In a polymerization reaction involving a free radical initiator, how would an increase in the degree of polymerization affect the thermal stability and mechanical properties of the resulting polymer chain, particularly in the context of addition polymerization?

A higher degree of polymerization means the chains are longer and have fewer chain‑ends per unit mass, so the polymer contains more covalent bonds that must be broken for decomposition, which raises its thermal stability. The same longer chains give the material a higher modulus and tensile strength because the load is distributed over a larger number of bonds, but they also make the polymer more brittle because there are fewer chain ends to absorb energy. In addition polymerization, for example, a poly(methyl methacrylate) sample with an average chain length of 200 monomer units will melt at a higher temperature and be tougher than one with only 50 units, yet it may crack more easily under impact. Thus, increasing the degree of polymerization generally improves heat resistance and stiffness while potentially reducing toughness.