### Methods for Porosity Measurement  
This study focused on investigating the porosity of LIB composite electrodes coated on a non-porous current collector foil. Therefore, methods like porometry, that rely on a capillary flow through porous specimen, e.g. battery separators, are not discussed here. As mentioned in Section 1.1, the most common way to measure porosity is via the  
Figure 1: Scheme of the porosity, structure, and components of an electrode. The total porosity, \(\varepsilon\), is the sum of \(\varepsilon_{acc}\) (blue) and \(\varepsilon_{inacc}\) (red). thickness and mass of the electrode, assuming the values for calculating \(\rho_{\textit{flux}}\) are known. The thickness can be measured by a gauge that also determines the accuracy of this method, because weight and area can be determined more precisely than thickness. Determination and description of porosity via the pore size distribution (PSD) can be accomplished by small-angle scattering techniques (via X-ray or neutrons) [9; 10], gas physisorption [11; 12; 13; 14] (mostly with nitrogen), mercury intrusion porosimetry (MIP) [15; 16; 17; 18], the Archimedes' principle with a displacement medium (e.g., water or glycerol) [19], or standard contact porosimetry [20; 21]. The latter is based on a capillary equilibrium of any liquid between the porous sample and a standard, and it is used for pore sizes between 1 nm to 300 \(\upmu\)m (comparable to MIP). Except for MIP, all mentioned techniques are non-destructive. With imaging methods, two- or three-dimensional structure models of a sample can be derived and used to determine porosity and PSD. Scanning electron microscopy (SEM) can be applied for surface and cross-sectional analysis (2D) [6; 22; 23]; combined with a focus ion beam (FIB), it can result in FIB/SEM tomography (3D) [24; 25; 26; 27]. Non-destructive tomography techniques utilize neutrons or X-ray radiation [28; 29; 30; 26] and can visualize a larger sample volume than FIB/SEM (e.g., 500 \(\times\) 110 \(\times\) 250 \(\upmu\)m compared to 31.3 \(\times\) 34.5 \(\times\) 16.8 \(\upmu\)m [26]) but with a lower resolution (e.g., a voxel edge length of 438 nm compared to 33.6 nm [26]), depending on the setup. Recently, digital modeling of electrode structures and manufacturing processes has become more relevant [5; 32]. From different electrode paste compositions to calendering and electrochemical performance, several microstructures and the resulting porosities can be investigated. In the future, artificial intelligence could, on the basis of the fundamental understanding of the correlation between materials, microstructure, and electrochemical performance, enable model-based identification of the most suitable microstructures for a specific application [33]. This study is one step toward achieving this fundamental understanding of the experiments. Modeling, especially, shows the challenges of understanding the microstructure of an electrode. The total porosity is only one parameter to characterize the morphology of electrodes after calendering. For the same value for total porosity of different electrodes, the distribution of AM, CB, binder, and pores could be heterogeneous and result in different structural properties and, ultimately, diverse electrochemical performances. The shape of the pores and pore connectivity affect the electronic as well as the ionic conductivity [34]. Moreover, attention should be paid to the influence of inactive materials (IMs) (i.e., CB and binder) on the microstructure and the transport phenomena within the electrode. Since these two components cannot often be considered separately from each other, they are usually described as a unit: the carbon and binder domain (CBD). Underestimating the importance of the CBD is frequently the reason for large differences between electrochemical experiments regarding Li-ion conductivity in positive electrodes and digital model electrodes derived from tomography measurements or those that are digitally generated [27; 35; 36; 37].