Reptation model theoretical results

Diffusion of flexible macromolecules in solutions and gel media has also been studied extensively [35,97]. The Zimm model for diffusion of flexible chains in polymer melts predicts that the diffusion coefficient of a flexible polymer in solution depends on polymer length to the 1/2 power, D N. This theoretical result has also been confirmed by experimental data [97,122]. The reptation theory for diffusion of flexible polymers in highly restricted environments predicts a dependence D [97,122,127]. Results of various... 

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. 

Though it is desirable to confirm the experimental results, the comparison of the theoretical formulas (148) with the experimental results (150) indicates that, insofar as the influence of the ambient macromolecules on the dynamics of a chosen macromolecule is concerned, the ambient macromolecules are equivalent to a certain relaxing medium. The reptation effect is 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 linear viscoelastic 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 has to be included when one considers the non-linear effects in viscoelasticity. 

We want to emphasize that a logarithmic time dependence of d and w, and the corresponding decrease of V, are not expected for a Newtonian liquid [42]. Moreover, our results cover times shorter than the longest relaxation time in equilibrated bulk samples (i.e., the reptation time). Thus, the visco-elastic properties of PS certainly affect our dewetting experiments. Thus, a detailed theoretical model has been developed that takes into account residual stresses, interfacial friction (i.e., slippage), and visco-elasticity [42,44,46],... 

These results pointed out several aspects of miiversahty in polymer viscoelasticity and led to some theoretical modelings. However, a promising way to describe the entanglement effect in a concentrated long-chain system had not appeared until de Gennes suggested the idea of reptation... 

Thus we see that the N dependence of Dg changes from the Rouse type Dg 1/iV to the reptation type Dg 1/iV as the chain length increases and crosses over rie. However, it is too early to conclude with this result that the premise of the reptation idea has been justified theoretically, because Skolnick et al. [ 14] have shown that an equation similar to eq 2.39 can be obtained from a different dynamic model, as explained below. 

In the next section, we review in more detail the relevant theoretical concepts. In Section 4.3, we discuss the different simulation methods, both Monte Carlo and molecular dynamics, which have been used to study both the static and dynamic properties of a melt. We also show why it is essential to use a coarse-grained model, instead of a more realistic model, if one is to have any chance of addressing the issues related to whether reptation theory is correct or not. In Section 4.4, we review the progress which has been made recently in understanding the motion of long linear chains in a melt. In Section 4.5, we consider the properties of highly crosslinked networks or rubbers. Finally, in Section 4.6, we briefly summarize our main results and present our outlook for future simulations in this area. 

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