Highly entangled polymers

The viscosity scales, from Eq. (1), as Tj-GoTi-gp since and are the characteristic modus and relaxation times appearing respectively in the integral. The plateau modulus is independent of molecular weight for highly entangled polymers [1] but inversely proportional to so... 

First detailed studies of the dynamic structure factor of highly entangled polymer melts were reported at the beginning of the 90 s. At that time the attainable Fourier times were limited to about 40 ns. On this time scale, NSE has already played a crucial role in helping to understand the dynamics of polymeric systems [49, 50, 72, 73]. At that time the existence of an entanglement length scale in a linear polymer was been proven [72]. However, with the available time resolution, it was not possible to separate the predictions of the different confinement models addressed above. 

An important role in the present model is played by the strongly non-linear elastic response of the rubber matrix that transmits the stress between the filler clusters. We refer here to an extended tube model of rubber elasticity, which is based on the following fundamental assumptions. The network chains in a highly entangled polymer network are heavily restricted in their fluctuations due to packing effects. This restriction is described by virtual tubes around the network chains that hinder the fluctuation. When the network elongates, these tubes deform non-affinely with a deformation exponent v=l/2. The tube radius in spatial direction p of the main axis system depends on the deformation ratio as follows ... 

Since the Navier s slip hypothesis of the last century, most experiments have failed to obtain positive evidence for a slip boundary condition on macroscopic scales in low molar mass liquids. However, Navier s notion of slip turns out to be extremely useful and convenient for the latest description of flow anomalies of highly entangled polymer melts including linear polyethylenes (LPE). The ability of a melt/solid interface to possess two profoundly different states as shown by Fig. 4a,b clearly reveals the potential role of interfacial slip in governing various melt flow phenomena in high pressure extrusion. Before reviewing recent experimental studies that have elucidated the molecular origins of different flow... 

Both expressions predict that x is higher than Xg for monodisperse samples with N higher than about 12 [15] or 4 [17]. This means that a pure reptation description is correct for highly entangled polymers as shown in section 3.1. 

Figure 1 Typical flow curve for highly entangled polymer melt extrusion through two-dimensional or axisymmetric dies.

The flow curves characterizing the extrusion of highly entangled polymer melts in conventional dies (metal, with any reasonable degree of roughness and having no special prior treatment) thus show that such flows are governed by ... 

Let us consider the flow of a highly entangled polymer in an axisymmetrical die of diameter D and length L. In the case of polymers, when the shear rates are sufficiently high or within a certain shear rate domain, variations in viscosity as a function of shear rate may be represented by a power law [30] ... 

HIGHLY ENTANGLED POLYMERS - FLOW WITH SLIP... 

In the case of the highly entangled polymers (LG2, LG3, PB, LLDPE, etc.), the Figure 3 type pressure loss curves show a jump in flow rate, indicating the triggering of sUp along the die walls. When one observes the appearance of the extruded rod, this phenomenon is superimposed on melt fractm-e. It occurs in various ways, depending on the type of installation used. 

Figure 4.1. a Highly entangled polymer chains in a semidilute polymer solution, h When zoomed in, the entangled chains can he regarded as consisting of blohs. 

This having been said, there are major unsettled theoretical issues regarding highly entangled polymer melts, and it is likely that the problems discussed in this chapter will be better understood when the fundamental issues in polymer physics have been resolved. 

F., and Marrucd, G. (2004) Highly entangled polymer primitive chain network simulations based on dynamic tube dilation. /. Chem. Phys., 121 (24), 12650-12654. 

K. E. Evans and S. F. Edwards, Computer Simulation of the Dynamics of Highly Entangled Polymers. Part 2 — Static Properties of the Primitive Chain , J. Chem. Soc., Faraday Trans. 2,11,1981, pp 1913-1927. 

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