## 3 Results and Discussion
### Inline Monitoring and Polymerisation Rate Determination
Exemplary here were the acrylic acid polymerisations in isopropyl alcohol (150 g/L) initiated with 1 mol% AIBN. (**b**) Normalised concentration profile for a fit with first order kinetics considering only the first 30% of the reaction conversion. Curves for 70 °C and 75 °C are congruent. However, if the error of these fits is determined for the whole reaction range (>95% conversion) (local fit, global error), a constant yet significantly higher error can be achieved when fitting at least up to a conversion of 30%. Higher errors are to be expected for fits up to higher conversions due to the increasing relevance of the Raman measurement fluctuations. The error for the fit up to a conversion of 10% is not displayed on the graph because of its high value of 0.54. If the error of the global fit for the reaction order \(n>1\) is considered in the respective conversion ranges, a constantly decreasing error results, which on the one hand is always lower than the global error for the fits according to reaction order 1 and from a fit up to 80% conversion is also lower than the corresponding local error for \(n=1\). As an example, for fitting the concentration profiles using the first order, the fit up to a conversion of 30% is shown. Up to that point an approximately constant local and global error can be obtained. This is shown in Figure 4(b). It shows that although the beginning of the reaction can be well represented, the monomer content is overestimated towards the middle of the reaction and underestimated in the end. This error increases with increasing temperature. Explanations as to why a reaction order of 1 cannot be assumed are discussed in more detail in the following. The raw data was fitted using the integrated differential equation for reactions of any reaction order \(n\) with \([AA]_{0}\) and \([AA]\) denoting the initial and current acrylic acid concentration, respectively, and \(k_{\text{n}}\) being the reaction rate constant:  
\[[AA]=\frac{[AA]_{0}}{\sqrt[n-1]{1+(n-1)[AA]_{0}^{n-1}k_{n}t}}\, \tag{2}\]  
Here, the average deviation from the calculated concentration to the fitted ideal kinetics according to Equation (2) is 4%. Since the data can be well represented by ideal kinetics, it can be concluded that the Trommsdorff-Norrish effect plays a subordinate role in the performed reactions. This suggests that the expected chain-regulation function of the solvent could provide for low molar masses and therefore uniform mixing. Based on the accuracy of fit of the data in Figure 4, the conversion of the reactions can be calculated by dividing each concentration data point by the maximum measured concentration, shown in Figure 6.  
The conversion chart shows that for 0.5 mol% of initiator used, a conversion of 80% was reached after 151, 111, 76 and 59 min, respectively, for each temperature. Doubling the AIBN concentration to 1.0 mol% led to noticeably steeper curves, shortening the reaction time up to an 80% conversion 1.5- to 3-fold and allowing for a conversion close to 100% after the displayed 180 min for 70 \({}^{\circ}\)C and 75 \({}^{\circ}\)C.  
In free radical homopolymers, the polymerisation rate \(R_{\text{p}}\) is defined as the decay of the monomer concentration over time. In complex forms of polymerisations where the steady-state radical concentration also depends on the monomer concentration  
Figure 6: Conversion of acrylic acid polymerisations in isopropyl alcohol (150 g/L) at different temperatures determined by Raman spectroscopy: 0.5 mol% AIBN (**a**), and 1.0 mol% AIBN (**b**). \([M]\), the polymerisation rate is proportional to the initiator and monomer concentration with their respective reaction orders \(\alpha\) and \(\beta\)[10; 13; 26] and can be generally defined as:  
\[R_{\mathrm{p}}=-\frac{\mathrm{d}[M]}{\mathrm{d}t}=k\ [I]^{\alpha}\ [M]^{\beta}. \tag{3}\]  
In this study, AIBN was used as an initiator. Because it is widely used and well known for free radical polymerisations, it is safe to assume classical kinetic considerations.