Derivation of the Universal Scaling Equation of the Hydrodynamic Scaling Model via Renormalization Group Analysis

The Altenberger−Dahler positive-function renormalization group (PFRG) method is shown to yield the universal scaling equation D s = D o exp(−αc ν) of the hydrodynamic scaling model for polymer self-diffusion. Here D o is the bare polymer self-diffusion coefficient at some low concentration, c is the...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Macromolecules 1998-04, Vol.31 (7), p.2317-2327
1. Verfasser: Phillies, George D. J
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The Altenberger−Dahler positive-function renormalization group (PFRG) method is shown to yield the universal scaling equation D s = D o exp(−αc ν) of the hydrodynamic scaling model for polymer self-diffusion. Here D o is the bare polymer self-diffusion coefficient at some low concentration, c is the (potentially high) polymer concentration, and ν and α are a scaling coefficient and scaling prefactor, respectively. To integrate the Lie equations of motion of the PFRG and obtain the universal scaling equation, the Kirkwood−Risemann model for polymer hydrodynamics is extended analytically to determine leading terms of the chain−chain and (for the first time) chain−chain−chain translation−translation hydrodynamic interaction tensors , , , , and , as well as many of their translational−rotational and rotational−rotational analogues.
ISSN:0024-9297
1520-5835
DOI:10.1021/ma971116r