Entanglements densities

The techniques described above have been used to demonstrate that failure can occur by (1) simple chain pull-out, (2) chain scission close to the interface, or (3) chain scission within one of the blocks (typically PS). The transition from chain pull-out to scission is essentially controlled by molecular weight whilst the location of the scission seems to depend on the entanglement density. Fig. 2 shows the transition between (2) and (3) as E is increased. 

The percolation parameters (p — Pc) associated with the disentanglement process are derived as follows p is the normalized entanglement density defined as... 

The model was tested against solution polymerization data for MMA reported by Schulz and Haborth (11). The minimization of error in fitting the model to the data resulted in negative values for a. This is physically unrealistic, and suggests that the model needs modification. Further work is intended which will refine the choice of initial condition for application of the model and/or change the inverse dependency of on entanglement density to power greater than unity. 

Non-linear viscoelastic flow phenomena are one of the most characteristic features of polymeric liquids. A matter of very emphasised interest is the first normal stress difference. It is a well-accepted fact that the first normal stress difference Nj is similar to G, a measure of the amount of energy which can be stored reversibly in a viscoelastic fluid, whereas t12 is considered as the portion that is dissipated as viscous flow [49-51]. For concentrated solutions Lodge s theory [52] of an elastic network also predicts normal stresses, which should be associated with the entanglement density. 

Fig. 28 Schematic illustration of entanglement density ve for thin FCSC, small ECSC, and large ECSC, respectively. Entanglements are assumed to exist on the surface of the crystal or in the amorphous layers between lamellae. ve increases with an increase of lamellar thickness /...

From the foregoing it will be clear that whenever entanglements and long chain branching are both present the dynamics in a polymer melt are highly co-operative. The orientational relaxation time of chain segments is exponentially dependent on both the contour distance to the nearest effective free end and on the effective entanglement density of its enviroiunent at all previous timescales. 

The viscoelastic response of the UHMWPE pseudo-gels depends also on the solution concentration. As shown in Figure 10, the G increased with concentration at frequency 50 sec"l over the temperature range from -20 C to 100 C. This is probably due to the higher entanglement density and/or higher crystallinity in the higher concentration solution. 

Fractional reduction in entanglement density due to steady shear flow g(0) = E/Eo (Part 8). 

Fig. 5 Critical stress intensity factor K c of commercial polymers versus the square root of entanglement density ve (after [18])...

Instead of Me, a frequently used characteristic is the entanglement density, ve, given by ... 

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