## 3 Results and Discussion
### The Changes of C-PC Contents in the Extracts Under Various Storage Conditions
It was clearly and first shown that the exposure of light to C-PC significantly accelerates the decrease of the concentrations of C-PC in the extract, and implied that the stability of C-PC should be more greatly affected by simultaneous exposure at high temperature and light for a relatively long period of storage, the conditions of which might reflect actual storage in many industrial fields [27; 28]. Kinetic Analysis of the Decrease of C-PC with Light and without Light Stored at Various Temperatures  
In considering the decreasing patterns of C-PC in Figures 2 and 3, the results of fitting the data in Figures 2 and 3 to Equations (1) and (2) proved that the changes of residual C-PC concentrations in the extract without light followed first-order reaction kinetics, showing clear straight lines in employing Equation (1) for all three different storage temperatures (Figure 4a) but not well fit to Equation (2) (Figure 4b). On the contrary, as shown in Figure 5, the decrease of C-PC contents in the extracts under light illumination clearly followed second-order kinetic at all of three storage temperatures (Figure 5b), showing continuous drop of C-PC contents until 14 days of storage and slowly decreased after that, especially a great decrease at 40 \({}^{\circ}\)C of high temperature rather than at 4 \({}^{\circ}\)C.  
Figure 3: The residual concentration of C-PC in the _Spirulina platensis_ extract at three different temperatures with light for two months of storage. To confirm the above approximate analysis of two different data sets in Figures 4 and 5, Table 1 shows the results of the estimating rate constants of kinetic analysis by fitting the data in Figures 2 and 3 to the Equations (1) and (2) along with linear regression coefficients (R\({}^{2}\)), which correspond to the results in Figures 4a and 5b. All of the data in Figures 4a and 5b were well fitted to Equations (1) and (2), respectively, having fairly good regression coefficients of the ranges of 0.9932 to 0.9997 for all the cases. Rate constant of Equation (1) as first-order kinetic was estimated as 0.0020 (1/day) in Figure 4a at 4 \({}^{\circ}\)C of storage temperatures and 0.0108 (1/day) at 40 \({}^{\circ}\)C, respectively. Compared to the rate constants of first order kinetics, the rate constants of second order kinetics (the cases exposed with light) were higher than the cases of no light at all three storage temperatures; 0.0020 vs. 0.0023 (1/day) at 4 \({}^{\circ}\)C, 0.0053 vs. 0.0065 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Storage condition** & **Temperature (\({}^{\circ}\)C)** & **Rate Constant (1/day)** & **R\({}^{2}\)** \\ \hline \multirow{3}{*}{Dark} & 4 & \(k_{1(4)}\) * & 0.0020 & 0.9957 \\  & 25 & \(k_{1(25)}\) * & 0.0053 & 0.9997 \\  & 40 & \(k_{1(40)}\) * & 0.0108 & 0.9932 \\ \hline \multirow{3}{*}{Light} & 4 & \(k_{2(4)}\) ** & 0.0023 & 0.9990 \\  & 25 & \(k_{2(25)}\) ** & 0.0065 & 0.9951 \\  & 40 & \(k_{2(40)}\) ** & 0.0138 & 0.9970 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of estimating first and second order rate constants of decreasing the C-pyocyan (C-PC) contents exposed to light and no light at three different storage temperatures. Figure 4: Results of first (**a**) and second order (**b**) plots of the decrease of C-PC contents in the extract at three different storage temperatures of 4 \({}^{\circ}\)C, 25 \({}^{\circ}\)C and 40 \({}^{\circ}\)C without light in Figure 2.  
Figure 5: Results of first (**a**) and second order (**b**) plots of the decrease of C-PC contents in the extract at three different storage temperatures of 4 \({}^{\circ}\)C, 25 \({}^{\circ}\)C and 40 \({}^{\circ}\)C with light in Figure 3.  
(1/day) at 25 \({}^{\circ}\)C and 0.0108 vs. 0.0138 at 40 \({}^{\circ}\)C, respectively, which can also confirm the hypothesis that the rate of decreasing and/or breaking intact C-PC was faster than the case of no light at any range of temperature.