# Recombination of Poly(Acrylic Acid) Radicals in Acidic Aqueous Solutions: A Pulse Radiolysis Study
## 3 Results and Discussion
### Generation and Detection of Free Radicals  
Ionizing radiation is known as a clean and easy to control way to generate polymer radicals [75; 76; 77]. In dilute aqueous solutions, practically all the radiation energy is absorbed by water. Radiolysis of water leads to the formation of various short-lived, highly reactive intermediates [78; 79; 80]. At the timescales when reactions with solutes present in millimolar concentrations are possible, the main reactive species are hydroxyl radicals, hydrogen atoms, and hydrated electrons (reaction 2). Their radiation-chemical yields, in the units of 10\({}^{-7}\) mol J\({}^{-1}\), are 2.8, 0.6, and 2.8, respectively. In acidic solutions, hydrated electrons are converted to hydrogen atoms (reaction 3, \(k\) = 2.3 \(\times\) 10\({}^{10}\) dm\({}^{3}\) mol\({}^{-1}\) s\({}^{-1}\)[81]). In order to increase the yield of hydroxyl radicals, it is customary to saturate solutions with nitrous oxide, which transforms e\({}_{\text{aq}}\)\({}^{-}\) into \({}^{\bullet}\)OH (reaction 4, \(k\) = 9.1 \(\times\) 10\({}^{9}\) dm\({}^{3}\) mol\({}^{-1}\) s\({}^{-1}\)[82]). However, in acidic solutions the efficiency of the latter process is limited by the competing reaction (3). \[\text{H}_{2}\text{O}\rightarrow{}^{\bullet}\text{OH},\,\text{H}^{\bullet},\, \text{e}_{\text{aq}}\,^{-},\text{H}_{2}\text{O}_{2},\,\text{H}_{2},\,\text{H}_{3 }\text{O}^{+} \tag{2}\]  
\[\text{H}_{3}\text{O}^{+}+\text{e}_{\text{aq}}\,^{-}\rightarrow\text{H}^{ \bullet}+\text{H}_{2}\text{O} \tag{3}\]  
\[\text{N}_{2}\text{O}+\text{e}_{\text{aq}}\,^{-}+\text{H}_{2}\text{O} \rightarrow{}^{\bullet}\text{OH}+\text{OH}^{-}+\text{N}_{2} \tag{4}\]  
Hydroxyl radicals and hydrogen atoms are known to react with PAA by hydrogen abstraction, a process that leads to the formation of two types of carbon-centered radicals, \(\alpha\) and \(\beta\), located randomly along PAA chains (reaction 5). While the rate constants of \({}^{\bullet}\)OH attack on macromolecules may depend on both molecular weight and concentration [83], for conditions similar to our work a value of \(k\) = 9 \(\times\) 10\({}^{7}\) dm\({}^{3}\) mol\({}^{-1}\) s\({}^{-1}\) has been reported  
Figure 2: Critical hydrodynamic concentration (\(c^{\bullet}\)) of PAA and OAA in aqueous solutions as a function of pH, as determined by viscometry at 25.0 \(\pm\) 0.1 \({}^{\circ}\)C.  
for the protonated PAA, and \(k\) = 2.2 \(\times\) 10\({}^{8}\) dm\({}^{3}\) mol\({}^{-1}\) s\({}^{-1}\) for the deprotonated chains, the reaction of H\({}^{\bullet}\) being somewhat slower [53]. Previous studies indicate that initially around 30% of \(\alpha\)-radicals **1** and 70% of \(\beta\)-radicals **2** are formed (reactions 5.1 and 5.2, respectively) [50]. These radicals, when in the protonated forms, show a featureless spectrum in UV, with absorbance raising towards shorter wavelengths [50; 53; 54]. Since no spectral evolution is observed during their decay at low pH, it is inferred that that the reactivity of \(\alpha\)-radicals and \(\beta\)-radicals in recombination reactions is similar; therefore, it can be kinetically considered as a single process. It should be noted that these reactions, in particular at low polymer concentrations and under pulse radiolysis conditions, have to compete with fast mutual recombination of \({}^{\bullet}\)OH radicals and H\({}^{\bullet}\) atoms; therefore, one cannot expect that all \({}^{\bullet}\)OH and H\({}^{\bullet}\) formed in the system would finally yield PAA radicals.