# Recombination of Poly(Acrylic Acid) Radicals in Acidic Aqueous Solutions: A Pulse Radiolysis Study
## 1 Introduction  
Changes in public awareness and the related drive to move from an economy based on fossil resources to the new one, based on renewable materials, are also reflected in the field of polymers and plastics. While much activity is focused on replacing commodity synthetic polymers by their green-sourced and biodegradable equivalents, this does not mean that synthetic polymers have no place in the future economy. Specialty polymers, used in new organic electronics and photovoltaics, biomaterials, drug delivery systems, etc., will definitely make use of the extraordinary properties that synthetic polymers can provide. These applications require the possibilities of synthesizing polymers of precisely known and well-controlled architecture, such as can be provided by modern synthetic methods based, for instance, on controlled radical polymerization [1, 2, 3, 4, 5]. To achieve full control over the processes involved in the synthesis of these specialty polymers and products, it is desirable to know the detailed kinetics and mechanisms of the involved elementarychemical reactions. In free-radical polymerization, our knowledge on propagation kinetics has been greatly increased in the last two decades due to a new experimental approach: PLP-SEC (Pulsed Laser Polymerization-Gel Permeation Chromatography) [6; 7; 8; 9]. Much attention has also been devoted to the termination reaction, i.e., recombination of two terminal radicals on the growing polymer chains, but it seems that the picture is not yet complete, especially when it comes to termination rate constant dependence on molecular weight and polymer concentration, and also to pinpointing the rate-determining process [10; 11; 12; 13; 14]. The importance of polymer radical recombination is not limited to polymerization. Polymer crosslinking processes in which radicals generated randomly on macromolecules come into proximity and recombine to form a covalent bond are also of high importance if we take into account the broad variety of products based on crosslinked polymers. If we limit the scope of our discussion to hydrophilic polymers being crosslinked in aqueous solution, kinetic features of the radical recombination process control the final outcome and character of the products, being either macroscopic (wall-to-wall) hydrogels or nanogels [15; 16]. The former are formed when intermolecular recombination prevails, and the latter are products of predominantly intramolecular crosslinking, i.e., recombination taking place between the radicals initially located on the same polymer chain. While macroscopic hydrogels have been known and used, mainly in medicine, since the 1960s [17; 18; 19; 20; 21; 22; 23; 24; 25; 26], nanogels are relatively new materials; interest in their synthesis and applications has risen rapidly in parallel with the developments in nanomedicine, controlled drug delivery, gene therapy, and targeted radiopharmaceuticals [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. While there are many methods to synthesize nanogels, those allowing controlled direct generation of many free radicals on macromolecules in solution seem to be very attractive. Pulses of ionizing radiation applied to aqueous polymer solutions are used to generate, in an instant, a known average number of radicals on each chain in a system that is free of any additives (initiators, monomers, crosslinking agents, surfactants), making this procedure particularly suitable to obtain nanogels for medical applications [15; 28; 39; 40; 41; 42; 43; 44]. In this work we use this approach to generate free radicals on polymer chains and study the kinetics of their recombination. Our aim is to learn about the kinetic features of these reactions, including its classical or non-classical character, to see how kinetics are influenced by various parameters, to learn how we can kinetically differentiate the intra- and intermolecular recombination, as well as to provide some hints as to the nature of the rate-determining step of intermolecular recombination of polymer radicals.