Conformational end effects in unperturbed chains and star-branched polymers

End effects in unperturbed chains with a specified number of bonds, n, have previously been characterized using the conformations at individual bonds and the mean square unperturbed dimensions of subchains situated at various positions along the chain. Both criteria have found that the end effects are extremely weak in typical flexible chains, such as unperturbed polyethylene. Of course, these criteria detect no end effect at all in a freely jointed chain. This conclusion requires modification if the end effects are defined differently, using the mean square radius of gyration of the n+1 chain atoms about chain atom i, denoted 〈 s i 2 〉 0 . The values of 〈 s i 2 〉 0 depend on i in all chains, including the freely jointed chain. The range for the volume specified by 〈 s i 2 〉 0 3 / 2 suggests that the average density of chain segments about a terminal atom is roughly 1/3 of the average density of chain segments about the atom midway along the contour of any long unperturbed chain. The severity of these end effects in finite chains depends on the detailed local structure, becoming more severe for more extended chains. The end effect detected by 〈 s i 2 〉 0 in regular freely jointed star-branched polymers becomes more severe as the number of branches increases.