Entangled regime

In elongational flow, the entanglement regime was observed at much lower concentrations, even below [r ] c = 0.1 [169], The effect was initially thought to be the result of coil expansion in flow, but was later discarded in favor of the lifetime for entanglement formation, under dynamic conditions of flow. 

Compared to the available clear-cut comparisons between NSE results and simulations for short Rouse chains, the situation in the entangled regime is less satisfactory. The molecular dynamics (MD) simulation of ensembles of suffi-... 

We have examined the influence of diphenyl ether and anisole on the association of the polystyryllithium and the 1,1-diphenyl-methyllithium active centers in benzene solution. The analytical tool used was the vacuum viscometry method (1 .2. 2. ) which utilizes concentrated solutions of polystyryllithium and the terminated polymer in the entanglement regime. Our results show that the presence of these ethers can alter the association states of the foregoing active centers. These findings parallel previous work (2) involving tetrahydrofuran. 

The viscometric method relies on the relation (in the entanglement regime) ... 

Worsfold found that the degree of association as measured from viscosity was less than that indicated by the light scattering and spectroscopic results. It was therefore concluded that the association dissociation rates were comparable to the chain entanglement lifetime. As a consequence, Worsfold concluded that viscosity measurements involving concentrated solutions of poly(dienyl)lithium in the entanglement regime could not detect the presence of, for example, star-shaped tetramers if the equilibrium... 

In the present paper, after a rapid presentation of the reptation model in its simplest version, in order to pinpoint the underlying hypothesis, we discuss the interest of complementary self diffusion and viscoelastic measurements, and present the currently available methods for measuring diffusion in entangled polymer systems. Then, results obtained on polydimethylsiloxane (PDMS), a model liquid polymer well above its glass temperature at room temperature will be described, and the consequences on the limits of the entangled regime as seen from diffusion measurements, compared to what is observed in rheometry, will be discussed. 

In the entangled regime, the limiting compliance of monodisperse samples is... 

Below e entangled regime, the limiting compliance follows approximately a linear dependence with molecular weight according to Rouse s theory (see section 6) ... 

It is interesting that in principle any value of k will lead to creation of entanglement. The reason for this is our prior knowledge to the entangling pulse. Here the atoms are in the coherent state which is as well defined in terms of variances as possible for separable states. We only need an "infinitesimal" extra knowledge about the spin state to go into the entangled regime. 

As the concentration was increased, droplets and beaded fibers were observed in the semidilute unentangled regime and beaded as well as uniform fibers were observed in the semidilute entangled regime. Uniform fiber formation was observed at c/c 6 for all the narrow MWD polymers (M of 12, 470-205, 800 g/mol] but for the relatively broad MWD polymers (M of 34,070 and 95,800 g/ mol], uniform fibers were not formed until higher concentrations, c/c 10, were utilized. ... 

We are dnis led to an extrapolation length b, in the entangled regime, of the form ... 

Fig. 18. Double logarithmic representation of the viscosity vs scaled molecular weight for a series of polymers, showing the change from a weak (nearly linear) dependence of viscosity on molecular weight to the entangled regime where rjo a After Berry and Fox (57), with permission.

The diffusion coefficient in the entangled regime decreases as with inaeasing polymer concentration. 

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