The Rouse model is frequently used in
polymer physics Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation and polymerisation of polymers and monomers respectively.P. Flory, ''Principles of ...
.
The Rouse model describes the conformational dynamics of an ideal chain. In this model, the single chain diffusion is represented by
Brownian motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).
This pattern of motion typically consists of random fluctuations in a particle's position insi ...
of beads connected by harmonic springs. There are no
excluded volume The concept of excluded volume was introduced by Werner Kuhn in 1934 and applied to polymer molecules shortly thereafter by Paul Flory. Excluded volume gives rise to depletion forces.
In liquid state theory
In liquid state theory, the 'exclude ...
interactions between the beads and each bead is subjected to a random thermal force and a drag force as in
Langevin dynamics
In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems. It was originally developed by French physicist Paul Langevin. The approach is characterized by the use of simplified models while acco ...
. This model was proposed by
Prince E. Rouse in 1953. The mathematical formalism of the dynamics of Rouse model is described here.
An important extension to include hydrodynamic interactions mediated by the solvent between different parts of the chain was worked out by
Bruno Zimm in 1956.
[
Bruno H. Zimm, ''Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss'', J. Chem. Phys. 24, 269 (1956).] Whilst the Rouse model applies to polymer melts, the
Zimm model Zimm may refer to:
* Bruno H. Zimm (1920–2005), American polymer chemist and DNA researcher
* Bruno Louis Zimm (1867-1943) American sculptor
* Maurice Zimm (1909–2005), American radio, television and film writer
* ZentralInstitut für Mathema ...
applies to polymer in solution where the hydrodynamic interaction is not screened.
In solution, the Rouse-Zimm model predicts ''D~1/N
ν'' which is consistent with the experiments.
In a polymer melt, the Rouse model correctly predicts long-time diffusion only for chains shorter than the entanglement length. For long chains with noticeable
entanglement, the Rouse model holds only up to a crossover time τ
e. For longer times the chain can only move within a tube formed by the surrounding chains. This slow motion is usually approximated by the
reptation
A peculiarity of thermal motion of very long linear macromolecules in ''entangled'' polymer melts or concentrated polymer solutions is reptation. Derived from the word reptile, reptation suggests the movement of entangled polymer chains as bein ...
model.
[{{Cite book, last=Doi, first=M., url=https://www.worldcat.org/oclc/59185784, title=The theory of polymer dynamics, date=1986, others=S. F. Edwards, isbn=0-19-851976-1, location=Oxford, oclc=59185784]
References
Polymer physics