Cross-section of a simulated negative electrode pore for a one-eighth unit cell model (i.e., symmetric electrolyte) showing the transient accumulation of positive ions at the surface of the pore over 1000ns. For a full pore, this section can be copied 3 times and rotated 90, 180 and 270 degrees respectively.
Furlani research group developed 3D computational models for the rational design of electronic double layer (EDL) supercapacitors.
Figure 1: Schematic of an electric double layer capacitor with mesoporous electrodes
In an electric double layer capacitor (EDLC) an electrolyte containing positive and negative ions is connected between an anode and cathode as shown in Figure. 1. The ions separate and accumulate on the surface of the oppositely charged electrodes in response to an applied voltage. Energy is stored in an EDLC via the formation of the closely-spaced layers of charge at the electrode-electrolyte interfaces. The separation distance between the ions and the charged electrode can be considered as the distance between the “plates" of the capacitor. This minuscule separation, on the order of angstroms, coupled with the large surface area of highly porous electrodes, enables EDLCs to have a significantly higher capacitance than traditional capacitors. Moreover, physical storage of charge, instead of chemical storage, prevents the degradation of the electrochemical cells over nearly unlimited charge/discharge cycles.
Figure 2: EDL supercapacitor with idealized mesoporous electrodes that consist of uniform cylindrical pores.
We are developing 3D computational models for the rational desin of EDL supercapacitors. The device models predict the capacitance as a function of key electrode and electrolyte properties: electrode thickness, porosity, pore dimensions, ionic concentration, diameter and valence etc. Since fabricated electrode morphologies are too complex to model directly, they are approximated using idealized mesoporous electrode structures, e.g., with ordered cylindrical and rectangular nanopores respectively as shown in Figure. 2.
We use a modified Poisson-Boltzmann model (MPB) to predict the steady-state behavior of EDLCs. A key feature of the MPB model is that it limits the accumulation of ionic charge based on the finite size of the ions. In the MPB model the electrostatic potential Ψ in the electrolyte is determined via the numerical solution of Poisson’s equation.
where zi and ci are the valency and local molar concentrations of the ionic species i and N is the total number of ionic species. The equilibrium concentration ci(Ψ)of an ion species is given by the Boltzmann distribution, e.g. for a symmetric binary electrolyte, N =2, z1 = z2 the concentrations of anions and cations, c1 and c2, respectively, are given by
We solve the nonlinear PDE Eq. 1 for the potential then use this to compute the charge distribution and capacitance etc. An example of the analysis going the accumulation of positive ions on the surface of the cathode is shown in Figure. 3. The decrease in gravimetric capacitance of the EDLC as a function of hydrated ion diameter is shown in Figure. 4.
Figure 3. Charge accumulation at the electrode-electrolyte interface: unit cell of computational model and cross-section of a simulated negative electrode pore for a one-eighth unit cell model (i.e. symmetric electrolyte) shows the steady-state accumulation of positive ions at the surface of the cathode. For a full pore, this cross section is mirrored across the boundary at the right.
Figure 4. Gravimetric capacitance as a function of hydrated ion diameter for an organic electrolyte.