# Predicting Dissolution Kinetics of Tricalcium Silicate Using Deep Learning and Analytical Models
## 1 Introduction
The symbols used in these models are defined as follows: \(\Delta G_{r}\) is the Gibbs free energy of the overall reaction; \(T\) is the temperature; \(R\) is the gas constant; \(A\) is the effective surface area of material; \(a_{i}\) is the ion activity of species \(i\); \(E_{a}\) is the activation energy; \(n\), \(n_{i}\), \(k\), and \(k_{i}\) are constants; and \(g(l)\) is the function of ionic strength. The analytical model developed by [PERSON] et al. [27] is based on the transition state theory and the Burton-Cabrera-Frank theory. It shows that the dissolution rate of a mineral depends exponentially on the Gibbs free energy of the overall dissolution and the temperature. However, this model cannot accurately predict the dissolution kinetics of a solid-solvent system that is near the equilibrium. This is because the model does not account for the transition from step retreat to dislocation-controlled dissolution. The model developed by [PERSON] et al. [28] accounts for various factors such as surface area, temperature, ionic strength, H\({}^{+}\) concentration in the solvent, and the change in Gibbs free energy related to dissolution. This model is widely used in the cement community to predict the dissolution kinetics of C\({}_{3}\)S [6]. In addition to modeling from a thermodynamic perspective, several studies [29; 30; 31; 32; 33] have explained the dissolution kinetics of minerals using the ion leaching theory. [PERSON]'s model [29] accounts for both H\({}^{+}\) and OH\({}^{-}\) in the leaching process, as these ions leach species from mineral surfaces with different activation energies. Other studies [32; 33; 34; 35; 36] have found that cations (excluding H\({}^{+}\)) in solvents can also contribute to mineral surface leaching. [PERSON] et al. [32] have emphasized the role of the ion activity ratio of H\({}^{+}\) to cations in mineral dissolution kinetics. This model divides the process into two scenarios: if the ion activity ratio is small, a large number of cations remain on the material surface, which dominates the leaching and dissolution processes; if the ratio is large, the dissolution rate is independent of cations. This model has been used to predict the dissolution kinetics of various minerals [33]. Although previous studies have proposed various models for predicting dissolution kinetics of minerals based on disparate theories, none of these models can predict the dissolution kinetics of C\({}_{3}\)S in a high-fidelity manner with a coefficient of determination (\(R^{2}\)) above 0.90. This is because there are several knowledge gaps in the state-of-the-art analytical models. First, it is not possible to account for all the influential variables (e.g., ions in the solvent; physicochemical properties of C\({}_{3}\)S particles; temperature; etc.) in a single analytical model. Moreover, it is difficult to incorporate a variable into analytical models without a clear understanding of its role in the dissolution process. Next, coefficients are not generic, thus requiring additional calibration while applying the model to a new C\({}_{3}\)S-solvent systems. Lastly, some parameters (e.g., ion activity; Gibbs free energy; activation energy; etc.) are obtained from additional quantitative and qualitative analyses of experimental results, which makes the model difficult to use and increases the likelihood of human error. Measuring the dissolution rate of C\({}_{3}\)S is a challenge because the solubility of calcium silicate hydrate is much lower than that of C\({}_{3}\)S, which means calcium silicate hydrate will precipitate before C\({}_{3}\)S completely dissolves, unless a very small amount of C\({}_{3}\)S is used. As a result, only a few studies have attempted to measure the C\({}_{3}\)S dissolution rate.