Rouse-like dynamics

Calculations based on a Rouse-like dynamics (Ferry, 1980), applied to the percolation clusters, give... 

When reptation is used to develop a description of the linear viscoelasticity of polymer melts [5, 6], the same underlying hypothesis ismade, and the same phenomenological parameter Ng appears. Basically, to describe the relaxation after a step strain, for example, each chain is assumed to first reorganise inside its deformed tube, with a Rouse-like dynamics, and then to slowly return to isotropy, relaxing the deformed tube by reptation (see the paper by Montfort et al in this book). Along these lines, the plateau relaxation modulus, the steady state compliance and the zero shear viscosity should be respectively ... 

One can try to locate a critical polymerisation index above which the data are no longer compatible with a Rouse-like dynamics, Ng = 500, lager than the Ng= 100 value determined from the diffusion measurements in a frozen matrix. This is an illustration of the fact that the two processes. Rouse motion and entangled motion are in competition the slowest process is the one which is indeed observed.When the matrix chains are mobile, the entangled dynamics becomes more rapid than pure reptation, and the Rouse motion can dominate the dynamics for larger molecular weights than when the matrix chains are immobile. 

In fact, in the crossover region, the chains are still entangled (this appears on the diffusion data with N P), but they do not obey the simple reptation nor the simple-Rouse-like dynamics. This fact may be of practical importance in situations where the entcmglements... 

Figure 6 Product of riD versus the index of polymerisation of the PDMS, for N P (full circles) and for N=P (open squares). From this plot, a critical index of polymerisation for a departure from Rouse - like dynamics Ne = 500 can be estimated.

The simulations yield MTsc d11 for the scaling of the molecular weight Mtsc of the terminal subchains with thickness d. Assuming for the terminal subchains Rouse-like dynamics (the confinement-induced mode is faster... 

The scaling model predicts the chain in semidilute solution exhibits Rouse-like dynamics, with a relaxation time given by... 

In particular, the non-local Onsager coefficient Arousc that mimics Rouse-like dynamics (cf. Eq. 114) corresponds to a local Onsager coefficient in the EP Dynamics... 

Obviously, if the chain is short enough and Rq < d, it does not feel the tube and one recovers a Rouse-like dynamics. 

Figure 5.7 Evolution of the ordering field, XN, in the course of the expanded ensemble simulation along both branches. The system parameters are identical to Figure 5.5. Smart Monte Carlo moves are used to update the molecular conformations. The local segment motion gives rise to Rouse-like dynamics for all but the very first Monte Carlo steps. Time is measured in units of the Rouse-time of the...

Figure 46 shows the time dependence of the mean squared segment displacement as predicted by the harmonic radial potential theory [70]. The three anomalous diffusion limits, (I)de> (H)de> and (III)de> of the tube/repta-tion model are well reproduced. Note the extended width of the transition regimes between these limits, which should be kept in mind when discussing experimental data with respect to a crossover between different dynamic limits. Increasing the effective tube diameter is accompanied by the gradual transition to Rouse-like dynamics of an unconfined chain (where entanglement effects are not considered). 

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