# A Study on the Conductivity and Infrared Spectroscopy of Elastic Polymer Composite Materials
## 4 Discussion  
### Temperature Coefficient of Resistance for Graphite's Physiorption  
Since physisorption occurs without a chemical reaction, it does not need activation energy and can therefore occur easily and at low temperature. The adsorption is an exothermic reaction, so the resistance produced by the elastic polymer composite materials' physisorption is directly proportional to the temperature. The main force of physisorption is based on the weak van der Waals and easily affected by temperature, so temperature has a great impact on resistance. Conservation of energy dictates that electron transfer between an electrode and a redox system in solution or adsorbed on the electrode surface is fastest when the energy of the electron is equal in the metal and in the thermally activated redox system [43; 44]. The elastic polymer composite materials were doped with a 46.3 M concentration of graphite, for which the influence of temperature on resistance is shown in Figure 13. The characteristic equations of resistivity (\(\rho\)) and temperature are as follows:  
\[\rho=\left\{\begin{array}{c}\rho_{0},\ \rm{if}\ T_{\rm e}<T_{0}\\ \rho_{0}+(\rho_{\rm f}-\rho_{0})\cdot e^{-Q_{\rm f}\cdot Q_{\rm m}\cdot(\frac{ T_{\rm e}-T_{\rm o}}{T_{\rm o}})},\ \rm{if}\ T_{\rm e}<T_{\rm f}\\ \rho=\left(\rho_{\rm c}-\rho_{\rm ppl}\right)\cdot\frac{T_{\rm e}-T_{\rm e}}{T_ {\rm e}-T_{\rm f}},\ \rm{if}\ T_{\rm e}<T_{\rm e}<T_{\rm c}\\ \left(\rho_{\rm nl}-\rho_{\rm c}\right)\cdot\frac{T_{\rm nl}-T_{\rm c}}{T_{\rm nl }-T_{\rm c}},\ \rm{if}\ T_{\rm c}<T_{\rm e}<T_{\rm nl}\\ \rho_{\rm c}\cdot e^{-Q_{\rm f}\cdot T_{\rm nl}}\cdot\frac{T_{\rm e}-T_{\rm c}}{ T_{\rm nl}-T_{\rm c}},\ \rm{if}\ T_{\rm e}>T_{\rm c}\end{array}\right. \tag{5}\]  
In Formula (5), \(T_{0}\) is the temperature at which absorption starts; \(\rho_{0}\) is the resistivity at temperature T\({}_{0}\); \(T_{\rm pl}\) is the initial temperature of the positive temperature coefficient on the linear region; \(\rho_{\rm ppl}\) is the resistivity when the temperature is at T\({}_{\rm pl}\); \(T_{\rm c}\) is the critical temperature of the positive and negative temperature coefficients of the elastic polymer composite materials; \(\rho_{\rm c}\) is the resistivity when the temperature is at T\({}_{\rm c}\); \(T_{\rm nl}\) is the cut-off temperature of the negative temperature coefficient on the linear region; \(\rho_{\rm nl}\) is the resistivity when the temperature is at T\({}_{\rm nl}\); \(T_{\rm m}\) is the melting temperature of the elastic polymer composite materials; \(\rho_{\rm m}\) is the resistivity when the temperature is at T\({}_{\rm m}\); \(T_{\rm e}\) is the temperature of the testing environment; and \(Q_{\rm Td}\) is the thermodynamics characteristic of the material that is dimensionless, and graphite's \(Q_{\rm Td}\) is 2. The \(D_{\rm m}\) is the thermal desorption characteristic of the material that is also dimensionless, and graphite's \(D_{\rm m}\) is 3.  
For the elastic polymer composite materials doped with 46.3 M concentration of graphite, T\({}_{0}\) = 267 K, T\({}_{\rm pl}\) = 312 K, T\({}_{\rm c}\) = 319 K, T\({}_{\rm nl}\) = 322.5 K, T\({}_{\rm m}\) = 343 K, \(\rho_{0}\) = 1.296 \(\times\) 10\({}^{3}\)\(\Omega\)-cm, \(\rho_{\rm pl}\) = 4.88 \(\times\) 10\({}^{4}\)\(\Omega\)-cm, \(\rho_{\rm c}\) = 5.712 \(\times\) 10\({}^{4}\)\(\Omega\)-cm, \(\rho_{\rm nl}\) = 4.936 \(\times\) 10\({}^{4}\)\(\Omega\)-cm, and \(\rho_{\rm m}\) = 7.04 \(\times\) 10\({}^{3}\)\(\Omega\)-cm.