Polyelectrolyte membrane fuel cells (PEMFCs) are a promising class of alternative energy devices with potential applications in transportation, portable electronics and stationary power devices that possess high efficiencies and are also environmentally friendly. Nafion® is the benchmark polyelectrolyte membrane (PEM) for PEMFC applications because of its high proton conductivity at high relative humidity (RH) as well as excellent oxidative stability. However, its relatively high cost and poor performance at low RH and high temperature (> 80 °C) has limited the full-scale commercialization of PEMFCs. Disulfonated poly(arylene ether sulfone) multiblock copolymers have emerged as very promising alternative PEMs for replacing Nafion® due to their improved thermal, chemical and mechanical stability as well as improved proton conductivity under low RH conditions. However, the long hydrophilic sequences (typically >10,000 g/mol) required to achieve high proton conductivity usually lead to excessive water swelling which degrade membrane dimensional stability. This dissertation reports a fundamentally new approach to address this grand challenge by introducing shape-persistent triptycene units into the hydrophobic sequences of multiblock copolymers. A series of novel triptycene-containing multiblock copolymers were developed and their potential for PEM applications was investigated. Different hydrophilic (BPS100, TRP100) and hydrophobic (TRP0, BPS0) oligomers were utilized in the synthesis of the multiblock copolymers in order to study the effect of the copolymer chemical composition on the fundamental membrane properties. The triptycene units, especially those in long hydrophobic sequences, induced strong supramolecular chain-threading and interlocking interactions that effectively suppress water swelling. Consequently, unlike in previously reported multiblock copolymer systems, the water swelling of the triptycene-containing copolymers did not increase proportionally with water uptake. This combination of high water uptake and low swelling ratio of these copolymers resulted in excellent proton conductivity and membrane dimensional stability under fully hydrated conditions. These new triptycene-containing materials have great potential for applications in polyelectrolyte membrane fuel cells.