Static scaling behavior of high-molecular-weight polymers in dilute solution: A reexamination

Previous theories of dilute polymer solutions have failed to distinguish clearly between two very different ways of taking the long-chain limit: I) N?8 at fixed temperature T, and II) N?8, T?T _? with x=N ^? (T?T _?) fixed, where ? is a suitable crossover exponent. I argue that the modern two-parameters theory (continuum Edwards model) applies to case II–not case I–and in fact gives exactly the crossover scaling functions for x? 0 modulo two nonuniversal scale factors. A Wilson-type renormalization group clarifies the connection between crossover scaling functions and continuum field theories.