The optimal reaction conditions for synthesizing polyethylene oxide PEO with a high molecular weight and low polydispersity index from ethylene oxide monomer are as follows:1. Temperature: The optimal temperature for synthesizing PEO is in the range of 40-60C. Lower temperatures can slow down the reaction rate, while higher temperatures can cause side reactions and chain termination, leading to lower molecular weight and higher polydispersity index.2. Pressure: The pressure should be maintained at a moderate level, typically around 1-5 atm. Higher pressures can increase the reaction rate, but may also lead to side reactions and chain termination.3. Catalyst: The choice of catalyst is crucial for controlling the molecular weight and polydispersity index of PEO. Anionic catalysts, such as potassium alkoxides e.g., potassium tert-butoxide , are commonly used for this purpose. These catalysts provide good control over the polymerization process, resulting in high molecular weight PEO with low polydispersity index. Additionally, the use of controlled/living polymerization techniques, such as reversible addition-fragmentation chain transfer RAFT polymerization or atom transfer radical polymerization ATRP , can further improve the control over molecular weight and polydispersity index.In summary, to synthesize high molecular weight PEO with low polydispersity index from ethylene oxide monomer, the reaction should be carried out at a temperature of 40-60C, a pressure of 1-5 atm, and using anionic catalysts like potassium alkoxides or controlled/living polymerization techniques.