Predicting the Tube Diameter in Melts and Solutions

A simple conjecture relating chain dimensions to the “tube diameter”, which represents the topological confining effect of entanglements on a chain, works well for all flexible entangled polymer melts. I extend this conjecture to semidilute solutions: first for ϑ solvents, where it is shown to be equivalent to the Colby−Rubinstein scaling picture, and then for good solvents. In the latter case, it turns out that the number of “blobs” per entanglement strand B is not a constant as had been previously assumed, but depends on the ratio of the packing length to the swelling length. This unified picture is consistent with existing data on semidilute solutions.