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 being analogous to snakes slithering through one another. Pierre-Gilles de Gennes introduced (and named) the concept of reptation into polymer physics in 1971 to explain the dependence of the mobility of a macromolecule on its length. Reptation is used as a mechanism to explain viscous flow in an amorphous polymer. Sam Edwards and Masao Doi later refined reptation theory.

Two closely related concepts are reptons and entanglement. A repton is a mobile point residing in the cells of a lattice, connected by bonds. Entanglement means the topological restriction of molecular motion by other chains.

Reptation theory describes the effect of polymer chain entanglements on the relationship between molecular mass and chain relaxation time. The theory predicts that, in entangled systems, the relaxation time τ is proportional to the cube of molecular mass, M: τ ∝ M ³. The prediction of the theory can be arrived at by a relatively simple argument. First, each polymer chain is envisioned as occupying a tube of length L, through which it may move with snake-like motion (creating new sections of tube as it moves). Furthermore, if we consider a time scale comparable to τ, we may focus on the overall, global motion of the chain. Thus, we define the tube mobility as

where v is the velocity of the chain when it is pulled by a force, f. μ_tube will be inversely proportional to the degree of polymerization (and thus also inversely proportional to chain weight).

The diffusivity of the chain through the tube may then be written as

By then recalling that in 1-dimension the mean squared displacement due to Brownian motion is given by

we obtain

The time necessary for a polymer chain to displace the length of its original tube is then