Viscosity-temperature Functions

TABLE 15.7 Group contributions to the molar viscosity-temperature function (g J,/3/mol4/3)... 

Molar thermal decomposition function, 763, 767 Molar thermal expansivity, 89 Molar viscosity-temperature function, 543 Molar volume (s)... 

The average molecular weight, polydispersity, temperature, hydrostatic pressure, and shear rate dependences of polymer melt viscosity will be discussed in Chapter 13, resulting in a set of correlations which can be used to obtain a rough estimate of melt viscosity as a function of all of these variables. A new correlation will be presented for the molar viscosity-temperature function. The dependences of the zero-shear viscosity of concentrated polymer solutions on the average molecular weight and on the temperature will also be discussed. Finally, a new model that was developed to predict the shear viscosities of dispersions of particles in both polymeric fluids and ordinary molecular fluids will be presented. 

Et1oo is the activation energy for viscous flow at zero shear rate in the limit of T E can be estimated [7] in terms of the molar viscosity-temperature function HT1 by using Equation 13.12. Hp is expressed in units of g F1/3"mole"4/3 and normally estimated by using group contributions. For example, the use of group contributions gives HT)=4020 g J1/3 mole-4/3 for polystyrene, so that the use of Equation 13.12 with Hp=4020 and M=104.15 results in ET OO =57504 J/mole, in comparison with the experimental value [7] of 59000 J/mole. 

Because of the limited amount of reliable data for E oo, only a limited number of group contributions is available [7,12] for the molar viscosity-temperature function HT) used to estimate this property via Equation 13.12. It is, therefore, useful to develop a correlation to allow the prediction of this quantity when the required group contributions are not all available. The correlation developed for this purpose will be presented in Section 13.C.2. 

The molar viscosity-temperature function HT) can be expressed [7] as a sum of two terms ... 

Table 13.1. Additive portion HT)sum of the molar viscosity-temperature function calculated by using group contributions, molar intrinsic viscosity function J and correction index NHt) used in the correlation, and fitted or predicted (fit/pre) values of for 140 polymers. For 60 of... 

Figure 13.3. A fit using the molar intrinsic viscosity function J, for the simply additive portion Hnsum °f e molar viscosity-temperature function H. is in g T1/3-mole 4/3.

Table 13.2. Observed activation energies for viscous flow of polymers at zero shear rate as T—>°o (E J [7], and the values of predicted by using the correlation developed for the molar viscosity-temperature function in this section. E is in units of 1()3 J/mole.

Wright11 suggested that m be termed the viscosity-temperature function (VTF). This last equation becomes... 

W. A. Wright, The Viscosity-Temperature Function, ASTM Bulletin July 84—86 (1956). 

It is not yet possible to give a reliable explanation of all these phenomena (when considering them in detail, still more complications are encountered ), but some indications can be borrowed from viscosity data which seem to lead to the key for unravelling these problems. The viscosity-temperature function of molten sulphur... 

The temperature dependence of melt viscosity at temperatures considerably above T approximates an exponential function of the Arrhenius type. However, near the glass transition the viscosity temperature relationship for many polymers is in better agreement with the WLF treatment (24). 

From the y(jc) functions and the two melt temperatures used, and by using the viscosity curves from rheological examinations (Fig. 11), viscosity distributions T](jc) of the two pure components were easily determined, as shown in Figs. 15a and 15b. Subsequently, the viscosity ratio functions 6(jc) were also calculated (Fig. 16). All four curves fall slightly from the core to the outside. 

Figure 15 Calculated viscosity as function of the halved sample thickness for two melt temperatures and for (a) injection volume flux of 8 cmVs and (b) injection volume flux of 80 cm /s.

Oil fuel pipeline systems transfer oil from storage to the oil burner at specified conditions of pressure, viscosity, temperature and rate of flow. There can be considerable variety in the choice of system, but its design (particularly correct pipe sizing and temperature control) is most important if it is to function satisfactorily. 

Viscosity is normally measured at two different temperatures typically 100°F (38°C) and 210°F (99°C). For many FCC feeds, the sample is too thick to flow at 100°F and the sample is heated to about 130°F. The viscosity data at two temperatures are plotted on a viscosity-temperature chart (see Appendix 1), which shows viscosity over a wide temperature range [4]. Viscosity is not a linear function of temperature and the scales on these charts are adjusted to make the relationship linear. 

The relaxation of gaseous methane, ethane and propane is by the spin-rotation mechanism and each pure component can be correlated with density and temperature [15]. However, the relaxation rate is also a function of the collision cross section of each component and this must be taken into account for mixtures [16]. This is in contrast to the liquid hydrocarbons and their mixtures that relax by dipole-dipole interactions and thus correlate with the viscosity/temperature ratio. 

Fig. 3.6.2 Relaxation time of pure alkanes or methane saturated alkanes as a function of viscosity, temperature and gas/oil ratio (GOR, m3 nT3) [13]. The solid line is for zero GOR. The dashed lines are for the indicated GOR.

Fig. 10. Complex dynamic viscosity as function of temperature for three different aliphatic hyperbranched polyesters based on bismethylol propionic acid and having different end-group structure - (O) propionate end-groups, ( ) benzoate end-groups, ( ) hydroxyl end-groups [118]...

Fig. 6.26 Local viscosity as function of the polymer concentration C scaled to the solvent viscosity ry for PS in the good solvent d-benzene at two temperatures (open circles T=30.6 °C, plus 65 °C). And in cyclohexane at the 0-temperature (full circles). (Reprinted with permission from [327]. Copyright 1996 The American Physical Society)...

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