Einstein Explains Water Transport in C-S-H

Water transport is critical for the durability and confinement performance of cement-based materials. C-S-H, the primary phase in hydrated cement-based materials, is nanoporous, contributing therefore to water transport. To understand water transport in C-S-H, it is necessary to deploy well-suited techniques and theoretical framework to deal with the nanoscale. Einstein linked the dynamics of a diffusing particulate system described by the mean-squared displacement (MSD) to the (self)-diffusion. The self-diffusion is, in turn, related to viscosity via the Stoke-Einstein relation. Using (equilibrium) molecular simulations, the self-diffusion of water in C-S-H is computed via the Einstein MSD equation. Using non-equilibrium molecular simulations of pressure-gradient-driven flows in C-S-H, it is shown that the Stokes-Einstein equation captures viscosity changes with the pore size expected in nanoporous materials. These results suggest that a fundamental link between diffusion and permeability can be established for C-S-H. Further, mean-field homogenization is deployed to get the effective diffusion and permeability of C-S-H at the gel scale. The results obtained are in good agreement with the available experimental data. In particular, it is finally possible to explain why the water permeability of the C-S-H gel (7 × 10⁻²³ m²), as early calculated by Powers based on experiments, is so low. The strategy deployed here can be extended in future work to understand ion transport and unsaturated transport in C-S-H.