A model for the fatigue life of thin-film carbon nanotube-based supercapacitors

The effects of cyclic loading on the mechanical performance and fatigue life of a novel carbon nanotube supercapacitor are investigated. The highly flexible supercapacitor is a monolithic, pre-fabricated, fully functional film made of a nanostructured free-standing layer in which ions are stored within two vertically aligned multi-walled carbon nanotube (MWCNs) electrodes that are monolithically interspaced by a solution of microcrystalline cellulose in a room temperature ionic liquid electrolyte. To study the cyclic mechanical response of such nanostructured multilayer composite, an original framework is adopted by combining the equivalent continuum approach of EshelbyeMoryeTanaka and a Weibull-like approach for the evolution of debonding carbon nanotubes electrodes. One- and three-layer models of the supercapacitor are proposed. Cyclic tests are numerically carried out in strain control. A fatigue life limit is determined by considering a confidence interval for the number of cycles corresponding to the states at which the effective elastic modulus of the partially debonded nanostructured portion of the supercapacitor is reduced by a percentage between 20% and 30%. The simulated cyclic tests yield Wholertype fatigue curves showing the fatigue life limit as the maximum number of cycles N for each strain amplitude. The sensitivity of the fatigue life with respect to meaningful parameters such as the interfacial strength between the MWCNs and cellulose is investigated. Frequency-response functions of the multilayer nanostructured composite are further computed as function of the strain amplitude during cyclic tests.