A molecular approach to chain entanglement in linear polymers

The phenomenon of chain entanglement in undiluted linear amorphous polymers is treated by calculating the probability of forming closed intramolecular loops. Adoption of the rotational isomeric state model of polymer chains permits an appropriate accounting of the detailed molecular structure to be made through the configurational characteristics of the polymer. The second (〈r〉₀) and fourth (〈r〉₀) moments of the vector r_hk connecting groups h and k in the isolated polymer chain and averaged over all chain conformations are calculated and used to evaluate the probability W_x(0) that r_hk is 0, or that an intramolecular loop of x = k ? h bonds is formed. Several linear polymers with widely differing molecular structures are treated. An attempt is made to correlate the degree of chain entanglement they manifest in the bulk with their ability to fold back upon themselves to form closed intramolecular loops.