## 2 Results and Discussion
It is tempting to attribute the decrease of the percolation threshold to an increase in the aspect ratio of the segregated carbon phase, as the threshold typically depends on the shape of the conductive filler in many composite materials [53; 54; 55]. For instance, [PERSON] et al. computed in a case study the insulator-conductor transition in SiOC/C-based materials, showing that the percolation threshold decreases from 20 to 5 vol.% as the shape of the conductive filler is changed from spherical to rod-like [35]. However, no reliable information on the aspect ratio can be obtained for SiOC/C, due to the random 3D carbon morphology and the lack of suitable characterization methods. The observed temperature-dependent shift for \(\phi_{\text{crii}}\) in the SiOC/C ceramics may therefore be also attributed to changes within the carbon network itself, e.g., the decrease of defects concentration and/or better alignment of carbon sheets allowing enhanced electrical transport in conjugated bonds. This possibility has been addressed upon assessing the critical exponent \(t\) in the studied SiOC/C samples cf. \(\sigma_{\text{C}}=\sigma_{0}\cdot(\phi-\ \Phi_{\sigma\text{crii}})^{t}\), where \(\sigma_{0}\) is a proportionality constant, \(\sigma_{\text{C}}\) the conductivity of the composite, \(\phi_{\text{crii}}\). the critical concentration below the composite that is insulating (percolation threshold) and \(t\) the critical exponent. The value of the critical exponent \(t\) is known to depend on the lattice dimensionality and was calculated to possess a value of ca. 2.0 in three-dimensional lattices/systems [56; 57]. Figure 4: Evolution of the average distance between defects L\({}_{\text{D}}\) within the carbon of SiOC/C synthesized at different temperatures. The empty symbols correspond to a graphene-based material in which the disorder and defect concentration were altered upon argon ion bombardment [52]. Deviations from this behavior have been reported for many different composites [58]. According to [PERSON], these deviations can be assigned to tunneling-percolation processes with strong fluctuations in tunneling distances thus causing high values for \(t\), even up to 6.0 [59; 60]. Non-universal behavior is frequently observed in dispersed composites, whereas universal behavior is seen more often in clustered samples [58]. The non-universal behavior may result from tunneling/hopping processes between two adjacent conductive particles [61], e.g., taking quantum mechanics into account the critical exponent becomes dependent on the mean tunneling distance and in principle does not obey any upper limit. As clearly shown in Figure 6, the value of \(t\) in SiOC/C sample series prepared at 1600 \({}^{\circ}\)C (with a percolation threshold at 6 vol.%) was ca. 4.3 and thus these materials should be considered as being significantly different than three-dimensional systems, for which the geometry and aspect ratio of the conductive phase mainly determined their behavior. The \(t\) value obtained for the SiOC/C ceramics in the present study were similar to those obtained, e.g., for RuO\({}_{2}\)/silica composites (\(t=3.8\)) [58]. Figure 5: The electrical conductivity of SiOC/C as a function of the sp\({}^{2}\) carbon for three different temperature series (a-C: amorphous carbon). The data were obtained from two-point conductivity measurements. Literature values [19; 33; 35; 38; 62; 63; 64; 65] are added for the sake of comparison. Figure 6: Electrical conductivity of SiOC/C materials as a function of the sp\({}^{2}\) carbon concentration. Figure 1:0 The upper dashed line represents the universal behavior with a slope of \(t=2\). The empty circles represent the electrical conductivity of piezoresistive RuO\({}_{2}\)/silica composites with varying RuO\({}_{2}\) content [58]. Only sparse information about the conduction mechanism in PDCs is available in the literature.