Scaling Analysis of Polymer Dynamics

  • Wenbing HuEmail author


In dilute solutions, diffusion of a single chain can be described by a non-draining mode of the coil. In the concentrated bulk phase, diffusion of a short chain can be described by a free-draining mode of the bead-spring Rouse chain, while diffusion of a long chain can be described by the tube model for a Rouse chain reptating along the primitive path. Scaling analysis is a powerful tool to learn their characteristic dynamics in various time scales.


Brownian Motion Hydrodynamic Interaction Polymer Coil Simple Fluid Ideal Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Colby R, Fetters LJ, Graessley WW (1987) Melt viscosity - molecular weight relationship for linear polymers. Macromolecules 20:2226–2237CrossRefGoogle Scholar
  2. De Gennes PG (1971) Reptation of a polymer chain in a presence of fixed obstacles. J Chem Phys 55:572–579CrossRefGoogle Scholar
  3. Des Cloizeaux J, Jannink G (1990) Polymers in solution: their modelling and structure. Oxford University Press, OxfordGoogle Scholar
  4. Doi M (1983) Explanation for the 3.4 power-law for viscosity of polymeric liquids on the basis of the tube model. J Polym Sci Polym Phys 21:667–684Google Scholar
  5. Edwards SF (1967) The statistical mechanics of polymerized material. Proc Phys Soc 92:9–13CrossRefGoogle Scholar
  6. Einstein A (1905) Investigations on the theory of the Brownian movement. Ann Phys (Leipzig) 17:549–560Google Scholar
  7. Einstein A (1911) Eine neue Bestimmung der Molekuldimensionen. Ann Phys (Leipzig) 34:591–592Google Scholar
  8. Fox TG, Flory PJ (1948) Viscosity-molecular weight and viscosity- temperature relationships for polystyrene and polyisobutylene. J Am Chem Soc 70:2384–2395CrossRefGoogle Scholar
  9. Frischknecht AL, Milner ST (2000) Diffusion with contour length fluctuations in linear polymer melts. Macromolecules 33:5273–5277CrossRefGoogle Scholar
  10. Graessley WW (1982) Entangled linear, branched and network polymer systems-molecular theories. Adv Polym Sci 47:67–117CrossRefGoogle Scholar
  11. Houwink R (1940) Relation between the polymerization degree determined by osmotic and viscometric methods. J Prakt Chem 157:15–18CrossRefGoogle Scholar
  12. Kirkwood JG, Riseman J (1948) The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J Chem Phys 16:565–573CrossRefGoogle Scholar
  13. Kuhn W (1934) Fadenformiger Molekule in Losungen. Kolloid-Z 68:2–15CrossRefGoogle Scholar
  14. Liu CY, Keunings R, Bailly C (2006) Do deviations from reptation scaling of entangled polymer melts result from single or many chain effects? Phys Rev Lett 97:246001CrossRefGoogle Scholar
  15. Mark H (1938) Über die entstehung und eigenschaften hochpolymerer festkörper. In: Sänger R (ed) Der feste Körper. Hirzel, Leipzig, pp 65–104Google Scholar
  16. McLeish TCB (2002) Tube theory of entangled polymer dynamics. Adv Phys 51:1379–1527CrossRefGoogle Scholar
  17. Milner ST, McLeish TCB (1997) Parameter-free theory for stress relaxation in star polymer melts. Macromolecules 30:2159–2166CrossRefGoogle Scholar
  18. Nyquist H (1928) Thermal agitation of electric charge in conductors. Phys Rev 32:110–113CrossRefGoogle Scholar
  19. Rouse PE (1953) A theory of the linear viscoelastic properties of dilute solution of coiling polymers. J Chem Phys 21:1273–1280CrossRefGoogle Scholar
  20. Sperling LH (2006) Introduction to physical polymer science, 4th edn. Wiley, New York, p 526Google Scholar
  21. Staudinger H, Nodzu R (1930) Über hochpolymere Verbindungen, 36. Mitteil: Viscositäts-Untersuchungen an Paraffin-Lösungen. Berichte der Deutschen Chemischen Gesellschaft 63:721–724CrossRefGoogle Scholar
  22. Stokes GG (1851) On the effect of the internal friction of fluids on the motion of pendulums. Trans Camb Phil Soc 9(Pt. II):8–106Google Scholar
  23. Zimm BH (1956) Dynamics of polymer molecules in dilute solution: viscoelasticity. J Chem Phys 24:269–278CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Department of Polymer Science and Engineering School of Chemistry and Chemical EngineeringNanjing UniversityNanjingChina, People’s Republic

Personalised recommendations