To synthesize high molecular weight polyacrylamide, you can follow these general steps:

1. Acquire the necessary materials: You will need acrylamide monomer, a crosslinker (e.g., N,N'-methylenebisacrylamide), a free radical initiator (e.g., ammonium persulfate), a buffer solution, and a polymerization vessel.

2. Prepare the polymerization vessel: Clean the vessel thoroughly to ensure no contaminants are present. Make sure the vessel is dry before use.

3. Prepare the monomer solution: Dissolve the desired amount of acrylamide monomer along with the crosslinker (if needed) in an appropriate solvent. Common solvents include distilled water or a mixture of water and a small amount of electrolyte (such as a sodium phosphate buffer).

4. Add a free radical initiator: Dissolve the free radical initiator (e.g., ammonium persulfate) in a small amount of solvent and add it to the monomer solution. The initiator will initiate the polymerization reaction.

5. Initiate the polymerization reaction: Mix the solution thoroughly to ensure a homogenous mixture, then seal the vessel to prevent evaporation. Place the vessel in a temperature-controlled heating device (e.g., an oven or water bath) at a specific temperature based on the desired reaction rate.

6. Allow the polymerization to proceed: Leave the vessel undisturbed for a specific period to allow the polymerization reaction to occur. The reaction time can vary depending on the desired molecular weight and reaction conditions.

7. Quench the reaction: After the desired reaction time, stop the polymerization by adding a terminating agent such as urea or ammonium thiocyanate. This will deactivate any remaining free radicals and halt the polymerization process.

8. Purify the polyacrylamide: Remove the polyacrylamide gel from the vessel and wash it with a suitable solvent (e.g., water or alcohol) to remove any impurities or unreacted monomers. Repeat the washing process multiple times.

9. Dry and store the polyacrylamide: Dry the purified polyacrylamide thoroughly, either by air-drying or using a drying oven. Store the polymer in a cool and dry place to prevent degradation.

It is important to note that the synthesis of polyacrylamide requires careful handling due to the potential hazards associated with acrylamide monomer, which is toxic and a potential skin sensitizer. Always follow appropriate safety precautions, including wearing appropriate personal protective equipment (PPE), working in a well-ventilated area, and following specific guidelines and regulations established by your institution or supplier.