Polymer master rheograms

Table Cl Details of data used for master rheograms of filled polymers in Figures 6.32-6.39 (Source Ch. 6 Refs [50] and [149]) ... 

In order to exemplify the method of master curve generation, low-density polyethylene (LDFE) is diosen as a representative case and a step-by-step procedure is outlined, lowing four graphs before the final master curve is given. In the case of all other polymers, the master rheograms are directly presented. 

The viscosity versus shear rate data for VCVA was obtained from a book [35] and a research paper [80]. The data were for a limited shear rate fiom 0.1 to 600/s and covered a limited temperature range from 140°C to 180°C (Bible B2 of Appendix B). Nevertheless, this coverage was within the useful and relevant range for this polymer. A total of 32 data points were used [77] for unifying the curve to form the master rheogram for VCVA shown in Fig. 4.33. 

The viscosity versus shear rate data for HDPE/PMMA blend were obtained [87] from only a single source [89] and at a solitary temperature of 160°C (Table B3 of pendix B). However, an exhaustive range of 12 compositions including the pure HDPE and pure PMMA polymer were covered. The data were available only in the low-shear-rate range from 0.01 to 1/s. Using a set of 36 data points, the master rheogram shown in Fig. 4.39 was created. 

The master rheograms for filled polymers have been given by Shenoy et al. [95] on a limited number of systems. These are for filled systems of LDPE, HOPE, PP, PS, Nyltm, PET, and PC using date from Refs. 33,44,59-61,65, %-102. The various filled polymer systems analyzed by them are summarized in Table BS of pendix B. 

Tables 6.S-6.8 list the model constants and the range of applicability based on the modified Carreau model, the modified Ellis model, the modified Ostwald-de Waele power-law model, and the General Rheological [11] model, respectively, for the master rheograms of most of the polymers discussed in Chapter 4.

The tests were performed to check how close the predictions from the master curve are to the actual data of viscosity versus shear rate. For most polymers, the error in the predicted value was limited to a maximum of 20%. The minimum deviation was less than 3%, as in the case of PET. For some polymers, however, the maximum mror in the case of some data was within a broader band of 40%. The reason for diis is that the master rheogram itself had a broad bandwidth. Because most of the data were coalesced from existing literature data, the errors in the miginal data naturally oeep into the predictions from the master curve. It is known fiiat, even with the most sophisticated equi ments, errors to the extent of S0% can oeq> in if proper care is not taken when generating the data. Thus, the blame for the broader error band in the case of some polymers, that too only in file low-medium shear-rate ran s, does not rest entirely with file master curve. If the original data which are used for forming the master curve are error-free, then automatically the master curve predictions would be very accurate, as fiie unification tedmique itself is very reliable. 

The chapters that need comments are those from Chapter 4 onward. For example, in Chapter 4, a different type of unification approach is described and used for obtaining master rheograms for a number of polymers which include... 

The polymer processor normally has ready access to the MFI value of the raw material that he intends to use. The master rheograms provide the quickest and simplest method for obtaining viscosity versus shear rate data at the temperature of interest simply through the use of the appropriate MFI value. The master rheograms are unique for each generic type of polymer over a wide range of shear rates, excepting the very low and very hi shear rates wherein the effect of molecular-wei t distribution is felt. 

In the case of extensional viscosity, unified curves have been presented for a limited number of cases and the data used for coalescence are also-limited. Because of the difficulties in measurement of extensional viscosity, the reliability of the data is often questionable. Because the original data cannot be as trustworthy as in the case of shear viscosity or complex viscoaty data, the master curves of extensional data should be looked at in the same light. In the case dt shear viscosify, the master rheograms for the filled polymers have been shown to be the same as those for the unfilled system. is, of course, true in the medium to high shear-rate region. In the low-shear-rate region, however, the effects of yield stress would dominate and the uniqueness of the curve will be... 

Chapter 4 gives master rheograms for a long list of polymers but, by no means, includes all known thermc lastics. It is, therefore, beneficial to establish the master rheograms for the thermoplastics not considered in the book along with any new polymers, time and again, when they get developed in the future. 

The upgraded master rheograms have been given in Chapter 5 for a handful of polymers. A systematic study can be initiated so that master rheograms of (q X versus (W /M ,) y/MFI can be established for all polymers... 

Table B5 Details of Data Used foi Master Rheograms of Filled Polymers... 

Table B7 Details of Data Used for Master Rheograms of Recyded Polymers in Figs. 4.46-4.48...

The fourth chapter begins with the origin and definition of MFI. It then develops the fundamentals of the unification technique based on a strong theoretical rationale. A demonstration of the use of this technique is followed by ample master rheograms of shear viscosity for a long list of common homopolymers, copolymers, blends, PVC formulations, and filled and recycled polymers. 

The fifth chapter upgrades the master rheogram in the low-shear-rate region where coalescence is impaired by differences in the molecular-weight distribution of the polymers. Further, extensions of the unification tedinique are discussed to establish the parameters for obtaining master curves for other rheological parameters such as normal stress difiference, complex viscosity, storage modulus, and extensional viscosity. 

The flow parameter that is readily accessible to most processors is the melt flow index (MFI). The MFI is either specified by the thermoplastics raw material supplier or can be easily measured using a relatively ine nsive apparatus. It is a single-point viscosity measurement at a relatively low shear rate and temperature. Earlier, it was often said that MFI gives a dot when actually what is needed is a plot for the polymer processors. However, this is not true now because of a unique approach developed for estimating the rheogram merely from the knowledge of the MFI. This approach is discussed in detail in this chapter, and unified master rheograms for most polymers are presented. 

In order to generate master rheograms, the authors went through an elaborate process of data collection and analysis. One, two, or all three of the following methods were employed for data collection in the case of each polymer. 

Viscosity versus shear rate curves for two different compositions of a hydroxy benzoic acid/poly(ethylene terephthalate) copolymer (HBA/PET) at various temperatures were used [84] in the formation of the master rheogram for the liquid-crystalline polymer shown in Fig. 4.37. The data for 80 mole% of HBA at six different temperatures ranging from 275°C to 330 C were taken from Ref. 42. In order to eliminate operator and interlaboratory errors, the data on the same composition at one representative temperature of 275°C was also used from another source [85]. The other composition of HBA/PET chosen was 60 mole% and again from two different sources [42,86]. From one source [42], the viscosity data for 60 mole% of HBA at three different temperatures between 210°C and 300 C was used, where as from the other [86], three different temperatures between 260°C and 285 C was used. A total of 51 data points covering a shear-rate range from 2 to 8000/s have been included (Table B3 of Appendix B) in the unification process to form the master rheogram in Fig. 4.37. 

Although only three different types of polymers are presented, it can be seen conclusively that the master curves generated hold good for virgin as well as reprocessed material. Thus, the master curves reported for virgin polymers in Figs. 4.11-4.43 could be used reliably as master rheograms of reprocessed materials. 

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