How do diesel-fuel ignition improvers work?

An important descriptor of diesel fuel is its Cetane Number: this is an indicator of the time delay between injection and spontaneous ignition of fuel in a standard diesel engine running under specified conditions; the shorter the ignition delay, the higher the cetane number. Thus, those groupings of atoms within a hydrocarbon molecule that are beneficial in conferring a resistance to spontaneous ignition in a gasoline, i.e. a high octane number, are undesirable when they occur in a diesel fuel, and vice versa. The cetane number scale uses two standard compounds, cetane (n-hexadecane) defined as 100, and heptamethyl-nonane defined as 15, so that, assuming linear mixing, a 1:1 mixture would have a cetane number of 57.5, a 1:2 mixture would have one of 43.3, &c. Long-chain paraffins tend to have high cetane numbers, e.g. n-dodecane = 80, n-tridecane = 83, in addition to cetane itself = 100. On the other hand, hydrocarbons containing benzene rings tend to have very low cetane numbers, e.g. diphenyl = 21, diphenylmethane = 11 and 1,2-diphenyl-ethane = 1. Extremely low cetane numbers are also found for hydrocarbons with a benzene ring carrying short-chain substituents, e.g. xylene = –10 and m-di-iso-propyl-benzene = –12, but as the side chain becomes longer, the cetane number rises, to 26 for n-hexyl-benzene and to 50 for n-nonyl-benzene. Substances containing fused rings also exhibit very low cetane numbers, e.g. α-methyl-naphthalene = 0. A corollary is that the minimum spontaneous ignition temperatures for aromatic hydrocarbons are higher than for non-aromatics. Legislated National Standards usually require that the cetane number of commercial diesel fuel shall exceed a certain value, say 40. Most diesel engines do not perform well with fuels of cetane number below this: for