Entangled polymer melts

Figure C2.1.13. (a) Schematic representation of an entangled polymer melt, (b) Restriction of tire lateral motion of a particular chain by tire otlier chains. The entanglement points tliat restrict tire motion of a chain define a temporary tube along which tire chain reptates.

NSE Studies on Entangled Polymer Melts Poly(tetrahydrofurane) (PTHF)... 

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. 

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... 

Estimation of the molar mass of a bulk supramolecular polymer by extrapolation of values determined in solution is always questionable. Therefore, a method based on transverse relaxation measurements of bulk samples was proposed [198]. It takes advantage of the fact that the strength of residual dipolar interactions depends on the molar mass in entangled polymer melts. 

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 ... 

OBSERVATION OF UNSTABLE FLOW FOR SLIGHTLY TO MODERATELY ENTANGLED POLYMERS - MELT FRACTURE... 

W Graessley. Viscoelasticity and diffusion in entangled polymer melt. In M Nagasawa, ed. Molecular Conformation and Dynamics of Macromolecules in Condensed Systems pp (163-184). Amsterdam Elsevier, 1988. 

For t the dynamics of entangled polymer melts are described by the Rouse model. Owing to the fact that x, Eq. (11.33) can be written as... 

Since monomers are space-filling in the melt, the number density of entanglement strands is just the reciprocal of the entanglement strand volume, leading to a simple expression for the plateau modulus of an entangled polymer melt [Eq. (7.47)]. 

The reptation ideas discussed above will now be combined with the relaxation ideas discussed in Chapter 8 to describe the stress relaxation modiihis G t) for an entangled polymer melt. On length scales smaller than the tube diameter a, topological interactions are unimportant and the dynamics are similar to those in unentangled polymer melts and are described by the Rouse model. The entanglement strand of monomers relaxes by Rouse motion with relaxation time Tg [Eq. (9.10)] ... 

The reptation model prediction for the viscosity of an entangled polymer melt is determined by integrating Eq. (9.20) ... 

In entangled polymer melts this diffusion occurs along the contour of the tube, with the mean-square monomer displacement in space determined using Eq. (9.71) ... 

Molecular dynamics simulation of a chain with N = 400 monomers in an entangled polymer melt. Forty configurations of the chain are shown at equally spaced time intervals up to the Rouse time of the chain. Picture---------... 

Consider an entangled polymer melt of At-mers with monomeric friction... 

Jordan, E.A. Donald, A.M. Fetters, L.J. Klein, J. Transition from linear to star-B branched diffusion in entangled polymer melts. Polym. Prep. 1989, 30 (1), 63-64. 

High-resolution proton DQ MAS NMR is used as a new technique that is capable of revealing complex motional processes in entangled polymer melts. Theoretical analysis shows the connection of quantities relating anisotropic polymer dynamics to data obtained from our DQ-MAS NMR experiment. With this technique, dynamic chain ordering as well as scaling laws consistent with the reptation model was previously observed for polybutadiene (PB). 

We propose that the non-Newtonian flow relaxation of the pure entangled polymer fluid can be identified with the relaxation time 0 of Equation 13.39, and estimate it by using the scaling relation for entangled polymer melts given by Equation 13.40. 

This equation indeed gives good account of the observed N/pY >-dependence of xr by applying the r T) from simulations. They attempted to justify this equation by taking an equation from Schweizer s (1989) formally exact, nonlinear generalized Langevin equation (GLE) for a flexible probe polymer in a dense entangled polymer melt (see Eq. (3.50) in Schweizer). They rewrote this same equation in the form... 

It is noteworthy that when Schweizer worked out his equation for entangled polymer melts, he did not obtain a stretch exponential that has exponent P = 0.57 or 0.59 that would have let him obtain the experimental or the dependence of the terminal relaxation time in order to be consistent with the experiment. On the other hand, as hinted by Schweizer (1989), Property (ii) of the CM when applied to terminal chain relaxation time xr of PI in blends with PtBS leads to the relation,... 

FIGURE 1.4 Diagramatic representation of an entangled polymer melt. 

Liu, C. Y., Keunings, R., and Bailly, C., 2006. Do deviations from reptation scaling of entangled polymer melts result from single- or many[Pg.229]

Shanbhag, S., and Larson, R. G., 2006. Identification of topological constraints in entangled polymer melts using the bond-fluctuation model. Macromolecules, 39(6) 2413-2417. 

Fenchenko studied free induction decays and transverse relaxation in entangled polymer melts. He considered both the effects of the dipolar interactions between spins in different polymer chains and within an isolated segment along s single chain. Sebastiao and co-workers presented a unifying model for molecular dynamics and NMR relaxation for chiral and non-chiral nematic liquid crystals. The model included molecular rotations/ reorientations, translational self-diffusion as well as collective motions. For the chiral nematic phase, an additional relaxation mechanism was proposed, associated with rotations induced by translational diffusion along the helical axis. The model was applied to interpret experimental data, to which we return below. 

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