Explain the concept of 'atom economy' in green polymer synthesis.

Atom economy is a concept in green chemistry that refers to the efficiency of a chemical reaction in terms of how many of the starting atoms are incorporated into the desired product. It is defined as the ratio of the molecular weight of the desired product to the sum of the molecular weights of all reactants, expressed as a percentage. A reaction with high atom economy is one where most of the atoms from the reactants end up in the product, minimizing the amount of waste generated. In the context of green polymer synthesis, atom economy is a crucial consideration for reducing the environmental impact of polymer production. Polymerization reactions that have high atom economy are preferred, as they minimize the generation of byproducts and waste materials. For example, addition polymerization reactions, where monomers directly add to each other to form a polymer without the loss of any atoms, typically have high atom economy. Ring-opening polymerization (ROP) also often exhibits high atom economy if the ring-opening process incorporates all the atoms of the cyclic monomer into the polymer chain. Condensation polymerization reactions, on the other hand, often have lower atom economy because they involve the elimination of small molecules, such as water or alcohols, as byproducts. These byproducts represent wasted atoms and reduce the overall efficiency of the reaction. Therefore, when designing green polymer syntheses, chemists aim to maximize atom economy by selecting reactions and catalysts that minimize waste generation and maximize the incorporation of starting materials into the desired polymer product.