Statistics of a single polymer chain*

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Abstract
Computer simulation and small-angle-x-ray scattering techniques have been used to study chain statistics in dilute solution. Monte Carlo techniques were used to probe the properties of short sequences within a polymer chain of 300 units whose monomers interact with a square well potential. These results show that above the theta point internal sequences are swollen compared to an isolated chain of the same degree of polymerization. Application of simple perturbation theory shows that this effect arises from interaction with monomers external to the sequence. The structure factor was also obtained from these Monte Carlo calculations and no evidence for crossover as predicted from “thermal blob” theory was observed. Dilute solutions of polystyrene in cyclopentane were studied by low angle x-ray scattering as a function of temperature, from the theta point into the good solvent regime. Like the Monte Carlo results, the experimental structure factor showed no evidence of crossover. In both cases the structure factor showed power law dependence on the scattering vector with an exponent which varied continuously from approximately -2 at the theta point to −5/3 in the good solvent regime.