## 2 Materials and Methods  
The positive electrodes consisted of 95 wt% AM (LiNi\({}_{0.6}\)Mn\({}_{0.2}\)Co\({}_{0.2}\)O\({}_{2}\) (NMC622), BASF, \(\rho_{\text{atfl}}\) (measured) = 4.76 g cm\({}^{-3}\)), 2 wt% CB (SuperC65, Imersy, \(\rho_{\text{atfl}}\) (measured) = 2.25 g cm\({}^{-3}\)), and 3 wt% of polyvinylidene difluoride (PVdF, Kureha, \(\rho_{\text{fluc}}\) = 1.77 g cm\({}^{-3}\)) binder. The components were mixed and homogenized with the solvent N-methyl-2-pyrrolidone (NMP) in an intensive mixer _Labormischer_ R02 VAC (EIRICH EVACTHERM) and coated on an aluminum current collector from UACJ. The areal capacity was set to 4 mAh cm\({}^{-2}\). By means of calendering, the electrodes were set to five different porosities from uncalendered (\(\approx\)44%) to 18%. Calendering was performed using a hydraulic roll-press calender (CLG-ZM-300Y) with varying loads of up to 1500 kN (maximum load as specified by the manufacturer) for the lowest porosity of 18%. The porosity investigation of the electrodes was performed with the same samples of each porosity (punched to 12 mm diameter) for all methods, starting with non-destructive techniques and ending with MIP. The total porosity, \(\varepsilon\), was determined with a gauge for at least 60 samples for each porosity. The specific surface areas of the electrodes and pore sizes up to 400 nm were measured with nitrogen ad-/desorption on a Micromeritics ASAP 2020 Surface and Porosity Analyzer (degassing at 120 \({}^{\circ}\)C for 12 h). The amount of coating material ranged from 3-4 g. The specific surface area was determined by the Brunauer-Emmett-Teller (BET) method [11], and the PSD was calculated with the model of Barrett, Joyner, and Halenda (BJH) [12]. Skeletal density \(\rho_{\text{skd}}\) (and \(\varepsilon_{\text{inacc}}\)) was determined with a helium pycnometer (Micromeritics AccuPyc II 1340) after three measurements with ten cycles each: three measurements to obtain converging results and ten measurements within these three cycles for statistics and trends. The values for \(\rho_{\text{skd}}\) were used for calculations in MIP. The latter was performed on 60 samples using a Pascal 140-440 (Pressurization by Automatic Speed-up and Continuous Adjustment Logic) porosimeter (Thermo Fischer Scientific (Waltham, MA, USA); distribution by Porotec GmbH). The pressure range was set to 0.01-400 MPa, whereas pore radii in the range of 110-0.0037 \(\upmu\)m can be determined (based on the Washburn model [15]). The porosimeter procedure consisted of two steps: a low-pressure region from 0.01-0.4 MPa (110-3.6 \(\upmu\)m pore size) and after a sample transfer a high-pressure region from 0.1-400 MPa (13-0.0037 \(\upmu\)m). Since the D90 value of the AM secondary particles was determined to be 14 \(\upmu\)m, which defines the pore sizes in the electrode, the evaluation of the mercury intrusion data was limited to the high-pressure region. Larger voids (13-110 \(\upmu\)m) were attributed to the space between the samples in the dilatometer [17]. The mercury in the capillary formed a plate capacitor with the metal sleeve around the dilatometer, the capacitance of which was proportional to the height of the mercury column in the metal sleeve. The intrusion of mercury into the sample was measured by a change in capacitance. Analysis of the MIP results was performed using the SOLID software (Solver of Intrusion Data, version 1.2.1), which included a calculation of the specific surface areas of the electrodes based on the PSD and a pore shape model. Possible pore shapes within the software were cylindrical/plate, conical, and spherical. For surface, cross-sectional, and tomography images via SEM and FIB an AURIGA Crossbeam workstation from Zeiss with a field emission gun (Schottky-type) was used. The tomography was prepared by a FIB milling process, using a high brightness liquid gallium ion source.