Exploring the Ion Solvation Environments in Solid-State Polymer Electrolytes through Free-Energy Sampling

Abstract

The success of polyethylene oxide (PEO) in solid-state polymer electrolytes for lithium-ion batteries is well established. Recently, in order to understand this success and to explore possible alternatives, we studied polyacetal electrolytes to deepen the understanding of the effect of the local chemical structure on ion transport. Advanced molecular dynamics techniques using newly developed, tailored interaction potentials have helped elucidate the various coordination environments of ions in these systems. In particular, the competition between cation−anion pairing and coordination by the polymer has been explored using freeenergy sampling (metadynamics). At equivalent reduced temperatures, with respect to the polymer-specific glass-transition temperature, two-dimensional free-energy plots reveal the existence of multiple coordination environments for the lithium (Li) ions in these systems and their relative stabilities. Furthermore, we observe that the Li-ion movement in PEO follows a serial, stepwise pathway when moving from one coordination state to another, whereas this happens in a more continuous and concerted fashion in a polyacetal such as poly(1,3-dioxalane) [P(EO-MO)]. The implication is that interconversion between coordination states of the Li ions may be easier in P(EO-MO). However, the overarching observation from our free-energy analysis is that Li-ion coordination is dominated by the polymer (in either case) and contact-ion pairs are rare. We rationalize the observed higher increase in glasstransition temperature (T g ) with salt loading in polyacetals as due to intermolecular Li-ion coordination involving multiple polymer chains, rather than just one chain for PEO-based electrolytes. This interchain coupling in the polyacetals, resulting in the higher T g , works against any gains due to variations in Li-ion coordination that might enhance transport processes over PEO. Further research is required to overcome the interdependence between local coordination and macroscopic properties to compete with PEO electrolytes at the same absolute working temperature. 36 through the free volume of the polymers assisted by the 37 segmental motion, with reasonable conductivity possible above 38 the glass-transition temperature. 6 Therefore, effective dissolu-39 tion of the cations and a low glass-transition temperature are 40 key to good ionic properties in these systems. 13 Unfortunately, 41 slow ionic conductivities and low transference numbers in

Understanding the Impact of Multi-Chain Ion Coordination in Poly(ether-Acetal) Electrolytes

“…A closer look at the coordination environments shows that in PEO, the inter-chain coordinated state primarily comprises 3 oxygen atoms coming from each chain, while in P­(EO-MO), we see a much wider basin that encompasses 3 or 4 oxygen atoms coming from each chain. Furthermore, we observe that a single chain of P­(EO-MO) cannot easily provide 7 oxygen atoms from a single chain, and therefore, the higher total fully polymer coordination we had observed in our previous work comes from multiple chains due to the ability of one of the coordinating P­(EO-MO) chains to provide 4 oxygen atoms. An analysis of the strain on these chains to provide the oxygen atoms for coordination indicates that if a PEO chain strains itself to provide 4 oxygen atoms, it can provide all the necessary 6 oxygen atoms without much effort, unlike P­(EO-MO), where beyond 4 oxygen atoms, the strain energy to provide more oxygen atoms keeps increasing.…”

“… Top-left panel: 2D free-energy analysis of solvation of a Li cation and TFSI anion in PEO at a concentration of r = 0.08 from our previous work with coordination with respect to oxygen atoms of ether/acetal and oxygen atoms of TFSI anions used as collective variables. Top-right panel: 2D free-energy analysis of inter- vs. intra-chain solvation of a Li cation in the same system with coordination with respect to oxygen atoms of ether/acetal from a specific chain and coordination with respect to other ether/acetal oxygen atoms used as collective variables.…”

“…Similar to our previous analysis, we calculate the probability ( p i ) of a Li ion being in a given coordination state by using an approximate partition function p normali = e − β normalΔ G i ∑ j e − β normalΔ G j where β = 1 k normalB T and Δ G i is the relative free energy of a specific coordination environment (see Tables and ).…”

“…The collective variable used to describe the various solvation environments in these systems was the coordination number (CN) of the lithium ion with various types of oxygen atoms. , For a better understanding of intra- versus inter-chain coordination, the collective variables used are the CN of the lithium ion with oxygen atoms from a specific chain of the polymer with respect to oxygen atoms from other chains. For the concentration study, the collective variables used, as before, were the CN of the Li ion with oxygen atoms from the polymer and CN of the Li ion with oxygen atoms from TFSI anion. The various parameters used for the metadynamics simulations such as height (H, kcal/mol) and width (W, unitless) of the Gaussian hills, frequency of hill addition (F, freq, steps), and the cutoff used for measuring the CN of the Li ion with the polymer (inter and intra) and TFSI oxygen atoms ( r 0 normalL normali − normalP normalo normall normaly and r 0 normalL normali − normalT normalF normalS normalI , Å) for the production runs are all listed in Table S5, and the effective simulation time of each calculation ( t , ns) is listed in Table S6.…”

“…Molecular dynamics (MD) has been a vital tool in exploring and understanding the solvation structure and its effect on transport properties in solid polymer electrolyte (SPE) systems. − In our previous work, we had used both a regular classical molecular dynamics protocol and advanced molecular dynamics calculations (free-energy sampling using metadynamics) to compare PEO with the most efficacious of the designed polyacetals , with dissolved LiTFSI salt to gain insights into the various coordination environments that exist, their relative stabilites, and how they might affect macroscopic transport properties. We showed that PEO has a stepwise pathway, with bond breaking and forming happening one after the other to move from one Li-ion coordination environment to another, while P­(EO-MO) has a much more direct pathway, with the bond breaking and forming happening in a more concerted fashion.…”