Polymeric liquids viscosity curve

In order to evaluate the viscosity of a polymeric liquid at finite rates of deformation, two parameters must be determined, i.e. (i) the critical shear rate y (y=l/7.) at which T) becomes a function of the of deformation, and (ii) the slope in the linear range of the flow curve. 

The time dependency of the stress-strain rate relationship can be omitted for polymeric liquids in many practical situations. Now, let us consider Figure 22.6, which is a typical plot for viscosity in terms of shear rate for a polymer melt. Two different regions can be observed in the flgure. In the first region, which occurs at moderate low shear rate values, there is a smooth variation of polymer viscosity. In the second region, there is a more pronounced decrease of viscosity as shear rate is further increased. This section of the curve is often described mathematically by a power-law model that expresses the relationship between shear rate and the viscosity stated in Equation 22.9, as discussed in... 

The cone-and-plate and parallel-plate rheometers are rotational devices used to characterize the viscosity of molten polymers. The type of information obtained from these two types of rheometers is very similar. Both types of rheometers can be used to evaluate the shear rate-viscosity behavior at relatively low vales of shear rate therefore, allowing the experimental determination of the first region of the curve shown in Figure 22.6 and thus the determination of the zero-shear-rate viscosity. The rheological behavior observed in this region of the shear rate-viscosity curve cannot be described by the power-law model. On the other hand, besides describing the polymer viscosity at low shear rates, the cone-and-plate and parallel-plate rheometers are also useful as dynamic rheometers and they can yield more information about the stmcture/flow behavior of liquid polymeric materials, especially molten polymers. 

With the growth of flow rate from low values, the elements of the reactive mass with the longest residence time are carried out from the reactor, i.e. those that have reacted to the maximal depth and have the maximal viscosity. Instead, the reactor is refilled with a fresh mixture of minimal viscosity. The effect of non-monotony of the P(Q) curve in isothermal flow of polymerizing liquid was independently discovered in Refs. [34, 35], and moreover, in Ref. [34] its qualitative experimental confirmation (instabilities during the operation of the corresponding multipass heat exchangers) was reported. 

FIGURE 11.2 Typical viscosity curve for a polymeric liquid. Includes relationship with physical operations and constitutive models. 

Measurements of the common physical constants such as boiling point or refractive index are not sufficiently sensitive to determine the trace amounts of impurities in question. Besides the common spectroscopic methods, techniques like gas chromatography (GC), high-pressure liquid chromatography (HPLC), or thin-layer chromatography (TLC) are useful. The surest criterion for the absence of interfering foreign compounds lies in the polymerization itself the purification is repeated until test polymerizations on the course of the reaction under standard conditions are reproducible (conversion-time curve, viscosity number of the polymers). 

For a nematic polymer in a transition region from LC to isotropic state, maximal viscosity is observed at low shear rates j. For a smectic polymer in the same temperature range only a break in the curve is observed on a lgq — 1/T plot. This difference is apparently determined by the same reasons that control the difference in rheological behaviour of low-molecular nematics and smectics 126). A polymeric character of liquid crystals is revealed in higher values of the activation energy (Ef) of viscous flow in a mesophase, e.g., Ef for a smectic polymer is 103 kJ/mole, for a nematic polymer3 80-140kJ/mole. 

The curve of the apparent viscosity data versus temperature for PP/PU/APP is reported in the Figure 10.9. In the first step (200°C-240°C), the viscosity of the material decreases when the temperature increases following the behavior of a thermoplastic material. Even though we observe in this step a carbonization of the material surface, the polymeric matrix has been preserved under the surface. In the 240°C-300°C temperature range, the viscosity value slightly decreases and its value remains close to the low apparent viscosity of the material molten at 240°C. The sample appears as completely carbonized and liquid. The plateau may then be explained by the chemical transformation of the material (formation of phosphoric acid esters and aromatic species).33... 

The energy barrier, U, that molecules have to overcome in order to become attached to a nucleus surface is of importance in the solidification of silicate melts and organic liquids, especially of polymeric substances. In this case U signifies the activation energy in the process of the diffusion of a molecule (or its segments) from the bulk of the liquid phase to the surface of a nucleus. A drastic decrease in the diffusion rate in such liquids, related to the increase in viscosity as the temperature is lowered, causes a maximum to appear in the curve representing nuclei formation frequency as a function of temperature. The position of this maximum corresponds to some supercooling, AT as shown in Fig. IV-9. ... 

It is worth noting that there are two basically different situations of the viscosity variation during the polymerization process. First the reative mass remains liquid, i.e. its ability to shear flow is maintained r](t - cc) reactive mass loses possibility to flow (gap)ri(P P ) - oo at a certain critical conversion, p = p < 1. Both cases are of real technological interest the corresponding curves are given in Fig. 2. 

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