## 3 Results and Discussion
### Inline Monitoring and Polymerisation Rate Determination
The square root proportionality of the propagation rate to the initiator concentration (\(\alpha=0.5\)) is implied [27]. Since the polymerisations shown in this work were also carried out at three different initiator concentrations, this assumption can also be confirmed by the straight line in Figure 7. Ideally, the straight line in the graph would intersect the origin, which is not the case here. This is presumably due to the fact that no lower initiator concentrations than 0.5 mol% were used. Another possible reason would be that radicals are being scavenged by, e.g., MEHQ (4-methoxyphenyl), which was included in the acrylic acid as a stabiliser. However, this effect should be negligible in the absence of dissolved molecular oxygen [28] and was also confirmed again for our experimental set-up (Figure A2). From this, the rate constant \(k\) is defined as a product of the chain propagation rate constant \(k_{\mathrm{p}}\) with the classical description for the concentration of growing chains depending on the square root of the initiator concentration [27]. Here, \(f\) is the initiator efficiency, \(k_{\mathrm{d}}\) and \(k_{\mathrm{t}}\) stand for the initiator decomposition and polymer chain termination rate constant, respectively:  
Figure 3:0  
It is worth noting, however, that kinetics in the case of AA polymerisations are much more complex. Because growing AA polymer chains undergo backbiting and transfer reactions, it is important to differentiate between secondary and tertiary radicals and their different rate constants [3]. Additionally, it has been found that the polymerisation rate of AA is highly dependent on the degree of neutralisation [2; 4; 10; 11; 14]. This is explained by the increase of ionised species with an increasing pH, resulting in different types of propagation rate constants between the differently ionised species [2; 14]. In our study, the acrylic acid solution was not neutralised and only a single initial monomer concentration was used. Nonetheless, the pH value was measured throughout the reaction. It should be noted that the pH value obtained here cannot be directly compared with the meaning of the pH value in aqueous solutions [29], but it serves as a reproducible reference value in the experimental procedure. In the beginning, the solution of AA in isopropanol (150 g/L) had a pH of 3.0. After 15 min (60 \({}^{\circ}\)C, 0.5 mol% AIBN), the pH had risen to 3.6 and a final value of 4.0 was reached at the end of the reaction. Figure 3:1 Linear dependence of the square root of the initiator concentration on the initial polymerisation rate. While the classical assumption for the monomer reaction order \(\beta\) in Equation (3) would suggest a value of 1, previous studies have suggested orders above 1 due to an interaction of the monomer with the initiator itself or its caged radicals [10]. While [PERSON]\(\acute{\text{e}}\) et al., [PERSON] et al. and [PERSON] et al. found the order to be 1.5 [10; 11; 30; 31], others such as [PERSON] et al. and [PERSON] et al., respectively, suggested values of 2 and 1.16-1.25 [2; 32]. In this work, we could confirm a reaction order of 1.73 \(\pm\) 0.15 in isopropyl alcohol across three different initiator concentrations. The resulting data from the experiments for the reaction order \(n\) and \(k_{\text{n}}\) are listed in Figure 3:2  
In comparison to data found in the literature [10; 11; 31; 32; 33] for the acidic (non-neutralised) AA polymerisation in water across different pH values at mostly temperatures between 50-60 \({}^{\circ}\)C, the rate constants found for isopropyl alcohol in this work are noticeably (up to 10-fold) slower. In acidic water (pH < 4) with different initiators and different concentrations thereof, rate constants were ranging from 0.14 to 0.90 L-mol\({}^{-1}\cdot\)min\({}^{-1}\) at 50-60 \({}^{\circ}\)C [31; 32; 33]. The observed rates in isopropanol seem more comparable to neutralised AA polymerisations in water, ranging from 0.003 to 0.045 L-mol\({}^{-1}\cdot\)min\({}^{-1}\), also at 50-60 \({}^{\circ}\)C [31; 32; 33].