The optimal catalyst for the polymerization of styrene monomer to produce high molecular weight polystyrene with controlled molecular weight distribution and low polydispersity index PDI is a combination of a well-defined initiator and a controlled/living polymerization technique. One of the most effective methods for achieving this is Atom Transfer Radical Polymerization ATRP .In ATRP, a transition metal complex usually copper-based is used as the catalyst, and an alkyl halide is used as the initiator. The most common catalyst system for styrene polymerization is a combination of copper I bromide CuBr and a nitrogen-based ligand, such as 2,2'-bipyridine bpy or tris 2-pyridylmethyl amine TPMA .The reaction conditions for ATRP of styrene are as follows:1. Temperature: The optimal temperature for styrene polymerization using ATRP is typically between 60-110C. Higher temperatures can increase the rate of polymerization, but may also lead to side reactions and loss of control over molecular weight distribution.2. Solvent: A suitable solvent for styrene polymerization should be non-polar or slightly polar, such as toluene, dimethylformamide DMF , or dimethyl sulfoxide DMSO . The solvent should also be compatible with the catalyst system and not interfere with the polymerization process.3. Monomer-to-initiator ratio: The ratio of styrene monomer to initiator should be carefully controlled to achieve the desired molecular weight and PDI. A higher monomer-to-initiator ratio will result in higher molecular weight polymers, while a lower ratio will produce polymers with lower molecular weight.4. Catalyst concentration: The concentration of the catalyst should be optimized to ensure efficient initiation and propagation of the polymerization reaction while minimizing side reactions and catalyst deactivation.5. Reaction time: The polymerization reaction should be allowed to proceed until the desired conversion of styrene monomer is achieved. The reaction time will depend on the specific reaction conditions and catalyst system used.By carefully controlling these reaction conditions and using a well-defined ATRP catalyst system, it is possible to produce high molecular weight polystyrene with a controlled molecular weight distribution and low polydispersity index.