RHEOLOGICAL MODELS FOR UNIFIED CURVES

In Chapters 4 and S, a number of unified curves have been presented for a variety of polymers of different generic types. These curves can be readily used for generating specific material parameter versus shear rate curves at any required temperature of interest merely from the knowledge of the MFI at that temperature. As ASTM test conditions [1,2] have to be conferred to during MFI test measurements, the MFI at the ASTM test temperature needs to be converted to the MFI value at the required temperature of interest. This could be done through the use of the modified Arrhenius-type Eq. (4.14) or the modified (Williams-Landel-Feny) WLF-type Eq. (4.15) described in Sec. 4.2.4. 

Care must be taken to use the appropriate activation energy E value [3,4] and the appropriate glass-transition temperature T, value in the respective equations. The value of E must be determined [3] within a nanow temperature band around the temperature of interest, so that the obtained value has higher accuracy. In the case of copolymers [4], extra caution has to be exercised because of the presence of dual values so that the appropriate value alone is chosen. 

The Tg values for various polymers are summarized in Table 1.5 for ready reference. It is important [5] to use the appropriate value of Tg in order to minimize errors in MFI estimation. The value of Tg could vary within a broad range from 10°C to 15 C, especially in the case of amorphous polymers. The values of the heat distortion temperatures of various grades of polystyrene (PS) are reported in Table 6.1. The heat distortion temperature, being a thermomechanical property of a polymer, is qualitatively related to the glass-transition 

Source Ref. 5 (Reprinted with kind permission from Steinkopff Verlag Darmstadt.) 

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Shenoy, A. V. and Saini, D. R., Rheological models for unified curves for simplified design calculations in polymer processing, RheoL Acta, 23, 368-377 (1984). 

The rheological models for unified conq>lex viscosity versus frequency curves can be ea y written based on the modified Cox-Mertz rule discussed in Quarter 5. Thus, using Eq. (5.5), the modified Carreau model for complex viscosity can be written from Eq. (6.1) as... 

Hguro 6.1 Evaluation of Genml Rheological model constants for unified curves of viscoitity versus ear rate. 

In order to simplify the final step in generating the required material parameter versus shear rate curves from by the above procedure, appropriate rheological models have been suggested for fitting the unified curves. 

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