The optimized temperature and reaction conditions for the synthesis of polystyrene from styrene monomers using free radical polymerization are as follows:1. Temperature: The optimal temperature for the polymerization of styrene is typically in the range of 60-120C. The exact temperature depends on the initiator used and the desired molecular weight of the polystyrene. Higher temperatures can lead to faster reaction rates, but may also result in shorter polymer chains due to increased termination reactions.2. Initiator: Free radical initiators such as benzoyl peroxide BPO , azobisisobutyronitrile AIBN , or 2,2'-azobis 2-methylpropionitrile AMBN are commonly used for the polymerization of styrene. The initiator concentration should be optimized to achieve the desired molecular weight and reaction rate. A typical initiator concentration is in the range of 0.1-1 wt% relative to the styrene monomer.3. Solvent: The polymerization of styrene can be carried out in bulk without solvent , in solution, or in an emulsion. Bulk polymerization is the simplest method, but it can lead to high reaction temperatures and poor heat transfer. Solution polymerization allows for better heat transfer and control of the reaction, but requires a suitable solvent such as toluene or ethylbenzene. Emulsion polymerization is used to produce polystyrene latex particles and requires the use of surfactants and water as the continuous phase.4. Reaction atmosphere: The polymerization should be carried out under an inert atmosphere e.g., nitrogen or argon to prevent the formation of side products due to the reaction of styrene or the initiator with oxygen.5. Reaction time: The reaction time depends on the desired molecular weight and conversion of styrene monomers. Typically, the reaction is allowed to proceed until a high conversion >90% is achieved, which can take several hours to days, depending on the reaction conditions.6. Termination: The reaction can be terminated by cooling the reaction mixture to room temperature and exposing it to air, which quenches the free radicals. Alternatively, a radical scavenger such as hydroquinone or butylated hydroxytoluene BHT can be added to terminate the reaction.In summary, the optimal conditions for the synthesis of polystyrene from styrene monomers using free radical polymerization depend on the specific initiator, temperature, solvent if used , and reaction time. These parameters should be optimized to achieve the desired molecular weight, conversion, and reaction rate.