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.]

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

Cited by in corpus (17)

• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• Nonperturbative renormalization group approach to frustrated magnets
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• Monte Carlo Methods for the Self-Avoiding Walk
• Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model
• Classical-to-critical crossovers from field theory
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Crossover scaling from classical to nonclassical critical behavior
• Crossover behavior in three-dimensional dilute spin systems
• Four-dimensional polymer collapse II: Pseudo-First-Order Transition in Interacting Self-avoiding Walks
• Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
• Two-parameter model predictions and theta-point crossover for linear-polymer solutions
• Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
• Hyperscaling for polymer rings
• Consistent coarse-graining strategy for polymer solutions in the thermal crossover from Good to Theta solvent
• Pseudo-First-Order Transition in Interacting Self-avoiding Walks and Trails
• Corrections to scaling in multicomponent polymer solutions