# A Systematic Experimental and Computational Analysis of Commercially Available Aliphatic Polyesters
## 3 Results
Indeed, the short fragments, which diffuse out of the matrix and are responsible for mass loss, have a carboxyl end group that can partially dissociate in water solutions. After 3 weeks, PDLG 5002 has lost about 80% of its initial mass, consistently, with the high degradation extent. On the other hand, about 5 weeks are needed to achieve a significant dissolution of the PDLG 5004 and PDLG 5010 samples. Mass loss, as well as water uptake, become significant for PDLG 7507 after about 8 weeks. Focusing on PDLG 5004 and RG505 with hydroxyapatite, mass loss remained negligible in the investigated time span, but water uptake started increasing from the beginning. Mathematical modeling was employed here to provide a quantitative estimation of degradation kinetics, thanks to a validated modeling framework that proved to be a reliable choice for bulk-eroding aliphatic polyesters [18; 19; 20]. For each investigated material, the hydrolysis kinetic constant \(k_{d}\) was fitted from experimental data in order to best reproduce the number and weight average molecular weights as a function of time. The quality of the fit was evaluated by computing the \(R^{2}\) parameters for both \(MW_{n}\) and \(MW_{w}\). These values are summarized in Table 2. The model input parameters, as well as the initial values and numerical procedures, are reported in the Supporting Information section. Figure 4: Lactic units content in the copolymer as a function of degradation time. Values are expressed as the arithmetic average of three independent measurements \(\pm\) standard deviation. A comparison between the model results and experimental data for the number and weight average molecular weights is reported in Figure 6.  
The model results are in very good agreement with the experimental data. Focusing on PDLG 5002, 5004, and 5010 materials, the kinetic constants do not show a clear trend as a function of initial molecular weight, but the values are very close each other, suggesting that the degradation kinetics are similar for these three polymers. In principle, it could be expected that \(k_{d}\) decreases as the initial molecular weight increases, since slower degradation kinetics are usually observed for high molecular weight polymers. The average value of the kinetic constant can be estimated as \(1.45\pm 0.07\times 10^{-3}\) cm\({}^{6}\) mol\({}^{-2}\) s\({}^{-1}\). On the other hand, RG 505 exhibits a slightly lower degradation kinetic constant, equal to \(1.23\times 10^{-3}\) cm\({}^{6}\) mol\({}^{-2}\) s\({}^{-1}\). Overall, the kinetic constant values of PLGA 50/50 formulations lie in a reasonably comparable range. The hydrolysis kinetic constant for PDLG 7507 is equal to \(9.67\times 10^{-4}\) cm\({}^{6}\) mol\({}^{-2}\) s\({}^{-1}\), which is significantly lower than the values for the PLGA 50/50 polymers. Focusing on the polymer/hydroxyapatite compounds, the impact of hydroxyapatite on the degradation kinetics is not explicitly included in the kinetic scheme of the model but is lumped into the estimated kinetic \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Polymer** & \(k_{d}\) **(cm\({}^{6}\) mol\({}^{-2}\) s\({}^{-1}\))** & **R\({}^{2}\) (MW\({}_{n}\)) (-)** & **R\({}^{2}\) (MW\({}_{w}\)) (-)** \\ \hline PDLG 5002 & \(1.36\times 10^{-3}\) & 0.96 & 0.96 \\ \hline PDLG 5004 & \(1.52\times 10^{-3}\) & 0.94 & 0.92 \\ \hline PDLG 5010 & \(1.46\times 10^{-3}\) & 0.97 & 0.97 \\ \hline RG505 & \(1.23\times 10^{-3}\) & 0.99 & 0.98 \\ \hline PDLG 7507 & \(9.67\times 10^{-4}\) & 0.95 & 0.96 \\ \hline RG505 + HA & \(1.01\times 10^{-3}\) & 0.99 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hydrolysis kinetic constant \(k_{d}\) and \(R^{2}\) values for each data set. Figure 5: Mass loss (**a**), water uptake (**b**), and pH of the surrounding medium (**c**) as a function of degradation time. Values are expressed as the arithmetic average of three independent measurements \(\pm\) standard deviation. constant.