Electrolytic solutions contain mobile ions that can pass current, and are essential components of any solution-phase electrochemical system. The Nernst–Planck–Poisson equations describe the electrodynamics and transport dynamics of electrolytic solutions. This thesis applies modern numerical and mathematical techniques in order to solve these equations, and hence determine the behaviour of electrochemical systems involving charge transport. The following systems are studied: a liquid junction where a concentration gradient causes charge transport; an ideally polarisable electrode where an applied potential difference causes charge transport; and an electrochemical cell where electrolysis causes charge transport. The nanometre Debye length and nanosecond Debye time scales are shown to control charge separation in electrolytic solutions. At equilibrium, charge separation is confined to within a Debye length scale of a charged electrode surface. Non-equilibrium charge separation is compensated in solution on a Debye time scale following a perturbation, whereafter electroneutrality dictates charge transport. The mechanism for the recovery of electroneutrality involves both migration and diffusion, and is non-linear for larger electrical potentials. Charge separation is an extremely important consideration on length scales comparable to the Debye length. The predicted features of capacitive charging and electrolysis at nanoelectrodes are shown to differ qualitatively from the behaviour of larger electrodes. Nanoscale charge separation can influence the behaviour of a larger system if it limits the overall rate of mass transport or electron transfer. This thesis advocates the use of numerical methods to solve the Nernst–Planck–Poisson equations, in order to avoid the simplifying approximations required by traditional analytical methods. As this thesis demonstrates, this methodology can reveal the behaviour of increasingly elaborate electrochemical systems, while illustrating the self-consistency and generality of fundamental theories concerning charge transport.

Lorsqu'un solide est en contact avec un liquide, des phénomènes physico-chimiques conduisent à polariser l'interface. Deux zones de charge, de signe opposé, apparaissent à cette interface, une dans le solide et l'autre dans le liquide, formant ainsi la double couche électrique (DCE). Par rapport à la littérature existante, l’originalité de ce travail est de s’intéresser à la DCE à l’interface acier inoxydable 304L /film passif d’oxyde/ solution de NaCl (0.01M) en couplant des caractérisations électrochimiques, électriques et physiques. Une méthodologie de caractérisation par voie électrochimique en utilisant les méthodes de spectroscopie d’impédance (SIE) et de voltammétrie cyclique (CV) a été mise au point pour accéder à deux paramètres: la capacité effective et la densité surfacique de charge. Des modifications de la concentration de l'électrolyte, du potentiel appliqué et de l'état de surface ont ensuite été réalisées : la capacité effective de la DCE dépend principalement de la concentration et du potentiel et la densité surfacique de charge croît avec la concentration. Dans la gamme étudiée, la rugosité a une faible influence sur la capacité effective mesurée. Des analyses physico-chimiques de la surface ont permis de caractériser les films passifs formés sur l'acier, sans révéler de différences significatives entre les surfaces avant et après immersion. Un autre paramètre caractéristique de la DCE, la densité volumique de charge à la paroi, a été aussi déterminé par la méthode d'électrisation par écoulement du liquide. Les 3 méthodes de caractérisation (SIE, CV et électrisation) confirment l'influence de la concentration sur les caractéristiques de la DCE. / When a metal is immersed in an electrolyte, a charge distribution is created at the interface and a potential is set up across the two phases. The separation between charges give rise to what are known as electric double layers (EDL). Compared to the usual solid/liquid interfaces investigated in the literature, this study is dedicated to the EDL at the stainless steel 304L / passive film / NaCl (0.01M) interface by combining electrochemical, electrical and physical methods. First, a methodology has been set up to characterise the EDL by the electrochemical methods: Electrochemical Impedance Spectroscopy (EIS) and cyclic voltammetry (CV). Both the effective capacity and the surface charge density were evaluated. Then, several parameters were investigated such as the electrolyte concentration, the applied potential and the influence on the EDL of the surface preparation. The results showed that the double layer capacitance depends mainly on the concentration of the electrolyte and on the applied potential. The roughness seems to have a poor influence on the measured capacitance. Various physico-chemical analysis were performed in order to characterise the passive films formed at the surface: no significant difference could have been evidence between the surfaces before and after immersion. Finally, the volume charge density was also determined by the liquid flow electrification measurement. Whatever the characterization techniques used (EIS, CV or flow electrification), the same trend was observed with regard to the influence of the concentration on the characteristics of the EDL.

L’objectif de ce travail est d’élaborer des matériaux composites modèles nanotubes de carbone/polymères permettant de tirer profit des propriétés des nanotubes de carbone à l’échelle macroscopique. L’obtention de tels matériaux nécessitant une fonctionnalisation homogène entre les nanotubes de carbone et les polymères, les nanotubes de carbone utilisés doivent être individuels et de même réactivité chimique, donc de même diamètre. Ainsi, ils doivent être synthétisés par CVD par des nanoparticules catalytiques monodisperses et supportées. Dans la première partie, nous avons élaboré une nouvelle méthode générique de synthèse de nanoparticules d’oxydes métalliques supportées. Nous avons principalement détaillé la synthèse de nanoparticules de Fe2O3 dont la distribution en taille est de 1.1 ± 0.3 nm. Dans la deuxième partie, après avoir étudié la stabilité thermique de ces nanoparticules, nous les avons utilisées pour catalyser la croissance des nanotubes de carbone monofeuillets individuels par CVD. La caractérisation des nanotubes obtenus par Raman indique une distribution en diamètre exceptionnellement étroite de 1.27 ± 0.15 nm. Dans la troisième partie, nous avons tout d’abord étudié la mise en solution des nanotubes de carbone par fonctionnalisation non covalente avec un polymère hydrosoluble le POE portant un motif pyrène en bout de chaîne et mis en évidence un phénomène de déplétion qui limite la solubilisation des nanotubes. Nous avons ensuite élaboré des matériaux composites nanotubes de carbone/rrP3HT par fonctionnalisation covalente et non covalente et nous avons étudié l’efficacité de séparation de charge dans les deux cas de fonctionnalisations. / The aim of this work is to develop composite materials carbon nanotubes/polymers to take advantage of properties of carbon nanotubes at macroscopic scale. To get such materials, homogeneous functionalization between carbon nanotubes and polymers is required, carbon nanotubes must be individual with the same chemical reactivity, therefore the same diameter. Thus, they must be synthesized by CVD from monodispersed and supported catalyst nanoparticles. In the first part, we developed a new universal method for the synthesis of metal oxide supported nanoparticles. We mainly detailed the synthesis of Fe2O3 nanoparticles with size distribution of 1.1 ± 0.3 nm. In the second part, after studying the thermal stability of these nanoparticles, we used them to catalyze the growth of individual single wall carbon nanotubes by CVD. The caracterisation of the obtained nanotubes by Raman show exceptionally narrow diameter distribution of 1.27 ± 0.15 nm. In the third section, we first studied the dispersion of carbon nanotubes by noncovalent functionalization withhydro-soluble polymer POE with pyrene as end group and revealed depletion phenomena that limit the solubilization of nanotubes. Then we developed composite materials carbon nanotubes/rrP3HT by covalent and noncovalent functionalisation and we studied the efficiency of charge separation in both cases of functionalization.

This thesis deals with out-of-equilibrium transport phenomena in strongly correlated low-dimensional fermionic systems, with special emphasis on π-conjugated molecular materials. The focus of this work is to study real-time dynamics of spin and charge transport in these systems in order to investigate non-equilibrium transport in single-molecule electronic and spintronic devices. Chapter 1 describes the electronic structure and dynamics of strongly correlated fermionic systems in general, and in one-dimension, in particular. For this purpose, effective low-energy model Hamiltonians (used in this work) are discussed. Whenever applicable, approximate analytical and numerical methods commonly used in the literature to deal with these model Hamiltonians, are outlined. In the context of one-dimensional strongly correlated fermionic systems, analytical techniques like the Bethe ansatz and bosonization, and numerical procedures like exact diagonalization and DMRG, used for solving finite systems, are discussed in detail. Chapter 2 provides an overview of the different zero-temperature (T = 0) time-dependent DMRG algorithms, which have been used to study out-of-equilibrium time-dependent phenomena in low-dimensional strongly correlated systems. In Chapter 3 we employ the time-dependent DMRG algorithm proposed by Luo, Xiang and Wang [Phys. Rev. Lett. 91, 049701 (2003)], to study the role of dimerization and electronic correlations on the dynamics of spin-charge separation. We employ the H¨uckel and Hubbard models for our studies. We have modified the algorithm proposed by Luo et. al to overcome some of its limitations. Chapter 4 presents a generalized adaptive time-dependent density matrix renormalization group (DMRG) scheme developed by us, called the Double Time Window Targeting (DTWT) technique, which is capable of giving accurate results with lesser computational resources than required by the existing methods. This procedure originates from the amalgamation of the features of pace keeping DMRG algorithm, first proposed by Luo et. al, [Phys.Rev. Lett. 91, 049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin and White [Phys. Rev. B 72, 020404 (2005)]. In chapter 5 we apply the Double Time Window Targeting (DTWT) technique, which was discussed in the previous chapter, for studying real-time quantum dynamics of spin-charge separation in π-conjugated polymers. We employ the Pariser-Parr-Pople (PPP) model which has long-range electron-electron interactions. For investigating real-time dynamics of spin and charge transport, we inject a hole at one end of polyene chains of different lengths and study the temporal evolution of its spin and charge degrees of freedom, using the DTWT td-DMRG algorithm. Chapter 6 we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes (D- (CH)x- A) chains, also known as push-pull polyenes. We employ long-range correlated model Hamiltonian for the D- (CH)x- A system and, real-time DMRG dynamics for time propagating the wave packet obtained by injecting a hole at a terminal site in the ground state of the system. Our studies reveal that the end groups do not affect the spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these with the polymethineimine (CN)x system in which besides electron affinities, the nature of pz orbitals in conjugation also alternate from site to site. Chapter 7 presents our investigation on the effect of static electron-phonon coupling (dimerization) on the dynamics of spin-charge separation in particular, and transport in general, in π-conjugated polyene chains. The polyenes are modeled by the Pariser-Parr-Pople Hamiltonian, having long-range electron-electron correlations. Our studies reveal that spin and charge velocities depend both on the chain length and dimerization. The spin and charge velocities increase as dimerization increases, but the amount of charge and spin transported along the chain decrease with enhancement in dimerization. Furthermore, in the range 0.3≤ δ≤0.5, it is observed that the dynamics of spin-charge separation becomes complicated, and the charge degree of freedom is affected more by electron-phonon coupling compared to the spin degree of freedom.

Das Verstehen der elektronischen Prozesse in Nano-Hybridsystemen, bestehend aus Molekülen und Halbleiterstrukturen, eröffnet neue Möglichkeiten für optoelektronische Bauteile. Dafür benötigt es nanoskopische und gleichzeitig atomare Modelle und somit angepasste Rechenmethoden. Insbesondere "Standard"-Ansätze für die Dynamik offener Quantensysteme werden mit zunehmender Systemgröße jedoch sehr ineffizient. In dieser Arbeit wird eine neue Methode basierend auf einer stochastischen Schrödinger-Gleichung etablieren. Diese umgeht die numerischen Limits der Quanten-Mastergleichung und ermöglicht Simulationen von imposanter Größe. Ihr enormes Potenzial wird hier in Studien zu Anregungsenergietransfer und Ladungsseparation an zwei realistischen Nano-Hybridsystemen demonstriert: para-sexiphenyl Moleküle auf einer flachen ZnO Oberfläche (6P/ZnO), und ein tubuläres C8S3 Farbstoffaggregat gekoppelt an einen CdSe Nanokristall (TFA/NK). Im 6P/ZnO System findet nach optischer Anregung Energietransfer vom 6P Anteil zum ZnO statt. Direkt an der Grenzfläche können Frenkel-Exzitonen zusätzlich Ladungsseparation initiieren, wobei Elektronen ins ZnO transferiert werden und Löcher im 6P Anteil verbleiben. Beide Mechanismen werden mittels laserpulsinduzierter ultraschneller Wellenfunktionsdynamik simuliert. Danach wird die langsamere dissipative Lochkinetik im 6P Anteil studiert. Hierfür wird die eigene Simulationstechnik der stochastischen Schrödinger-Gleichung verwendet. Die Studie an der TFA/NK Grenzfläche basiert auf einer gigantischen equilibrierten Aggregatstruktur aus 4140 Molekülen. Ein generalisiertes Frenkel-Exzitonenmodell wird benutzt. Der Ansatz der stochastischen Schrödinger-Gleichung ermöglicht bemerkenswerte Einblicke in die Aggregat-interne Exzitonenrelaxation. Danach werden inkohärente Raten des Exzitonentransfers zum NK berechnet. Unterschiedliche räumliche Konfigurationen werden untersucht und es wird diskutiert, warum das Förster-Modell hier keine Gültigkeit besitzt. / Understanding the electronic processes in hybrid nano-systems based on molecular and semiconductor elements opens new possibilities for optoelectronic devices. Therefore, it requires for models which are both nanoscopic and atomistic, and so for adapted computational methods. In particular, "standard" methods for open quantum system dynamics however become very inefficient with increasing system size. In this regard, it is a key challenge of this thesis, to establish a new stochastic Schrödinger equation technique. It bypasses the computational limits of the quantum master equation and enables dissipative simulations of imposing dimensionality. Its enormous potential is demonstrated in studies on excitation energy transfer and charge separation processes in two realistic nanoscale hybrid systems: para-sexiphenyl molecules deposited on a flat ZnO surface (6P/ZnO), and a tubular dye aggregate of C8S3 cyanines coupled to a CdSe nanocrystal (TDA/NC). After optical excitation, the 6P/ZnO system exhibits exciton transfer from the 6P part to the ZnO. Close to the interface, Frenkel excitons may further initiate charge separation where electrons enter the ZnO and holes remain in the 6P part. Both mechanisms are simulated in terms of laser-pulse induced ultrafast wave packet dynamics. Afterwards, slower dissipative hole motion in the 6P part is studied. For this purpose, the own stochastic Schrödinger equation simulation technique is applied. The study on the TDA/NC interface is based on a gigantic equilibrated nuclear structure of the aggregate including 4140 dyes. A generalized Frenkel exciton model is employed. Thanks to the stochastic Schrödinger equation approach, energy relaxation in the exciton band of the TDA is simulated in outstanding quality and extend. Then, incoherent rates for exciton transfer to the NC are computed. Different spatial configurations are studied and it is discussed why the Förster model possesses no validity here.