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Multiblock poly(arylene ether sulfone) copolymers are attractive for polyelectrolyte membrane fuel cell applications due to their reportedly improved proton conductivity under partially hydrated conditions and better mechanical/thermal stability compared to Nafion. However, the long hydrophilic sequences required to achieve high conductivity usually lead to excessive water uptake and swelling, which degrade membrane dimensional stability. Herein, we report a fundamentally new approach to address this grand challenge by introducing shape-persistent triptycene units into the hydrophobic sequences of multiblock copolymers, which induce strong supramolecular chain-threading and interlocking interactions that effectively suppress water swelling. Consequently, unlike previously reported multiblock copolymer systems, the water swelling of the triptycene-containing multiblock copolymers did not increase proportionally with water uptake. This combination of high water uptake and low swelling behavior of these copolymers resulted in excellent proton conductivity and membrane dimensional stability under fully hydrated conditions. In particular, the triptycene-containing multiblock copolymer film with the longest hydrophilic block length (i.e., BPSH100-TRP0-15k-15k) had a water uptake of 105%, an excellent proton conductivity of 0.150 S/cm, and a volume swelling ratio of just 29% (more than 42% reduction compared to Nafion 212).