Fig. 14

The partition function for polymer position (Z) calculated from the number of positions a polymer can occupy for a given length of polymer (s), number of chain ends (N = 2), and types of vertices (\(\sigma_{p}\)). \(\sigma_{p}\) is proportional to the number of ways the segment vertices can flex. A No flexible vertices, therefore the partition function is only proportional to the number of chain ends to the power of the chain end vertex constant (\(\sigma_{1}\)), or \(Z \sim N^{{2\sigma_{1} }}\). B There are 2 chain ends and a vertex with 4 possible configurations, or \(Z \sim N^{{2\sigma_{1} }} s^{{ \sigma_{4} + 2\sigma_{1} }}\). C There are 2 chain ends and a vertex with 6 possible configurations, or \(Z \sim N^{{2\sigma_{1} }} s^{{ \sigma_{6} + 2\sigma_{1} }}\). From reference [81]