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Closed-loop phase diagrams are known in systems with specific intermolecular interactions^,,,. In weakly interacting systems, however, such behaviour has never been observed. Here, diblock copolymers formed from polystyrene covalently linked to poly (n-pentylmethacrylate), P(S-b-nPMA), which have only weak segmental interactions, are shown to exhibit a closed-loop phase behaviour over a narrow range of molecular weight. The endothermic transitions from the disordered to ordered and back to the disordered state, as a function of increasing temperature, are dominantly entropic in origin. The morphology and rheological properties of P(S-b-nPMA) undergo characteristic changes at the transitions. Whereas the disorder-to-order transition temperature increases with decreasing molecular weight, the order-to-disorder transition temperature decreases. At a limiting molecular weight, the closed-loop vanishes …