Disentangling time

Keywords Crazing Creep Molecular deformation mechanisms Disentanglement Time-dependent strength Toughness... 

Besides, analysing the effect of MW of PMMA on the increase in craze dimensions with time [44], leads to the conclusion that the molecules in the craze fibrils are not fully stretched, retaining folds and thus keeping entangled. So, it supports the consideration of r(crc) as a disentanglement time. 

Pc> Pb> Pf cumulative number fraction of grid squares that exhibit craze formation, craze fibril breakdown, and catastrophic fracture, respectively probability that a given entangled strand survives craze fibril formation disentanglement time of i strands in a fibril that survive fibril formation craze interface velocity volume fraction of polymer within craze... 

Figure 8. Disentanglement time (t ) as a function of solution concentration.

Criticality in Concentration. The sharp downturn of the disentanglement time vs. concentration curve for the flare effect (Figure 8) indicates that the flare sets in within a narrow concentration range as C is increased. This is the critical concentration already identified as C. The postulation of the existence of a critical lower concentration is consistent with the concept of a network, because for a network to arise there needs to be a pathway of contact across the whole macroscopic system, the establishment of which, as common with all such percolation problems, is a critical phenomenon. In our case the minimum contact criterion is clearly the existence of coil overlap. 

A model for anomalous transport [60] was extended to dissolution and the appropriate boundary condition for the rubbery-solvent interface, S, took into account the disentanglement time derived above. As in the approach of Papanu et al. [57], thermodynamics of swollen networks was used to estimate the concentration at the rubbery-solvent interface, S. 

The concept of the dissolution clock was introduced. Initially, the clock is set to zero at each point in the polymer. The clock measures time only after the solvent concentration at that point reaches a critical value. When the clock time becomes equal to the disentanglement time, the polymer at that point dissolves. This is pictorially shown in Fig. 26. 

Fig. 26. Solvent volume fraction history at a spatial point. When the solvent volume fraction is equal to the critical gel volume fraction, the dissolution clock starts, ti. When the clock time, t2, is equal to the disentanglement time, t, the polymer at this point is dissolved...

The situation is dynamic. The position of any segment is continuously changing so that a characteristic disentanglement time can be... 

As the flow velocity relates to the disentangling time, this also holds for the melt viscosity. Indeed, po and the disentangling time for entangled melts show the same dependence on the molecular weight. Figure 5.13 collects the results of viscosity measurements for various polymers. As should be noted, a power law behavior... 

Rouse-modes with m < m do not exist. They become replaced by other relaxation processes, and the third term in Eq. (6.109) describes this contribution. The relaxation strength is identical to that of the replaced Rouse-modes, as this part remains unrelaxed after the decay of all modes with m>m. Writing the correlation function for the long-term part in the form (t/ra) implies the assumption that, similar to the Rouse-modes, also this part is controlled by a single characteristic time, the disentangling time ra, only. As introduced here, (f/ra) is a general normalized function... 

Doi and Edwards analysed the described disentangling process of the primitive chain in more detail. As in the case of the Rouse-motion, the dynamics of the disentangling process can also be represented as a superposition of independent modes. Again, only one time constant, the disentangling time Td, is included, and it sets the time scale for the complete process. In the Doi-Edwards treatment, ra is identified with the longest relaxation time. Calculations result in an expression for the time dependent shear modulus in the terminal flow region. It has the form... 

Although the data tend to agree more with the reptation model than other models, it is difficult to distinguish on this basis alone. For the reptation model the relaxation of the modes is expected to follow eq. (4.10) for times up to for N/p > Ng. Then the relaxation time should increase by a factor N/Ne with a plateau in between. The plateau value is expected to be around exp(—7iiouse(Ae)/Tp) and last up to the disentanglement time. We should mention here that this time is dependent on the mode number p, as was shown for the case of chain in a straight tube. Here one however has to deal with the problem that for the present N/Ne values, the free chain ends dominate the relaxation spectrum, as seen above for the mean-square displacements. Thus we used an approach similar to the idea employed in... 

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