Polyacrylamide (PAM) can be prepared via different methods, depending on the desired application and the desired properties of the polymer. Here are two common methods for the preparation of polyacrylamide:

1. Free Radical Polymerization:

   - Monomer Selection: Acrylamide (CH2=CHCONH2) is typically used as the main monomer for polyacrylamide synthesis.

   - Initiator Selection: Free radical initiators, such as ammonium persulfate (APS) or potassium persulfate (KPS), are commonly used to initiate the polymerization reaction.

   - Crosslinking Agent (Optional): If a crosslinked polyacrylamide hydrogel is desired, a crosslinking agent such as N,N'-methylenebisacrylamide (BIS) can be added to the monomer solution in a controlled amount.

   - Polymerization Process: Typically, the monomer, initiator, and crosslinking agent (if applicable) are dissolved in an appropriate solvent, such as water, and then subjected to polymerization. This can be done by heating the solution under controlled conditions or by using a suitable catalyst.

   - Purification and Drying: After the polymerization is complete, the resulting polyacrylamide can be purified and dried to obtain the final product.

2. Solution Polymerization:

   - Monomer Dissolution: Acrylamide monomer is dissolved in a suitable solvent, such as water, to form a monomer solution.

   - Initiator Addition: An initiator, such as APS or KPS, is added to the monomer solution.

   - Polymerization Process: The monomer solution is then heated under controlled conditions to initiate the polymerization reaction. This typically involves maintaining the temperature at a specific range for a certain duration.

   - Purification and Drying: The resulting polyacrylamide solution is often subjected to purification steps, such as filtration or precipitation, to remove impurities. Finally, the purified polyacrylamide can be dried to obtain the desired product.

Both of these methods can be used to prepare linear or crosslinked polyacrylamide depending on the specific requirements of the application. It is important to note that handling acrylamide and its monomers should be done with caution, as it is a toxic compound. Proper safety measures and guidelines must be followed during the process.