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

Alan D. Sokal
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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) $N \to\infty$, $T \to T_θ$ with $x \equiv N^ϕ(T-T_θ)$ 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.]

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Alan D. Sokal. 1993-05-08. Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution: A Reexamination. https://doi.org/10.1209/0295-5075%2F27%2F9%2F005%2010.1209%2F0295-5075%2F30%2F2%2F011

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