## 3 Results and Discussion
### Calculation of Diffusion Coefficient in Cement Bodies with \(\gamma\)-C\({}_{2}\)S
\[\frac{\mathrm{C}_{\mathrm{x}}}{\mathrm{C}_{0}}=\ 1\ -\ \mathrm{erf}\bigg{(}\frac{ \mathrm{x}}{\sqrt[2]{\mathrm{D}t}}\bigg{)} \tag{13}\]  
Figure 8: Carbonation in an OPC/\(\gamma\)-C\({}_{2}\)S paste specimen. Figure 7: Densification on the surface of the pastes due to carbonation. Using Equation (13), knowing the surface concentration \(\mathrm{C_{o}}\) and the concentration at distance x, \(\mathrm{C_{x}}\), the diffusion coefficient is calculated as D. However, because not all the data are available, Equation (14), which is a modification of Equation (5), can be used. \[\mathrm{x^{1}}=\ \mathrm{k\sqrt{Dt}} \tag{14}\]  
This simplifies the calculations because although the concentrations at the carbonation front are not known, the diffusion depth x\({}^{1}\) (mm) and time t (years) are known; therefore, D can be calculated. Using Equation (14), the diffusion coefficient can be calculated using the time of diffusion and depth of diffusion. The diffusion coefficients calculated for the different paste specimens in the experiment are shown in Figure 9. The diffusion coefficient shows a tendency to increase until the reaction time of 1 day and then decreases. As the substitution rate of \(\mathrm{\gamma}\)-\(\mathrm{C_{2}S}\) increases, the diffusion coefficient tends to decrease. This is due to \(\mathrm{CaCO_{3}}\), a carbonation product formed in the pores, reducing the porosity of the hardened cement paste, lowering the diffusion coefficient. Carbon Dioxide Capture by OPC/\(\mathrm{\gamma}\)-\(\mathrm{C_{2}S}\) Cementitious Materials  
The \(\mathrm{CO_{2}}\) released from cement manufacture mostly comes from burning limestone. \[\mathrm{CaCO_{3}}\ \rightarrow\ \mathrm{CaO}+\mathrm{CO_{2}(g)} \tag{15}\]  
Some of the reported \(\mathrm{CO_{2}}\) emissions from the cement industry come from the transportation of materials (especially raw materials) and power generation. However, when cement is used in construction, it reverses the reaction in Equation (15), such that CaO reacts with \(\mathrm{CO_{2}}\) after a very long time to eventually produce \(\mathrm{CaCO_{3}}\), as given in Equation (16) [19]. \[\frac{\mathrm{d}\mathrm{C}}{\mathrm{d}t}=\ D\frac{\mathrm{d}^{2}\mathrm{C}}{ \mathrm{d}x^{2}} \tag{10}\]0  
Concrete takes up \(\mathrm{CO_{2}}\) when constructing normal houses, infrastructure works such as bridges and roads, and in demolished buildings. The rate of carbonation is difficult to calculate because it depends on several factors. However, because the coefficient D in Equation (14) changes over time, a number of researchers have simplified this by using Equation (17), which is based on a simplification of [PERSON]'s second law to obtain the carbonation depth in concrete [19]. \[\frac{\mathrm{d}\mathrm{C}}{\mathrm{d}t}=\ D\frac{\mathrm{d}^{2}\mathrm{C}}{ \mathrm{d}x^{2}} \tag{10}\]1  
where x is the depth of carbonation (mm), t is the carbonation time (years), and k is the carbonation rate factor. Different situations require different values of K, that is, for the environment in which the concrete is carbonated, whether it is indoors or outdoors, covered/sheltered or open, and whether it is buried or under water; therefore, there is a need for correction factors,  
\[\frac{\mathrm{d}\mathrm{C}}{\mathrm{d}t}=\ D\frac{\mathrm{d}^{2}\mathrm{C}}{ \mathrm{d}x^{2}} \tag{10}\]2 Diffusion coefficients of specimens from measurements taken. k, involved in the different cases, all of which contribute to the value of K, such that K = k\({}_{1}\)\(\times\) k\({}_{2}\)\(\times\) k\({}_{3}\)\(\times\) k\({}_{4}\). Different correction values of k were proposed by [PERSON] for a systematic method of calculating CO\({}_{2}\) uptake [19; 20; 21]. \[\frac{\mathrm{d}\mathrm{C}}{\mathrm{d}t}=\ D\frac{\mathrm{d}^{2}\mathrm{C}}{ \mathrm{d}x^{2}} \tag{10}\]3  
It is sometimes convenient to combine some k values such that K = k\({}_{1}\)\(\times\) k\({}_{2}\)\(\times\) k\({}_{3}\). CO\({}_{2}\) capture can be calculated using Equation (18) [19; 21].