A universal equivalent circuit for carbon-based supercapacitors

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

Electron transfer reactions in ternary systems on silica gel surfaces: evidence for radical cation diffusion

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 reflectance laser flash photolysis spectroscopy. Azulene has been shown to enhance the rate of electron transfer in the ternary system, proving 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

Modelling of distributed time constants in carbon based supercapacitors

Modelling of distributed time constants in carbon based supercapacitor

Energy and electron transfer reactions on silica gel and titania-silica mixed oxide surfaces

The energy and electron transfer reactions of anthracene co-adsorbed with an electron donor on silica gel and titania-silica mixed oxides have been studied by a combination of steady state reflectance, emission spectroscopy, and nanosecond diffuse reflectance laser flash photolysis. Bimolecular rate constants for energy and electron transfer between anthracene and azulene have been measured; kinetic analysis of the decay of the anthracene triplet state and radical cation show that the kinetic parameters depend on the titania content of the sample and the azulene loading. The rate of energy and electron transfer reactions increases as a function of azulene loading and decreases with increasing titania content in titania-silica mixed oxides. These findings indicate that the observed rate of reaction is determined by the rate of diffusion of anthracene on the titania-silica surfaces whereas, in contrast, the observed rate of reaction on silica gel is predominantly governed by the rate of diffusion of azulene

Quantum design of ionic liquids for extreme chemical inertness and a new theory of the glass transition

In many modern technologies (such as batteries and supercapacitors), there is a strong need for redox-stable ionic liquids. Experimentally, the stability of ionic liquids can be quantified by the voltage range over which electron tunneling does not occur, but so far, quantum theory has not been applied systematically to this problem. Here, we report the electrochemical reduction of a series of quaternary ammonium cations in the presence of bis(trifluoromethylsulfonyl)imide (TFSI) anions and use nonadiabatic electron transfer theory to explicate the results. We find that increasing the chain length of the alkyl groups confers improved chemical inertness at all accessible temperatures. Simultaneously, decreasing the symmetry of the quaternary ammonium cations lowers the melting points of the corresponding ionic liquids, in two cases yielding highly inert solvents at room temperature. These are called hexyltriethylammonium TFSI (HTE-TFSI) and butyltrimethylammonium TFSI (BTM-TFSI). Indeed, the latter are two of the most redox-stable solvents in the history of electrochemistry. To gain insight into their properties, very high precision electrical conductivity measurements have been carried out in the range +20 °C to +190 °C. In both cases, the data conform to the Vogel-Tammann-Fulcher (VTF) equation with “six nines” precision (R 2 > 0.999999). The critical temperature for the onset of conductivity coincides with the glass transition temperature T g. This is compelling evidence that ionic liquids are, in fact, softened glasses. Finally, by focusing on the previously unsuspected connection between the molecular degrees of freedom of ionic liquids and their bulk conductivities, we are able to propose a new theory of the glass transition. This should have utility far beyond ionic liquids, in areas as diverse as glassy metals and polymer science

Activation energies of photoinduced unimolecular, bimolecular and termolecular processes on silica gel surfaces

Activation energies for energy and electron transfer have been measured in various systems on silica gel. In the case of ion-electron recombination, a facile technique involving fluorescence recovery is described which complements diffuse reflectance spectroscopy in the study of these systems. In bimolecular anthracene/azulene systems, activation energies have been shown to be independent of pre-treatment temperature in the range 25–210 °C, demonstrating that physisorbed water plays little role in determining diffusion rates on silica gel. In a ternary anthracene/azulene/perylene system, we have for the first time presented comparative activation energies for the diffusion of azulene and its radical cation, and have shown a greater activation energy for diffusion of the latter species

Probing the interplay between factors determining reaction rates on silica gel using termolecular systems

In this study we have compared energy and electron transfer reactions in termolecular systems using a nanosecond diffuse reflectance laser flash photolysis technique. We have previously investigated these processes on silica gel surfaces for bimolecular systems and electron transfer in termolecular systems. The latter systems involved electron transfer between three arene molecules with azulene acting as a molecular shuttle. In this study we present an alternative electron transfer system using trans β-carotene as an electron donor in order to effectively immobilise all species except the shuttle, providing the first unambiguous evidence for radical ion mobility. In the energy transfer system we use naphthalene, a structural isomer of azulene, as the shuttle, facilitating energy transfer from a selectively excited benzophenone sensitiser to 9-cyanoanthracene. Bimolecular rate constants for all of these processes have been measured and new insights into the factors determining the rates of these reactions on silica gel have been obtained

The modelling of carbon-based supercapacitors: distributions of time constants and Pascal Equivalent Circuits

Supercapacitors are an emerging technology with applications in pulse power, motive power, and energy storage. However, their carbon electrodes show a variety of non-ideal behaviours that have so far eluded explanation. These include Voltage Decay after charging, Voltage Rebound after discharging, and Dispersed Kinetics at long times. In the present work, we establish that a vertical ladder network of RC components can reproduce all these puzzling phenomena. Both software and hardware realizations of the network are described. In general, porous carbon electrodes contain random distributions of resistance R and capacitance C, with a wider spread of log R values than log C values. To understand what this implies, a simplified model is developed in which log R is treated as a Gaussian random variable while log C is treated as a constant. From this model, a new family of equivalent circuits is developed in which the continuous distribution of log R values is replaced by a discrete set of log R values drawn from a geometric series. We call these Pascal Equivalent Circuits. Their behaviour is shown to resemble closely that of real supercapacitors. The results confirm that distributions of RC time constants dominate the behaviour of real supercapacitors

Ternary mixtures of sulfolanes and ionic liquids for use in high-temperature supercapacitors

Ionic liquids are a natural choice for supercapacitor electrolytes. However, their cost is currently high. In the present work, we report the use of ternary mixtures of sulfolane, 3-methyl sulfolane, and quaternary ammonium salts (quats) as low-cost alternatives. Sulfolane was chosen because it has a high Hildebrand solubility parameter (δ H = 27.2 MPa 1/2 ) and an exceptionally high dipole moment (μ = 4.7 D), which means that it mixes readily with ionic liquids. It also has a high flash point (165 °C), a high boiling point (285 °C), and a wide two-electrode (full-cell) voltage stability window ( > 7 V). The only problem is its high freezing point (27 °C). However, by using a eutectic mixture of sulfolane with 3-methyl sulfolane, we could depress the freezing point to -17 °C. A second goal of the present work was to increase the electrical conductivity of the electrolyte beyond its present-day value of 2.1 mS cm -1 at 25 °C, currently provided by butyltrimethylammonium bis(trifluoromethylsulfonyl)imide (BTM-TFSI). We explored two methods of doing this: (1) mixing the ionic liquid with the sulfolane eutectic and (2) replacing the low-mobility TFSI anion with the high-mobility MTC anion (methanetricarbonitrile). At the optimum composition, the conductivity reached 12.2 mS cm -1 at 25 °C

Supplementary data for: Low temperature performance evaluation of electrochemical energy storage technologies.

Underlying dataset used for the publication: Low temperature performance evaluation of electrochemical energy storage technologies. https://doi.org/10.1016/j.applthermaleng.2021.116750Data includes raw discharge, max power and EIS files in .cor .z .tdms and .mat files. Data is also provided as a separate matlab file Test_data_cells.mat which also contains data of all cells in a single file. Matlab .fig files for interactive figures are included in addition to the script used to plot the figures.Please contact [email protected] for questions </div