Understanding the Impact of Grafted Chain Length in Polymer Electrolytes with Nonlinear Architectures.

The development of safe and high-performance solid polymer electrolytes (SPEs) is central to advancing solid-state lithium batteries. Recently, there has been an emergence of promising SPEs that combine poly-(ethylene oxide) (PEO) with other components in nonlinear architectures including block, bottlebrush, and star structures, yet rational design of nonlinear architectures remains elusive. Here we employ coordination star polymers (CSPs) with precisely defined arm numbers and tunable PEO arm lengths to study the structural factors governing ion transport. Systematic experiments combined with coarse-grained molecular dynamics simulations reveal a universal conductivity maximum at medium arm lengths, arising from a balance between the conformational confinement of short arms and the crystallization tendency of long arms. This behavior aligns well with the Daoud-Cotton model, which describes concentrated and semi-diluted regimes along the polymer arms. The resulting framework establishes transferable design rules that link arm length, arm number, and chain dynamics to ionic conductivity. Beyond CSPs, these principles provide a predictive foundation for engineering star, comb, and bottlebrush electrolytes with optimized performance.