## 2 Derivation of Discrete Solid Phases (DSPs) from Cemdata07 Solid Solution End-Members
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & **Mole** & \multirow{2}{*}{**DSP Dissolution Reactions**} & \multirow{2}{*}{**Log K**} & \multicolumn{2}{c}{**Analytical Expression**} & \multirow{2}{*}{**Vol**} \\  & & & & **(25 \({}^{\circ}\)C)** & & **(Equation (1))** & & **(cm\({}^{3}\)/mol)** \\ \cline{3-6}  & **X\({}_{\text{i}}\)** & **X\({}_{\text{j}}\)** & & & **a** & **C** & **d** \\ \hline Tobermorite & \multirow{3}{*}{1} & \multirow{3}{*}{0} & (CaO)0.8333(SiO\({}_{2}\))1.0000(H\({}_{2}\)O) & & & & 3.06440 & \\ II & & & 1.3330 \(+\) 1.6666 H\({}^{+}\) 0.8333 Ca\({}^{+}\)2 \({}^{+}\) & 11.1373 & \(-\)13.91062 & \(\times\) 10\({}^{3}\) & 5.962965 & 59 \\  & & & 2.1663 H\({}_{2}\)O + 1.0000 SiO\({}_{2}\) & & & & \\ \hline TobJenSS & \multirow{3}{*}{0.8} & (CaO)1.0000(SiO\({}_{2}\))1.0000(H\({}_{2}\)O) & & & & & \\ CS100 & & & 1.4864 \(+\) 2.0000 H\({}^{+}\) = 1.0000 Ca\({}^{+}\)2 \({}^{+}\) & 14.5527 & \(-\)15.22546 & \(\times\) 14.86636 & \(\times\) 10\({}^{3}\) & 6.357638 & 62.8 \\ \hline TobJenSS & \multirow{3}{*}{0.6} & (CaO)1.1667(SiO\({}_{2}\))1.0000(H\({}_{2}\)O) & & & & & \\ CS117 & & & 1.6398 \(+\) 2.3334 H\({}^{+}\) = 1.1667 Ca\({}^{+}\)2 \({}^{+}\) & 18.1104 & \(-\)16.39794 & \(\times\) 10\({}^{3}\) & 6.752311 & 66.6 \\  & & & 2.8065 H\({}_{2}\)O + 1.0000 SiO\({}_{2}\) & & & & \\ \hline TobJenSS & \multirow{3}{*}{0.4} & (CaO)1.3333(SiO\({}_{2}\))1.0000(H\({}_{2}\)O) & & & & & \\ CS133 & & & 1.7932 \(+\) 2.6666 H\({}^{+}\) = 1.3333 Ca\({}^{+}\)2 \({}^{+}\) & 21.7431 & \(-\)17.49397 & \(\times\) 10\({}^{3}\) & 7.146450 & 70.4 \\  & & & 3.1265 H\({}_{2}\)O + 1.0000 SiO\({}_{2}\) & & & & \\ \hline TobJenSS & \multirow{3}{*}{0.2} & (CaO)1.5000(SiO\({}_{2}\))1.0000(H\({}_{2}\)O) & & & & & \\ CS150 & & & 1.9466 \(+\) 3.0000 H\({}^{+}\) = 1.5000 Ca\({}^{+}\)2 \({}^{+}\) & 25.4508 & \(-\)18.51652 & \(\times\) 10\({}^{3}\) & 7.541123 & 74.2 \\  & & & 3.4466 H\({}_{2}\)O + 1.0000 SiO\({}_{2}\) & & & & \\ \hline \hline \multirow{3}{*}{Jennite} & \multirow{3}{*}{0} & \multirow{3}{*}{1} & (CaO)1.6667(SiO\({}_{2}\))1.0000(H\({}_{2}\)O) & & & & & \\  & & & 2.1000 \(+\) 3.3334 H\({}^{+}\) = 1.6667 Ca\({}^{+}\)2 \({}^{+}\) & 29.3008 & \(-\)19.39671 & \(\times\) 10\({}^{3}\) & 7.935796 & 78 \\ \cline{1-1} \cline{3-6}  & & & 3.7667 H\({}_{2}\)O + 1.0000 SiO\({}_{2}\) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: End-members and DSP for the CSH model. metals (K and Na) by the C-S-H gel [26]. To minimise the computing time, all input data were defined in an Excel spreadsheet and transferred directly into the PHREEQC input file. The above shows how the C-S-H gel's solubility could be modelled as a series of DSPs, which, here, were derived from the jennite and tobermorite-II end-members provided in the cemdata07 database. However, a solid solution model was not needed to model the OPC hydration, which, in fact, only required portlandite and a suitable C-S-H gel phase of a fixed calcium to silica (Ca/Si) ratio between 1.6 and 1.8 and a water/Si (H/Si) molar ratio between 2.0 and 2.1. In the DSP model presented in [19], these values were closely matched by the CSH(165) phase, which had a Ca/S ratio of 1.65 and H/Si ratio of 2.1167. As shown in Figure 1, the TobJenSS_CS150 DSP was the only one predicting the precipitation of the C-S-H gel, which, with a Ca/Si ratio of 1.50 and H/Si ratio of 1.947, was not suitable to represent the C-S-H gel in the hydrated OPC. The jennite and tobermorite-II model should, therefore, only be used in cement blends where lower C/S ratios are purposefully targeted by the addition of supplementary cementitious materials (SCMs). Going forward, only the TobJenSS_CS150 phase (Table 2) was used in the analysis to represent the C-S-H gel in the PHREEQC model used here.