Alan D.Sokal
Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution:
A Reexamination
(178K, ps)
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 $x \equiv N^\phi (T-T_\theta)$ 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.]