## 3 Results and Discussion
### Inline Monitoring and Polymerisation Rate Determination  
Similar to the widespread application of NIR spectroscopy for in situ monitoring of chemical reactions, particularly polymerisation reactions [23; 24], Raman spectroscopy can be employed. Previous research by [PERSON] et al. has shown that the integral of the C=C stretching vibration band can be correlated linearly to the acrylic acid (AA) concentration in aqueous solutions from 20 g/L up to 400 g/L [25]. Because the Raman spectrum of isopropyl alcohol does not overlap with this band, the AA concentration could be measured throughout the whole polymerisation reaction. AA concentration profiles of the reactions carried out with 0.5 mol% and 1.0 mol% AIBN regarding the AA content are shown in Figure 4.  
Here, the shown data points were acquired by multiplying the normalised concentration acquired from the band integration with the initial AA concentration. Raman measurements can have some fluctuations due to temperature changes, variations in viscosity, ascending bubbles, and the stirred reaction mass. However, depending on the desired spectra resolution, Raman laser intensity and the optical path length of the immersion probe, a single spectrum can be acquired in a fraction of a second. Over the course of the reaction, if spectra are acquired every 32 s, the data are sufficient to fit the concentration profiles using ideal kinetics. Under the initially classically expected assumption of a monomer reaction order of 1, however, curve fitting did not lead to a coverage of all measurement values during the reactions. Therefore, only if the reaction is to be examined up to lower conversions of about 30%, is it tenable to express the reaction with an order of  
Figure 3: Temperature profile of acrylic acid polymerisations in isopropyl alcohol (150 g/L) initiated with AIBN (1 mol%). Solid lines show the temperatures in the reactor vessel, dotted lines display the corresponding jacket temperatures. 1 (see Figure 5a). The fit error \(\sigma^{2}\) is calculated as the sum of squares described as follows (Equation (1)):  
\[\sigma^{2}=\sum_{i=1}^{N}\frac{\left[P_{i,\text{meas}}-P_{i,\text{calc}}\right] ^{2}}{N-K}, \tag{1}\]  
where \(P\) denotes the fitted value (in this case the normalised concentration), \(N\) the amount of data points and \(K\) the number of parameters to adjust the fit. In order to determine to what extent the reaction with a fit according to a reaction order \(n=1\) is valid, the data points were only fitted up to a certain conversion section (in 10% steps); this is plotted in Figure 5a. The error resulting from this fit is called the local error of the local fit. From these so-called local fits, the error that results when all measuring points of a reaction, i.e., the entire conversion range, are considered is then determined. This is called the global error of the local fit. In addition, these errors were compared with the fit used for the later described final evaluation according to reaction orders of \(n>1\) (Equation (2)). For this purpose the fit applied to the entire reaction was used, but the error was determined in the respective conversion interval. It can be concluded from the graph in Figure 5a that the local fit errors for \(n=1\), for the fit up to a 20% conversion to the fit up to a 70% conversion,  
Figure 4: Concentration profiles of acrylic acid polymerisations in isopropyl alcohol (150 g/L) initiated with AIBN: 0.5 mol% (**a**), and 1.0 mol% (**b**). Crosses denote the normalised integral of the C=C stretching vibration band acquired by Raman spectroscopy, multiplied by the initial acrylic acid concentration. Solid lines are fitted according to \(n\)-th order kinetics. Figure 5: (**a**) Plot of the respective fit errors for the fit of all conversion curves or concentration profiles according to reaction order \(n=1\) and \(n>1\) up to a certain conversion. The local error describes the error in the respective conversion range, the global error includes all measuring points of the reaction.