## Appendix A  
Table 10 lists the electrochemical parameters values associated to the uncycled porous electrodes. With the subscripts \({}^{(a),(b),(c)}\) in Table 10 denoting for the origin of the parameters as follows: (a) experimentally determined; (b) literature and (c) estimated. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameters** & **Graphite** & **NMC** \\ \hline Electrode thickness & 79 \(\times\) 10\({}^{-6}\) m \({}^{(a)}\) & 70 \(\times\) 10\({}^{-6}\) m \({}^{(a)}\) \\ Volume fraction of AM & 0.52 \({}^{(c)}\) & 0.45 \({}^{(c)}\) \\ Volume fraction of electrolyte (i.e., porosity) & 0.31 \({}^{(c)}\) & 0.37 \({}^{(c)}\) \\ Current collector thickness & 14 \(\times\) 10\({}^{-6}\) m \({}^{(a)}\) & 21 \(\times\) 10\({}^{-6}\) m \({}^{(a)}\) \\ Solid phase electrode potential & Figure 4 [V] \({}^{(a)}\) & Figure 2 [V] \({}^{(a)}\) \\ Maximum lithium ions concentration & 34,984 mol/m\({}^{3}\)\({}^{(a)}\) & 48,900 mol/m\({}^{3}\)\({}^{(a)}\), [47] \\ AM particle (equivalent) radius & 5.40 \(\times\) 10\({}^{-6}\) m \({}^{(a)}\) & 3.44 \(\times\) 10\({}^{-6}\) m \({}^{(a)}\) \\ \(Li^{+}\) diffusion coefficient in the solid phase & [47] [V] \({}^{(a)}\) & [47] [V] \({}^{(a)}\) \\ \(Li^{+}\) diffusion coefficient activation Energy & 18.7 \(\times\) 10\({}^{3}\) J/mol \({}^{(a)}\) & 27.6 \(\times\) 10\({}^{3}\) J/mol \({}^{(a)}\) \\ Reaction rate constant & 9 \(\times\) 10\({}^{-13}\) m/s \({}^{(c)}\) & 8.5 \(\times\) 10\({}^{-12}\) m/s \({}^{(c)}\) \\ Electrode electronic conductivity & 100 S/m \({}^{(b)}\), [48] & 0.6 S/m \({}^{(c)}\) \\ Current collector electronic conductivity & 5.998 \(\times\) 10\({}^{7}\) S/m \({}^{(b)}\), [48] & 3.774 \(\times\) 10\({}^{7}\) S/m \({}^{(b)}\), [49] \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Electrochemical parameters values: uncycled porous electrodes. With the subscripts \({}^{(a),(b),(c)}\) in Table 14 denoting for the origin of the parameters as follows: (a) experimentally determined; (b) literature and (c) estimated. In Tables 15 and 14, for the experimental determination of the parameters associated to the superscript (a), both NMC and Graphite electrodes sheets were recovered from the uncycled and cycled battery cells according to the procedure detailed in [47]. The electrodes thickness and the current collectors thickness were measured by means of a thickness gauge (i.e., electometer). Solid phase electrode potential of both Graphite and NMC electrodes were measured by charging first 18 mm diameter electrodes punches (in EL cells containers (Hamburg, Germany)) to their upper cut-off potential using a CC-CV method (C/30-0.5 C) (as referred in [47]) and discharging them subsequently to their lower cut-off voltage with C/30 (ca. 250 \(\upmu\)A). Maximum lithium ions concentration in both electrodes were determined from XRD (X-ray Diffraction) experiments as referred by the procedure in [47]. Radius of active material (AM) particles in both electrodes were determined from the analysis of SEM (Scanning Electron Microscopy) micrographs as referred in [47]. _Li\({}^{+}\)_ diffusion coefficient in the solid phase in both electrodes were determined from GITT (Galvanostatic Intermittent Titration Technique) according to the procedure detailed in [47]. The activation Energy associated to the _Li\({}^{+}\)_ diffusion coefficient in the electrodes was determined during the discharge of the electrodes at each 10% discharge step, by means of an incremental temperature profile between 20 \({}^{\circ}\)C and 30 \({}^{\circ}\)C including 5 steps, each of 2.5 \({}^{\circ}\)C increment. The volume fraction of active material (AM) and electrolyte in both electrodes, the electrochemical reaction rate constant associated to both electrodes, as well as the electronic conductivity of the NMC electrode were estimated. The estimation of these parameters was performed using a non linear least square based algorithm, which was implemented via MATLAB(r) as referred in [50].