Coupled electro-chemo-viscoelastic constitutive model for a supercapacitor electrode

The motion of ions in supercapacitor electrodes produces internal stresses that cause viscoelastic strains. In addition, stresses may be due to external forces applied to structural supercapacitors, which are multifunctional materials that simultaneously store energy and carry structural loads. There are currently no thermodynamics-based models for the coupled electro-chemo-viscoelastic response of electrodes. Here, the same thermodynamics model is used for both the viscoelastic response and the electrochemical response. This mathematical equivalence is a reference from which to study coupling between the viscoelastic and electrochemical responses. The model has two inputs (stress or strain and electric potential or specific charge) and two outputs (strain or stress and specific charge or electric potential). The coupling is studied by adding three constants in the free energy. The convexity of the free energy and the stability of the free response limit the magnitude of the coupling. The unit response matrix is derived, and results are given for the time and frequency domains. The effect of an applied potential on stress is shown to be much more significant than the converse effect. The model compares well to an experiment consisting of a cyclic electric current applied during stress relaxation.