The optimal temperature and pressure for the efficient synthesis of polyethylene oxide PEO from ethylene oxide EO monomer depend on the catalyst and reaction conditions used. Generally, the polymerization of EO is carried out using anionic or cationic catalysts.For anionic polymerization, the typical temperature range is between 20C to 60C, while the pressure is maintained at atmospheric pressure or slightly above. The use of a higher temperature can lead to a faster reaction rate, but it may also result in a lower molecular weight of the resulting PEO.For cationic polymerization, the temperature range is usually between 0C to 40C, and the pressure is maintained at atmospheric pressure or slightly above. Lower temperatures are preferred in this case to minimize side reactions and achieve a higher molecular weight PEO.The yield and molecular weight of the resulting PEO are influenced by the temperature and pressure conditions, as well as the catalyst concentration, reaction time, and monomer-to-catalyst ratio. Higher temperatures generally lead to faster reaction rates, but they can also cause side reactions and lower molecular weight PEO. Lower temperatures can result in higher molecular weight PEO, but the reaction rate may be slower.Pressure has a less significant effect on the polymerization process, but maintaining a slightly elevated pressure can help ensure that the ethylene oxide monomer remains in the liquid phase, which is necessary for the polymerization to occur.In summary, the optimal temperature and pressure for the efficient synthesis of PEO from EO monomer depend on the specific catalyst and reaction conditions used. Generally, a temperature range of 0C to 60C and atmospheric pressure or slightly above are used to achieve a balance between reaction rate, yield, and molecular weight of the resulting polymer.