Ionic Conductivity and Ion Transfer Mechanism in Solid Polymer Electrolytes

Typically in SPEs, the Li+-ions are dissolved in a polymer matrix and Li+-ion transport occurs only in the amorphous phase of the polymer above their glass transition temperature where polymer chain motion creates a dynamic, disordered environment that plays a critical role in facilitating ion transport [40-44]. However, in SPEs with high lithium-ion conductivity, the polymer not only dissolves the lithium salt, but it is also able to couple with lithium-ions. Hence, the local relaxation and segmental motion of amorphous regions within the polymer chain at or above the glass transition temperature (T„) plays a significant role in the ionic conductivity of SPEs [40,45]. In addition, the number of free Li+-cations also significantly affects the Li+- transportability within the SPE. Hence, ionic conductivity of SPEs is greatly influenced by the effective number of mobile ions (free ions), the elementary electric charge, and the ion mobility. The effective number of mobile ions greatly depends on the degree of salt dissociation in the polymer host, which is significantly affected by the chemical nature of the host polymer matrix. As previously mentioned, the polar groups in the polymer, such as -O-, =0, C=0), -F, —S—, C=N, —NH—, etc., are effective building blocks for dissolving and dissociating lithium salts. In polyethylene oxide, for example, the lone pair of oxygens (ether linkages) on the PEO segment is coordinated with the lithium-ion by Coulombic interaction, helping to improve the segmental motion and the dissociation of lithium salts into the respective anion and cation. In the process, PEO acts as a solvent, and the lithium salt dissolves into the PEO matrix. Similarly, other atoms such as =0, —C=0, -F, —S—, —NH—, —C=N also play a similar role. Hence, Li+-ions are located at suitable coordination sites (e.g., -O- in polyethylene oxide, -F in PVdF or PVdF-co-HFP, —C=N in PAN, and -NR in polyamide) in the polar chains of the polymer. The polymer chains undergo constant local segmental motion, which results in the appearance of free volumes [46,47]. The challenges and perspectives of lithium-ion transport in a solid- state electrolyte [48] are depicted in Figure 1.3. In SPEs, under the electric field, the migration movement of Li+-cations is from one coordination point to another along the polymer segment, or they jump from one segment to another through these free volumes. Hence, the mechanism of ion motion may involve the formation of time-dependent pathways in the polymer matrix, the short-range transport of ions temporarily attached to the polymer chain, and ion hopping between an ionic cluster or coordination center. The Li+-ion transport mechanism of solid polymer electrolytes based on PEO [46,47] is showm in Figure 1.4. In 2001, this concept of ionic conduction in SPEs was overturned by Bruce et al. [49]. In their study, they showed that the ionic conductivity (Li+-ion conductivity) in the static, ordered environment of the crystalline phase can be greater than that in the equivalent amorphous material above T„. The study also demonstrated that ion transport in crystalline polymer electrolytes can be dominated by cations, whereas both ions are generally mobile in the amorphous phase [50].

Based on experimental studies of ionic conductivity in PEO-based crystalline complexes formed with six ether oxygens per cation, Stoeva et al. [51] proposed that in the crystalline phase of P(EO)6:LiX (X = PF6, AsF6, SbF6, all these compounds are iso-structural), pairs of PEO chains fold to form cylindrical tunnels, within w'hich the Li+ cations are located and coordinated w'ith ether oxygens, while the anions are located outside these tunnels in the inter-chain space and do not coordinate w'ith cations. The structure of a PE06:LiAsF6 crystalline complex suggests that Li+-ion transport along the tunnels may be possible in the crystalline 6:1 complex. These Li+-ions

Challenges and perspectives of lithium-ion transport in a solid-state electrolyte

FIGURE 1.3 Challenges and perspectives of lithium-ion transport in a solid-state electrolyte.

Schematic illustration of the lithium-ion transport mechanism in polyethylene oxide (PEO)-based solid polymer electrolytes

FIGURE 1.4 Schematic illustration of the lithium-ion transport mechanism in polyethylene oxide (PEO)-based solid polymer electrolytes.

can migrate from one site to another along these cylindrical tunnels without the aid of segmental motion [51]. To compare ionic conductivity in the static, ordered environment of a crystalline polymer electrolyte with the dynamic and disordered environment of an amorphous polymer electrolyte above 7j„ Stoeva et al. [51] prepared crystalline and amorphous forms of PE06:LiSbF6. The variation in ionic conductivity as a function of temperature for the crystalline and amorphous PE06:LiSbF6 materials is shown in Figure 1.5. A temperature-dependent ionic conductivity study shows that the ionic conductivity in crystalline PE06:LiSbF6 is higher than for the same composition in the amorphous state, even above 7]. [51]. The crystalline phase reaches conductivity more than one order of magnitude higher than the amorphous phase at the lowest temperatures. Nuclear magnetic resonance (NMR) studies on these electrolytes demonstrated that PF6 ions do not move with respect to polymer chains, indicating that the ionic conductivity is dominated by Li+-ions; that is, the cation transport number Tu+ = 1.

Generally, ion transport in solids involves ions hopping between adjacent sites. In the conventional view of ionic conductivity in polymer electrolytes, ions move in a dynamic environment created by the polymer chain motion in the amorphous phase above Tr A crankshaft-like motion associated with short segments of the polymer chains randomly creates suitable coordination sites adjacent to the ions, so that these ions may hop from one site to another. Such segmental modes, involving the motion of groups of atoms on the polymer chains, are usually relatively slow, limiting the hopping rate and therefore the maximum conductivity.

By considering the ionic conductivity in crystalline ceramic materials such as Na6Al203, RbAg4l5, the lithium superionic conductor (LISICONs) (Li|4Zn(Ge04)4) [52,53], or Li05La05TiO3 [54], it can also be claimed that ion transport is favored in crystalline polymer electrolytes. Some of these crystalline ceramic materials display the highest known ionic conductivities in the solid state, exceeding by 1-3 orders of magnitude the maximum conductivity of conventional amorphous polymer electrolytes. For instance, RbAg4I5 has a conductivity of over 10 1 S cm1, and Li0 5La0 5Ti03

Ionic conductivity

FIGURE 1.5 Ionic conductivity (S cm-') of amorphous (open circles) and crystalline (filled circles) PEOfj:LiSbF6 as a function of temperature. Adapted and reproduced with permission from Reference [51]. Copyright 2003 American Chemical Society.

achieves 10~3 S crrr1 [53,54] at room temperature. High ionic conductivity can also be obtained in plastic crystals where ion transport is aided by rotational disorder [55]. In their later studies [56-58], Bruce et al. [49] proposed that modifying these stoichiometric crystalline complexes by replacing a few mol.% of XF6 ions with monovalent ions having very different shapes and sizes such as N(S02CF3)2 or anions with different charges such as SiF62- can increase the ionic conductivity by 1.5-2 orders of magnitude. However, the opposite results were reported by Henderson et al. after examining the ionic conductivity of the same crystalline SPEs, P(EO)6-LiX (X = PF6, AsF6, SbF6) [59,60]. Sun et al. [61] have also reported comparable ionic conductivities in amorphous and crystalline di-block copolymers. Even though a large number of studies have reported on the ion transfer mechanism in solid polymer electrolytes, more systematic microscopic studies on ionic conductivity as a function of temperature (temperature-dependent ionic conductivity) would provide more clear information on the ion transfer mechanism. Hence, a comprehensive description of lithium-ion transportation in SPEs is challenging because the systems are complicated and no simple structural-property correlation has yet been derived.

A good understanding of conducting mechanisms is necessary for the design of solid polymer electrolytes with practical application in lithium-ion batteries. Solid polymer electrolytes are a complex system that contains materials with multiple conducting species that make a more complex conduction mechanism. As per the equation, о = F £АД£( (where F, Rr and E, are the Faraday constant, the number of charge carriers, the ionic charge of the charge carriers, and the ionic mobility, respectively), the conductivity (o) of such a complex system is primarily governed by two parameters: (i) the number of charge carriers and (ii) the mobility of the charge carriers.

The temperature-dependent ionic conductivity of the SPE system often follows two dominant conduction mechanisms: (i) the Arrhenius type or the Vogel- Tammann-Fulcher (VTF) type [29,62,63]. The VTF equation was devised early in the 20th century for describing the diffusion process in glassy and disordered materials [60] from quasi-thermodynamic models with free volume and configurational entropy, and its behavior can be related to ion motion coupled with the long-range motions of the polymer segments. In general, for a polymer electrolyte, the log a vs. 1 IT curves are typically nonlinear or slightly curved, so the activation energy for the ionic conduction £a can be obtained using the Vogel-Tammann-Fulcher model [cr = а0Гп- exp{EJR(T - 7'0)|] instead of the simple Arrhenius model (o = cr0 exp(EJRT)) used for the treatment of linear Arrhenius plots. This indicates that the conduction mechanism not only involves the increasing dissociation of lithium salt and the lowering of ionic coupling but also an ionic hopping motion coupled with relaxation/ breathing and/or the segmental motion of polymeric chains [64-67]. Flere, o0 is the pre-exponential factor, which is related to the number of charge carriers Л7; £a is the activation energy for the ionic conductivity which can be calculated from the nonlinear least-squares fitting of the data from plots of log о vs. 1/7; and T0 is the equilibrium glass transition temperature (T0 s T„ - 50 K). The materials that obey the linear Arrhenius equation indicate that ion transport occurs in such materials via a simple hopping mechanism decoupled from relaxation, breathing, and the segmental motion of polymeric chains [62]. Based on ionic conductivity studies of PEO and polyphenylene oxide (PPO) salt complexes, the ionic conductivity can be related to frequency and temperature using the William-Landel-Ferry (WLF) equation, considering the relaxation process of polymer molecular chain motion in an amorphous system. The expression is

Here, cjiT., is the conductivity of the relevant ions at glass transition temperature Tg, and Cl and C2 are the WLF parameters in the free volume equation of ion migration, respectively.

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