Geometry-Controlled Diffusion in Bicontinuous Cubic Lipid Networks

Bicontinuous cubic lipid phases exhibit complex internal aqueous networks that strongly influence molecular transport, yet a predictive framework linking internal geometry to effective diffusion remains lacking. In this study, we isolate and quantify the role of geometry alone in governing diffusive transport within bicontinuous cubic lipid networks by modeling diffusion in idealized triply periodic minimal surface geometries, namely the gyroid, diamond, and primitive phases. Monte Carlo random-walk simulations were performed with tracer particles confined to the aqueous domains and reflecting boundaries at the lipid interface, and effective diffusion coefficients were extracted from the long-time mean-squared displacement while tortuosity was independently quantified from geometric path-length statistics. The simulations reveal a clear hierarchy of transport efficiency across cubic phases, with the gyroid exhibiting the highest effective diffusion, followed by the diamond and primitive geometries. Despite identical volume fractions and microscopic diffusion parameters, substantial differences in macroscopic transport emerge solely from geometric connectivity and path elongation, and when normalized diffusion coefficients are plotted against tortuosity, data from all geometries collapse onto a common scaling relationship, identifying tortuosity as a unifying geometric descriptor of transport. These results establish geometry as the dominant control parameter governing diffusion in bicontinuous cubic lipid networks and provide a geometry-only predictive framework that offers a minimal baseline for interpreting experimental transport measurements in cubic lipid phases and supports the rational design of cubosome-based systems with tunable transport properties.