Estimation of thermodynamic quantities via in-situ monitoring and modelling at the early-stage of ettringite formation

Early stage of solid formation from solution is a matter of debate, particularly nucleation and early growth. Existing thermodynamic models based on bulk equilibrium assumptions often fail to capture these elusive stages and consequently the nature of early-stage formation. This work focuses on estimating key quantities, such as interfacial energy, early crystal growth rate, and the freshly formed solid solubility through in-situ monitoring and numerical modelling. As case study, we focus on ettringite, a critical solid formed during early hydration of cement. A highly controlled, dilute, titration-precipitation method was employed to deconvolute the early stages of solid formation. The process was monitored using Ca2+ ion selective electrodes (ISE), along with optical, pH, and conductivity probes. Their data were incorporated into a model based on classical nucleation theory (CNT) and monovariate population balance. This integrated approach provides a better baseline, offering meaningful insights into an essential reaction of real cement. In our study, where the growth is limited by Ca2+ diffusion, the fresh solid solubility (log Ksp,fresh) was found to be -40.7±0.02, and solid-liquid interfacial energies for primary and secondary nucleation were 22.7± 0.06 and 19.2±0.05 mJ/m2, respectively. Additionally, the evolution of needle dimensions was estimated in the experimental timeline. The proposed model was subsequently extended to describe ettringite formation in model cement, providing physically consistent estimation of nucleation and growth rates and insights into the complex dynamics of cement hydration.