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My understanding of knocking is that in a spark ignition engine as the fuel is being compressed it heats up. The heat causes some of the oxygen to break up into oxygen radicals the $\ce{O^.}$ radicals react with the fuel grabbing parts of the fuel and creating radicals. These radicals react with molecular Oxygen thus releasing oxygen radicals to go on and continue the chain reaction.

I can understand how adding ethanol to fuel would fix this as $\ce{O^. + H3CCH2OH → H2O + H3CCHO}$ would mop up the oxygen radicals. But how does tetraethyl lead fix this?

Or is my understanding of knocking and cold flame just wrong?

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Engine combustion reactions are complex but Tetraethyl Lead (TEL) slows thermal combustion

It is important to understand what causes knocking in internal combustion engines. In diesel engines the heat cause by compression is what ignites the fuel. They typically use linear hydrocarbon fuels as they are more likely to auto-combust under compression. Petrol (gasoline) engines are designed differently and the combustion is initiated by a spark. Combustion initiated by compression or heat is undesirable as the engine no longer controls when the ignition happens. Typical fuels contain more branched chain, aromatics and unsaturated hydrocarbons. If early combustion does happen it can damage the engine and is called "knocking".

The important issue with all antiknock agents is to inhibit early combustion caused by compression and heat. And this is exactly what TEL has been observed to do.

And it wasn't discovered from theory. It was found to work by experimenting with a large variety of alternatives (and, unfortunately, economics, not safety, dominated the choice over other possibilities).

But what is the mechanism? This is harder to determine as there are a large variety of radical reactions possible in air/fuel mixtures. It isn't likely that the key step is the production of oxygen radicals (dioxygen is already a diradical under normal atmospheric conditions). But it is reasonable to assume that highly reactive hydrocarbon radicals play a part (the radicals produced from the linear hydrocarbons in diesel fuel would be more reactive than those from petrol/gasoline fuel). And it is also reasonable that TEL would "mop up" some of the potential radicals produced from heat and compression in a standard spark engine. Inhibiting these, even to a small extent, seems to be enough to reduce the propagation speed of those unwanted early side reactions so that knocking does not initiate early combustion.

BTW, though ethanol does work, it takes about 10% of it in the fuel. Better keep that for drinking and develop other, better and non-toxic, agents.

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