# Recombination of Poly(Acrylic Acid) Radicals in Acidic Aqueous Solutions: A Pulse Radiolysis Study
## 3 Results and Discussion
### Radical Lifetime as a Function of pH  
Carbon-centered PAA radicals can undergo a number of reactions ([50], for a general discussion on polymer radical reactions see also [16]). Those involving one radical include H-transfer, which leads to transformation of \(\beta\)-radicals into the more stable \(\alpha\)-radicals, as well as \(\beta\)-fragmentation leading to chain scission. Both these processes are relatively slow, and they show up with considerable yields only in neutral and alkaline solutions, when the lifetime of PAA radicals is long (see below). A potential reaction of PAA radical with hydrogen peroxide formed by \({}^{\bullet}\)OH self-combination (due to incomplete scavenging of \({}^{\bullet}\)OH radicals by PAA at the lowest polymer concentrations used in this work) is also too slow to compete with reactions between two polymer radicals, at least in an acidic medium. Reactions involving two PAA radicals (recombination) are crosslinking and disproportionation. Crosslinking results in formation of a C-C covalent bond between the former radical sites, while disproportionation does not create a crosslink, but a double bond on one of the former radical sites. The ratio between crosslinking and disproportionation is largely set by the polymer chemistry and cannot be easily influenced. Studies on 2,4-dimethylglutaric acid used as a structural model of PAA indicate that in acidic solution the fraction of crosslinking events is around 44%, indicating the importance of the disproportionation pathway [84]. Since the rate-determining step of crosslinking and disproportionation is the same, i.e., coming of two radical-bearing chain segments into proximity, in kinetic studies we do not differentiate between them, considering them as two kinetically equivalent components of radical decay, and we use the term \"recombination\" to denote the sum of these processes. The two latter reactions are the only processes leading to a decrease in the radical concentration in the system, since in the previously mentioned H-transfer and chain scission the number of radicals is preserved, and the potential radical transfer back to the solvent is thermodynamically unfavorable. Therefore, the lifetime of polymer radicals depends to a large extent on how easy it is for two radical-bearing chain segments to approach each other. In polyelectrolytes, in the absence of other factors such as steric barriers, this depends mainly on the presence and strength of repulsive electrostatic interactions between chain segments due to the ionized functional groups. Already in the 1970s [PERSON] and [PERSON] demonstrated such an effect by studying radical decay in copolymers of vinyl alcohol and acrylic acid [85]. The increasing fraction of dissociated acrylic acid units led to a significant decrease in the radical recombination rate. In previous studies on PAA homopolymers, a strong pH effect on the radical lifetime has been reported [50; 52]. Lifetimes observed for fully charged PAA were several orders of magnitude longer than for the case of protonated carboxylic groups. Very long lifetimes of radicals derived from fully charged polyelectrolytes have also been found for poly(methacrylic acid) [86] and poly(styrene sulfonate) [87]. In our study we have confirmed this earlier observation by pulse-irradiating oxygen-free solutions of PAA, OAA, and PA at various pH and following the decay of substrate-derived radicals. Already from the kinetic traces of PAA radicals (Figure 3a) it is evident that at pH 2 the radicals decayed fast. Their first half-life was less than a millisecond. In contrast, no decay was detectable on the same timescale for pH 5 and 9; actually, even some increase was observed resulting from the slow H-transfer taking place. The same effect, albeit less pronounced, was observed for OAA (Figure 4a). For propionic acid (Figure 4b), radical decay was observed within the first millisecond at all pH values, although the fastest reaction was still seen at pH 2.