# Development on Solid Polymer Electrolytes for Electrochemical Devices
## 2 Ion Transport Properties and Conduction Mechanism in SPEs  
Ionic conductivity is one vital characteristic in determining whether the SPE is practical and efficient for device applications. The ionic conductivity of an electrolyte is calculated by using the bulk resistance from the Nyquist impedance plot. The electrolyte is subjected to a small potential typically 10 mV to ensure a linear current-voltage relationship for impedance measurement. According to the Nernst-Einstein relationship, the ionic conductivity, \(\sigma\), is directly proportional to the diffusion coefficient of ions, \(D\), as shown in the following equation:  
\[\sigma=\frac{q^{2}n}{k_{b}T}D \tag{1}\]  
where \(q\) is elementary charge, \(n\) is the number of ions, \(k_{b}\) is Boltzmann constant and \(T\) is temperature. Since the electrolyte consists of salts that can ionize into cations and anions, Equation (1) can be written as follows:  
\[\sigma=\sigma_{+}+\sigma_{-}=\frac{q^{2}}{k_{b}T}\left(n_{+}D_{+}+n_{-}D_{-}\right) \tag{2}\]  
where \(\sigma_{+}\) and \(\sigma_{-}\) are the ionic conductivity of cations and anions respectively, \(n_{+}\) is the number of cations, \(n_{-}\) is the number of anions, \(D_{+}\) is the cationic diffusion coefficient and \(D_{-}\) is the anionic diffusion coefficient. The movement of ions are varied in the electrolyte systems depending on the solvation environment (liquid, solid and gel). As aforementioned, a polymer electrolyte generally consists of inorganic salts solvated in a polymer matrix that contains functional groups, such as -OH, -C=O, -NH\({}_{2}\) and -COC-. The functional groups help to solvate salts into ions via electrostatic interaction. It has been acknowledged for the past three decades that the motion of ions in polymer matrix is coupled with the segmental movement of the polymer chains, and this is described as the Brownian motion by many researchers [14]. Therefore, it is believed that the ion movements can only occur in amorphous polymers where the polymer chains are freely moveable to transport the ions. It is well-known that the motion and flexibility of polymer chains are higher in polymer matrix that possess low glass transition temperature, \(T_{\rm g}\). Hence, the selection of polymer is crucial in the development of polymer electrolyte. The relation between conductivity and \(T_{\rm g}\) can be explained by the Vogel-Tammann-Fulcher (VTF) equation:  
\[\sigma=\sigma_{o}T^{1/2}exp\left(\frac{-B}{T-\left(T_{g}-50{\rm K}\right)}\right) \tag{3}\]  
where \(\sigma_{o}\) is the prefactor and \(B\) is related to the activation energy. \(T_{\rm g}\) can also be determined from differential scanning calorimetry (DSC). Based on Equations (2) and (3), the conductivity of a polymer electrolyte can be amplified by increasing the number density of mobile ions and lowering the \(T_{\rm g}\). Another approach is by decoupling ion diffusion with the polymer chains. A simplest way to fulfil the above criteria is by adding high dielectric constant plasticizers into the polymer electrolyte. A high dielectric constant can weaken the attraction forces between the ions in the salt and thus enhances the salt dissociation and the increase in number density of mobile ions [3]. Plasticizers also facilitate the pathway of ions transportation by increasing the amorphousness of the polymer electrolyte film and providing the additional coordination sites for ions to conduct. [PERSON] and [PERSON] [4] have investigated the role of propylene carbonate (PC) as plasticizer in PEO-based electrolytes having lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) via Monte Carlo and molecular dynamics simulations. They found that the conductivity showed significant improvement with the addition of PC due to the increase in mobility of TFSI' ions [4]. The lithium ions' diffusion remained unchanged and showed stronger interaction with the ethylene oxide oxygen as compared to the carbonate oxygen.