussed with comparison to the symmetrical case.

In this doctoral project, a relatively new form of carbon material, with unique narrow pore size distribution around 7 Å and with uniform structure, has been electrochemically characterised using the single particle microelectrode technique. The carbon has been used as electrode material for supercapacitors. This type of capacitors is used as high power energy buffers in hybrid vehicles and for stationary power backup. The principle for the microelectrode technique consists of connecting a carbon particle with a carbon fibre by means of a micromanipulator. The single particle and carbon fibre together form a microelectrode. Combination of this technique with electroanalytical methods such as cyclic voltammetry and potential step measurements allows for the survey of electrochemical phenomena and for the determination of ion transport parameters inside the nanopores. A mathematical model based on Fick’s second law, for diffusion of ions inside the nanopores at non steady state, was used for the determination of effective diffusion coefficients (Deff). The coefficients were calculated from an asymptotic solution of Fick’s equation, applied for a thin layer adjacent to the external surface of the carbon particles and valid for the current response in a short time region. Another asymptotic solution was obtained, using spherical geometry and valid for the current response in a long time region. In this doctoral work, the carbon particles have been exposed to potential cycling, which mimics that of large electrodes during operation of a double layer capacitor. The potential-current response, E-I, for the nanoporous carbon, shows a pure capacitive behaviour between –0.5 V and 0.1 V vs. the Hg|HgO reference electrode. The detection of the faradaic processes beyond these potentials was possible by lowering of the voltammometric sweep rate. The electrochemical processes occurring at positive and at negative potential were investigated separately. Cyclic voltammometric measurements showed that the chemisorption of hydroxyl groups, occurring between 0.1 and 0.3 V, leads to a mild oxidation of the carbon structure, resulting in surface groups containing an oxygen atom at a specific carbon site (e.g., phenolic or quinine type). These oxygen-containing surface groups caused an increase of the specific capacitance, which remained constant throughout a number of voltammometric cycles. The Deff decreased on the other hand with the number of cycles. The Deff decreases also with the positive potential. The evaluation of Deff indicates adsorption of hydroxyl groups and an increase of the effective tortuosity of the pore system. The oxidation of the carbon particles, between 0 and 0.5 V, leads to more extensive oxidation and to surface groups containing two oxygen atoms at a single carbon site, followed by formation of carbonate ions. The oxygen-containing surface groups and carbonate ions formed at these potentials do not contribute to the specific capacitance and drastically retard or obstruct the ion transport inside the nanopores. At negative potentials the carbon particles show a dominantly capacitive behaviour. The faradaic processes taking place below –0.5 V vs. Hg|HgO reference electrode are generation and adsorption of hydrogen. These processes do not perturb significantly the electrochemical and ion transport properties of the nanoporous carbon particles. It was found that hydrogen generation occurs at –0.5 V vs. Hg|HgO and that two hydrogen oxidation processes take place at positive potentials. The results indicate that the weakly adsorbed hydrogen undergoes oxidation between 0 and 0.1 V and that the strongly adsorbed hydrogen is oxidised at more positive potentials. The single particle technique was adapted for the determination of diffusion coefficients of an organic electrolyte. The different size of the anions and cations caused different transport characteristics at negative and positive potentials. Slow cycling was found important for ion penetration inside the nanopores and for the evaluation of the effective diffusion coefficients. The effective diffusion coefficients for the nanoporous carbon using aqueous 6M KOH and 0.1M TEABF4 in acetonitrile were estimated to 1.4 (±0.8).10-9 cm2 s-1 and 1.3 (±0.4) 10-8 cm2 s-1, respectively.

This thesis is concerned with kinetic characterisation of theinsertion compound LiMn2O4, which is used as positive electrodematerial in rechargeable lithium batteries. Three different typesof electrode configurations have been investigated, namely singleparticles, thin films and composite electrodes. Differentelectrochemical techniques, i.e. linear sweep voltammetry (LSV),electrochemical impedance spectroscopy (EIS), potential step, andgalvanostatic experiments were applied under various experimentalconditions. The majority of the experimental data were analysedby relevant mathematical models used for describing the reactionsteps of insertion compounds. It was concluded that a model based on interfacialcharge-transfer, solid-phase diffusion and an external iR-dropcould be fairly well fitted to LSV data measured on a singleelectrode system over a narrow range of sweep rates. However, itwas also found that the fitted parameter values vary greatly withthe characteristic length and the sweep rate. This indicates thatthe physical description used is too simple for explaining theelectrochemical responses measured over a large range of chargeand discharge rates. EIS was found to be a well-suited technique for separatingtime constants for different physical processes in the insertionand extraction reaction. It was demonstrated that the impedanceresponse is strongly dependent on the current collector used.According to the literature, reasonable values of theexchange-current density and solid-phase diffusion coefficientwere determined for various states-of-discharge, temperatures andelectrolyte compositions. Experiments were carried out in bothliquid and gel electrolytes. A method which improves thedistinction between the time constants related to thematerial’s intrinsic properties and possible porous effectsis presented. The method was applied to composite electrodes.This method utilises, in addition to the impedance responsemeasured in front of the electrode, also the impedance measuredat the backside of the electrode. Finally, the kinetics of a composite electrode was alsoinvestigated by in situ X-ray diffraction (in situ XRD) incombination with galvanostatic and potentiostatic experiments. Noevidence of lithium concentration gradients could be observedfrom XRD data, even at the highest rate applied (i.e. ~6C), thusexcluding solid-phase diffusion and also phase-boundary movement,as described by Fick’s law, as the ratelimiting step. <b>Key words:</b>linear sweep voltammetry, electrochemicalimpedance spectroscopy, potential step, in situ X-raydiffraction, microelectrodes, electrode kinetics, LiMn2O4cathode, rechargeable lithium batteries

<p>This thesis is concerned with kinetic characterisation of theinsertion compound LiMn2O4, which is used as positive electrodematerial in rechargeable lithium batteries. Three different typesof electrode configurations have been investigated, namely singleparticles, thin films and composite electrodes. Differentelectrochemical techniques, i.e. linear sweep voltammetry (LSV),electrochemical impedance spectroscopy (EIS), potential step, andgalvanostatic experiments were applied under various experimentalconditions. The majority of the experimental data were analysedby relevant mathematical models used for describing the reactionsteps of insertion compounds.</p><p>It was concluded that a model based on interfacialcharge-transfer, solid-phase diffusion and an external iR-dropcould be fairly well fitted to LSV data measured on a singleelectrode system over a narrow range of sweep rates. However, itwas also found that the fitted parameter values vary greatly withthe characteristic length and the sweep rate. This indicates thatthe physical description used is too simple for explaining theelectrochemical responses measured over a large range of chargeand discharge rates.</p><p>EIS was found to be a well-suited technique for separatingtime constants for different physical processes in the insertionand extraction reaction. It was demonstrated that the impedanceresponse is strongly dependent on the current collector used.According to the literature, reasonable values of theexchange-current density and solid-phase diffusion coefficientwere determined for various states-of-discharge, temperatures andelectrolyte compositions. Experiments were carried out in bothliquid and gel electrolytes. A method which improves thedistinction between the time constants related to thematerial’s intrinsic properties and possible porous effectsis presented. The method was applied to composite electrodes.This method utilises, in addition to the impedance responsemeasured in front of the electrode, also the impedance measuredat the backside of the electrode.</p><p>Finally, the kinetics of a composite electrode was alsoinvestigated by in situ X-ray diffraction (in situ XRD) incombination with galvanostatic and potentiostatic experiments. Noevidence of lithium concentration gradients could be observedfrom XRD data, even at the highest rate applied (i.e. ~6C), thusexcluding solid-phase diffusion and also phase-boundary movement,as described by Fick’s law, as the ratelimiting step.</p><p><b>Key words:</b>linear sweep voltammetry, electrochemicalimpedance spectroscopy, potential step, in situ X-raydiffraction, microelectrodes, electrode kinetics, LiMn2O4cathode, rechargeable lithium batteries</p>

Orientador: Stefano de Leo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-08-15T11:34:18Z (GMT). No. of bitstreams: 1 Silva_KeniaCristinaPereira_M.pdf: 5917573 bytes, checksum: 689b0e6d7c10b6ea1e4524486138cc7e (MD5) Previous issue date: 2010 / Resumo: O objetivo principal deste trabalho é estudar a equação de Schrödinger para um potencial quaterniônico tipo barreira. A solução analítica encontrada permite comparar qualitativamente as diferenças entre a mecânica quântica complexa e a mecânica quântica quaterniônica. Antes de apresentar a solução analítica da barreira, para um melhor entendimento da motivação que leva ao estudo de uma mecânica quântica quaterniônica, será analisado em detalhes (ondas planas e pacotes de onda) o potencial tipo degrau / Abstract: The main objective of this research is to study the Schrödinger equation for a quaternionic potential barrier. The analytical solution found allow us to compare qualitatively the differences between the complex quantum mechanics and the quaternionic quantum mechanics. Before presenting the barrier analytical solution, to a better understanding of the motivation that leads us to the study of quaternionic quantum mechanics, the potencial step will be discussed in detail (plane waves and wave packets) / Mestrado / Fisica-Matematica / Mestre em Matemática Aplicada

Mit Lösungen von 9,10-Diphenylanthracen und N(C2H5)4ClO4 oder N(C4H9)4ClO4 als Leitsalz im Lösungsmittel Acetonitril wurden Elektrochemilumineszenz (ECL)-Experimente durchgeführt. Dazu wurden die Elektroden mit Folgen von jeweils drei in bestimmten zeitlichen Abständen aufeinander folgenden Potentialsprüngen polarisiert. Es wird gezeigt, dass bei entsprechender Wahl der Potentiale und der Haltezeiten anodische und kathodische ECL-Emissionen gleicher Intensität erzeugt werden können. Sodann wurde ECL in den Derivaten von Poly(p-phenylen-vinylen), MEH-PPV und DB-PPV erzeugt. Diese leitfähigen Polymere wurden als dünne Schichten auf Platin-Elektroden aufgebracht und wie bei ECL aus der Lösungsphase in Acetonitril-Elektrolyten mit Tetralkylammonium-Leitsalzen Potentialsprüngen unterworfen. Bei geeigneter Einstellung der Potentialsprünge und Haltezeiten konnten anodische und kathodische ECL gleicher Intensität erhalten werden. Dies ist das erste Mal, dass symmetrische ECL mit polymerbeschichteten Elektroden erhalten wurde. Die Kinetik der ECL weicht deutlich von der aus der Lösungsphase ab. Der ECL-Prozess verläuft langsamer als in der Lösungsphase, und der Leitelektrolyt hat einen signifikanten Einfluss auf das elektrochemische Verhalten der Polymerschicht. Die Ursachen dafür wurden über Modellrechnungen analysiert, mit denen die Ladungstransportprozesse in der Polymerschicht simuliert wurden. In derartigen Simulationsrechnungen konnten die Geschwindigkeitskonstanten der ECL-Reaktion sowohl im Polymer als auch in der Lösung bestimmt werden. Um die Stabilität der Polymerschichten zu erhöhen, wurde versucht, die Polymerketten mit Synchrotronstrahlung zu vernetzen. Diese Experimente brachten nicht das erwartete Ergebnis. Die Ursachen dafür werden auf der Grundlage von Ex-Situ-Raman-spektroskopischen Untersuchungen diskutiert. / Electrochemiluminescence (ECL) has been generated in solution phase using 9,10-diphenylanthracene (DPA) with TEAClO4 (or TBAClO4) in acetonitrile solvent. Triple potential step was used for the generation of ECL. It was found that anodic and cathodic ECL of equal intensities can be generated by proper choice of potential step magnitude, width and the waiting period (tw) between successive triple potential steps. ECL was then generated in conducting polymers poly(2-ethylhexyloxy-5-methoxy-1,4-phenylenevinylene) (MEH-PPV) and poly(2,3-dibutoxy-1,4-phenylenevinylene) (DB-PPV) by coating them on Pt electrodes and subjecting to potential steps in tetraalkylammonium salt solutions with acetonitrile. Similar to the case of solution phase ECL, symmetrical anodic and cathodic ECL could be observed by the appropriate choice of the potential step parameters. But the kinetics of the ECL was found to be different from that of the solution phase ECL. The time scale of the ECL process was found to be longer than that in the solution phase ECL. The nature of supporting electrolyte had a remarkable impact on the electrochemistry of conducting polymers. The reasons were analyzed by theoretical calculations evoking the concept of charge transport characteristics of conducting polymers. The rate constants of the ECL process were calculated by separate simulation procedure in the solution phase as well as in the polymer phase ECL. To enhance the stability of conducting polymers, synchrotron radiation induced cross-linking was performed. The effects were different from expected which were analyzed and rationalized by ex-situ Raman spectroscopic studies.