## 3 Results and Discussion
### Mercury Intrusion Porosimetry and N\({}_{2}\)-Physisorption  
The most common technique to investigate the porosity and especially the PSD of LIB electrodes is MIP. As shown in Figure 2, MIP covers nearly all pore sizes, which occur in electrodes of LIBs besides micropores. The results of the intrusion experiments are shown in Figure 5. The specific volume of mercury (Hg), \(\
u_{Hg}\), within the electrodes during in-/extrusion is depicted in Figure 5a. From the intrusion data, the PSD (Figure 5b) can be calculated, assuming Hg is a perfect non-wetting liquid with a constant contact angle to the electrode material surface. Releasing pressure after intrusion results in an extrusion of Hg from the electrode. This process is influenced by the shape and size of the pores. For uncalendered electrodes, nearly all the intruded Hg stays trapped in the electrode after pressure release, while only half of the Hg remains inside in case of electrodes with the lowest porosity (marked in Figure 5a). One reason could be the change in pore shape from spherical (for uncalendered electrodes) to more conical-like pores (for lower porosities). Spherical pores have a larger ratio of pore body size to pore throat size, which increases the amount of Hg-entrapment [43]. [PERSON] and [PERSON] suggest further reasons for the Hg-entrapment being spatially extended structural heterogeneities, a snap-off in narrow poreslocated next to much larger pore elements (marked in Figure 5(c5)), and the contact angle hysteresis [43]. A change in pore shape, even at constant porosity, alters the electronic and ionic conductivity of battery electrodes [34]. Thus, the pore shape directly influences the electrochemical performance of LIBs and electrodes. Furthermore, the surface area of pores increases when changing from spherical to more conical and slit-like pores. This is important for interface chemistry (electrolyte additive research) and for calculating the ionic conductivity of the electrolyte within the electrode (tortuosity, currently under investigation). Additional insights are expected when comparing MIP and N\({}_{2}\)-physisorption, discussed hereafter. More structural heterogeneities of uncalendered electrodes compared to calendered electrodes and, therefore, a higher amount of Hg-entrapment can be confirmed with the PSD results in Figure 5b. The PSD graph shows the differential specific pore volume with respect to the logarithm of the pore diameter (_dvHg/dlogD_) as a function of the pore size. A bimodal distribution can be identified for all investigated electrode porosities with a major fraction of pore sizes (highest peak) at 3 \(\upmu\)m for uncalendered electrodes. This peak shifts to smaller pore sizes for lower electrode porosities down to nearly 400 nm for electrodes with 18% total porosity. A second peak at \(\approx\)100 nm stays almost constant for all investigated electrode porosities and can be attributed to pores within or between CBD clusters [27]. At pore sizes below 100 nm, the specific pore volume increases for the lower porosity electrodes. The reasons for this increase are, on the one hand, the compression of larger pores, and on the other hand the creation of smaller pores resulting from AM particle cracking, starting here at 30% porosity towards lower porosities. The peak shift with lower porosity results in a decrease in structural heterogeneities because the PSD becomes more uniform. Contrary to this, the increase in the number of pores below 100 nm for the electrode with the lower porosity and the overall densification of the electrode resulted in a more tortuous pore network and, thus, a lower effective ionic conductivity within the electrode/electrolyte assembly. In addition to the PSD, the bulk sample volume, _Vbulk (Hg)_, can be measured after covering the electrodes with Hg and before applying a pressure for intrusion, since Hg is considered to be a perfect non-wetting liquid. With _Vbulk (Hg)_ and the sample mass, _msample_, _public (Hg)_ can be calculated.