Cosmic strings in general relativity

In this thesis we examine the properties of Cosmic Strings in the theory of General Relativity. We begin by considering static Cosmic Strings in flat space-time. We derive the field equations for the Cosmic String and show that the solution depends upon a single scaling parameter a which is constructed from the physical constants. Using this result we construct 1-parameter families of solutions which depend on an auxiliary parameter e and which describe the thin-string limit of a Cosmic String. By interpreting these solutions as elements of the simplified Colombeau algebra we may interpret the relativistic energy density Too of the thin string as an element of the Colombeau algebra with delta-function mass-per-unit-length. Furthermore, for a critically coupled Cosmic String the energy momentum tensor in the thin-string limit may be given a distributional interpretation. We also solve the string equations numerically for various values of a. This is done by compactifying the space-time to include infinity as part of the numerical grid and then using a relaxation method to suppress exponentially growing un-physical solutions. In curved space-time we derive the equations for the scalar and vector fields which are now coupled to the geometric variables through Einstein's equations. We again examine the thin-string limit in the Colombeau algebra by considering a 1-parameter family of solutions. We derive an expression for the deficit angle in terms of the distributional energy-momentum tensor of the thin string. We use this result to investigate the gravitational lensing properties of the string and relate this to the deficit angle. In the special case of a cone we find the scattering angle is equal to the deficit angle. We also solve the coupled equations numerically using techniques similar to those used in flat space-time. The second part of the thesis involves the dynamics of Cosmic Strings. Einstein's equations then lead to wave equations for both the matter and metric variables. However, the space-time is not asymptotically flat and this leads to problems in applying the appropriate boundary conditions. By using a Geroch transformation it is possible to reformulate the equations in terms of geometrical variables defined on an asymptotically flat (2+l)-dimensional space-time. Three exact vacuum solutions describing gravitational radiation due to Weber-Wheeler, Xanthopoulos and Piran et al. are used to excite thestring which is found to oscillate with frequencies which are proportional to the masses of the scalar and vector fields of the string. This is in agreement with the exact results obtained using the linearised equations of the thin dynamic string.The behaviour of the dynamic string is studied by solving the equations numerically using an implicit fully characteristic scheme. The use of the Geroch transformation allowsus to compactify the space-time and include null infinity as part of the numerical grid. This enables us to use the correct boundary conditions at infinity and hence suppressun-physical divergent solutions. The code is tested by comparing the results with exactsolutions, by checking that it agrees with the static code and by undertaking a time dependent convergence test. The code is found to be accurate, stable and exhibit clear second order convergence

An All-Organic Proton Battery

Rechargeable batteries that use organic matter as the capacity-carrying material have previously been considered a technology for the future. Earlier batteries in which both the anode and cathode consisted of organic material required significant amounts of conductive additives and were often based on metal-ion electrolytes containing Li⁺ or Na⁺. However, we have used conducting poly­(3,4-ethylenedioxythiophene) (PEDOT), functionalized with anthraquinone (PEDOT-AQ) or benzonquinone (PEDOT-BQ) pendant groups as the negative and positive electrode materials, respectively, to make an all-organic proton battery devoid of metals. The electrolyte consists of a proton donor and acceptor slurry containing substituted pyridinium triflates and the corresponding pyridine base. This slurry allows the 2e^–/2H⁺ quinone/hydroquinone redox reactions while suppressing proton reduction in the battery cell. By using strong (acidic) proton donors, the formal potential of the quinone redox reactions is tuned into the potential region in which the PEDOT backbone is conductive, thus eliminating the need for conducting additives. In this all-organic proton battery cell, PEDOT-AQ and PEDOT-BQ deliver 103 and 120 mAh g^–1, which correspond to 78% and 75%, respectively, of the theoretical specific capacity of the materials at an average cell potential of 0.5 V. We show that PEDOT-BQ determines the cycling stability of the device while PEDOT-AQ provides excellent reversibility for at least 1000 cycles. This proof-of-concept shows the feasibility of assembling all-organic proton batteries which require no conductive additives and also reveals where the challenges and opportunities lie on the path to producing plastic batteries

Investigation of the Redox Chemistry of Isoindole-4,7-diones

Quinone derivatives have been proposed as active components in lithium ion battery (LIB) electrode materials. In this work the electrochemistry of a series of substituted isoindole-4,7-diones (IIDs) was investigated. Three new IID derivatives were synthesized and characterized by various electrochemical and spectroscopic techniques. Polymerization was attempted to achieve a conducting polymer with redox active quinone side groups, which would be advantageous in a LIB application. A combination of <i>in situ</i> spectroelectrochemical measurements and density functional theory (DFT) calculations was used to investigate the proton coupled redox reactions of the IIDs. Results from a previous computational study of the IIDs were compared with experimental data here, and the agreement was very good. The energy of the spectroscopic transitions in the UV and in the visible region showed different correlation with redox potential and quinone substituent in the series of IIDs. This behavior was rationalized by examination of the involved molecular orbitals. The results indicated that the properties of the quinone unit, such as the redox potential, could be selectively varied by substitution

Activation Barriers Provide Insight into the Mechanism of Self-Discharge in Polypyrrole

Conducting polymers are envisioned to play a significant role in the development of organic matter based electrical energy conversion and storage systems. However, successful utilization of conducting polymers relies on a fundamental understanding of their inherent possibilities and limitations. In this report we studied the temperature dependence of the self-discharge in polypyrrole and show that the rate of self-discharge is kinetically controlled by a polymer intrinsic endergonic electron transfer reaction forming a reactive intermediate. We further show that this intermediate is intimately linked to a process known as overoxidation. This process is general for most, if not all, p-doped conducting polymers irrespective of medium. The results herein are therefore expected to significantly impact the development of future energy storage systems with conducting polymer based components

Computational Electrochemistry Study of 16 Isoindole-4,7-diones as Candidates for Organic Cathode Materials

Prediction of the redox behavior of electroactive molecules enables screening of a variety of compounds and can serve as a guideline in the search for organic molecules for use as cathode materials in, for example, Li ion batteries. In this study, we present a computational strategy, based on density functional theory, to calculate redox potentials and acid dissociation constants for a series of 16 isoindole-4,7-dione (IID) derivatives. The calculations take all possible electron and proton transfers into account, and the results were found to correlate very well with electrochemical and spectroscopic measurements. The possibility of polymerizing the IID derivatives was also assessed computationally, as polymerization serves as a straightforward route to immobilize the active material. Three of the considered IIDs (5,6-dicyano-2-methyl-isoindole-4,7-dione, 5,6-dihydroxy-2-methyl-isoindole-4,7-dione, and 2-methyl-5-(trifluoromethyl)-isoindole-4,7-dione) are predicted to be particularly interesting for making polymers for organic cathodes because these are calculated to have high redox potentials and high specific capacities and to be readily polymerizable. The presented strategy is general and can be applied in the prediction of the electrochemical behavior of quinones as well as other systems involving proton and electron transfers

A Comparative Study of the Effects of Rinsing and Aging of Polypyrrole/Nanocellulose Composites on Their Electrochemical Properties

The effects of polymerization conditions, rinsing, and storage on composites composed of polypyrrole (PPy) and Cladophora nanocellulose in terms of purity, chemical composition, conductivity, and electroactivity were investigated using conductivity measurements, cyclic voltammetry, FTIR-ATR, XPS, and ICP-AES. A clear correlation between rinsing volume and PPy degradation was found using water- or NaCl-rinsing solutions as evidenced by conductivity and electroactivity losses. It was further found, through FTIR-ATR as well as XPS-measurements, that this degradation was caused by incorporation of hydroxyl groups in the PPy-layer. The extent of degradation correlated with a shift in the FTIR-ATR peak around 1300 cm^–1, showing that FTIR-ATR may be used as a quick diagnostic tool to evaluate the extent of degradation. By the use of acidic rinsing solution, this degradation effect was eliminated and resulted in superior samples in terms of both conductivity and electroactivity and also in a more efficient removal of reactants. Upon ambient storage, over a period of 200 days, a gradual decrease in conductivity was found for initially highly conductive samples. The electroactivity, on the other hand, was relatively unaffected by storage, showing that conductivity measurements alone are ineffective to determine the degree of polymer degradation if the water content is not controlled. Also, FTIR-ATR measurements indicated that the oxidation state did not change to any large extent upon storage and that only minor degradation of PPy occurred. The results presented herein thus offer valuable guidelines on how to develop simple and reliable postsynthesis treatments of conducting polymer–paper composites with performance fulfilling requirements on stability, electroactivity, and purity in applications such as environmentally friendly energy storage devices and biomedical applications

Quantification of Human Kallikrein‑2 in Clinical Samples by Selected Reaction Monitoring

Recently, the number of mass spectrometry-based quantification assays has been increased, partially due to the global efforts of chromosome-centric human proteome project (C-HPP). Our goal at the Chromosome 19 Consortium is to provide novel selected reaction monitoring (SRM) assays of proteins coded on chromosome 19. We have selected the two most useful signature peptides (NSQVWLGR and HNLFEPEDTGQR) of human kallikrein-2 (hK2 – NX_P20151) and developed an SRM assay. Details of the analytical parameters, including multiple transitions by peptides, are presented. The endogenous levels of hK2 were determined in clinical samples (<i>n</i> = 35). The limit of quantification was also estimated by spiking heavy isotope-labeled peptides into seminal plasma samples at various concentrations (LOQ ≈ 29 ng/mL)

Enthalpic versus Entropic Contribution to the Quinone Formal Potential in a Polypyrrole-Based Conducting Redox Polymer

A conducting redox polymer (CPR) based on pyrrole with a hydroquinone pendant group was synthesized through electropolymerization of the corresponding monomer. The formal potential (<i>E</i>⁰′) in aqueous solution at different pH as well as in MeCN containing equal amounts of pyridinium-triflates and the corresponding free pyridine with different p<i>K</i>_a was investigated. <i>E</i>⁰′ could be completely recovered in MeCN, and by utilizing pyridine bases with different donor–acceptor strengths, a decrease of 61 meV/p<i>K</i>_a was found that corresponded exactly to the pH dependence of <i>E</i>⁰′ in aqueous electrolyte. To separate the entropic and enthalpic contributions to <i>E</i>⁰′, temperature-dependent electrochemistry was performed. Two different modes of operation with changing pH/p<i>K</i>_a between the two media were revealed. In MeCN, <i>E</i>⁰′ varies only because of the enthalpic contribution as the entropic contribution is unaffected by change in p<i>K</i>_a. In water, there is primarily an entropic contribution to <i>E</i>⁰′ with changing pH due to solvation of the proton. The presented results are expected to open up for new design possibilities of CRPs based on ion-coordinating redox groups for electrical energy storage

Probing Polymer–Pendant Interactions in the Conducting Redox Polymer Poly(pyrrol-3-ylhydroquinone)

Conducting polymers with redox active pendant groups show properties typical of both conducting polymers (i.e., capacitive charging and intrinsic conductivity) and redox polymers (i.e., electrochemical surface response at the formal potential of the pendant groups). The two components can also exert significant interaction on each other during their separate electrochemical reactions. In poly­(pyrrol-3-ylhydroquinone), a polypyrrole derivative functionalized with hydroquinone units, the redox conversion of the pendant groups has a large impact on the polymer backbone. This interaction is manifested by a loss of bipolaron states during the hydroquinone oxidation, leading to a decreasing p-doping level with increasing potential, something which, to the best of our knowledge, has never been observed for a conducting polymer. Another effect is a contraction of the polymer film, and subsequent mass loss due to solvent expulsion upon hydroquinone oxidation, which counteracts the normal swelling of polypyrrole with increased potential. The conducting redox polymer under investigation has been synthesized via two routes, leading to different fractions of subunits bearing redox active hydroquinone groups. While the redox potentials are unaffected by the synthesis route, the backbone/pendant group interaction varies notably depending on the degree of quinone functionalization. This type of polymers could find use in, e.g., organic energy storage materials, since the polymer backbone both increases the electronic conductivity and prevents dissolution of the active material, as well as in actuator application, due to polymer contraction over the relatively narrow potential region where the pendant group redox chemistry occurs

Synthesis and Redox Properties of Thiophene Terephthalate Building Blocks for Low-Potential Conducting Redox Polymers

Terephthalate-substituted thiophene derivatives are promising redox-active components for anode materials in lithium-ion batteries. In this study, we present the synthesis of substituted 2-(thiophen-3-yl)­terephthalate derivatives (TTDs) as suitable monomers for thiophene-based conducting redox polymers, along with their characterization by electrochemical and spectroscopic techniques. Density functional theory (DFT) calculations, utilizing the universal solvation model based on solute electron density (SMD), were used to predict both the first and the second reduction potentials of these TTDs. The computational results showed good agreement with the experimental data in nonaqueous acetonitrile solvent, with mean absolute errors of 30 and 40 mV for the first and second reduction steps, respectively. Time-dependent (TD) DFT calculations on TTDs indicated terephthalate local transitions at both 200 and 240 nm and charge-transfer transitions above 300 nm by examination of the involved molecular orbitals