The transport behavior of inverse bicontinuous cubic phases is experimentally investigated as the combined outcome of solute molecular structure and geometrical details of the confining symmetry. Molecular diffusion is discussed in relation to curvature, bottlenecks and interfacial properties of each cubic phase. Point-like molecules show faster diffusion across the double diamond (Pn3m) symmetry, while unfolded macromolecules display better performance inside the double primitive (Im3m) cubic phase. The former observation is in agreement with previous simulation work, whereas the latter indicates that dedicated theory needs to be developed for diffusing polymers. Further, the effect of electrostatic interactions is assessed by a study of diffusion of nanoparticles, and is rationalized via a combination of simulations and theoretical considerations as the result of a competition between water mobility and geometrical features of the channel.

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