Simulation of average stress values in por-Si-H₂O structures near the phase transition point of water

A theoretical model to predict the values of average stresses in silicon-based mesoporous structures with adsorbed water frozen under conditions of spatial limitation (confinement) has been developed. These stresses arise near the phase transition point of water due to differences in the thermal coefficients of linear expansion of the inhomogeneity elements of the materials under study. Knowledge of the average stress values makes it possible to predict changes in the melting/freezing temperature of water and the resistance to mechanical destruction (stability) of the water-saturated structures under consideration during thermal cycling near the ice-water phase transition point (in the temperature range 233–273 K). The model is based on the generalized singular approximation of the random fields theory in a version of the self-consistency method and makes it possible to consider the influence on the values of the average stress tensor components of a water-saturated mesoporous material of the presence of a layer of silicon dioxide on the pore surfaces, the structure of the inhomogeneous medium and the volume fraction of the components. Numerical model calculations were carried out and the dependences of the values of the average stress tensor components on the volumetric content of water frozen in the porous silicon matrix were studied. Numerical simulation showed that an increase in both the characteristic size (the ratio of the thickness of the silicon dioxide layer to the radius of the pore) and the volume fraction of frozen water leads to an increase in the values of the average stress tensor components.