The topology of fullerenes

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website

THE MOSTAR INDEX OF FULLERENES IN TERMS OF AUTOMORPHISM GROUP

Let $G$ be a connected graph. For an edge $e=uv\in E(G)$, suppose $n(u)$ and $n(v)$ are respectively, the number of vertices of $G$ lying closer to vertex $u$ than to vertex $v$ and the number of vertices of $G$ lying closer to vertex $v$ than to vertex $u$. The Mostar index is a topological index which is defined as $Mo(G)=\sum_{e\in E(G)}f(e)$, where $f(e) = |n(u)-n(v)|$. In this paper, we will compute the Mostar index of a family of fullerene graphs in terms of the automorphism group. 

On the diverse bonding situations in nanostructures : an ab initio computational study

This computational study investigates diverse bonding situations in nanostructures (carbon nanotubes, fullerenes, metal compounds) spanning a broad range of energies. Weak, dispersive interactions and covalent metal-ligand and metal-metal bonding are examined. The results of efficient density functional calculations are compared to those of correlated wavefunction calculations on model systems. This rigorous validation is crucial in evaluating the balance between computational cost and accuracy

Towards More Efficient Enhanced Sampling Methods To Study Phase Transitions

The most familiar phase transitions observed in nature are associated with a change in the state of matter (solid, liquid, and gas). In some rare cases this may involve the plasma phase. Such transitions are often referred to as first order phase transitions and often occur commonly such as during the melting of snow or freezing of lakes and rivers during winter. This project focuses on the most ubiquitous phase changes such as, liquid-solid and vapor-liquid as well as the less prevalent vapor-solid transitions. These types of phase transitions are also known as classical phase transitions. They usually involve symmetry breaking and can be identified by a singularity in the free energy or one of its derivatives. More modern classification of phase transitions relies on the order parameters as exemplified by the Landau\u27s theory. An order parameter is a quantity that takes a value of zero in the disordered phase and assumes finite values in the ordered phase. In the case of liquid-vapor transition, the order parameter is the density. The study of phase transitions is often complicated by the amount of time required by these phase changes and the presence of a high free energy barrier. Consequently, changes occurring close to coexistence are hard or even impossible to follow via conventional experimental techniques. Molecular simulation is therefore the method of choice to study these processes. Molecular simulations are numerical experiments carried out on model systems and have a number of advantages over traditional experiments. Simulations do not have any limitation as to the type of molecules or conditions under which they can be applied. Current simulation methods used to accomplish this task, such as the grand canonical and Gibbs ensemble Monte Carlo methods, employ the concept of particles insertion and deletion moves or requires the knowledge of at least one point at coexistence. These types of moves are extremely inefficient when dense fluids are involved and limit the accuracy of these methods. To circumvent these difficulties, non-Boltzmann sampling methods such as the umbrella sampling and Wang-Landau sampling techniques, have been employed to study these phase transitions. Vapor-solid and liquid-solid phase transitions were studied using a combination of hybrid Monte Carlo (HMC) and the umbrella sampling on a system of C60 molecules. The crystallization process occurs in two steps, nucleation and growth. The nucleation step is an activated process that involves a high free energy barrier. The free energy barrier is overcome through a series of HMC steps. The growth step on the other hand is studied by means of unconstrained molecular dynamics (MD). This study illustrates that the body centered cubic structure plays no role in the crystallization of C60. This is because only the face centered cubic and the hexagonal closed parked crystal structures were observed in both the nucleation and growth steps. In addition, the growth process is observed to follow a complex mechanism known as cross nucleation. The process of cross nucleation has also been observed in model fluids such as Lennard-Jones fluid and in the experimental study of D-mannitol. Hybrid Monte Carlo and configurational bias Monte Carlo (CBMC) were combined with the Wang-Landau (WL) sample method to study the vapor-liquid equilibria of Polycyclic aromatic hydrocarbons (PAHs) with four fused benzene rings and &alpha-olefins (C2 - C6 respectively. These studies are conducted in the isothermal-isobaric (NPT) ensemble to avoid the particle insertion and deletion moves that resulted in low acceptance rates in previous simulations. These studies led to the prediction of the critical temperatures, pressures and densities of both systems

Applications of finite reflection groups in Fourier analysis and symmetry breaking of polytopes

Cette thèse présente une étude des applications des groupes de réflexion finis aux problems liés aux réseaux bidimensionnels et aux polytopes tridimensionnels. Plusieurs familles de fonctions orbitales, appelées fonctions orbitales de Weyl, sont associées aux groupes de réflexion cristallographique. Les propriétés exceptionnelles de ces fonctions, telles que l’orthogonalité continue et discrète, permettent une analyse de type Fourier sur le domaine fondamental d’un groupe de Weyl affine correspondant. Dans cette considération, les fonctions d’orbite de Weyl constituent des outils efficaces pour les transformées discrètes de type Fourier correspondantes connues sous le nom de transformées de Fourier–Weyl. Cette recherche limite notre attention aux fonctions d’orbite de Weyl symétriques et antisymétriques à deux variables du groupe de réflexion cristallographique A2. L’objectif principal est de décomposer deux types de transformations de Fourier–Weyl du réseau de poids correspondant en transformées plus petites en utilisant la technique de division centrale. Pour les cas non cristallographiques, nous définissons les indices de degré pair et impair pour les orbites des groupes de réflexion non cristallographique avec une symétrie quintuple en utilisant un remplacement de représentation-orbite. De plus, nous formulons l’algorithme qui permet de déterminer les structures de polytopes imbriquées. Par ailleurs, compte tenu de la pertinence de la symétrie icosaédrique pour la description de diverses molécules sphériques et virus, nous étudions la brisure de symétrie des polytopes doubles de type non cristallographique et des structures tubulaires associées. De plus, nous appliquons une procédure de stellation à la famille des polytopes considérés. Puisque cette recherche se concentre en partie sur les fullerènes icosaédriques, nous présentons la construction des nanotubes de carbone correspondants. De plus, l’approche considérée pour les cas non cristallographiques est appliquée aux structures cristallographiques. Nous considérons un mécanisme de brisure de symétrie appliqué aux polytopes obtenus en utilisant les groupes Weyl tridimensionnels pour déterminer leurs extensions structurelles possibles en nanotubes.This thesis presents a study of applications of finite reflection groups to the problems related to two-dimensional lattices and three-dimensional polytopes. Several families of orbit functions, known as Weyl orbit functions, are associated with the crystallographic reflection groups. The exceptional properties of these functions, such as continuous and discrete orthogonality, permit Fourier-like analysis on the fundamental domain of a corresponding affine Weyl group. In this consideration, Weyl orbit functions constitute efficient tools for corresponding Fourier-like discrete transforms known as Fourier–Weyl transforms. This research restricts our attention to the two-variable symmetric and antisymmetric Weyl orbit functions of the crystallographic reflection group A2. The main goal is to decompose two types of the corresponding weight lattice Fourier–Weyl transforms into smaller transforms using the central splitting technique. For the non-crystallographic cases, we define the even- and odd-degree indices for orbits of the non-crystallographic reflection groups with 5-fold symmetry by using a representation-orbit replacement. Besides, we formulate the algorithm that allows determining the structures of nested polytopes. Moreover, in light of the relevance of the icosahedral symmetry to the description of various spherical molecules and viruses, we study symmetry breaking of the dual polytopes of non-crystallographic type and related tube-like structures. As well, we apply a stellation procedure to the family of considered polytopes. Since this research partly focuses on the icosahedral fullerenes, we present the construction of the corresponding carbon nanotubes. Furthermore, the approach considered for the non-crystallographic cases is applied to crystallographic structures. We consider a symmetry-breaking mechanism applied to the polytopes obtained using the three-dimensional Weyl groups to determine their possible structural extensions into nanotubes

Modelling the optical, kinetic, and thermodynamic properties of soot precursor molecules

This thesis investigates the optical, kinetic, and thermodynamic properties of soot precursor molecules, namely polyaromatic hydrocarbons (PAHs), by applying \textit{ab initio} quantum chemical methods. In particular, density functional theory (DFT) is applied to study the properties of several different types of PAHs, including curved PAHs, localized $\pi$-radical PAHs, and cross-linked PAHs. These studies help model the gas phase chemistry that leads to the formation of these different types of PAHs, and also help assess their relevance to the formation of soot. The optical band gaps (OBGs) of curved, cross-linked, and radical PAHs are computed using a DFT method corroborated with UV/Visible spectroscopy measurements. Curved PAHs are shown to increase the OBG due to hybridisation changes. In contrast, $\pi$-radical character was found to decrease the band gap. Crosslinks are observed to minimally impact the OBG of the monomers. The effect of $\sigma$-radicals on the OBG was also shown to be negligible. The results suggest that curved and $\pi$-radical PAHs of moderate size can also explain the optical properties of flames. The persistence of the polarity of curved aromatics in flame conditions is investigated by using DFT to calculate their barriers and rates of inversion. Curved PAHs above 11--15 ($\approx$ 0.8 nm) rings in size were seen to be unable to invert at flame temperatures. This is seen to be a function of the number of pentagons, and hence curvature. \textit{Ab initio} quantum molecular dynamics of a 1 nm curved PAH and C\textsubscript{3}H\textsubscript{3}\textsuperscript{+} chemi-ion suggest molecular dipole fluctuations of 10--20\%, with the chemi-ion and PAH being bound for the entire simulation. This suggests curved PAHs are persistently polar at 1500~K and can bind substantially to ions in flames. The kinetics of seven-member ring formation in PAHs containing a five-member ring is investigated. Seven-member ring formation by the hydrogen-abstraction-acetylene-addition (HACA) mechanism is studied for two different PAHs, one closed shell and one resonance-stabilised-radical (RSR) PAH. The seven-member ring forms more quickly for the RSR PAH. Seven-member ring formation by four different bay closure processes is also studied. The rate constants determined for the pathways are then used in kinetic simulations in 0D homogeneous reactors. The hydrogen abstraction based pathway is seen to dominate until higher temperatures, where the carbene pathway takes over. The results suggest that seven-member ring formation in PAHs containing a five-member ring is possible at flame temperatures. The impact of localized $\pi$-radicals on soot formation is explored by developing a simple mechanism for their formation and computing their relative concentrations under flame conditions using 0D homogeneous reactor simulations. It is seen that flame temperatures at the onset of nucleation (1400--1500~K) promote the formation of localized $\pi$-radicals on rim-based pentagonal rings, whilst lower temperatures favor fully saturated rings, and higher temperatures favor the $\sigma$-radical. A kinetic Monte Carlo study indicates that multiple localized $\pi$-radicals can form on a single PAH suggesting localized $\pi$-radicals on rim-based pentagonal rings could be important to understanding the mechanism of soot formation. The rate and equilibrium constants of cross-linking reactions between PAHs of various reactive edge types is computed. The forward rate constants confirms that reactions involving aryl $\sigma$-radicals are generally fast, but the reactions between aryl $\sigma$-radicals and localized $\pi$-radicals were notably faster than others. Computed equilibrium constants showed that reactions involving $\sigma$ and $\pi$-radical PAHs are the most favorable at flame temperatures. Calculations for larger PAHs showed that the formation of bonded-and-stacked structures results in substantially enhanced equilibrium constants for the reaction of two large localized $\pi$-radicals. This suggests that combined physical and chemical interactions between larger $\pi$-radical PAHs could be important in flame environments.Johnson Matthey National Research Foundation of Singapor

Oligothiophene Materials for Organic Solar Cells - Photophysics and Device Properties

The rapidly increasing power conversion efficiencies (PCEs) of organic solar cells (OSCs) above 10% were made possible by concerted international research activities in the last few years, aiming to understand the processes that lead to the generation of free charge carriers following photon absorption. Despite these efforts, many details are still unknown, especially how these processes can be improved already at the drawing board of molecular design. To unveil this information, dicyanovinyl end-capped oligothiophene derivatives (DCVnTs) are used as a model system in this thesis, allowing to investigate the impact of small structural changes on the molecular properties and the final solar cells. On thin films of a methylated DCV4T derivative, the influence of the measurement temperature on the charge carrier generation process is investigated. The observed temperature activation in photoinduced absorption (PIA) measurements is attributed to an increased charge carrier mobility, increasing the distance between the charges at the donor/acceptor (D/A) interface and, thus, facilitating their final dissociation. The correlation between the activation energy and the mobility is confirmed using a DCV6T derivative with lower mobility , exhibiting a higher activation energy for charge carrier generation. Another parameter to influence the charge carrier generation process is the molecular structure. Here, alkyl side chains with varying length are introduced and their influence on the intramolecular energy levels as well as the absorption and emission properties in pristine and blend films with the acceptor C60 are examined. The observed differences in intermolecular order (higher order for shorter side chains) and phase separation in blend layers (larger phase separation for shorter side chains) are confirmed in PIA measurements upon comparing the temperature dependence of the triplet exciton lifetimes. A proposed correlation between the side chain length and the coupling between D and A, which is crucial for efficient charge transfer, is not confirmed. The presented flat heterojunction solar cells underline this conclusion, giving similar photocurrent densities for all compounds. Differences in PCE are related to shifts of the energy levels and the morphology of the blend layer in bulk heterojunction devices. Furthermore, the impact of the electric field on the charge carrier generation yield is investigated in a proof-of-principle study, introducing PIA measurements in transmission geometry realized using semitransparent solar cells. The recombination analysis of the photogenerated charge carriers reveals two recombination components. Trapped charge carriers or bound charge pairs at the D/A interface are proposed as an explanation for this result. The miscibility of D and A, which can be influenced by heating the substrate during layer deposition, is of crucial importance to obtain high PCEs. In this work, the unusual negative influence of the substrate temperature on DCV4T:C60 blend layers in solar cells is investigated. By using optical measurements and structure determination tools, a rearrangement of the DCV4T crystallites is found to be responsible for the reduced absorption and, therefore, photocurrent at higher substrate temperature. The proposed blend morphology at a substrate temperature of 90° C is characterized by a nearly complete demixing of the D and A phases. This investigation is of particular relevance, because it shows the microscopic origins of a behavior that is contrary to the increase of the PCE upon substrate heating usually reported in literature. Finally, the optimization steps to achieve a record PCE of 7.7% using a DCV5T derivative as donor material are presented, including the optimization of the substrate temperature, the active layer thickness, and the transport layers.:Abstract - Kurzfassung Publications Contents 1 Introduction 2 Elementary Processes in Organic Semiconductors 2.1 Introduction 2.2 Optical Excitations in Organic Materials 2.2.1 Introduction 2.2.2 Radiative Processes: Absorption and Emission 2.2.3 Non-radiative Relaxation Processes 2.2.4 Triplet Excitons and Intersystem Crossing 2.3 Polarization Effects and Disorder 2.4 Transport Processes in Disordered Organic Materials 2.4.1 Charge Transport 2.4.1.1 The Bässler Model 2.4.1.2 Marcus Theory for Electron Transfer 2.4.1.3 Small Polaron Model 2.4.1.4 Functional Dependencies of the Charge Carrier Mobility 2.4.2 Diffusive Motion 2.4.3 Exciton Transfer Mechanisms 2.4.4 Characteristics of Exciton Diffusion 2.5 Charge Photogeneration in Pristine Materials 3 Organic Photovoltaics 3.1 General Introduction to Solar Cell Physics 3.2 Introduction to the Donor/Acceptor Heterojunction Concept 3.3 The Open-Circuit Voltage in Organic Solar Cells 3.4 Doping of Organic Semiconductors 3.5 Introduction to the p-i-n Concept 3.6 Charge Transfer Excitons in Donor/Acceptor Heterojunction Systems 3.6.1 Introduction 3.6.2 Verification of Charge Transfer Excitons in Donor/Acceptor Systems 3.7 The Process Cascade for Free Charge Carrier Generation in Donor/Acceptor Heterojunction Systems 3.7.1 The Initial Charge Transfer Step 3.7.2 The Binding Energy of the Charge Transfer Exciton 3.7.3 \"Hot\" Charge Transfer Exciton Dissociation 3.7.4 \"Cold\" Charge Transfer Exciton Dissociation 3.7.5 Supposed Influence Factors on Charge Transfer Exciton Dissociation 3.7.6 Recombination Pathways for Charge Transfer Excitons 3.7.7 Free Charge Carrier Formation and Recombination 4 Experimental Methods 4.1 Sample Preparation 4.2 Material Characterization Methods 4.2.1 Optical Characterization 4.2.2 Cyclic Voltammetry 4.2.3 Ultraviolet Photoelectron Spectroscopy 4.2.4 Atomic Force Microscopy 4.2.5 Grazing Incidence X-Ray Diffraction 4.2.6 Organic Field-Effect Transistor 4.3 Photoinduced Absorption Spectroscopy 4.3.1 Introduction 4.3.2 Derivation of the PIA Signal 4.3.3 Recombination Dynamics 4.3.4 Intensity Dependence of the PIA Signal 4.4 Solar Cell Characterization 4.4.1 External Quantum Efficiency 4.4.2 Spectral Mismatch Correction 4.4.3 Current-Voltage Characteristics 4.4.4 Optical Device Simulations 4.4.5 Optical Device Transmission Measurements 5 The Oligothiophene Material System 5.1 Introduction 5.2 Thermal Stability 5.3 Energy Levels 5.4 Optical Properties of the Pristine Materials 5.5 The Donor/Acceptor Couple: DCVnT and C60 5.6 Solar Cell Devices 5.7 Summary 6 Temperature Dependence of Charge Carrier Generation 6.1 Introduction 6.2 Principal Introduction to the PIA Measurements 6.2.1 Interpretation of the Spectra 6.2.2 Interpretation of the Frequency Scans 6.3 Temperature Dependence of the Spectra 6.4 Discussion of the Temperature Dependent Processes in the Blend Layer 6.5 Temperature Activated Free Charge Carrier Generation 6.5.1 Evaluation of the Activation Energy for the DCV4T-Me:C60 Blend 6.5.2 Comparison to a Sexithiophene Derivative (DCV6T-Me) 6.6 Summary 7 Side Chain Investigation on Quaterthiophene Derivatives 7.1 Energy Levels 7.2 Optical Properties 7.2.1 Solution and Pristine Films 7.2.2 Mixed Films with C60 7.3 Influence of the Side Chain Length on the Intermolecular Coupling 7.3.1 PIA Spectra of Pristine and Blend Layers at 10K 7.3.2 Recombination Analysis for Pristine and Blend Films at 10K 7.4 The Influence of the Side Chain Length on the Offset Charge Carrier Generation Rate at Low Temperature 7.5 In the High-Temperature Limit: Implications for Solar Cell Devices 7.5.1 PIA Spectra in Pristine and Blend Films at 200K 7.5.2 Recombination Analysis: Triplet Excitons and Free Charge Carriers 7.6 Solar Cells 7.6.1 Flat Heterojunction Devices 7.6.2 Bulk Heterojunction Devices 7.7 Summary 8 Electric-Field Dependent PIA Measurements on Complete Solar Cell Devices 8.1 Introduction 8.2 Semitransparent Organic Solar Cells 8.3 Photoinduced Absorption Measurements 8.4 Summary and Outlook 9 The Effect of Substrate Heating During Layer Deposition on the Performance of DCV4T:C60 BHJ Solar Cells 9.1 Introduction 9.2 The Importance of Morphology Control for BHJ Solar Cells 9.3 The Impact of Substrate Heating on DCV4T:C60 BHJ Solar Cells 9.4 Absorption and Photoluminescence 9.5 Topographical Investigations (AFM) 9.6 X-ray Investigations 9.6.1 1D GIXRD Measurements 9.6.2 2D GIXRD Measurements 9.7 Proposed Morphological Picture and Confirmation Measurements 9.7.1 Morphology Sketch of the DCV4T:C60 Blend Layer 9.7.2 Confirmation Measurements 9.8 The Equivalence of Temperature and Time 9.9 Summary 10 Record Solar Cells Using DCV5T-Me33 as Donor Material 10.1 Introduction 10.2 The Influence of the Substrate Temperature 10.3 Determination of the Optical Constants 10.4 Stack Optimization 10.5 Summary and Outlook 11 Conclusions and Outlook 11.1 Summary of the Photophysical Investigations 11.2 Summary of Device Investigations 11.3 Future Challenges Appendix A Detailed Description of the Experimental Setup for PIA Spectroscopy Appendix B Determination of the Triplet Level by Differential PL Measurements Appendix C Additional Tables and Figures Appendix D Reproducibility of the Solar Cell Results (Statistics) Appendix E Lists Bibliography AcknowledgmentsDer rasante Anstieg des Wirkungsgrads von organischen Solarzellen über die Marke von 10% war nur durch länderübergreifende Forschungsaktivitäten während der letzten Jahre möglich. Trotz der gemeinsamen Anstrengungen, die Prozesse, die zwischen der Absorption der Photonen und der Ladungsträgererzeugung liegen, genauer zu verstehen, sind einige Fragen jedoch immer noch ungelöst, z.B. wie diese Prozesse schon auf dem Reißbrett durch die gezielte Änderung bestimmter Molekülstrukturen optimiert werden können. Um dieses Ziel zu erreichen, werden in dieser Arbeit Dicyanovinyl-substituierte Oligothiophene (DCVnTs) verwendet. Diese Materialien bieten die Möglichkeit, kleine strukturelle Änderungen vorzunehmen, deren Einfluss auf die molekularen und auf die Solarzelleneigenschaften untersucht werden soll. Der Einfluss der Messtemperatur auf den Prozess der Ladungsträgertrennung wird hier an einer methylierten DCV4T-Verbindung in einer dünnen Schicht untersucht. Die bei photoinduzierter Absorptionsspektroskopie (PIA) beobachtete Aktivierung dieses Prozesses mit zunehmender Temperatur wird auf eine erhöhte Ladungsträgerbeweglichkeit zurückgeführt. Der dadurch erhöhte effektive Abstand der Ladungen an der Grenzfläche zwischen Donator (D) und Akzeptor (A) erleichtert die endgültige Trennung der Ladungsträger. Durch den Vergleich mit einer DCV6T-Verbindung wird der Zusammenhang zwischen der Aktivierungsenergie und der Beweglichkeit bekräftigt. Die kleinere Beweglichkeit äußert sich dabei in einer größeren Aktivierungsenergie. Darüber hinaus kann der Ladungsträgergenerationsprozess auch von der Molekülstruktur abhängen. In dieser Arbeit wird untersucht, wie sich die Länge von Alkylseitenketten auf die Energieniveaus der Moleküle, aber auch auf die Absorptions- und Lumineszenzeigenschaften der Materialien in reinen und in Mischschichten mit dem Akzeptor C60 äußert. Die ermittelten Unterschiede bezüglich der Molekülordnung (geordneter für kürzere Seitenketten) und der Phasengrößen in Mischschichten (größere Phasen bei kürzerer Kettenlänge) werden in der Untersuchung der Temperaturabhängigkeit der Lebensdauer von Triplettexzitonen mittels PIA-Messungen bestätigt. Für Solarzellen ist von Bedeutung, ob sich die Seitenkettenlänge auf die Wechselwirkung zwischen D und A auswirkt. Der vermutete Zusammenhang wird hier nicht bestätigt. Ein ähnlicher Photostrom für alle untersuchten Verbindungen in Solarzellen mit planaren Heteroübergängen unterstreicht diese Schlussfolgerung. Unterschiede im Wirkungsgrad werden auf Änderungen der Energieniveaus und die Morphologie in Mischschichtsolarzellen zurückgeführt. Des Weiteren wird in einer Machbarkeitsstudie der Einfluss des elektrischen Felds auf die Generationsausbeute freier Ladungsträger untersucht. Dafür werden halbtransparente Solarzellen verwendet, die es ermöglichen, PIA-Messungen in Transmissionsgeometrie durchzuführen. Als mögliche Erklärung für das Auftreten zweier Rekombinationskomponenten in der Analyse des Rekombinationsverhaltens der durch Licht erzeugten Ladungsträger werden eingefangene Ladungsträger und gebundene Ladungsträgerpaare an der D/A-Grenzfläche genannt. Das Mischverhalten von D und A kann durch ein Heizen des Substrates während des Verdampfungsprozesses eingestellt werden, was von entscheidender Bedeutung für eine weitere Steigerung des Wirkungsgrades ist. Für DCV4T:C60-Mischschichtsolarzellen wird jedoch eine Verschlechterung des Wirkungsgrads zu höheren Substrattemperaturen beobachtet. Durch optische Messungen und Methoden zur Schichtstrukturbestimmung wird dieser Effekt auf eine Umordnung der DCV4T-Kristallite für hohe Substrattemperaturen und die damit verbundene Verringerung der Absorption und damit auch des Photostroms zurückgeführt. Bei einer Substrattemperatur von 90° C sind die D- und A-Komponenten fast vollständig entmischt. Dieses Beispiel ist von besonderer Bedeutung, weil hier die Ursachen für ein Verhalten aufgezeigt werden, das entgegen den Beispielen aus der Literatur eine Abnahme des Wirkungsgrads beim Aufdampfen der aktiven Schicht auf ein geheiztes Substrat zeigt. Schließlich werden die Optimierungsschritte dargelegt, mit denen Solarzellen mit einer DCV5T-Verbindung als Donatormaterial auf einen Rekordwirkungsgrad von 7,7% gebracht werden. Dabei wird die Substrattemperatur, die Dicke der aktiven Schicht und die Transportschichten angepasst.:Abstract - Kurzfassung Publications Contents 1 Introduction 2 Elementary Processes in Organic Semiconductors 2.1 Introduction 2.2 Optical Excitations in Organic Materials 2.2.1 Introduction 2.2.2 Radiative Processes: Absorption and Emission 2.2.3 Non-radiative Relaxation Processes 2.2.4 Triplet Excitons and Intersystem Crossing 2.3 Polarization Effects and Disorder 2.4 Transport Processes in Disordered Organic Materials 2.4.1 Charge Transport 2.4.1.1 The Bässler Model 2.4.1.2 Marcus Theory for Electron Transfer 2.4.1.3 Small Polaron Model 2.4.1.4 Functional Dependencies of the Charge Carrier Mobility 2.4.2 Diffusive Motion 2.4.3 Exciton Transfer Mechanisms 2.4.4 Characteristics of Exciton Diffusion 2.5 Charge Photogeneration in Pristine Materials 3 Organic Photovoltaics 3.1 General Introduction to Solar Cell Physics 3.2 Introduction to the Donor/Acceptor Heterojunction Concept 3.3 The Open-Circuit Voltage in Organic Solar Cells 3.4 Doping of Organic Semiconductors 3.5 Introduction to the p-i-n Concept 3.6 Charge Transfer Excitons in Donor/Acceptor Heterojunction Systems 3.6.1 Introduction 3.6.2 Verification of Charge Transfer Excitons in Donor/Acceptor Systems 3.7 The Process Cascade for Free Charge Carrier Generation in Donor/Acceptor Heterojunction Systems 3.7.1 The Initial Charge Transfer Step 3.7.2 The Binding Energy of the Charge Transfer Exciton 3.7.3 \"Hot\" Charge Transfer Exciton Dissociation 3.7.4 \"Cold\" Charge Transfer Exciton Dissociation 3.7.5 Supposed Influence Factors on Charge Transfer Exciton Dissociation 3.7.6 Recombination Pathways for Charge Transfer Excitons 3.7.7 Free Charge Carrier Formation and Recombination 4 Experimental Methods 4.1 Sample Preparation 4.2 Material Characterization Methods 4.2.1 Optical Characterization 4.2.2 Cyclic Voltammetry 4.2.3 Ultraviolet Photoelectron Spectroscopy 4.2.4 Atomic Force Microscopy 4.2.5 Grazing Incidence X-Ray Diffraction 4.2.6 Organic Field-Effect Transistor 4.3 Photoinduced Absorption Spectroscopy 4.3.1 Introduction 4.3.2 Derivation of the PIA Signal 4.3.3 Recombination Dynamics 4.3.4 Intensity Dependence of the PIA Signal 4.4 Solar Cell Characterization 4.4.1 External Quantum Efficiency 4.4.2 Spectral Mismatch Correction 4.4.3 Current-Voltage Characteristics 4.4.4 Optical Device Simulations 4.4.5 Optical Device Transmission Measurements 5 The Oligothiophene Material System 5.1 Introduction 5.2 Thermal Stability 5.3 Energy Levels 5.4 Optical Properties of the Pristine Materials 5.5 The Donor/Acceptor Couple: DCVnT and C60 5.6 Solar Cell Devices 5.7 Summary 6 Temperature Dependence of Charge Carrier Generation 6.1 Introduction 6.2 Principal Introduction to the PIA Measurements 6.2.1 Interpretation of the Spectra 6.2.2 Interpretation of the Frequency Scans 6.3 Temperature Dependence of the Spectra 6.4 Discussion of the Temperature Dependent Processes in the Blend Layer 6.5 Temperature Activated Free Charge Carrier Generation 6.5.1 Evaluation of the Activation Energy for the DCV4T-Me:C60 Blend 6.5.2 Comparison to a Sexithiophene Derivative (DCV6T-Me) 6.6 Summary 7 Side Chain Investigation on Quaterthiophene Derivatives 7.1 Energy Levels 7.2 Optical Properties 7.2.1 Solution and Pristine Films 7.2.2 Mixed Films with C60 7.3 Influence of the Side Chain Length on the Intermolecular Coupling 7.3.1 PIA Spectra of Pristine and Blend Layers at 10K 7.3.2 Recombination Analysis for Pristine and Blend Films at 10K 7.4 The Influence of the Side Chain Length on the Offset Charge Carrier Generation Rate at Low Temperature 7.5 In the High-Temperature Limit: Implications for Solar Cell Devices 7.5.1 PIA Spectra in Pristine and Blend Films at 200K 7.5.2 Recombination Analysis: Triplet Excitons and Free Charge Carriers 7.6 Solar Cells 7.6.1 Flat Heterojunction Devices 7.6.2 Bulk Heterojunction Devices 7.7 Summary 8 Electric-Field Dependent PIA Measurements on Complete Solar Cell Devices 8.1 Introduction 8.2 Semitransparent Organic Solar Cells 8.3 Photoinduced Absorption Measurements 8.4 Summary and Outlook 9 The Effect of Substrate Heating During Layer Deposition on the Performance of DCV4T:C60 BHJ Solar Cells 9.1 Introduction 9.2 The Importance of Morphology Control for BHJ Solar Cells 9.3 The Impact of Substrate Heating on DCV4T:C60 BHJ Solar Cells 9.4 Absorption and Photoluminescence 9.5 Topographical Investigations (AFM) 9.6 X-ray Investigations 9.6.1 1D GIXRD Measurements 9.6.2 2D GIXRD Measurements 9.7 Proposed Morphological Picture and Confirmation Measurements 9.7.1 Morphology Sketch of the DCV4T:C60 Blend Layer 9.7.2 Confirmation Measurements 9.8 The Equivalence of Temperature and Time 9.9 Summary 10 Record Solar Cells Using DCV5T-Me33 as Donor Material 10.1 Introduction 10.2 The Influence of the Substrate Temperature 10.3 Determination of the Optical Constants 10.4 Stack Optimization 10.5 Summary and Outlook 11 Conclusions and Outlook 11.1 Summary of the Photophysical Investigations 11.2 Summary of Device Investigations 11.3 Future Challenges Appendix A Detailed Description of the Experimental Setup for PIA Spectroscopy Appendix B Determination of the Triplet Level by Differential PL Measurements Appendix C Additional Tables and Figures Appendix D Reproducibility of the Solar Cell Results (Statistics) Appendix E Lists Bibliography Acknowledgment