## 4 Discussion and Conclusions  
In this study, the non-linear electrical properties of pyrogallol-formaldehyde are investigated. It is shown that the resistance of this material can be reversibly switched using electrical pulses or voltage ramps. The resistance change is believed to be caused by Joule heating, which leads to the formation of a hot conducting filament across the sample. It is also demonstrated that the ZrO\({}_{2}\) nanoparticles improve the sample conductivity but do not have a direct role in the NDR properties nor in the metastable changes in sample resistance. The rise in temperature caused by Joule heating is not expected to be high enough to cause significant changes in the carbon bonds or graphitization. Carbon exists in various forms, including the low-resistivity sp2-dominated graphitic form and the high-resistivity sp3-dominated diamond form. It is known that heating carbon to temperatures above 600 \({}^{\circ}\)C under controlled conditions (pyrolysis) can alter the sp2/sp3 ratio or cluster existing sp2 sites, but these changes in carbon bonds result in permanent changes in resistance, which cannot account for the fully reversible changes in resistance reported in this study. The electric field may also play a role in the observed resistance changes. Previous studies using a scanning tunnelling microscope probe have shown that high electric fields can induce structural changes in amorphous carbon [22]. While the electric field applied to our samples was below 3 kV/cm, it is possible that the combination of heat and electric field led to changes in carbon rearrangements. Further research is needed to clarify the role of both heat and electric field, including studies that vary sample thickness and combine electrical measurements with structural techniques. The samples studied in this research are porous, with a large surface area to volume ratio, and they can absorb atmospheric species such as oxygen and water. Evidence for absorbed water was found in the Fourier transform infrared spectroscopy (FTIR) spectrum of the PF/ZrO\({}_{2}\) samples [17]. It is expected that surface/bulk effects from the interaction with adsorbates significantly affect the material's conductivity. It is also known that trapped water, behaving as supercritical water, can mediate chemical reactions and affect the electrical conductivity of carbon-based materials [23]. The effects of absorbed water on the electrical conductivity of carbon-based materials are discussed in a comprehensive review by [PERSON] [21]. We speculate that upon heating, absorbed chemical species may diffuse out from the hot filament to nearby regions, and when the filament  
Figure 5: Set of I-V curves measured in pulsed mode and programmed with consecutive Joule heating pulses. Applied pulses were at constant current (20 \(\upmu\)A) and increasing duration. The inset shows the incremental change in conductance as a function of the length of the heating pulse. cools down, the chemical species may diffuse back, restoring the original conductivity. However, further work is needed to understand the role of absorbed oxygen and water in the reversible changes in resistance caused by Joule heat. The fine adjustment of electrical properties makes pyroggallol-formaldehyde/ZrO composites appealing for various electronic devices, including volatile memory devices, devices that mimic the long-term plasticity of biological synapses, threshold switching devices, and oscillator circuits that utilize negative differential resistance properties. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13021069/s1](https://www.mdpi.com/article/10.3390/app13021069/s1)]([https://www.mdpi.com/article/10.3390/app13021069/s1](https://www.mdpi.com/article/10.3390/app13021069/s1)), Figure S1: Comparison between the electrical conductivity of the pyrogallol-formaldehyde sample with the sample doped with 5% of ZrO\({}_{2}\) nanoparticles. The conductivity was measured for several pyrolysis temperatures.