Polystyrene extensional viscosity

For polymer melts where the low shear rate limiting viscosity value is r ), r 3t]0 (14). Examples of extensional viscosity growth, either to a steady t](i ) value or to a strainhardening-like mode, are shown in Fig. 3.6 for the linear nonbranched polystyrene (PS), a high density polyethylene (HDPE) that is only slightly branched with short branches, and a long chain-branched low density polyethylene (LDPE) (15). 

Figure 3.39 Uniaxial extensional viscosity rj as a function of time following start-up of steady uniaxial extension at the extension rates e indicated. Data are shown for an unbranched polystyrene (PS I), a high-density polyethylene with short, unentangled side branches (HOPE I), and two low-density polyethylenes (LDPE III and lUPAC A), with long side branches. (From Laun 1984, with permission from the Universidad Nacional Autonoma de Mexico.)------------------------------...

Gupta RK, Nguyen DA, Sridhar T (1991) Extensional viscosity of dilute polystyrene solutions effect of concentration and molecular weight. Phys Fluid 12 1296-1318... 

Vinogradov et used a more sophisticated setup compared to that of Cogswell, and showed the equivalence of extensional viscosity data obtained using a constant stretch rate instrument and a constant stress instrument for molten polystyrene. An unexpected feature of the constant stress results was that the strain rate was found to decrease initially, as expected, but it then exhibited a minimum before becoming constant. This implies a maximum in the tensile stress growth coefficient and, in that respect, this behavior was similar to that of linear low density polyethylene as reported by Schlund and Utracki< ) among others. 

A. E. Everage and R. L. Ballman, Extensional viscosity of amorphous polystyrene, J. Appl. Polym. Sci. 

Jones DM, Walters K, WilUams PR (1987) The Extensional Viscosity of Mobile Polymer Solutions. Rheol Acta 26 20-30 McKineley GH, Sridhar T (2002) Filament-Stretching Rheome-try of Complex Huids. Annu Rev Huid Mech 34 375-415 Li L, Larson RG, Sridhar T (2000) Brownian Dynamics Simulation of Dilute Polystyrene Solutions. J Rheol 4 291-322 Gupta RK, Nguyen DA, Sridhar T (1991) Extensional Viscosity of Dilute Polystyrene Solutions Effect of Concentration and Molecular Weight. Phys Huid 12 1296-1318... 

Figure 9.1 shows the variation of extensional viscosity with extensional rate for the three filled polystyrene systems containing Ti02, CB and CaCOa. A comparison between Figure 9.1 and Figure 6.1 indicates the fillers appear in the same sequence when their levels of increases are considered. The highest viscosity increase occurs in CaCOj filled system, the lowest in Ti02 filled system and the medium in CB filled system both in extensional as well as shear flow. This naturally leads to the conclusion ttiat the effect of filler type on the extension viscous properties would be qualitatively akin to the effect on the shear viscous properties. 

Figure 9.1 Variation of steady state extensional viscosity with extensional rate for filled polystyrene melts at 30vol% of various types of fillers as indicated. (Reprinted from Ref. 29 with kind permission from American Chemical Society, vyashington DC. USA)...

Figure 9.4 shows the extensional viscosity vs. time curves for unfilled polystyrene melt at different extensional rates. It was found [19] that the extensional viscosity may tend to become constant at very low deformaticm rates, but become unbounded at higher and higher deformation rates. With filler concentration at low loading levels of 5 and 10% of carbon black filler, it weis fotmd [19] that the plots resembled those in Figure 9.4. However, at higher filler concentrations, constant extensional viscosities were achieved with time and these values were found to decrease with increasing extensional rate as shown in Figures 9.5 ctnd 9.6 for 20 and 25 vol% carbon black loading.

FIgur 9.5 Variation of extensional viscosity with time at different extensional rates for 20vol% carbon black filled polystyrene melt at 170°C. (Reprinted from Ref. 19 with kind permission from Society of Plastics Engineers Inc., Connecticut, USA.)... 

Figure 9.11 shows the effect of surface treatment on extensional viscosity for 30% calcium carbonate filled polystyrene [27]. The data are presented in two forms, namely steady state extensional viscosity vs. extensional rate in Figure 9.11(a) and steady state extensional viscosity vs. tensile stress in Figure 9.11(b). Irrespective of the type of data representation, it is seen that surface treated calcium carbonate reduces the level of extensional viscosity and brings it closer to that of the unfilled polymer. The yield stress value is reduced considerably though the values of the ratio of yield stress in extension to that of shear is still maintained nearer to the von Mises value of 1.73 as can be seen from Table 9.1. Surface treatment tends to modify the forces of particle-particle interaction and hence show reduced yield stress values due to lowering of the interaction forces [2,27]. 

A typical example of extensional flow is the flow at the entrance of a capillary die. Cogswell [83] has shown that the pressure losses through sudi dies can be used as a measure of the extensional viscomty. This method has not lined popularity because of the skepticism in acc ting the complex converging-flow patterns at the die entrance as representative of true extensional flow with constant extensional rate. Cogswell [84] did suggest later that the die should be lubricated to reduce the shear flow and the profile of the die wall should vary at all cross sections in such a way as to ensure constant extensional rate along the die axis. Such a rheometer has been known to be developed and used for extensional viscosity data of polystyrene melt [85]. 

Orr and Sridhar demonstrate that the extensional viscosity shows a dependence on strain history, even for relatively low-molecular-weight (50 kDa) polystyrene at elevated concentration (25 wt%) in dioctylphthalate(24). For polymers being... 

Another end-separation method was recently described by Bach et al. [201]. Their filamentstretching rheometer (FSR) is an adaptation of a device originally developed for dilute polymer solutions [202,203 ] and later used for concentrated solutions [203,204]. As shown in Fig. 1024, the filament is formed from a small sample by stretching it between two cylindrical, steel fixtures to which it is attached by the direct adhesion of the sample to the metal. The strain in this device is not uniform, and the measurement is based on the portion of the filament midway between the end fixtures, where its diameter is a minimum. As a result, several preliminary experiments are required to establish an empirical relationship between the radius at this point, where the Hencky strain is -2[ln(R/Ro)] and the distance between the fixtures, L (t). The data for e < 1.0 are not reliable, but steady state was reached in experiments by Bach et al. for an LDPE and an LLDPE, making it possible to determine the extensional viscosity [201]. The results agreed with data from an RME. This technique has also been used to demonstrate extension thickening in linear polystyrene [204]. 

Figure 11.11 Comparison of the predictions of the DEMG model (solid line) and MLD model (dashed and dotted lines) to experimental data (symbols) for the uniaxial extensional viscosity rif (e) versus extension rate f. The data are for a 6% solution of 10.2 million molecular weight polystyrene In diethyl phthalate at 21 °C.The parameters used In the MLD and DEMG theories are G 5 = 294 Pa for both models = 21 s, and Tj = 0.51 s for the DEMG theory, and = 83.4 s, and Tj = 1.08 s for the "Mllner-McLeish" method of obtaining the time constants for the MLD model (dashed line), and Tj = 123 s, and Tj = 1.58 s for the "Doi-Kuzuu" method (dotted line). From Bhattacharjeeeta/. [49).

Figure 11.13 Steady-state uniaxial extensional viscosity normalized by the zero shear viscosity versus Weissenberg number Wi = re for nearly monodisperse polystyrene melts with molecular weights of 200,000 (-i-) and 390,000 ( ), where r is roughly the reptation time.The line is the prediction of the Doi-Edwards theory (from Bach etal. [56]).

FIGURE 3.15 Comparison of predictions for extensional viscosity (rj) for three constitutive equations (WM, UCM, and PTT) with experimental data for polystyrene (St5Ton 678) at 190 °C. (Data from Gotsis, 1987.)... 

Fig. 3.6 Extensional growth viscosity versus time for polystyrene (top), HDPE, and LDPE. [S. A. Khan, R. K. Prud homme, and R. G. Larson, Rheol. Acta, 26, 144 (1987).]...

---