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Structure of polymers, fully strechted or coiled?

In the context of structure-property relationships, one can treat the structure of polymer molecules with flexible bonds. If the bonds are flexible, then the orientation of the segments of a polymer is random. In this case, the random walk (RW) model is useful for simulation. The RW represents a sequence of N displacements in a random direction. For the simulation of a configuration of a polymer molecule, each move corresponds to a segment of the molecule. As a measure for the shape of the polymer is the mean square end-to-end distance <R2>.

polymer configuration

Already through the haptic simulation the students arrive at the relationship <R2>=N, which corresponds to a coiled structure rather than an elongated molecule. Further applications of such simulations are the behavior in constrained geometry as well as for rubber elasticity.

confined polymer