# Predicting Dissolution Kinetics of Tricalcium Silicate Using Deep Learning and Analytical Models
## 1 Introduction  
Portland cement (PC) is the fundamental material for modern infrastructure, but its production contributes significantly to global CO\({}_{2}\) emissions, accounting for about 9% of total emissions [1, 2, 3]. To improve the sustainability and performance of PC, it is important to understand the hydration reaction of its primary component, tricalcium silicate (C\({}_{3}\)S). C\({}_{3}\)S is the most abundant component in PC, making up more than 50% of its composition [4, 5, 6]. When C\({}_{3}\)S reacts with water, it undergoes a series of chemical reactions that result in the dissolution of calcium and silicate ions, followed by the formation of calcium silicate hydrate and portlandite [4]. While the phase transformations that occur at later stages of the hydration are well documented [4, 7], the dissolution kinetics of C\({}_{3}\)S at early stages remains a controversial subject. However, it is important to understand the dissolution kinetics of C\({}_{3}\)S when it is undersaturated with respect to solvent. The undersaturation of C\({}_{3}\)S solution presents the initial and induction periods of cement hydration [4, 6]. The dissolution mechanisms of C\({}_{3}\)S are different when the solution is in undersaturation and saturation (i.e., hydration products form) [6, 8]. By studying the dissolution behaviors of C\({}_{3}\)S, we can gain a better understanding of the factors that affect the hydration kinetics of cement. This knowledge can be used to develop novel cement formulations and improve cement performance. Despite many studies that have sought to uncover the mechanisms (e.g., protective phase [9; 10; 11] and double layer theory [12]) behind the dissolution of C\({}_{3}\)S and minerals in recent decades, a definitive rate-controlling mechanism remains elusive due to the complex interaction of physicochemical parameters between solids and aqueous solvents. The most widely accepted theory to explain the dissolution kinetics of C\({}_{3}\)S and minerals is the inverse crystal nucleation theory [6; 13; 14]. This theory posits that, similar to the process of crystal growth, the dissolution of C\({}_{3}\)S and minerals is primarily determined by the density of pre-existing steps on the surface of minerals [14]. These steps are formed by dislocation defects and the nucleation of two-dimensional vacancy islands at impurities or homogenous sites. The growth of vacancy islands on a surface is determined by the Gibbs-Thomson effect, a thermodynamic principle that dictates their critical size [15; 16]. If a vacancy exceeds this critical size, it will continue to grow. At the critical size, the free energy change reaches a maximum, creating an energy barrier that must be overcome for vacancy growth to continue. The energy barriers that must be overcome by the vacancy islands have a proportional relationship with the interfacial energy, but an inverse relationship with the degree of undersaturation [15; 16]. While the solution is near the equilibrium, the density of steps of the solid is dominated by dislocation defects, as the energy barriers are too high for vacancy islands to overcome. Except for surface defects, other experimental parameters--for example, solvent chemistry [8; 17], surface geometry [18; 19; 20; 21; 22; 23], and mineral composition [24; 25; 26]--also substantially influence the dissolution kinetics of C\({}_{3}\)S and minerals. By incorporating these parameters into analytical models, it is possible to reveal underlying structures between dissolution kinetics and physicochemical properties of minerals and solvents. The following review focuses on existing analytical models (shown in Table 1) that have been used to predict the dissolution kinetics of C\({}_{3}\)S and minerals. Some of these models have been successful in accurately predicting the dissolution kinetics of minerals.