Rouse model
Encyclopedia
The Rouse model is frequently used in polymer physics
.
The Rouse model describes the conformational dynamics of an ideal chain. In this model, the single chain diffusion is represented by Brownian motion
of beads connected by harmonic springs. There are no excluded volume interactions between the beads and each bead is subjected to a random thermal force and a drag force as in Langevin dynamics
. This model was proposed by Prince E. Rouse in 1953.
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. Whilst the Rouse model overestimates the decrease of the diffusion coefficient D with the number of beads N as 1/N, the Zimm model predicts D~1/Nν which is consistent with the experimental data for dilute polymer solutions.
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 τe. 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
model.
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....
.
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
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
of beads connected by harmonic springs. There are no excluded volume interactions between the beads and each bead is subjected to a random thermal force and a drag force as in Langevin dynamics
Langevin dynamics
In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems, originally developed by the French physicist Paul Langevin...
. This model was proposed by Prince E. Rouse in 1953.
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. Whilst the Rouse model overestimates the decrease of the diffusion coefficient D with the number of beads N as 1/N, the Zimm model predicts D~1/Nν which is consistent with the experimental data for dilute polymer solutions.
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
Reptation
Reptation is the snake-like thermal motion of very long linear, entangled macromolecules in polymer melts or concentrated polymer solutions.Entanglement means the topological restriction of molecular motion by other chains....
the Rouse model holds only up to a crossover time τe. 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
Reptation
Reptation is the snake-like thermal motion of very long linear, entangled macromolecules in polymer melts or concentrated polymer solutions.Entanglement means the topological restriction of molecular motion by other chains....
model.