Reptation model chain

There are three basic time scales in the reptation model [49]. The first time Te Ml, describes the Rouse relaxation time between entanglements of molecular weight Me and is a local characteristic of the wriggling motion. The second time Tro M, describes the propagation of wriggle motions along the contour of the chain and is related to the Rouse relaxation time of the whole chain. The important... 

We present here a simple experiment, conceived to test both the reptation model and the minor chain model, by Welp et al. [50] and Agrawal et al. [51-53]. Consider the HDH/DHD interface formed with two layers of polystyrene with chain architectures shown in Fig. 5. In one of the layers, the central 50% of the chain is deuterated. This constitutes a triblock copolymer of labeled and normal polystyrene, which is, denoted HDH. In the second layer, the labeling has been reversed so that the two end fractions of the chain are deuterated, denoted by DHD. At temperatures above the glass transition temperature of the polystyrene ( 100°C), the polymer chains begin to interdiffuse across the... 

The scaling results above all pertain to local segmental relaxation, with the exception of the viscosity data in Figure 24.5. Higher temperature and lower times involve the chain dynamics, described, for example, by Rouse and reptation models [22,89]. These chain modes, as discussed above, have different T- and P-dependences than local segmental relaxation. 

The deformation of polymer chains in stretched and swollen networks can be investigated by SANS, A few such studies have been carried out, and some theoretical results based on Gaussian models of networks have been presented. The possible defects in network formation may invalidate an otherwise well planned experiment, and because of this uncertainty, conclusions based on current experiments must be viewed as tentative. It is also true that theoretical calculations have been restricted thus far to only a few simple models of an elastomeric network. An appropriate method of calculation for trapped entanglements has not been constructed, nor has any calculation of the SANS pattern of a network which is constrained according to the reptation models of de Gennes (24) or Doi-Edwards (25,26) appeared. 

The reptation model for polymer diffusion would predict that the thickness of the gel phase reflects the dynamics of disentanglement. The important factors here are chain length, solvent quality and temperature since they affect the dimensions of the polymer coils in the gel phase. The precursor phase, on the other hand, depends upon solvency and temperature only through the osmotic force it can generate in the system and the viscoelastic response of the system in the region of the front. These factors should be independent of the PMMA molecular weight. 

The reptation model predicts that the viscosity of a melt scales with the chain length to the third power while the diffusion coefficient decreases with the second power of the chain length. 

We now consider the predictions of the reptation model for the mean-square displacement of the chain segments. Figure 3.13 gives an overview. 

Fig. 3.14 Mean-square displacement of a chain segment in the reptation model. The exponents of the different power law regimes are noted along the respective lines...

It is not clear how improvements can be made without real progress on the difficult fundamental problems of diffusion in media with obstacles and cooperation of large-scale motions between interpenetrating chains which do not violate chain connectivity. The DeGennes reptation model (225) makes a significant contribution to the first problem, although in an admittedly simplified system. Rigorous calculations or computer simulations on well-defined models which relate to the second problem would be extremely valuable, even if the models themselves were not completely faithful representations of the assumed physical situation. It is not obvious how even to pose solvable problems, simplified or not, which relate to interchain cooperation. 

The reptation model (225) also appears to produce a Rouse spectrum at long times. In order to renew its configurations a chain must diffuse out of the tunnel defined by the fixed obstacles along its length. De Gennes calculates the autocorrelation function for the end-separation vector, obtaining... 

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 glass transition results from large scale conformational motion of the polymer chain backbone all moieties making up the structural unit of the polymer contribute to it. The main chain motions also satisfy the De Gennes reptation model (1971), where the chains move back and forth in snakelike motions. 

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