Novel approaches to the synthesis and treatment of cathode materials for lithium-ion batteries

Nous avons mis au point une approche novatrice pour la synthèse d’un matériau de cathode pour les piles lithium-ion basée sur la décomposition thermique de l’urée. Les hydroxydes de métal mixte (NixMnxCo(1-2x)(OH)2) ont été préparés (x = 0.00 à 0.50) et subséquemment utilisés comme précurseurs à la préparation de l’oxyde de métal mixte (LiNixMnxCo(1-2x)O2). Ces matériaux, ainsi que le phosphate de fer lithié (LiFePO4), sont pressentis comme matériaux de cathode commerciaux pour la prochaine génération de piles lithium-ion. Nous avons également développé un nouveau traitement post-synthèse afin d’améliorer la morphologie des hydroxydes. L’originalité de l’approche basée sur la décomposition thermique de l’urée réside dans l’utilisation inédite des hydroxydes comme précurseurs à la préparation d’oxydes de lithium mixtes par l’intermédiaire d’une technique de précipitation uniforme. De plus, nous proposons de nouvelles techniques de traitement s’adressant aux méthodes de synthèses traditionnelles. Les résultats obtenus par ces deux méthodes sont résumés dans deux articles soumis à des revues scientifiques. Tous les matériaux produits lors de cette recherche ont été analysés par diffraction des rayons X (DRX), microscope électronique à balayage (MEB), analyse thermique gravimétrique (ATG) et ont été caractérisés électrochimiquement. La performance électrochimique (nombre de cycles vs capacité) des matériaux de cathode a été conduite en mode galvanostatique.

Henry C. Carey et le système américain d’économie contre l’impérialisme du libre-échange britannique : son passage au New York Tribune

Les débats économiques au 19e siècle, loin d’être l’apanage du monde universitaire, étaient aux États-Unis un des principaux objets de contentieux entre les partis politiques et ceux-ci trouvaient écho dans la sphère publique. Les journaux étaient alors le principal moyen de communiquer les opinions des différents partis. La présente étude vise à mettre en contexte et cerner la position des écrits du plus important économiste américain de son époque, Henry Charles Carey (1793-1879), reconnu comme tel par J.S. Mill et Karl Marx en leur temps, lors de la décennie de 1850 dans le journal le plus influent de cette période, le New York Tribune. Pour ce faire, il a fallu au préalable identifier les articles non signés de Carey dans le journal, ce qui n’avait auparavant jamais été fait. Au moment d’écrire dans le principal organe américain qui défendait la protection aux États-Unis afin d’industrialiser le pays, Carey était alors le représentant le plus prééminent du système américain d’économie. Ce dernier, fondé sur les écrits d’Alexander Hamilton, prônait l’industrialisation des États-Unis et l’intervention de l’État pour défendre le bien commun, s’opposant ainsi à l’école libérale anglaise basée sur les écrits d’Adam Smith. Conceptuellement, la pensée économique de Carey se situe dans la tradition des Autres Canon, basée sur la production et l’innovation. Ceci le mena à s’opposer avec vigueur tant au malthusianisme qu’à la division internationale du travail, justifiée théoriquement par la thèse de l’avantage comparatif de Ricardo. En effet, dans son analyse, la volonté exprimée au milieu du 19e siècle par l’Angleterre de devenir l’atelier du monde et de faire du reste des nations des producteurs de matières premières sous un régime de libre-échange n’était rien d’autre que la continuation de la politique coloniale par d’autres moyens. Pour Carey, la spécialisation dans l’exportation de matières premières, notamment défendue par les planteurs du Sud des États-Unis, loin d’être bénéfique au pays, était le sûr gage de la pauvreté comme les cas de l’Irlande et de l’Inde le démontraient.

New supported transition metal complexes: synthesis, characterization and application as catalysts for oxidation/hydrodesulphurization reactions

This thesis deals with the synthesis and charcterisation of some supported transition metal complexes and their catalytic properties. Two industrially important reactions were carried out: i) cyclohexanol oxidation and ii) hydrodesulphurization of diesel. Thesis is divided into nine chapters. An overview of the heterogenised homogeneous systems is given in Chapter 1. Chapter 2 deals with the materials and methods used for the preparation and characterisation. Details regarding the synthesis and characterisation of zeolite encapsulated transition metal complexes are given in Chapter 3 to Chapter 7. In Chapter 8, the results of catalytic activity studies of the cyclohexanol oxidation using the zeolite encapsulated complexes are presented. Details of preparation of hydrodesulphurization catalysts through the molecular designed dispersion method, their characterization and catalytic activity studies are presented in Chapter 9. References are given at the end of the thesis.

Investigations of Nonlinear Optical Properties of certain organic photonic materials using Z-Scan and DFWM techniques

Nonlinear optical processes in organic compounds have attracted considerable interest in the field of science and technology because of their compelling technological promises in fields of optical communication,computing,switching and signal processing.As a result of the synthesis of novel organic compounds with varying degree of nonlinear optical strength, many practical devices based on these are getting realised giving new theoretical insights into the nonolinear optical behaviour of materials.Organic compounds like phthalocyanines and porphyrins have evoked great deal of interest in the field of photonic technology.The present thesis describes the results obtained from the investigations carried out on the nonlinear optical properties of certain organo-metallic compounds using Z-Scan and DFWM techniques.

Studies on new processing aids and other compounding ingredients in special purpose rubbers

In the first part of the study we probed the effectiveness of rice bran oil as a multipurpose compounding ingredient for nitrile (NBR) and chloroprene (CR) rubbers. This oil has already been successfully employed in the compounding of NR and SBR in this laboratory.In this context we thought it worthwhile to try this oil in the polar rubbers viz, NBR and CR also. The principle of like dissolves like as applicable to solvents is equally applicable while selecting a plasticiser, elastomer combination. Because of the compatibility considerations polar plasticisers are preferred for polar rubbers like NBR and CR. Although plasticisation is a physical phenomenon and no chemical reaction is involved, the chemical structure of plasticisers determines how much physical attraction there is between the rubber and the plasticiser. In this context it is interesting to note that the various fatty acids present in rice bran oil have a long paraffinic chain, characteristic of waxes, with an acid group at the end of the molecule. The paraffinic end of the molecule contributes lubricating effects and limits compatibility whereas the acid end group contributes some polarity and is also chemically reactive. Because of absorption of acid group on the surface of pigments, these acids will have active pigment wetting characteristics also. These factors justifies the role of rice bran oil as a co-activator and lubricating agent for NBR and CR. In fact in our study we successfully replaced stearic acid as co-activator and aromatic oillDOP as processing aid for CR and NBR with rice bran oil.This part of the study has got special significance in the fact that rubber industry now heavily depends on petroleum industry for process oils. The conventional process oils like aromatic, naphthenic and paraffinic oils are increasingly becoming costlier, as its resources in nature are fast depleting. Moreover aromatic process oils are reported to be carcinogenic because of the presence of higher levels of polycyclic aromatic compounds in these oils.As a result of these factors, a great amount research is going on world over for newer processing aids which are cost effective, nontoxic and performanance wise at par with the conventional ones used in the rubber industry. Trials with vegetable oils in this direction is worth trying.Antioxidants are usually added to the rubber compound to minimise ageing effects from heat, light, oxygen etc. As rice bran oil contains significant amount of tocopherols and oryzanol which are natural antioxidants, we replaced a phenolic antioxidant like styrenated phenol (SP) from the compound recipe of both the rubbers with RBO and ascertained whether this oil could function in the role of antioxidant as well.Preparation and use of epoxidised rice bran oil as plasticiser has already been reported.The crude rice bran oil having an iodine value of 92 was epoxidised in this laboratory using peracetic acid in presence of sulphuric acid as catalyst. The epoxy content of the epoxidised oil was determined volumetrically by treating a known weight of the oil with excess HCI and back titrating the residual HCI with standard alkali solution. The epoxidised oil having an epoxy content of 3.4% was tried in the compounding of NBR and CR as processing aids. And results of these investigations are also included in this chapter. In the second part of the study we tried how RBO/ERBO could perform when used as a processing aid in place of aromatic oil in the compounding of black filled NRCR blends. Elastomers cannot have all the properties required for a particular applications, so it is common practice in rubber industry to blend two elastomers to have desired property for the resulting blend.In this RBO/ERBO was tried as a processing aid for plasticisation, dispersion of fillers, and vulcanisation of black filled NR-CR blends.Aromatic oil was used as a control. The results of our study indicate that these oils could function as a processing aid and when added together with carbon black function as a cure accelerator also.PVC is compatible with nitrile rubber in all proportions, provided NBR has an acrylonitrile content of 25 to 40%. Lower or higher ACN content in NBR makes it incompatible with PVC.PVC is usually blended with NBR at high temperatures. In order to reduce torque during mixing, additional amounts of plasticisers like DOP are added. The plasticiser should be compatible both with PVC and NBR so as to get a homogeneous blend. Epoxidised soyaben oil is reported to have been used in the compounding of PVC as it can perfonn both as an efficient plasticiser and heat stabilizer.At present DOP constitute the largest consumed plasticiser in the PVC compounding. The migration of this plasticiser from food packaging materials made of PVC poses great health hazards as this is harmful to human body. In such a scenario we also thought it worthwhile to see whether DOP could be replaced by rice bran oil in the compounding of NBR-PVC blends Different blends of NBR-PVC were prepared with RBO and were vulcanized using sulphur and conventional accelerators. The various physical and mechanical properties of the vulcanisates were evaluated and compared with those prepared with DOP as the control plasticiser. Epoxidised rice bran oil was also tried as plasticiser for the preparation of NBR-PVC blends. A comparison of the processability and cure characteristics of the different blends prepared with DOP and ERBO showed that ERBO based blends have better processability and lower cure time values. However the elastographic maximum torque values are higher for the DOP based blends. Almost all of the physical properties evaluated are found to be slightly better for the DOP based blends over the ERBO based ones. However a notable feature of the ERBO based blends is the better percentage retention of elongation at break values after ageing over the DOP based blends. The results of these studies using rice bran oil and its epoxidised variety indicated that they could be used as efficient plasticisers in place of DOP and justifies their role as novel, nontoxic, and cheap plasticisers for NBR-PVC blends.

Photoacoustic and photothermal deflection studies on certain selected photonic materials“

The emergence of lasers in the early sixties has not only revolutionized the field of optics and communication but also paved new ways in the field of material characterization. Material studies using photothermal techniques possess certain unique characteristics and advantages over conventional methods. The most important aspect of photothennal techniques is their ability to perform noncontact and nondestructive measurement. Photoacoustics, photothermal deflection, thermal lens, photothermal radiometry and photopyroelectric methods are some of the commonly used and powerful techniques for the thermal and optical characterization of materials using lasers. In this thesis the applications of photoacoustic and photothermal deflection techniques for the thermal and optical characterization of different photonic materials, namely, semiconductors, liquid crystals and dye-doped polymers are discussed

Exploring oligo(p-phenylenevinylene) gelators as sensors and stimuli responsive materials

Gelation provides a unique medium, which often induces organization of molecules resulting in the modulation of their optical, morphological and electronic properties thereby opening a new world of fascinating materials with interesting physical properties at nano- meso- and macroscopic levels. Supramolecular gels based on linear π-systems have attracted much attention due to their inherent optical and electronic properties which find application in organic electronics, light harvesting and sensing. They exhibit reversible properties due to the dynamic nature of noncovalent forces. As a result, studies on such soft materials are currently a topic of great interest. Recently, researchers are actively involved in the development of sensors and stimuli-responsive materials based on self-assembled π-systems, which are also called smart materials. The present thesis is divided into four chapters

Investigations on Nonlinear and Radiative Properties of Certain Phatonic Materials

Light in its physical and philosophical sense has captured the imagination of human mind right from the dawn of civilization. The invention of lasers in the 60’s caused a renaissance in the field of optics. This intense, monochromatic, highly directional radiation created new frontiers in science and technology. The strong oscillating electric field of laser radiation creates a. polarisation response that is nonlinear in character in the medium through which it passes and the medium acts as a new source of optical field with alternate properties. It was in this context, that the field of optoelectronics which encompasses the generation, modulation, transmission etc. of optical radiation has gained tremendous importance. Organic molecules and polymeric systems have emerged as a class of promising materials of optoelectronics because they offer the flexibility, both at the molecular and bulk levels, to optimize the nonlinearity and other suitable properties for device applications. Organic nonlinear optical media, which yield large third-order nonlinearities, have been widely studied to develop optical devices like high speed switches, optical limiters etc. Transparent polymeric materials have found one of their most promising applicationsin lasers, in which they can be used as active elements with suitable laser dyes doped in it. The solid-matrix dye lasers make possible combination of the advantages of solid state lasers with the possibility of tuning the radiation over a broad spectral range. The polymeric matrices impregnated with organic dyes have not yet widely used because of the low resistance of the polymeric matrices to laser damage, their low dye photostability, and low dye stability over longer time of operation and storage. In this thesis we investigate the nonlinear and radiative properties of certain organic materials and doped polymeric matrix and their possible role in device development

A new inexpensive method for the preparation of acicular precursors for magnetic recording media

Magnetic materials meant for audio/video recording applications necessitate that polycrystalline materials be in acicular shape. So preparation of acicular precursors for magnetic storage materials assumes significance. The employment of aqueous solutions do not produce needle shape crystallites. Glycerol is one of the complexing media used for the precipitation of ferrous oxalate dihydrate. An inexpensive method using starch for preparation of acicular particles is described. The influence of an additive namely Gd on acicularity is also investigated

Investigations on TiO2 Based Nanocomposites as Potential Photonic Materials

This Study overviews the basics of TiO2with respect to its structure, properties and applications. A brief account of its structural, electronic and optical properties is provided. Various emerging technological applications utilising TiO2 is also discussed.Till now, exceptionally large number of fundamental studies and application-oriented research and developments has been carried out by many researchers worldwide in TiO2 with its low-dimensional nanomaterial form due to its various novel properties. These nanostructured materials have shown many favourable properties for potential applications, including pollutant photocatalytic decomposition, photovoltaic cells, sensors and so on. This thesis aims to make an in-depth investigation on different linear and nonlinear optical and structural characteristics of different phases of TiO2. Correspondingly, extensive challenges to synthesise different high quality TiO2 nanostructure derivatives such as nanotubes, nanospheres, nanoflowers etc. are continuing. Here, different nanostructures of anatase TiO2 were synthesised and analysed. Morphologically different nanostructures were found to have different impact on their physical and electronic properties such as varied surface area, dissimilar quantum confinement and hence diverged suitability for different applications. In view of the advantages of TiO2, it can act as an excellent matrix for nanoparticle composite films. These composite films may lead to several advantageous functional optical characteristics. Detailed investigations of these kinds of nanocomposites were also performed, only to find that these nanocomposites showed higher adeptness than their parent material. Fine tuning of these parameters helps researchers to achieve high proficiency in their respective applications. These innumerable opportunities aims to encompass the new progress in studies related to TiO2 for an efficient utilization in photo-catalytic or photo-voltaic applications under visible light, accentuate the future trends of TiO2-research in the environment as well as energy related fields serving promising applications benefitting the mankind. The last section of the thesis discusses the applicability of analysed nanomaterials for dye sensitised solar cells followed by future suggestions.

New studies on the versatile roles of Polyaniline and its composites in polymer based optoelectronic and energy storage devices

From the early stages of the twentieth century, polyaniline (PANI), a well-known and extensively studied conducting polymer has captured the attention of scientific community owing to its interesting electrical and optical properties. Starting from its structural properties, to the currently pursued optical, electrical and electrochemical properties, extensive investigations on pure PANI and its composites are still much relevant to explore its potentialities to the maximum extent. The synthesis of highly crystalline PANI films with ordered structure and high electrical conductivity has not been pursued in depth yet. Recently, nanostructured PANI and the nanocomposites of PANI have attracted a great deal of research attention owing to the possibilities of applications in optical switching devices, optoelectronics and energy storage devices. The work presented in the thesis is centered around the realization of highly conducting and structurally ordered PANI and its composites for applications mainly in the areas of nonlinear optics and electrochemical energy storage. Out of the vast variety of application fields of PANI, these two areas are specifically selected for the present studies, because of the following observations. The non-linear optical properties and the energy storing properties of PANI depend quite sensitively on the extent of conjugation of the polymer structure, the type and concentration of the dopants added and the type and size of the nano particles selected for making the nanocomposites. The first phase of the work is devoted to the synthesis of highly ordered and conducting films of PANI doped with various dopants and the structural, morphological and electrical characterization followed by the synthesis of metal nanoparticles incorporated PANI samples and the detailed optical characterization in the linear and nonlinear regimes. The second phase of the work comprises the investigations on the prospects of PANI in realizing polymer based rechargeable lithium ion cells with the inherent structural flexibility of polymer systems and environmental safety and stability. Secondary battery systems have become an inevitable part of daily life. They can be found in most of the portable electronic gadgets and recently they have started powering automobiles, although the power generated is low. The efficient storage of electrical energy generated from solar cells is achieved by using suitable secondary battery systems. The development of rechargeable battery systems having excellent charge storage capacity, cyclability, environmental friendliness and flexibility has yet to be realized in practice. Rechargeable Li-ion cells employing cathode active materials like LiCoO2, LiMn2O4, LiFePO4 have got remarkable charge storage capacity with least charge leakage when not in use. However, material toxicity, chance of cell explosion and lack of effective cell recycling mechanism pose significant risk factors which are to be addressed seriously. These cells also lack flexibility in their design due to the structural characteristics of the electrode materials. Global research is directed towards identifying new class of electrode materials with less risk factors and better structural stability and flexibility. Polymer based electrode materials with inherent flexibility, stability and eco-friendliness can be a suitable choice. One of the prime drawbacks of polymer based cathode materials is the low electronic conductivity. Hence the real task with this class of materials is to get better electronic conductivity with good electrical storage capability. Electronic conductivity can be enhanced by using proper dopants. In the designing of rechargeable Li-ion cells with polymer based cathode active materials, the key issue is to identify the optimum lithiation of the polymer cathode which can ensure the highest electronic conductivity and specific charge capacity possible The development of conducting polymer based rechargeable Li-ion cells with high specific capacity and excellent cycling characteristics is a highly competitive area among research and development groups, worldwide. Polymer based rechargeable batteries are specifically attractive due to the environmentally benign nature and the possible constructional flexibility they offer. Among polymers having electrical transport properties suitable for rechargeable battery applications, polyaniline is the most favoured one due to its tunable electrical conducting properties and the availability of cost effective precursor materials for its synthesis. The performance of a battery depends significantly on the characteristics of its integral parts, the cathode, anode and the electrolyte, which in turn depend on the materials used. Many research groups are involved in developing new electrode and electrolyte materials to enhance the overall performance efficiency of the battery. Currently explored electrolytes for Li ion battery applications are in liquid or gel form, which makes well-defined sealing essential. The use of solid electrolytes eliminates the need for containment of liquid electrolytes, which will certainly simplify the cell design and improve the safety and durability. The other advantages of polymer electrolytes include dimensional stability, safety and the ability to prevent lithium dendrite formation. One of the ultimate aims of the present work is to realize all solid state, flexible and environment friendly Li-ion cells with high specific capacity and excellent cycling stability. Part of the present work is hence focused on identifying good polymer based solid electrolytes essential for realizing all solid state polymer based Li ion cells.The present work is an attempt to study the versatile roles of polyaniline in two different fields of technological applications like nonlinear optics and energy storage. Conducting form of doped PANI films with good extent of crystallinity have been realized using a level surface assisted casting method in addition to the generally employed technique of spin coating. Metal nanoparticles embedded PANI offers a rich source for nonlinear optical studies and hence gold and silver nanoparticles have been used for making the nanocomposites in bulk and thin film forms. These PANI nanocomposites are found to exhibit quite dominant third order optical non-linearity. The highlight of these studies is the observation of the interesting phenomenon of the switching between saturable absorption (SA) and reverse saturable absorption (RSA) in the films of Ag/PANI and Au/PANI nanocomposites, which offers prospects of applications in optical switching. The investigations on the energy storage prospects of PANI were carried out on Li enriched PANI which was used as the cathode active material for assembling rechargeable Li-ion cells. For Li enrichment or Li doping of PANI, n-Butyllithium (n-BuLi) in hexanes was used. The Li doping as well as the Li-ion cell assembling were carried out in an argon filled glove box. Coin cells were assembled with Li doped PANI with different doping concentrations, as the cathode, LiPF6 as the electrolyte and Li metal as the anode. These coin cells are found to show reasonably good specific capacity around 22mAh/g and excellent cycling stability and coulombic efficiency around 99%. To improve the specific capacity, composites of Li doped PANI with inorganic cathode active materials like LiFePO4 and LiMn2O4 were synthesized and coin cells were assembled as mentioned earlier to assess the electrochemical capability. The cells assembled using the composite cathodes are found to show significant enhancement in specific capacity to around 40mAh/g. One of the other interesting observations is the complete blocking of the adverse effects of Jahn-Teller distortion, when the composite cathode, PANI-LiMn2O4 is used for assembling the Li-ion cells. This distortion is generally observed, near room temperature, when LiMn2O4 is used as the cathode, which significantly reduces the cycling stability of the cells.

Organic field-effect transistors and phototransistors based on amorphous materials

A comparison between the charge transport properties in low molecular amorphous thin films of spiro-linked compound and their corresponding parent compound has been demonstrated. The field-effect transistor method is used for extracting physical parameters such as field-effect mobility of charge carriers, ON/OFF ratios, and stability. In addition, phototransistors have been fabricated and demonstrated for the first time by using organic materials. In this case, asymmetrically spiro-linked compounds are used as active materials. The active materials used in this study can be divided into three classes, namely Spiro-linked compounds (symmetrically spiro-linked compounds), the corresponding parent-compounds, and photosensitive spiro-linked compounds (asymmetrically spiro-linked com-pounds). Some of symmetrically spiro-linked compounds used in this study were 2,2',7,7'-Tetrakis-(di-phenylamino)-9,9'-spirobifluorene (Spiro-TAD),2,2',7,7'-Tetrakis-(N,N'-di-p-methylphenylamino)-9,9'-spirobifluorene (Spiro-TTB), 2,2',7,7'-Tetra-(m-tolyl-phenylamino)-9,9'-spirobifluorene (Spiro-TPD), and 2,2Ž,7,7Ž-Tetra-(N-phenyl-1-naphtylamine)-9,9Ž-spirobifluorene (Spiro alpha-NPB). Related parent compounds of the symmetrically spiro-linked compound used in this study were N,N,N',N'-Tetraphenylbenzidine (TAD), N,N,N',N'-Tetrakis(4-methylphenyl)benzidine (TTB), N,N'-Bis(3-methylphenyl)-(1,1'-biphenyl)-4,4'-diamine (TPD), and N,N'-Diphenyl-N,N'-bis(1-naphthyl)-1,1'-biphenyl-4,4'-diamine (alpha-NPB). The photosensitive asymmetrically spiro-linked compounds used in this study were 2,7-bis-(N,N'-diphenylamino)-2',7'-bis(biphenyl-4-yl)-9,9'-spirobifluorene (Spiro-DPSP), and 2,7-bis-(N,N'-diphenylamino)-2',7'-bis(spirobifluorene-2-yl)-9,9'-spirobifluorene (Spiro-DPSP^2). It was found that the field-effect mobilities of charge carriers in thin films of symmetrically spiro-linked compounds and their corresponding parent compounds are in the same order of magnitude (~10^-5 cm^2/Vs). However, the thin films of the parent compounds were easily crystallized after the samples have been exposed in ambient atmosphere and at room temperature for three days. In contrast, the thin films and the transistor characteristics of symmetrically spiro-linked compound did not change significantly after the samples have been stored in ambient atmosphere and at room temperature for several months. Furthermore, temperature dependence of the mobility was analyzed in two models, namely the Arrhenius model and the Gaussian Disorder model. The Arrhenius model tends to give a high value of the prefactor mobility. However, it is difficult to distinguish whether the temperature behaviors of the material under consideration follows the Arrhenius model or the Gaussian Disorder model due to the narrow accessible range of the temperatures. For the first time, phototransistors have been fabricated and demonstrated by using organic materials. In this case, asymmetrically spiro-linked compounds are used as active materials. Intramolecular charge transfer between a bis(diphenylamino)biphenyl unit and a sexiphenyl unit leads to an increase in charge carrier density, providing the amplification effect. The operational responsivity of better than 1 A/W can be obtained for ultraviolet light at 370 nm, making the device interesting for sensor applications. This result offers a new potential application of organic thin film phototransistors as low-light level and low-cost visible blind ultraviolet photodetectors.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.