Crossover approach to scaling behavior in dilute polymer solutions: Theoryand simulation

We develop a crossover theory for dilute polymer solutions, analogous to cr ossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N* is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predi ctions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain len gths. Various properties of these chains were analyzed, including the end-t o-end distance distribution and mean-square radius of gyration. We find tha t the approach to the asymptotic scaling regime displays two types of cross over behavior, depending on the value of the model parameter (u) over bar, which is a measure of the strength of the monomer-monomer excluded volume i nteraction: (i) (u) over bar < 1 and (ii) (u) over bar > 1. In case (i), th e systemexhibits crossover from a Gaussian chain to the Kuhnian chain, as t he degree of polymerization increases. In case (ii), the system exhibits cr ossover from the rigid rod to a Kuhnian chain. Our crossover theory is foun d to work well for polymers with (u) over bar > 1 only near the asymptotic scaling regime. However, for (u) over bar, the theory works well in all reg imes. [S0021-9606(99)50505- 9].