Polymers reptation

The pom-pom polymer reptation model was developed by McLeish and Larson (60) to represent long chain-branched LDPE chains, which exhibit pronounced strain hardening in elongational flows. This idealized pom-pom molecule has a single backbone confined in a reptation tube, with multiple arms and branches protruding from each tube end, as shown in Fig. 3.12(a). Mb is the molecular weight of the backbone and Ma, that of the arms. 

The investigation of viscoelasticity of dilute blends confirms that the reptation dynamics does not determine correctly the terminal quantities characterising viscoelasticity of linear polymers. The reason for this, as has already been noted, that the reptation effect is an effect due to terms of order higher than the first in the equation of motion of the macromolecule, and it is actually the first-order terms that dominate the relaxation phenomena. Attempts to describe viscoelasticity without the leading linear terms lead to a distorted picture, so that one begins to understand the lack of success of the reptation model in the description of the viscoelasticity of polymers. Reptation is important and have to be included when one considers the non-linear effects in viscoelasticity. 

Tube length fluctuations modify the rheological response of entangled polymers. Reptation dynamics adds a regime to the mean-square monomer displacement that was not present in the free Rouse model. This extra regime is a characteristic signature of Rouse motion of a chain confined to a tube. 

Two-Dimensional Pulsed Field Electrophoresis Theoretical Background. Applying the polymer reptation model to conventional DNA electrophoresis is proving to be quite successful, especially in the case of field strength dependent electrophoretic mobilities. 

At t Xg, the whole polymer is confined in a deformed tube. As time passes, the polymer reptates, and at time t the parts of the polymer near the ends have disengaged from the deformed tube, while the part in the middle is still confined in the tube. Since only the segments in the deformed tube are oriented and contribute to the stress, the stress is proportional to the fraction (t) of the polymers still confined in the... 

Figure 4.6 Simplified model for polymer reptation, showing the tight tube created by contingent polymer chains plus possible plasticiser or solvent molecules.

Figure 33.11 A polymer reptates by moving inside a tube, defined by its neighboring chains.

D. W. Schaefer. Polymer reptation in semidilute solutions. /. Polymer Sci. Polymer 5ymp.,73(1985), 121-131. 

Returning to the problem of polymer reptation, we find, using Eq. (13.9.3), that the time needed for the chain to diliuse out of the constraining tube is given by... 

---