Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution: A Reexamination

Abstract

Previous theories of dilute polymer solutions have failed to distinguish clearly between two very different ways of taking the long-chain limit: (I) $N\to \infty$ at fixed temperature $T$, and (II) $N\to \infty$, $T\to T_{\theta }$ with $x\equiv N^{\varphi }(T-T_{\theta })$ fixed. I argue that the modern two-parameter theory (continuum Edwards model) applies to case II --- not case I --- and in fact gives exactly the crossover scaling functions for $x\ge 0$ modulo two nonuniversal scale factors. A Wilson-type renormalization group clarifies the connection between crossover scaling functions and continuum field theories. [Also contains a general discussion of the connection between the Wilson and field-theoretic renormalization groups. Comments solicited.]

Comments: 10 pages including 1 figure, 181159 bytes Postscript (NYU-TH-93/05/01)