A universal equivalent circuit is proposed for carbon-based supercapacitors. The circuit, which actually applies to all porous electrodes having non-branching pores, consists of a single vertical ladder network in series with an RC parallel network. This elegant arrangement explains the three most important shortcomings of present-day supercapacitors, namely open circuit voltage decay, capacitance loss at high frequency, and voltammetric distortion at high scan rate. It also explains the shape of the complex plane impedance plots of commercial devices and reveals why the equivalent series capacitance increases with temperature. Finally, the construction of a solid-state supercapacitor simulator is described. This device is based on a truncated version of the universal equivalent circuit, and it allows experimenters to explore the responses of different supercapacitor designs without having to modify real supercapacitors.

Triplet state and radical cation formation is observed following laser excitation of anthracene, phenanthrene and naphthalene (and their derivatives) adsorbed on silica gel. Energy- and electron-transfer reactions of these compounds with co-adsorbed azulene have been studied using a time-resolved diffuse reflectance laser flash photolysis technique. Triplet energy transfer from the arene derivative to azulene and electron transfer from azulene to the arene radical cation have been investigated in order to distinguish between diffusional and energetic control in these systems. Energy and electron transfer can be studied independently due to differing absorption properties and energy dependencies of production of the triplet states and radical cations. Transient decay kinetics for both electron and energy transfer have been modelled using two different rate constant distributions: a log Gaussian and a symmetrical Levy stable distribution. The latter model has also been demonstrated to be applicable to the decay of radical cations in the absence of an electron donor, which cannot be adequately described by the Gaussian model. Energy-transfer rates between the arene derivatives and azulene have been found to be close to the diffusion-controlled limit; however, in most cases, the rate of electron transfer is considerably lower. A correlation between the bimolecular rate constant and free energy of electron transfer has been found, indicating a Marcus inverted region. Compounds with bulky substituents show a further reduction in the rate of electron transfer, suggesting that an additional steric factor is involved in this process.

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Energy and electron transfer reactions between co-adsorbed molecules on silica gel have been studied using nanosecond time-resolved diffuse reflectance laser flash photolysis. The systems under investigation are anthracene and 9-carboxylic acid anthracene co-adsorbed with azulene, which undergo both triplet-triplet energy transfer and electron transfer from azulene to the anthracene radical cation following laser excitation. The decay traces have been analysed using a model which assumes a log gaussian distribution of rate constants and the methodology behind the optimisation of the fitting parameters is described. Bimolecular rate constants for energy and electron transfer between anthracene (and its derivative) and azulene have been obtained. Ground state association between anthracene and azulene has been observed, and an equilibrium constant for the process determined. The kinetic data is corrected for these ground state association effects which reduce the free azulene concentration. For both systems and for both the energy and electron transfer processes, analysis of the quenching data yields the same quenching constant. This indicates that the rate of reaction of anthracene (and the 9-carboxylic acid anthracene) on silica gel is predominantly governed by the rate of diffusion of the quencher.

Electron transfer reactions in ternary systems on silica gel surfaces: evidence for radical cation diffusion. Photochemical and Photobiological Sciences, 9 (7), pp. 937 -941.Additional Information:• This article was published in the journal, Photochemical and Photobio- Electron transfer reactions have been studied between 9-anthracenecarboxylic acid co-adsorbed with perylene on silica gel surfaces employing azulene as a molecular shuttle in order to facilitate hole transfer. In this paper we present for the first time a ternary system that unambiguously demonstrates an appreciable mobility of radical cations on the silica gel surface. Rates of hole transfer from the 9-anthracenecarboxylic acid radical cation to perylene via azulene have been studied using diffuse 10 reflectance laser flash photolysis spectroscopy. Azulene has been shown to enhance the rate of electron transfer in the ternary system, demonstrating significant mobility of the azulene and its radical cation species on silica gel surfaces. The data shows that the azulene radical cation can diffuse at an appreciable rate on the silica gel surface. Introduction 15The photochemistry and photophysics of molecules adsorbed to oxide surfaces and contained within zeolites has been the subject of a number of studies . The rapid mobility of molecules on oxide surfaces has been previously reported 2,6-11 and studied through both energy and electron transfer 20 reactions. The latter have also been studied on other porous materials such as clays 2,43-46 . Silica gel, which was employed in this study, is widely used in industry as a catalytic support and a greater understanding of reaction kinetics on these materials is significant in optimising these applications. 25Multi-photon ionisation of arenes and the subsequent electron transfer reactions of their radical cations on silica gel have been previously reported 3,4,13,14 and the influence of the nature and loading of the electron donor and electron acceptor compounds on the reaction rate investigated. The kinetics of 30 decay of radical ions on silica gel is not straightforward since the surface is heterogeneous in nature and rates rarely conform to simple exponential kinetics. We have used the model described by Albery et al 4,[12][13][14][15]50 to characterise our data sets, ensuring a comprehensive exploration of the 35 parameter space in order to obtain a global optimum value for the rate constants 13,14 .We have previously shown that energy and electron transfer reactions in these systems are dependent upon the rate of diffusion 13,14 , and in the case of azulene as energy acceptor / 40 electron donor, rates of reaction are largely determined by the rate of diffusion of this relatively more mobile species. We have demonstrated also that energetics play a role in determining electron transfer rates, and have shown a Marcustype dependence of rate on the free energy for electron 45 transfer 4,14 . In this study we also found evidence for some steric influence on reaction rates.In previous work we studied t...