On the pressure of water of crystallization at filler inclusions

On water uptake, plaster of Paris sets to gypsum, and the volume expansion associated with this particular hydration reaction has been long exploited to make casts for statuary. Immobilization of molecules of liquid water into the crystal lattice of water of crystallization gives rise to a decrease of entropy, and this is manifested by the so‐called heat of hydration. When it occurs at a calcium sulfate inclusion inside a polymer, the plaster of Paris → gypsum reaction generates a pressure, and the dependence of the equilibrium value of this pressure on temperature is expressed by Clapeyron's equation. From published data for the volume expansion Δ V and entropy decrease Δ S , it is shown that\documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{dp}}{{dT}} = \frac{{\Delta V}}{{\Delta S}} = - 50{\rm bar K}^{ - 1} $$\end{document} Using as a benchmark the fact that p is zero at 100°C, the temperature at which plaster of Paris, gypsum, and liquid solution can exist in thermodynamic equilibrium (1), we find that hydration at ambient temperatures of a typical calcium sulfate filler composition will, under conditions of thermodynamic equilibrium, generate sufficient pressure to cause internal cracking. Attention is drawn to the fact that creation of water of crystallization pressures of similar magnitude can be expected for any other filler that can exist in more than one state of hydration. As a corollary, the Clapeyron equation is used to make a similar analysis of the phenomenon of frost shattering in polymeric materials that contain free water.