# A Study on the Conductivity and Infrared Spectroscopy of Elastic Polymer Composite Materials
## 3 Results  
### Activated Carbon's Characteristic Equation  
The relationship between the activated carbon doping concentration (\(\mathrm{C_{d}}\)) and resistivity (\(\mathrm{\rho}\)) of the specimen is shown in Figure 11. The specimen's resistivity and doping concentration are in inverse proportion. At a temperature of 300 K, when the activated carbon doping concentration reaches 35 M, the electric conductivity increases rapidly, but when the activated carbon doping concentration increases to 45 M, the electric conductivity enters into a steady state. In the meanwhile, if the activated carbon doping concentration reaches 55 M, the adsorption of activated carbon is so strong that it causes the specimen's elasticity to reduce. Moreover, when the activated carbon doping concentration is 60 M, at which point adsorptive saturation is reached, many cracks are left on the surface of the hardened specimen. Increasing to 65 M causes adsorption over-saturation, and the activated carbon desorbs from the surface of the specimen. After many experiments, the equation for the resistance characteristic of the activated carbon doping concentration is derived as follows:  
\[\mathrm{\rho}=\left\{\begin{array}{ll}(\mathrm{\rho}_{c}-\mathrm{\rho}_{ \mathrm{s}})\frac{\mathrm{C}_{\mathrm{d}}-\mathrm{C}_{\mathrm{c}}}{\mathrm{C} _{\mathrm{c}}-\mathrm{C}_{\mathrm{c}}},&\mathrm{if}\ \mathrm{C}_{\mathrm{d}}>\mathrm{C}_{ \mathrm{c}}\\ (\mathrm{\rho}_{\mathrm{o}}-\mathrm{\rho}_{\mathrm{c}})\frac{\mathrm{C}_{ \mathrm{c}}-\mathrm{C}_{\mathrm{d}}}{\mathrm{C}_{\mathrm{c}}-\mathrm{C}_{ \mathrm{c}}},&\mathrm{C}_{\mathrm{d}}<\mathrm{C}_{\mathrm{c}}\end{array}\right. \tag{2}\]  
In Formula (2), \(\mathrm{C}_{0}\) is the minimum doping concentration required for the elastic polymer composite materials to become resistance materials; \(\mathrm{\rho}_{0}\) is the resistivity of \(\mathrm{C}_{0}\); \(\mathrm{C}_{\mathrm{c}}\) is the critical doping concentration at which the conductor is in a steady state; \(\mathrm{\rho}_{\mathrm{c}}\) is the resistivity of the critical doping concentration; \(\mathrm{C}_{\mathrm{s}}\) is the adsorption-saturated doping concentration; and \(\mathrm{\rho}_{\mathrm{s}}\) is the resistivity of the adsorption-saturated saturated doping concentration.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **A** & & **B** \\ \hline
**Element** & **Weight\%** & **Atomic\%** & **Weight\%** & **Atomic\%** \\ \hline C & & & 70.39 & 80.68 \\ \hline O & 39.41 & 56.57 & 14.83 & 12.76 \\ \hline Si & 14.70 & 12.02 & 4.90 & 2.40 \\ \hline Al & 8.24 & 7.01 & 2.59 & 1.32 \\ \hline Cl & 37.65 & 24.39 & 7.28 & 2.83 \\ \hline Total & 100 & & 100 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The EDX analysis result. (A) Elastic polymer composite materials doped with 0 M graphite specimen. (B) Elastic polymer composite materials doped with 40 M graphite specimen.  
Figure 10: EDX images of elastic polymer composite materials: (**a**) Composite with 0 M graphite doping. Elastic polymer composite materials without carbon powder doping. (**b**) Composite with 40 M graphite doping.  
At a temperature of 300 K, for the elastic polymer composite materials doped with activated carbon, C0 = 35 M, Cc = 45 M, Cs = 60 M, \(\rho_{0}\) = 4.456 \(\times\) 108 \(\Omega\)-cm, \(\rho_{\rm c}\) = 4 \(\times\) 106 \(\Omega\)-cm, and \(\rho_{\rm s}\) = 1.12 \(\times\) 104 \(\Omega\)-cm.