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Polyalkylenimines (PAIs) are a class of cationic polymer that have a generalized structure with secondary or tertiary amines in the main chain separated by alkylene spacers. Owing to the presence of the nucleophilic amine groups in the polymer backbone, their synthesis is more complicated compared to simpler vinyl-based polymers. This chapter will cover the synthesis of PAIs, their physical properties and a short review of applications, focusing on gene delivery. The chapter will only cover PAI homopolymers and excludes the convoluted area of block copolymers, as this is worth a full review by itself.

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