Cluster-continuum quantum mechanical models to guide the choice of anions for Li⁺-conducting ionomers

A quantum-mechanical investigation on Li poly(ethylene oxide)-based ionomers was performed in the cluster-continuum solvation model (CCM) that includes specific solvation in the first shell surrounding the cation, all surrounded by a polarizable continuum. A four-state model, including a free Li cation, Li⁺-anion pair, triple ion, and quadrupole was used to represent the states of Li⁺ within the ionomer in the CCM. The relative energy of each state was calculated for Li⁺ with various anions, with dimethyl ether representing the ether oxygen solvation. The population distribution of Li⁺ ions among states was estimated by applying Boltzmann statistics to the CCM energies. Entropy difference estimates are needed for populations to better match the true ionomer system. The total entropy change is considered to consist of four contributions: translational, rotational, electrostatic, and solvent immobilization entropies. The population of ion states is reported as a function of Bjerrum length divided by ion-pair separation with/without entropy considered to investigate the transition between states. Predicted concentrations of Li⁺-conducting states (free Li⁺ and positive triple ions) are compared among a series of anions to indicate favorable features for design of an optimal Li⁺- conducting ionomer; the perfluorotetraphenylborate anion maximizes the conducting positive triple ion population among the series of anions considered.