## 2 Materials and Methods
### Cycling Analysis  
The extent of conversion with cycling was monitored by thermogravimetric analysis (TGA) using a SETSYS Evolution 1750 TGA-DSC from Setaram. Two different experimental conditions were performed in order to carry out the different kinetic analysis methods.  
To carry out a kinetic analysis using the Coats-Redfern method, non-isothermal calcination and carbonation was performed under two atmospheric conditions: Calcination under inert atmosphere (100% N\({}_{2}\); maximum temperature 850 \({}^{\circ}\)C) followed by carbonation under a mixed atmosphere (25% v/v CO\({}_{2}\)); and calcination and carbonation under 100% CO\({}_{2}\) (maximum temperature 1000 \({}^{\circ}\)C). A total gas flow of 20 mL min\({}^{-1}\) was used for both conditions. Experimental conditions are detailed in Table 1. For each experiment, \(\sim\)18 mg of P-CaO (powder sample) was placed into a 100 \(\mu\)L alumina crucible and subjected to a temperature ramp from ambient to the maximum temperature, followed by subsequent cooling to ambient temperature. The experiment was repeated for four different heating rates (2.5, 5, 10, and 15 \({}^{\circ}\)C min\({}^{-1}\)).  
To implement generalized methods of kinetic analysis (i.e., intrinsic chemical reaction rate model and apparent model), it was necessary to carry out carbonation under isothermal conditions. For this case, P-CaO was heated to the set temperature (see Table 1) under 100% N\({}_{2}\) and held isothermally for 20 minutes. After this time, the gaseous atmosphere was adjusted to introduce 25% v/v CO\({}_{2}\) and held isothermally for 40 minutes to allow for carbonation. The sample was then cooled to ambient temperature. The heating and cooling rates were 10 \({}^{\circ}\)C min\({}^{-1}\) and a constant gas flow of 20 mL min\({}^{-1}\) was maintained.  
For all experiments, a blank was performed under the same conditions and subtracted from each experiment to correct weight signal drifts. For the decomposition reaction of P-CaCO\({}_{3}\) to P-CaO, the extent of reaction, \(\alpha\), was determined using the fractional weight loss:  
\[\alpha=\frac{m_{i}-m(t)}{m_{i}-m_{f}} \tag{2}\]  
where \(m_{i}\) is the initial mass of the sample in grams, \(m(t)\) is the mass of the sample in grams after \(t\) minutes and \(m_{f}\) is the final mass of the sample in grams (after calcination). The carbonation conversion of P-CaO to P-CaCO\({}_{3}\) was calculated as follows:  
\[X(t)=\left(\frac{m(t)-m_{i}}{m_{X=1}}\right)\times\left(\frac{M_{CaCO_{3}}}{M_ {CaCO_{3}}-M_{CaO}}\right) \tag{3}\]  
Figure 1: Materials synthesis procedure using Pechini synthesis.  
where \(m(t)\) is the mass of the sample in grams after \(t\) minutes under the carbonation atmosphere, \(m_{\rm i}\) is the initial mass of the sample in grams (before carbonation), \(m_{X=1}\) is the theoretical mass of the sample in grams after 100% carbonation conversion (43.97% mass gain), and \(M\) is the molar mass in g mol\({}^{-1}\).  
This expression differs slightly from the means of calculating carbonation conversion usually utilized in literature [46]. The rationale is that prior to calcination in the thermogravimetric analyzer, P-CaO may still include CaCO\({}_{3}\) phases due to incomplete calcination in the furnace and adsorption of atmospheric CO\({}_{2}\). As a result, \(m(t)\) must be measured with reference to the theoretical mass after 100% carbonation conversion (which would occur during the first temperature ramp), as opposed to the initial mass of P-CaO.