where the fundamental charge carrier are no longer single free ions but ionic clusters of different charge numbers z ij = iz + +jz -. α ij is the matrix element that defines the population of the cluster consisted of i cations and j anions, which is averaged over ensembles and long simulation time. D ij is the diffusion coefficient for each type of cluster, written in matrix form. Cation(s) and anion(s) are defined to belong to the same cluster if the cation is within the cutoff distance of one or more of the anions. It is worth noting that neutral cluster with z ij = 0 does not contribute to the total conductivity although it also diffuses. This is the first time that the cluster Nernst-Einstein (cNE) is applied to polymer-in-salt system other than PEO or PEO-based variants. Molecular dynamics ion hopping analysis. The ion hopping analysis is characterized by tracking the coordination environment change of one single ion. Time-dependent trajectory of cation coordination is traced based on a distance criterion (i.e., an atom contributes to the coordination of a cation when its distance to the cation is less than the coordination cutoff). Specifically, the coordination from the most electronegative nitrogen atoms of the polymer chains and the oxygen atoms of the anions is tracked over the simulation time. The consecutive indices corresponds to consecutive coordination from the same chain or anion, while the switch between two different consecutive line indicates a cation jump among chains.