Modern polymerization techniques enable syntheses of functional block copolymers with unusual thermal, electronic, and ionic conductivities. However, these new macromolecular syntheses often introduce significant molecular weight polydispersity (a chain length heterogeneity) into one or more of the copolymer blocks. Conventional wisdom stipulates that chain length uniformity (“monodispersity”) is a prerequisite for periodic nanoscale self-assembly of block copolymers. Few studies have questioned the validity and stringency of this preconceived notion. We are studying the melt-phase behavior of ABA-type triblock copolymers comprising either polydisperse A or B blocks. Contrary to conventional wisdom, polydisperse ABA BCPs also assemble into a rich array of periodic nanoscale structures with unexpectedly enhanced thermodynamic stabilities as compared to their monodisperse analogs. Based on these insights, we are now studying: (1) a series of new Li-ion conducting block copolymers for advanced batteries, and (2) new thermoplastic elastomers with unusual mechanical properties.