## 3 Results and Discussion
### Mercury Intrusion Porosimetry and N\({}_{2}\)-Physisorption
Furthermore, the total amount of intruded Hg _VHg_ yields information considering \(\varepsilon_{acc}\) down to pore sizes of 3.7 nm. Reducing _Vbulk (Hg)_ by _VHg_ results in the apparent density _\(\rho_{app}\)_.  
\[\rho_{app}=\frac{m_{sample}}{V_{bulk}\left(Hg\right)-V_{Hg}} \tag{2}\]  
If the electrodes show no structural changes during MIP (e.g., no compression) and contain no pore throats with a size < 3.7 nm, \(\rho_{app}\) should be close to \(\rho_{skel}\) (determined by He-pycnometry). By applying the different densities, various porosities can be calculated from the specific Hg-volume, _vHg_, for example:  
\[\varepsilon_{skel}(Hg)=\frac{\
u_{Hg}}{\
u_{Hg}+\frac{1}{\rho_{ total}}} \tag{3}\]  
as the total porosity from MIP. Using \(\rho_{skel}\) in Equation (3) yields the accessible porosity \(\varepsilon_{skel}\) (Hg), where closed pores are excluded. With \(\rho_{app}\), only the Hg-accessible (apparent) porosity _\(\varepsilon_{app}\) (Hg)_ is considered as shown in Figure 5(c4). The difference between \(\varepsilon_{skel}\) (Hg) and \(\varepsilon_{app}\) (Hg) results in the amount of pore volume accessible for helium but not for mercury. Inaccessible regions for Hg could also be due to too small pore entries of <3.7 nm or due to pressure-induced changes in the microstructure, e.g., changes in the elastic CBD. All calculated porosities from MIP are summarized, in comparison to the total porosity \(\varepsilon\) determined by gauge measurements, in Table 2. In addition, the specific pore surface area \(\sigma_{pore}\) was determined from PSD results. The total porosity derived by gauge measurements tends to be higher than derived by MIP. The main reason is the inaccuracy of gauge measurements indicated in Section 3.1. Electrodes with an \(\epsilon\) of 30% and the related reference electrodes with an \(\epsilon\) of 28% confirm this statement, since there is only an insignificant difference between the \(\epsilon_{xtal}\) (\(H\beta\)) of these samples. Furthermore, a gauge measurement overestimates the thickness of an electrode since only the thickest position of the electrode determines the result. This effect is amplified by structural heterogeneities of the samples. Thus, the largest difference between \(\varepsilon\) and \(\epsilon_{xtal}\) (\(H\beta\)) could be identified for uncalendered electrodes. In summary, to compare electrode microstructures, the porosity derived by MIP should be preferred to the porosity derived by gauge measurements. The difference between the accessible porosities \(\epsilon_{skel}\) (\(H\beta\)) and \(\epsilon_{app}\) (\(H\beta\)) decreases from 2.5 (for \(\varepsilon\) = 44%) to 0.5 (for \(\varepsilon\) = 18%) percentage points. Since the pore shape changes with calendering, more pores are accessible for Hg-intrusion at lower electrode porosities. Another explanation is that the strong calendered electrodes are less compressible and, thus, more stable against the high intrusion pressure, which results in a measured porosity closer to the true electrode porosity. For applications, such as LIBs, \(\epsilon_{app}\) (\(H\beta\)) could have more relevance in terms of electrochemical performance than \(\epsilon_{skel}\) (\(H\beta\)) since pore spaces with small entries of <3.7 nm, still accessible by He-gas, could be electrochemically inactive or cause high overpotentials due to the hindered Li-ion kinetics, especially at higher applied current densities. Further insights into microporosity could be gained by N\({}_{2}\)-physisorption. As a result of Figure 5, the change in pore shape and the increase in the pores with a size <100 nm for lower electrode porosity should lead to a change in the specific pore surface area, \(\sigma_{pore}\). In Table 2, an increase in \(\sigma_{pore}\) from 1.3 (\(\varepsilon\) = 44%) to 2.1 m\({}^{2}\) g\({}^{-1}\) (\(\varepsilon\) = 18%) can be identified, thus confirming the previous findings.