Free volume and conductivity in polymer electrolytes

Positron annihilation lifetime spectroscopy (PALS) and impedance spectroscopy (IS) have been employed to study the effect of temperature and pressure on the DC conductivity (σDC) and the mean hole volume (Vh) of a NaPF6 ethylene oxide based polyurethane electrolyte. The DC conductivity of the polymer electrolyte displayed a characteristic non-Arrhenius temperature dependence yielding acceptable values for both the "pseudo-activation energy" (B) and the "zero mobility temperature" (T0) from a VTF fit. Vh(T) showed a linear increase of 0.53 cm3 (mol K)−1. When extrapolating Vh(T) to 0 K a temperature very close to T0 from the VTF fit was obtained, which suggests a free volume mediated conductivity mechanism. This suggestion is further supported by the linear dependence of ln(σDC(T)) on Vh−1(T). Conductivity was measured as a function of pressure (σDC(P)) with ln(σDC(P)) showing a characteristic decrease with increasing pressure. The activation volumes (VA) calculated from these measurements ranged from 45 to 20 cm3 mol−1 over a temperature from 304 to 365 K. Critical volumes calculated from two current free-volume models were found to be unrealistic. Combining the extra volume required for ionic motion (VA) with the available free volume (Vh) at the same temperature poses a realistic and 'model-free' figure of 117 cm3 mol−1 for the critical volume at 304 K. This equates roughly to the volume of 3–4 EO units. The pressure dependence of free volume (Vh(P)) for a polymer electrolyte has been measured for the first time, and yielded a linear decrease in Vh with increasing pressure. A linear dependence of σDC(P) on Vh−1(P) was also found. A comparison of the isothermal and isobaric dependence of σDC on Vh−1 illustrates the contribution of factors other than free volume have on charge carrier number and mobility. This comparison shows that the variation of Vh with temperature and the variation of Vh with pressure affect the conductivity in very different ways. These results clearly show that free volume cannot be considered the sole factor responsible for conductivity in polymer electrolytes.