Master Rheograms

In order to generate master riieograms, 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. 

Method 1 scosity versus shear data was generated by the authors using the Weissenberg Rheogoniometer R19 in the lower-shear-rate regkm (10 -l(P/s) and on the Instron Capillary Rheometer Model 3211 in the higher shear-rate region (10-l(f/s). 

Method 2 scosity versus shear rate data was collected from published literature. 

Method 3 fiscosity versus shear rate data was obtained directly from manufacturers of polymers. 

The MFI values needed for the unification process were obtained from one 

Method A The MFI was actually measured using a Melt Flow Indexer Method B The MFI was estimated from the available shear stress versus shear rate curve in the manner discussed in Sec. 4.2.2. 

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Appendix C Data details and sources for 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]) ... 

All this was done in order to consolidate the master rheograms and eliminate any dependence that these might have on the measuring techniques, equipment, or operator. 

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 master rheogram for HDPE is shown in Fig. 4.12. The data used in this curve involve three sources [30,31,46] and includes 146 data points. The viscosity versus shear rate curves were available for a shear-rate range from 0.01 to 1000/s and at eight different temperatures from 170 C to 220°C (Ihble B1 of Appendix B). 

Figure 4.13 shows a plot of X MFI versus y/MFI, which is the master rheogram for UHMWPE that is grade and temperature invariant. 

The viscosity versus shear rate data for PS was obtained from three different manufacturers (1) J.P. Whelan, Amoco Chemicals Corporation, Naperville, Illinois. (2) Dow Chemicals, Midland Michigan, (3) H.A. Biletech, LTDC, Polysar Inc., Massachusetts. These data [33,51,52] along with those obtained from a research paper [53] were unified [30] to form the master rheogram as shown in Fig. 4.16. A total of 112 data points were used over a very broad range of shear rate (Ihble B1 of. ipendix B). 

The master rheogram for aorylic is shown in Fig. 4.18. Atotal of 105 data points covming a shear-rate range from 1 to 10,000/s have been used [56]. The bulk of the data has been taken from Westover [35] and conqilemented by 12 data... 

For polyacetal (POM), viscosity versus shear rate data were obtained from two sources [57,58]. One source was the renowned book on polyacetals by Barker and Price [57], whereas the other source was a research paper by Pritchard and Wissbrun [58]. Only 24 data points were analyzed and the master rheograms as shown in Fig. 4.19 were generated [56]. Even with limited data, two distinct master rheograms were revealed—one for linear polyacetal and the other for branched polyacetal. This is not an unexpected situation and is. similar to that observed earlier for polethylenes wherein HOPE (linear PE) and LDPE (branched PE) have two distinct master rheograms. 

The master rheogram for poly(ethylene terephthalate) (PEI) is shown in Fig. 4.21. cept for 4 data points taken from a research paper by Wu [61], the 169 data points were obtained from a single source, namely, the manufacturer [62]. All types of grades of PET (i.e., fiber, molding, tire cord, bottle) have been unified on the master rheogram [56]. in the case of nylon, the Newtonian plateau is very distinct and covers a wide range of shear rate. The deviation from the Newtonian behavior is also not too pronounced even at considerably higher shear rates. 

The viscosity versus shear rate data for polycarbonate (PC) covering a limited range of shear rate from 10 to 2000/s and temperatures from 2S0 C to 290°C were used [56] in obtaining the master rheogram shown in Fig. 4.22. Data on... 

The master rheogram for SAN is shown in Fig. 4.30. A total of 80 data points have been used [30], covering a limited shear-rate range from 20 to 600/s (Table B2 of Appendix B). The viscosity versus shear rate data was made available from the manufacturer [51]. This data was for two different grades of SAN (lyrll 860B and lyril 867B) at four different temperatures (200 C, 215 C, 230"C, and 250 C). 

The master rheogram for SBS is given in Fig. 4.31. This unified curve has been produced [77] using limited data from a single source [39]. The 27 data points included have been taken from viscosity versus shear rate curve spanning 6 temperatures between 110°C and 210 C and covering a shear-rate range from 0.1 to 1000/s (Table B2 of Appendix B). 

The master rheogram for ABS shown in Fig. 432 was formed [77] by using viscosity versus shear rate data from two research p rs [78,79], In one case [78], the available data were for one grade of ABS, namely, Kralastic MH at three different temperatures of 180°C, 200 C, and 220°C. In the other case [79], at a single temperature of 210°C, viscosity versus shear rate data for two... 

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 master rheogram for ethylene-vinyl acetate (EVA) is shown in Fig. 4.34. This unified curve was obtained [77] from limited data on just one grade of EVA, namely, ALAIHON EA A 3185. The viscosity versus shear rate data were available [40,41] at seven temperatures between 60°C and 125°C, covering a shear-rate range from 0.01 to 500/s (Table B2 of ipendix B). 

The viscosity versus shear rate data for polyester elastomer (Hytrel) were obtained from its technical brochure on rheology and handling suf lied by the manufacturer [81] (Table B2 of Appendix B). The data covered a shear-rate range of 10-3000/s for five different grades of Hytrel. For three of the grades, the data temperature was 220 C, whereas for the other two grades, they were 180 C and 240 C, respectively. A total of 20 data points were used [77] in the unification process to obtain the master rheogram for polyester elastomer (Hytrel) shown in Fig. 4.35. 

The master rheogram for olefinic-type thermoplastic elastomer (TPE) obtained by the unification [77] of viscosity versus shear rate data from two sources [82,83] is shown in Fig. 4.36. The data covers a number of different grades of TPE over a range of shear rate from 1 to 1000/s but is limited to the two temperatures of 20S C and 230°C. A total of 44 data points have been used in the unification process (Table B2 of Appendix B). 

The master rheogram [87] for PP/HDPE is shown in Fig. 4.38. the viscosity versus shear rate data were avaUable at one single temperature of 19(FC but... 

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. 

Only limited data on PS/PMMA blend have been used [87] in order to generate the master rheogram shown in Fig. 4.40. A total of three compositions (0.75/ 0.25, 0.50/0.50, 0.25/0.75) of PS/PMMA besides the pure components were used. The viscosity versus shear rate data coveting a shear-rate range of 20 to... 

The master rheogram for PS/POM blend shown in Fig. 4.41 is based on limited data [87] taken from a single source [91] at a fixed temperature of 210°C. A total of 20 data points were taken from the viscosity data that spanned a shear-rate range from 20 to 400/s for 3 compositions (0.9/0.1, 0.5/0.S, 0.2/0.8) of PS/ POM, in addition to the pure components (Table B3 of Appendix B). 

The master rheogram established [92] for PVC formulations is shown in Fig. 4.43. This was formed using exhaustive viscosity versus shear-rate data from... 

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. 

It was found [95] that the master rheograms for each of filled systems was no different from that for the unfilled systems over a broad range of shear rates. Only in the very low-shear-rate region, the master curve is not unique due to the yield stress behavior, which is known to occur for filled systems as can be seen from one typical curve shown in Fig. 4.44. This aspect was depicted [95] only for HDPE, where a clear fork was shown to exist in the low-shear-rate region. Although in other curves the forks were not shown [95], it does not imply their nonexistence. In fact, if sufficient data in the low-shear region on filled systems was available, then the fork would be present in all the curves. However, the matter of prime importance is that the master curve in the... 

UPGRADING THE VISCOSITY MASTER RHEOGRAM IN THE LOW SHEAR REGION... 

In the master rheograms of viscosity versus shear rate given in Chapter 4, the following four models have been suggested [10,11] covering a varied range of shear rates ... 

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