Reptation

[1] Derived from the word reptile, reptation suggests the movement of entangled polymer chains as being analogous to snakes slithering through one another.

[2] 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.

[3][4] Sir Sam Edwards and Masao Doi later refined reptation theory.

A repton is a mobile point residing in the cells of a lattice, connected by bonds.

[8][9] Entanglement means the topological restriction of molecular motion by other chains.

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. μtube 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 By noting that this time is comparable to the relaxation time, we establish that τ ∝ L2 / μtube.

Since the length of the tube is proportional to the degree of polymerization, and μtube is inversely proportional to the degree of polymerization, we observe that τ ∝ (DPn)3 (and so τ ∝ M3).

From the preceding analysis, we see that molecular mass has a very strong effect on relaxation time in entangled polymer systems.

Indeed, this is significantly different from the untangled case, where relaxation time is observed to be proportional to molecular mass.

The corresponding increase in relaxation time can result in viscoelastic behavior, which is often observed in polymer melts.

Note that the polymer’s zero-shear viscosity gives an approximation of the actual observed dependency, τ ∝ M3.4;[11] this relaxation time has nothing to do with the reptation relaxation time.

Entanglements with other polymer chains restrict polymer chain motion to a thin virtual tube passing through the restrictions.

The mechanism for movement of the chain through these restrictions is called reptation.

The mathematics of random walks can show that the average end-to-end distance of a section of a polymer chain, made up of

[15][16] The conditions of existence of reptation in the thermal motion of macromolecules of complex architecture (macromolecules in the form of branch, star, comb and others) have not been established yet.