Reptation mechanism, chain diffusion

A comparison of Eqs. 10.55 and 10.59 shows that the diffusivity of an isolated chain due to Brownian motion falls off more slowly with increasing chain size than the diffusivity of an entangled chain diffusing by the reptation mechanism. 

Polymer diffusion reptation and interdigitation R P WOOL Mechanisms for polymer chain diffusion... 

The Doi-Edwards theory assumes that reptation is the dominant mechanism for conformational relaxation of highly entangled linear chains. Each molecule has the dynamics of a Rouse chain, but its motions are now restricted spatially by a tube of uncrossable constraints, illustrated by the sketch in Fig. 3.38. The tube has a diameter corresponding to the mesh size, and each chain diffuses along its own tube at a rate that is governed by the Rouse diffusion coefficient (Eq. (3.37)). If the liquid is deformed, the tubes are distorted as in Fig. 3.39, and the resulting distortion of chain conformations produces a stress. The subsequent relaxation of stress with time corresponds precisely to the progressive movement of chains out of the distorted tubes and into random conformations by reptation. The theory contains two experimental parameters, the unattached mer diffusion coefficient T>o... 

Nevertheless, a value of a = -2 does not guarantee the presence of an entangled regime when H = Af as pointed out in previous section. Studying chain diffusion in a crosslinked matrix helps avoid the tube-renewal factor, the presence of permanent topological constraints is assured, and an independent measure of the diffusion coefficient for the free chain can be obtained but mechanisms in addition to reptation could still appear, i.e., fluctuations of network Junctions. 

Fig. 3 means that the additional mechanism which accelerates the chain diffusion with respect to pure reptation is only a function of the number of entanglements along the test chain, N/g = with g the number... 

Medium-to-high conversion - immediately after the onset of the gel effect. The diffusion mechanism is complex. Large chains become effectively immobile (on the timescale of the lifetime of a propagating radical) even though the chain ends may move by segmental diffusion, reptation, or reaction diffusion. Monomeric spedes and short chains may still diffuse rapidly. Short-long termination dominates. Initiator efficiencies may reduce with conversion. 

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

Most in depth studies of termination deal only with the low conversion regime. Logic dictates that simple center of mass diffusion and overall chain movement by reptation or many other mechanisms will be chain length dependent. At any instant, the overall rate coefficient for termination can be expressed as a weighted average of individual chain length dependent rate coefficients (eq. 20) 39... 

For 100 < P < 1000, the measured diffusion coefficients for N = P no longer follow the N 2 reptation prediction. In the same range of N values, D remains proportional to N 2 if P N, i.e. if the motion of the chains surrounding the test chain are frozen down during the diffusion time of the test chain. The comparison of the data obtained with N = P and with N P clearly puts into evidence the acceleration of the dynamics associated with the matrix chains, similarly to what has yet been observed with other polymers [11, 12, 42 to 44] or in solutions [10]. This acceleration, by a factor close to three, can be attributed to the constraint release mechanism [7, 8, 13], the effects of fluctuations of the test chain inside its tube [9] being a priori the same in the two situations P = N and P N. 

There are in fact two additional processes for relaxation which are quite natural to consider. One is the renewal of conformation by release of constraints which confine each chain, arising from diffusion of the surrounding chains which supply the con-straints This constraint release mechanism would operate in liquids, where the obstacles are themselves parts of reptating chains, but not in a network. 

The objectives of the present research were (i) to develop a solvent transport model accounting for diffusional and relaxational mechanisms, in addition to effects of the viscoelastic properties of the polymer on the dissolution behavior (ii) to perform a molecular analysis of the polymer chain disentanglement mechanism, and study the influence of various molecular parameters like the reptation diffusion coefficient, the disentanglement rate and die gel layer thickness on the phenomenon and (iii) to experimentally characterize the dissolution phenomenon by measuring the temporal evolution of the various fronts in the problem. 

The rate polymer diffusion in polymer media spans orders of magnitude. The mechanism of the process is unclear. It is very difficult to provide even a qualitative mechanistic picture how a long chain can move throughout a complex network of entanglements superimposed by the other macromolecules. The reptation theory of DeGennes [13] is probably only qualitatively true and only for very specific conditions. Simulations could be extremely helpful in at lest qualitative understanding of this process. 

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