Modelling and Experimental Studies on Dynamic Behaviour of Electrochemical Double Layer Capacitors

Abstract

lectrochemical double layer capacitors (EDLCs) can store and deliver electrical energy at high power density with long cycle life, and can absorb peak charge/discharge loads. EDLCs can be used with batteries to insulate the latter from the adverse e ects of shock loads. Other high technology applications also harness this feature of EDLCs. EDLCs store energy in the form of oppositely charged double layers on two electrodes. The electrodes are typically made of porous carbon which o ers high speci c surface area ( 1500 m2/g) and high capacitance at low cost. The high surface area is contributed by pores ranging from micropores (< 2 nm) to macropores (> 50 nm). The charging of an EDLC moves electrons from one electrode to other. This leads to buildup of double layers on electrode-electrolyte interfaces in pores. Connecting a load across an EDLC leads to ow of electrons through the load, discharge of double layers, movement of ions in pores and electrolyte, and decrease in capacitor's potential. There are two main issues with EDLCs that need to be addressed to take them to the next level in energy storage applications|low energy e ciency at moderate to high currents and high self-discharge. The objective of the work reported here is twofold: a) to obtain detailed and careful electrode speci c experimental measurements of dynamic characteristics of inhouse EDLCs with known structural details and physical properties, instead of the ones available commercially, and b) use comprehensive transport model based investigations to quantitatively understand factors that limit performance of EDLCs. In the rst part of the work, we present a detailed analysis of charge-redistribution (CR) in EDLCs using a macro-homogeneous transport model. CR manifests as rapid decrease in voltage beyond IR drop after charging is stopped, and recovery of voltage beyond IR recovery after discharging is stopped. The model considers local electrolyte concentration dependent ionic conductivity, nite electronic conductivity of porous solid matrix, constant capacitance of double layer, ionic

ux driven by potential and concentration gradients, di erent sizes of ions, and Bruggeman correction for ionic conductivity in pores. The model predicts that the depletion of ions in pores requires signi cant potential drop to move ions to ii build double layers. Its magnitude, predicted by the earlier models to reach an asymptotic value with time, is found in the present model to increase with time due to the depletion e ects. The model predicts CR to occur at two time scales|rapid changes in cell potential over a couple of seconds, driven purely by potential gradients across pores, and slow changes over time scale of hundreds of seconds, driven by electrolyte concentration gradients inside and outside the porous electrode. The large di erences in CR at two electrodes on account of involvement of di erent ions on them are highlighted. The model predicted two time scale relaxation of cell potential, one after the other, follows linear scaling with log t, but with di erent slopes. The magnitude of both the slopes is a ected by the extent of retardation of movement of ions in pores. The model shows that holding a rapidly charged EDLC for short intervals of potentiostatic charging alleviates CR induced loss of charging capacity substantially. An extensive experimental study is undertaken next to obtain discharge characteristics of carbon-H2SO4 EDLCs at di erent electrolyte concentrations. The low current measurements, in the absence of any transport limitations, show that charging and discharging cannot be explained using a single set of potential dependent capacitance values. With the focus of the thesis on discharge of EDLCs, the discharge current is varied over a large range. The experiments show close to 100% charge utilization at low discharge currents, which decrease to as much as 50% at high currents. The highly non-linear decrease observed in cell potential at high currents persists at the lowest currents used as well. These EDLCs are subjected to cyclic-voltammetry and impedance spectroscopy for their complete electrochemical characterization. In order to unambiguously delineate the dynamic e ects during discharge, the variation of potential di erence across each electrode at low currents is used to recover voltage and electrolyte concentration dependent electrode capacitance. The model predictions for time variation of cell and individual electrode potentials, obtained using i) measured capacitance, (i) measured electrolyte conductivity in bulk, and iii) Bruggeman correction for conductivity in pores, are in perfect agreement with the measurements at low discharge currents. At high discharge currents, the model substantially underpredicts the loss of charge utilization. The measured cell potential drops to zero far more rapidly and the cell iii potential recovery in open circuit mode is far too strong. Since there is no tted parameter in the model whose value can be altered, the model unambiguously points to much lower ionic conductivity in charged pores than what is given by the Bruggeman correction. With incorporation of additional retardation of movement of ions through correction factors for electrolyte conductivity in pores, the model quantitatively explains a large body of experimental data. The model also predicts the measured cyclic-voltammetry pro les well; the agreement between the two is excellent at high scan rates. The study thus highlights the need to understand the cause of unusually low ionic conductivities in charged porous electrodes. Self-discharge (SD) is the loss of stored energy when a device is not in use. In the second part of the thesis, we carried out an experimental and modelling study to understand SD better. The experimental study is focused on investigation of role played by SD in galvanostatic, potentiostatic, and open-circuit modes. The open circuit potential of the capacitor used in the present work decreased from 1.0 to 0.4 V in 31 h. The electrode speci c measurements highlight quite di erent rates of self-discharge at the two electrodes. The measurements show that a capacitor starting with the same open circuit potential, but with di erent histories such as maintaining it under a potentiostat versus letting it reach the same voltage as it self-discharges from a higher cell potential, lead to di erent self-discharge rates. When a capacitor is maintained at a xed cell potential by supplying it with the needed current, named oat current, our measurements show that potential di erences for the individual electrodes undergo slow internal adjustment. The measurements carried out at low currents to charge and discharge EDLC show that passing of a charging current through EDLC aggravates SD, while passing of an external current to discharge EDLC diminishes SD. The measurements performed on electrodes with di erent amount of active material on them and with di erent distance between the electrodes establish that self-discharge neither occurs uniformly everywhere in the electrodes nor does it occur by a mechanism controlled by projected area of the electrodes. The widely used Conway's diagnotic tools also do not lead to identi cation of any of the three widely held mechanisms for self-discharge. The model developed to predict charge-redistribution in EDLCs at short iv time scales is extended to predict slow self-discharge using the measured values of electrode potential dependent oat currents|the rate at which charge must be supplied to maintain cell potential constant|after four hours of maintaining EDLCs at desired potential. The model on the other hand requires substantially smaller values of oat currents to match experimental measurements on self-discharge during OCR. The additional measurements carried out over 50 h of potentiostatic holding show that the magnitude of the current required to keep cell potential constant keeps decreasing, while the individual electrode potentials stop readjusting just after about 6 h. The model quantitatively explains experimental observations on self-discharge under open circuit and galvanostatic discharge conditions. It successfully predicts the experimentally observed internal readjustment of electrode potentials on potentiostatic holding of our EDLC. The model validates the need to address the e ect of history on self-discharge rates for electrodes.