Reptation, chain

Figure C2.1.13. (a) Schematic representation of an entangled polymer melt, (b) Restriction of tire lateral motion of a particular chain by tire otlier chains. The entanglement points tliat restrict tire motion of a chain define a temporary tube along which tire chain reptates.

The ripple experiment works as follows In Fig. 6, HDH and DHD are depicted by open and filled circles where the filled circles represent the deuterium labeled portions of the molecule and the open circles are the normal (protonated) portions of the chains. Initially, the average concentration vs. depth of the labeled portions of the molecules is 0.5, as seen along the normal to the interface, unless chain-end segregation exists at / = 0. If the chains reptate, the chain ends diffuse across the interface before the chain centers. This will lead to a ripple or an excess of deuterium on the HDH side and a depletion on the DHD side of the interface as indicated in the concentration profile shown at the right in Fig. 6. However, when the molecules have diffused distances comparable to Rg, the ripple will vanish and a constant concentration profile at 0.5 will again be found. 

Entangled Polymer Liquids. Do Linear Chains Reptate ... 

T.P. Lodge, N.A. Rotstein, and S. Prager. Dynamics of entagled polymer liquids Do linear chains reptate In I. Prigogine and S.A. Rice, editors, Advances in Chemical Physics, volume 79, pages 1-132, New York, 1990. John Wiley Sons. 

Figure 1 Schematic representation of one chain among obstacles, a) The chain is constrained by the obstacles, b) By local fluctuations, the chain changes its conformation. The probability of forming a loop (dashed line) is very small (strong entropy loss), and the role of the extemities is dominant, c) The chain reptates like a snake in the virtual tube (thin line) envelope of all the topological constraints exerted on it by the obstacles. The tube is progressively redefined from the extremities, as schematically presented by the two situations at time t and t , with t >t.

The primitive chain reptates along itself with a diffusion constant that can be identified as the diffusion coefficient of the Rouse model. Under the action of a force /, the velocity of the polymer in the tube is v =f /, where is the overall friction coefficient of the chain. It is expected that C is related to the friction coefficient of the individual segments, Q, by the expression... 

Dynamics of Melts Chain Reptation Concluding Remarks References and Notes... 

Fig. 13 A-C.Rdease of a constraint on the primitive path by rqytation of a neighboring chain. Tte initial path (A) is altered when the end of a neighboring chain reptates past the path (B) and is replaced by a new diain (C). The result is a l ad random jump in conformation lower figure)...

Consider an isolated long probe P-mer entangled in a melt of shorter Wmers. Tube dilation assumes that as soon as short chains relax, stress in the long P-mer drops to zero. In particular, a version of tube dilation called double reptation imposes an exact symmetry between single chains in a tube and multi-chain processes. As one chain reptates away, stress at a common entanglement (stress point) is relaxed completely. In constraint release models, this stress relaxes only partially due to connectivity of the P-mer. 

Narasimhan B, Peppas NA. On the importance of chain reptation in models of dissolution of glassy polymers. Macromolecules 1996 29 3283-3291. 

In trying to answer these questions it is certainly instructive to examine previous fundamental experimental works in which such thin films have been employed. In particular, we have to mention studies on polymer interdiffusion in which thin polymer films were used for testing theoretical concepts of polymer physics [102-106]. Spin-coating was typically used to prepare the films because this process presents an easy way of obtaining smooth film of precisely controllable thickness, even in the nanometer range. This is an essential criterion for investigating, for example, polymer diffusion across an interface between two films. While these experiments successfully supported the model of chain reptation [102-106], they also indicated some deviations that hinted, for example, at the enrichment of chain ends at surfaces [104, 106]. 

Much effort has gone in trying to predict melt rheological response from the molecular structure. Physical chemists have considered the modes of vibration of short-chain molecules (to explain the low molecular weight shear viscosity data in Fig. 3.10), applied mathematicians have attempted to explain the non-Newtonian and elastic properties of melts from the lifetimes of temporary entanglements between molecules, while physicists have used the snake-like motions of sections of polymer chains (reptation) for the same purpose. None of these approaches has been completely successful. 

When component-one s molecular weight is below Me, the viscoelastic response of component one is described by the Rouse theory, and tj (proportional to tci if the component-one chain reptates) can be equated to zero as the component-one chains lose the reptational mechanism. Then Eq. (ll.A.l) is transformed to... 

Equation (12.5) contains two relaxation processes (v (t)v (t)) is to be randomized or relaxed by the chain reptational motion, and the change in with time represents the chain-tension relaxation. The former is much slower than the latter if the molecular weight is large. At t T q, the chain-tension relaxation process ends and ln t)) returns to its equihbrium value / the stress tensor T(t Teg) becomes... 

---