## 3 Results and Discussion
### Inline Monitoring and Polymerisation Rate Determination
However, it must be kept in consideration that AA polymerisation is strongly pH-dependent, but that the pH scale also behaves differently in solvents other than water [29]. Using the data from Figures 4 and 6, the rate of polymerisation can additionally be shown as a function of conversion (Figure 8). This graph shows that the maximum polymerisation rate was also the initial polymerisation rate. Initial polymerisation rates of 0.1-0.04 mol\(\cdot\)L\({}^{-1}\cdot\)min\({}^{-1}\) with 0.5 mol\(\%\) of \begin{table}
\begin{tabular}{c c c c c} \hline \(\boldsymbol{c_{0,\text{AIBN}}}\) [mol\(\cdot\)L\({}^{-1}\)] & \(\boldsymbol{c_{0,\text{AA}}}\) [mol\(\cdot\)L\({}^{-1}\)] & \(\boldsymbol{n}\) & **T** [\({}^{\circ}\)C] & \(\boldsymbol{k_{\text{n}}}\) [L\(\cdot\)mol\({}^{-1}\cdot\)min\({}^{-1}\)] \\ \hline
0.0102 & 2.03 & 1.56 & 60 & 0.0170 \\
0.0103 & 2.05 & 1.85 & 65 & 0.0308 \\
0.0102 & 2.05 & 1.74 & 70 & 0.0388 \\
0.0103 & 2.05 & 1.68 & 75 & 0.0477 \\ \hline
0.0209 & 2.08 & 1.72 & 60 & 0.0312 \\
0.0208 & 2.08 & 1.72 & 65 & 0.0440 \\
0.0208 & 2.08 & 1.60 & 70 & 0.0719 \\
0.0208 & 2.08 & 1.72 & 75 & 0.1543 \\ \hline
0.0312 & 2.08 & 1.90 & 60 & 0.0333 \\
0.0312 & 2.08 & 2.07 & 65 & 0.0616 \\
0.0312 & 2.08 & 1.58 & 70 & 0.0679 \\
0.0312 & 2.08 & 1.64 & 75 & 0.1015 \\ \hline \end{tabular}
\end{table} 
Table 1: Initial concentrations of acrylic acid (AA) and AIBN with their resulting reaction order and rate constants depending on the reaction temperature. Figure 8: Polymerisation rate of acrylic acid polymerisations in isopropyl alcohol (150 g/L) at different temperatures as a function of conversion determined by Raman spectroscopy: 0.5 mol\(\%\) AIBN (**a**), and 1.0 mol\(\%\) AIBN (**b**). AIBN and 0.35-0.06 mol\(\cdot\)L\({}^{-1}\cdot\)min\({}^{-1}\) with 1.0 mol\(\%\) of AIBN were observed, displaying a strong temperature dependence. The rates decreased with an increasing conversion, corresponding to the depletion of AA monomers. The commonly known autoacceleration of the polymerisation rate after the start of polymerisation due to the gel-effect [34] was not present here due to the short polymer chains. Rather, an almost linear decrease in the polymerisation rate, especially at 60 \({}^{\circ}\)C, could be observed. From the initial polymerisation rates, \(k\) values were calculated according to Equation (3) and their natural logarithm was plotted against the reciprocal reaction temperatures to solve the Arrhenius equation. Due to the fact that the classical Arrhenius plot could be distorted by the temperature drop caused by the initiator addition and the subsequent temperature stroke, the Arrhenius parameters were estimated within a basic simulation using Predici 11. For this purpose, the reactions carried out were fed into Predici with their recipes and the experimental temperature and concentration curves. Based on the values obtained from the Arrhenius plots, the initial values for the parameter estimation were determined. The algorithm tried to map the experimental concentration profiles with the simulated ones up to a conversion of 60\(\%\) (to cover the temperature profiles deviating from the ideal temperatures in Figure 3). This is shown in Figure 9 together with the development of the \(k\) values. The parameter estimation resulted in activation energies \(E_{\text{a}}\) of 57.6 \(\pm\) 0.8 kJ/mol for 0.5 mol\(\%\) of AIBN and 88.5 \(\pm\) 1.5 kJ/mol for 1.0 mol\(\%\) of AIBN. These values are lower than the activation energies determined by the classical linear regression (65 \(\pm\) 11 kJ/mol for 0.5 mol\(\%\) of AIBN and 102 \(\pm\) 14 kJ/mol for 1.0 mol\(\%\) of AIBN). The frequency factors were estimated to be 2.69 \(\times\) 10\({}^{5}\)\(\pm\) 3.80 \(\times\) 10\({}^{4}\) L\(\cdot\)mol\({}^{-1}\cdot\)s\({}^{-1}\) and 2.65 \(\times\) 10\({}^{10}\)\(\pm\) 6.61 \(\times\) 10\({}^{9}\) L\(\cdot\)mol\({}^{-1}\cdot\)s\({}^{-1}\), respectively. In the literature, reaction temperatures starting at 70 \({}^{\circ}\)C and above have showed a shift in the Arrhenius plot, resulting in different slopes [2,30].