Polyethyleneimine is a cationic polymer of repeating amine units, available as a linear or a branched architecture. The branched form carries primary, secondary, and tertiary amines, and it is this mixture that gives a high charge density over a wide pH range [1]. The positive charges condense DNA and RNA into nanoparticles, which is why the polymer is one of the most studied non-viral transfection agents [2]. The same charge density makes it cytotoxic and causes it to bind serum proteins, so the high-molecular-weight forms are usually modified by grafting poly(ethylene glycol) or by reducing the molar mass [3]. Immobilised on a support, the polymer chelates heavy metal ions and captures carbon dioxide, and it also serves to modify membrane surfaces [4]. The transfection efficiency and the cytotoxicity both rise with molar mass, and separating the two has not been achieved [5].