Viscosity internal

There remains an interpretation of ta to be found, ta exhibits an activation energy of about 0.43 0.1 eV, about three times as high as the C-C torsional barrier of 0.13 eV. The discrepancy must reflect the influence of the interactions with the environment and therefore ta appears to correspond to relaxation times most likely involving several correlated jumps. The experimental activation energy is in the range of that for the NMR correlation time associated with correlated conformational jumps in bulk PIB [136] (0.46 eV) and one could tentatively relate ta to the mechanism underlying this process (see later). 

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The dielectric constant of unsymmetrical molecules containing dipoles (polar molecules) will be dependent on the internal viscosity of the dielectric. If very hard frozen ethyl alcohol is used as the dielectric the dielectric constant is approximately 3 at the melting point, when the molecules are free to orient themselves, the dielectric constant is about 55. Further heating reduces the ratio by increasing the energy of molecular motions which tend to disorient the molecules but at room temperature the dielectric constant is still as high as 35. 

At low frequencies when power losses are low these values are also low but they increase when such frequencies are reached that the dipoles cannot keep in phase. After passing through a peak at some characteristic frequency they fall in value as the frequency further increases. This is because at such high frequencies there is no time for substantial dipole movement and so the power losses are reduced. Because of the dependence of the dipole movement on the internal viscosity, the power factor like the dielectric constant, is strongly dependent on temperature. 

In order to reconciliate high-frequency dynamic rheological data with theory, Cerf proposed an additional internal viscosity term which should be mainly molecular weight independent [37] ... 

The use of internal viscosity forces permit us to take into account kinetic effects associated with deformation rates which were beyond the scope of most polymer... 

The inclusion of internal viscosity raises considerably the free-energy storage capacity of a rapidly deforming macromolecule as compared to the idealized Hookean spring model and could play a decisive role in mechanochemical reactivity in transient elongational flow. 

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

It is expected, however, that the Gaussian representation is inadequate in transient elongational flow, even if the chain is only weakly deformed. During a fast deformation, the presence of non-equilibrium effects, like internal viscosity , noncrossability and self-entanglements will stiffen the molecular coil which is now capable of storing a much larger amount of elastic energy than that predicted from Eq. (113). 

Ohnesorge Number Oh = pL/(pLoD0f5 Compare internal viscosity force to surface tension force Walzel [398]... 

The description of the chain dynamics in terms of the Rouse model is not only limited by local stiffness effects but also by local dissipative relaxation processes like jumps over the barrier in the rotational potential. Thus, in order to extend the range of description, a combination of the modified Rouse model with a simple description of the rotational jump processes is asked for. Allegra et al. [213,214] introduced an internal viscosity as a force which arises due to a transient departure from configurational equilibrium, that relaxes by reorientational jumps. Thereby, the rotational relaxation processes are described by one single relaxation rate Tj. From an expression for the difference in free energy due to small excursions from equilibrium an explicit expression for the internal viscosity force in terms of a memory function is derived. The internal viscosity force acting on the k-th backbone atom becomes ... 

Internal viscosity (Section 4) provides another possible source of shear-rate dependence. For sufficiently rapid disturbances, a spring-bead model with internal viscosity acts like a rigid body for sufficiently slow disturbances it is flexible and indefinitely extensible. The analytical difficulties for coupled, non-linear spring-bead systems are equally severe in linear spring-bead systems with internal viscosity. Even the elastic dumbbell with internal viscosity has only been solved exactly in the limit of small e (559), where e is the ratio of internal friction coefficient to molecular (external) friction coefficient Co n. For this case, the viscosity decreases with shear rate. 

Similar arguments can be raised against internal viscosity as a primary cause of shear rate dependence in the viscosity. A recent review (339a) has shown that current many-bead theories predict differences in y0 and co0 when e is small and chosen to fit the oscillatory data. The approximate nature of these analyses leaves serious doubts about their predictions in steady-state flow, however. A new... 

Experimentally,(t] m -rjs)/(t]0 -t]s)less than unity, and shear rate dependence should practically disappear if only internal viscosity is considered. Such behavior is not of course observed. 

A final piece of evidence against both finite extensibility and internal viscosity is provided by flow birefringence studies. One would expect each to produce variations in the stress optical coefficient with shear rate, beginning near the onset of shear rate dependence in the viscosity (307). Experimentally, the stress-optical coefficient remains constant well beyond the onset of shear rate dependence in r for all ranges of polymer concentration (18,340). 

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