The synthesis of polystyrene from styrene monomer typically occurs through a process called free radical polymerization. Here is the step-by-step mechanism for this process:1. Initiation: A free radical initiator, such as benzoyl peroxide or azobisisobutyronitrile AIBN , is added to the styrene monomer. The initiator undergoes thermal decomposition, producing free radicals that can react with the styrene monomer.2. Propagation: The free radical reacts with the double bond of the styrene monomer, forming a new radical. This new radical can then react with another styrene monomer, creating a longer chain with a radical at the end. This process continues, with the chain growing in length as more styrene monomers are added.3. Termination: The polymerization reaction can be terminated in several ways, such as when two radicals react with each other, forming a stable covalent bond, or when a radical reacts with an inhibitor or a chain transfer agent.Several factors can affect the yield and quality of the resulting polystyrene:1. Temperature: The reaction rate and the degree of polymerization are both temperature-dependent. Higher temperatures can increase the reaction rate but may also lead to more side reactions and a lower molecular weight of the polymer.2. Concentration of initiator: The concentration of the initiator can affect the number of polymer chains formed and the overall reaction rate. A higher concentration of initiator can lead to a higher reaction rate but may result in shorter polymer chains.3. Reaction time: The longer the reaction time, the higher the degree of polymerization and the molecular weight of the resulting polystyrene. However, excessively long reaction times can lead to degradation of the polymer.4. Presence of impurities: Impurities in the styrene monomer or the initiator can lead to side reactions or chain transfer reactions, affecting the molecular weight and quality of the polystyrene.5. Polymerization method: Different polymerization methods, such as bulk, solution, suspension, or emulsion polymerization, can affect the yield and quality of the polystyrene. Each method has its advantages and disadvantages, and the choice of method depends on the desired properties of the final product.By carefully controlling these factors, chemists can optimize the yield and quality of the resulting polystyrene.