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Plastics melt on heating and Cotton burns.

When do substances burn with flame? Should they always contain volatile compounds for them to create the Flame?

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Your generalisation about plastics is too simple. And volatile components are not required for flames to exist.

Many plastics don't burn at all easily. Bakelite, many epoxy resins or kevlar, for example, neither burn easily or melt. PVC melts but doesn't easily burn. Polyethylene and polystyrene both melt and burn.

Flames are created by gas-phase oxidation reactions (at least in air, even more things will burn in fluorine but you don't see that happening very often as not many labs or kitchens have access to fluorine). But plenty of things containing no volatile components can be made to burn with flames.

Coke or charcoal, for example, are mostly carbon but can be burned and, when burning, will have flames. But those flames are not made by volatilising components of the substance but consist of the burning of partial oxidation products (often carbon monoxide) created by surface reactions on the solid. The purer the carbon the fewer the number of volatile components but once the reaction has started, there is enough energy to keep the solid reacting directly with oxygen to generate gaseous volatiles like CO.

Candles, unlike coal, are made from mixtures of long chain hydrocarbons. These can be volatilised by moderate heat and will then burn in air as gases. This is why candles are easy to light compared to coal and also why they contain a wick which both starts the reaction and acts to wick the liquified hydrocarbons into the hotter zones of the flame where they can be vaporised and burned.

So while flames require volatile components, they can come from partial reactions in the substance and don't have to be present before the fire starts.

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Burning is the result of a redox reaction between some sort of fuel source and oxygen in the air. Since cotton is a loosely packed substance, there is a lot of surface area for oxygen to react with it. In addition, cotton is mostly made up of cellulose, a compound that readily burns at low temperatures. On the other hand, plastics are made up of large hydrocarbons. Hydrocarbons are fuel sources; however, larger hydrocarbons require more energy to start combustion. Plastic should burn exothermically, but the energy required to start the process is too large for it to be ignited by a flame.

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