Modeling of Supercapacitors

A supercapacitor stores energy in electrical double layers at electrode/electrolyte interfaces. In molecular modeling of supercapacitors, the... 

Barsali S, Ceraolo M, Marracci M, Tellini B (2010) Frequency dependent parameter model of supercapacitor. Measurement 43 1683-1689... 

Classic equivalent model of supercapacitor circuit. ESR = equivalent serial resistor. EPR equivalent parallel resistor. 

S. Buller, M. Thele, R. De Doncker, and E. Karden, Impedance-based simulation models of supercapacitors and li-ion batteries for power electronic applications, IEEE Transactions on Industry Applications, vol. 41, no. 3, pp. 742-747, 2005. 

In the sixth paper of this chapter, Kierzek et al., mainly focus on modeling of pore formation vs surface area growth phenomena upon activation of coal and pitch-derived carbon precursors. These authors briefly touch on other precursor carbons as well. The properties of newly synthesized materials are being looked at from the point of view of their application as active materials in the supercapacitor electrodes. Editors thought this work by the Institute of Chemistiy and Technology of Petroleum and Coal in Poland, could be of genuine interest to the practical developers of carbon materials for the supercapacitor industry. 

Verbrugge M, Liu P. Microstructural analysis and mathematical modeling of electric double-layer supercapacitors. Journal of the Electrochemical Society 2005 152(5) D79-D87. 

Belhachemi F, Rael S, Davat B. A physical based model of power electric double-layer supercapacitors, IEEE-IAS 00, Rome, 2000. 

The field of supercapacitor modeling has been extremely active in recent years with many papers appearing each month. Here we will... 

The electrodes of supercapacitors, in particular carbon-based electrodes, have very complex microstructure. Consequently, many types of EDLs can exist in a supercapacitor. For example, some EDLs are formed near open surfaces that can be planar (e.g., flat graphene sheet), cylindrical (e.g., CNT), or spherical (e.g., OLC) some EDLs appear inside narrow pores (e.g., sUt-shaped and cylindrical (Mies). By taking each EDL as a separate capacitor, a supercapacitor can be considered as many capacitiM s connected in series and/or in parallel. Thus, it is reasonable to study some of these capacitors (i.e., EDLs) to gain insights into the charge storage mechanism in a real supercapacitor. Many different techniques can be used to model the EDLs, and here we focus on molecular simulations and density functional theory (DFT) calculations. 

Molecular dynamics (MD) and Monte Carlo (MC) simulations are popular molecular simulation techniques. These methods are well suited for modeling supercapacitor because EDLs in supercapacitors are essentially molecular phenomena, e.g., the thickness of EDLs in supercapacitors is typically less than a few nanometers. The uni(]ue advantage of these methods is that they provide direct information on both the microstructure (e.g., ion density distribution across EDL, which is difficult to measure experimentally) and the macroscopic properties (e.g., its capacitance) of EDLs. This allows one to establish the microscopic origins of the capacitance of supercapacitors and thus helps guide the design and selection of electrode/electrolyte materials for supercapacitors. MD simulation, as... 

Once the ion density distribution inside a modeled supercapacitor (or EDL) is determined using molecular simulations or DFT calculations, the macroscopic properties of supercapacitors can be computed. The most important property... 

DFT calculaticHi [8] and closer to the experimental data. This implies that adding the polarizability of electrode (even the imis) could help increase the accuracy of supercapacitor modeling. 

The bulk of EAP-based supercapacitor work to date has focused on Type I devices. Polypyrrole (PPy, Figure 9.4C) has been studied [147,151-153] for this application, with specific capacitance values ranging from 40 to 200 F/g. Garcia-Belmonte and Bisquert [151] electrochemically deposited PPy devices that exhibit specific capacitances of 100-200 F/cm with no apparent dependence on film thickness or porosity extensive modeling of impedance characteristics was used. Hashmi et aL [153] prepared PPy-based devices using proton and lithium-ion conducting polymer electrolytes. As is often observed, electrochemical performance suffered somewhat in polymeric electrolytes single electrode specific capacitances of 40-84 F/g were observed with stability of 1000 cycles over a 1 V window. 

A number of models describing supercapacitor resistor and capacitor behaviors used to mimic their performances in power systems have been reported and include classical equivalent, ladder circuit, and lumped or distributed parameter electrical and Debye polarization cell models [6]. An established design of a dynamic model of the often-used polymer electrolyte membrane fuel cell (PEMFC) is included in MATLAB and Simulink software to simulate performance under varying conditions specific to applications. 

Buller, S., E. Karden et al. 2002. Modeling the dynamic behavior of supercapacitors using impedance spectroscopy. IEEE Transactions on Power Electronics, 38,... 

The two-branch model of the supercapacitor may be presented with a third branch, made up of an indnctance and a parallel resistance which represents the leakage current. 

This identification procedure, based on the experimental analysis of the variation in voltage at the edges of supercapacitor, can be applied to identify the parameters of one or more cells. We can also use this method to identify the parameters of a module of supercapacitors connected in a series and/or in parallel. Thus, a supercapacitor module (irrespective of the number of cells used) can be modeled by a simple RC circuit. 

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