Abstract
We discuss the asymptotic high--molecular-weight behavior of flexible, weakly repulsive polymer chains in melts, both through an analogy to an O(n) model of magnets and directly. We show that such polymers are slightly expanded in two dimensions so that in the limit of very high molecular weight, polymers interpenetrate strongly and the fraction of the monomers belonging to a polymer within the radius of gyration of that polymer tends to zero logarithmically. The molecular-weight or length-scale dependence of the radius of gyration, osmotic pressure, and end-end scattering function is given. The range of parameters for which this behavior is expected is discussed.
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