## 3 Results and Discussion
### Interpretation of SIP Signatures  
To investigate the correlation between textural information (the grain size of the ground materials) and the electrical properties, we present in Figure 5 the principal component analysis (PCA) computed for each spectra measured in samples with well-defined grain size. In particular, we use the PCA to investigate the correlation between the grain size and the Cole-Cole parameters fitted to each measured spectra (see Tables 3-5). The PCA helps us compare more variables through the fitting to each other orthogonal lines on the set of observations [51]. We can determine the various accounts with the eigenvalues of  
system (Figure 5), which describe 88% (in the case of the graphite plugs), 83% (in the case of the disseminated graphite), and 99% (in the case of the commercial graphite samples) of the variation. Every parameter or component has a value between \(-1\) and \(1\). These values produce the coefficient matrix, giving the coordinates of the coefficients (see Figure 5). The longer the vector resolved within each component, the higher the influence of the parameter. In the case of the plug measurements, the PCA reveals that the sample volume correlates more to the chargeability than the normalized chargeability, and both contribute to the first principal component (Figure 5a). Figure 5b reveals that while the chargeability and maximum phase values contribute to the first principal component, the grain size, which correlates with the relaxation time the most, contributes the most to the second principal component. The graphite volume correlates more to the normalized chargeability than to the chargeability. Furthermore, in the case of measurements in synthetic graphite powder, the normalized chargeability correlates to the salt content (Figure 5c). The PCA reveals that the chargeability contributes to the first principal component, while the relaxation time contributes to the second principal component; simultaneously, the graphite volume (Figure 5a,b) contributes to both main principal components. Hence, it is clear that the volumetric content of graphite is the main parameter controlling SIP signatures. To establish an experimental model that links our electrical parameters with graphite content and grain size, we present in Figure 6 plots of the chargeability and normalized chargeability against the graphite content, and the relaxation time against the grain size. In Figure 6a, the chargeability (M) and the volumetric graphite content reveal a positive linear relationship in cases with graphite content below 10%. Figure 6a reveals that most of our laboratory measurements can be described with a power-law relationship between chargeability and the graphite content, including samples with 15% graphite. Such a model can be written as  
\[\varnothing=a+b\mathrm{M}^{c} \tag{4}\]  
where \(\varnothing\) represents the graphite volumetric content, and \(a\), \(b\), and \(c\) fitting constants. Equation (4) was observed for different grain sizes; however, we observed different \(b\) and \(c\) parameters for the small grain sizes (d1 and d2) in comparison to those needed for larger grain sizes (d3 and d4, dashed line in Figure 6a). Alternatively, in Figure 6b, we show the correlation between the normalized chargeability (M\({}_{\mathrm{n}}\)) and graphite volumetric content, which also needs to be adjusted for large grain sizes. Such a power-law relationship can be written as follows:  
\[\varnothing=e\mathrm{M}_{\mathrm{n}}^{f} \tag{5}\]  
where \(e\) and \(f\) represent fitting coefficients. As observed in Table 6, the use of Equation (5) results in a coefficient of correlation (\(R^{2}\)) higher than the one observed in Equation (4), likely because involving the normalized chargeability also permits to account for variations in the pore-fluid electrical conductivity (Equation (3)).