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Understanding the transport properties of water in self-assembled block copolymer morphologies is important for furthering the use of such materials as water-purifying membranes. In this study, we used coarse-grained dissipative particle dynamics simulations to clarify the influence of pore morphology on the self-diffusion of water in linear-triblock-copolymer membranes. We considered representative lamellar, cylindrical, and gyroid morphologies and present results for both the global and local diffusivities of water in the pores. Our results suggest that the diffusivity of water in the confined, polymer-coated pores differs from that in the unconfined bulk. Explicitly, in confinement, the mobility of water is reduced by the hydrodynamic friction arising from the hydrophilic blocks coating the pore walls. We demonstrate that in lamella and cylindrical morphologies, the latter effects can be rendered as a universal function of the pore size relative to the brush height of the hydrophilic blocks. [ABSTRACT FROM AUTHOR]