Structural Relaxation and Cation (Li+, H+, Na+) Diffusion in Crystalline Polymer Electrolytes: Ab Initio Molecular Dynamics Simulations

The ionic conductivity in crystalline polymer electrolytes is found to be greater than that in the equivalent amorphous materials when above T_g. Polyethylene oxide-alkali salt systems, such as PEO₆:XPF₆(X = H⁺, Li⁺, Na⁺), are of particular interest due to their unique structure.¹ The structure of PEO₆:XPF₆ is comprised of two polymer chains in which the alkali ions (i.e., Li⁺ or Na⁺) or protons reside in and being separated from the anions outside of the polymer chains (Fig. 1(a)). Instead, these cations are simultaneously coordinated by six ether oxygen ions of the PEO chains. Unlike the amorphous polymers, the cation diffusion in crystalline PEO₆:XPF₆ is highly directional, along z-axis of the PEO chains. Such process is facilitated with the interaction between cations and ether oxygen ions. Thus, it is essential to keep the PEO chains in the closed state during ion transport. Different structural modification approaches have been recently proposed to help improving ion conductivity. These approaches include: doping with larger anions, changing the end groups of polymer chains, and using poly-dispersed PEO.^2,3

In this work, ab initio molecular dynamics (AIMD) simulations have been undertaken to study the structural stability and cation transport in PEO₆:XPF₆(X = H⁺, Li⁺, Na⁺) systems with doped cation ions, including interstitials and vacancies. The simulations were performed using the VASP code.⁴ During the molecular dynamics simulation, the supercell is heated up to 300 K via repeated velocity rescaling for 1 ps; and then being maintained at 300 K for 2.5 ps in a NVT (canonical) ensemble. In the density functional (DFT) calculation, a generalized gradient approximation is applied within the projector-augmented-wave method in the VASP code. Ion diffusion barriers for cations were calculated using the nudged elastic band (NEB) method. The atomic positions and cell parameters of PEO₆:LiPF₆ were relaxed from the experimental structures, the other two systems are fitted based on the assumption that these three systems are isostructural and adopt the same space group. 

In the systems without doped cations (Fig. 1(b)), only the PEO chains in PEO₆:LiPF₆ maintain the chain shape, and lithium ions are constrained by the PEO chains. Interestingly, the calculated Li-O bond distance shows the Li-O bonding environment differs remarkably from previous studies. For PEO₆:HPF₆ system, although the protons still reside in the chains, the PEO chains are stretched in the x-y plane. This indicates that the protons have serious impact on the chain structure, resulting in distortions. In PEO₆:NaPF₆ system, the polymer chains are severely damaged with sodium ions outside of the PEO chains.  For systems doped with cation interstitials and vacancies, all three systems show more severe damages in PEO chains. This suggests the introduction of cation point defect cannot guarantee improvement of cation diffusion inside the PEO chains. Other measures, such as end group modification, have to be taken into consideration for enhancing mechanical strength of the PEO chains. Cation diffusion barriers are also calculated using NEB method at 0 K. A vacancy diffusion mechanism is considered in this study (Fig. 1(c)). The proton in PEO₆:HPF₆ has a small barrier (0.80 eV) when comparing with other two systems (Li⁺ in PEO₆:LiPF₆: 4.16 eV, Na⁺ in PEO₆:NaPF₆: 3.86 eV) (Fig. 1(d)). 

In summary, our AIMD simulations indicate that the introduction of cation point defects alone cannot guarantee improvement of cation transport inside the PEO chains. The diffusion barrier calculations clearly indicates the substantially high mobility of protons in comparison to the other cations in these crystalline polymers. 

Acknowledgement

The authors gratefully acknowledge the support by the U.S. Army Research Office under Contract No. W911NF-07-1-0085. 

References

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