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The Rheological Studies on the Polypropylene/ Supercritical Carbon Dioxide Mixture at Highly Non-Newtonian Region
CaMold Plastic Corp. www.camold.com
Abstract: The rheological behavior of PP/supercritical CO2(SCCO2) mixture at highly Non- Newtonian region was investigated in this study. The uniform CO2-containing PP melt was produced by using a modified injection machine equipped with an additional gas port and a specially designed screw. After measuring the pressure profile, the flow rate and the temperature inside a slit die at front of the barrel during injection process, the apparent viscosity of the melt was determined with shear heating correction at different shear rates. The shear rate experimented by this equipment had extended to an order of 1E4 1/s. The theoretical consideration based on Cross and Carreau models and combined with the Eyring model was proposed to describe the rheological behavior of PP/CO2 mixture. Then after Rabinowitsch correction, the true viscosity at different temperatures was obtained and compared. The results revealed that the viscosity of PP/CO2 melt could be well correlated by Cross-Carrueau models, and the viscosity of PP melt was strongly influenced and reduced by CO2 addition. But the magnitude of viscosity reduction was actually determined by either the shear rate or the temperature that could be the dominant mechanism at different stages. Under the same temperature, the viscosity was reduced more significantly at lower shear rates. However, as shear rates raised, the viscosity reduction diminished and eventually reached a stable value at extremely high shear rates. Moreover, the viscosity reduction would be greater as the temperature was lower, but it also diminished when the temperature increased. For this PP/CO2 system, the distribution of viscosity data could be well represented by the master curve that implied the adaptation of normalized corrections on both the temperature and the CO2 effects.
Introduction In recent years, with special characters (1), the supercritical fluid (SCF) has been widely utilized in the plastic foaming process as the replacement of conventional foaming agents such as Freon and organic solvents, to eliminate the damage of the Ozone layer and to prevent worsening air pollution (2). By manipulating the thermodynamic instability of SCF, an extremely high population density of up to 109~1015/cm3 of micro-bubbles with a dimension of 1~100μm, can be produced by spontaneous phase separation that controlled either by temperature raise (3~5) or by pressure release (6~9). These were batch procedures that usually need more than 24 hours for gas saturation. To improve the efficiency, the continuous process was also under development (10). As the rheological property of the Polymer/SCF mixture governs the operation conditions as well as the morphology and the quality of the final products, therefore, understanding the rheology of the mixture is of fundamental importance for both theoretical development and industrial application. In the early stage, Han et al. (11,12) carried out experiments to investigate the rheology of gas- charged molten polymers in foam extrusion. By installing a rectangular slit die with a glass window at the front of an extruder, the basic flow behavior of the blowing agent/polymer mixture was examined. It was found that the gas-charged polymer melt exhibited a curved pressure profile along the axial direction near the die exit, but the polymer without the blowing agent showed a linear profile. He proposed that the gas separation and bubble growth within the die were responsible for the observed curvature variance. The measured pressure for bubble inflation decreased with the increase of melt temperature, but increased with the escalation of the blowing agent concentration, which could be correlated by saturated solubility of gas in the polymer melt at various temperatures and pressures. It was also found that the bulk viscosity of gas-charged molten polymers decreased with the increase of the blowing agent concentration and with the increase of the melt temperature. Noticeably, the two-phase solution would be generated for an open system as pressure declined and gas separated at the region near die exit, its rheological property was actually different from a uniform single phase. Hence, the traditional rheometer had to be modified to measure the gas-containing polymer system. Gerhardt (13) had adapted a Back Pressure Assembly on a capillary extrusion rheometer to prevent the gas separation. The results from his investigation on PDMS (Polydimethylsiloxane)/SCF system showed that the viscosity of PDMS decreased with the increase of CO2 content, and the Newtonian plateau was more apparent for the PDMS/CO2 system. However, the shape of the flow curve looked similar to pure PDMS. The maximum value of the experimented shear rate in this study was 1500 1/s, but actually, the material used was a polymer solution instead of a polymer melt. Gendron (14) utilized a commercial on-line rheometer, which equipped a Melt Flow Monitor at the front of a twin screw extruder, and the closed slit die was applied to measure the rheological property of PP(polypropylene)/CO2 and PS(polystyrene)/CO2 systems. The results revealed that the addition of CO2 could plasticize the polymers and depress the glass temperature(Tg). These two effects would be comparable to the phenomenon that was induced by temperature increase, and the correlation of zero-shear viscosity with temperature variation could be well expressed by the generalized Arrhenius /Williams-Landel-Ferry (W-L-F) equation. The highest value of the experimented shear rate in this study was below 200 1/s. There were many research studies conducted by utilizing equipments similar to Han?s in the following: Lee et al. (15) investigated a PS/CO2 system by using the capillary die attached to the front of a single extruder. They found that the viscosity of polymer melt decreased with the increase of the gas amount, but it increased with the raise of pressure. Furthermore, Lee et al. (16) proposed to use the generalized Cross-Carreau model to describe the viscosity dependence on the temperature, the pressure, the gas content, and the shear rate. Their reported shear rate was in order of 1E2 1/s, which was low as limited by the apparatus used. Lee et al. (17) again adapted a wedge die to perform the same experiment on a PE(polyethylene)/PS blending system. After the Rabinowitsch correction, the true shear rate was achieved to 1E3 1/s. Their results revealed that the shear-thinning behavior of polymer melt was less sensitive as CO2 was added, which implied that the power law index was shifted to a higher value. Khan et al. (18) combined the modified free volume theory with the Sanchez-Lacombe equation of state, and used a composition-dependent shift factor to correlate the variation of viscosity with the composition for a PS/CO2 system. The reported highest shear rate was 1000 1/s, and the results showed that the viscosity of the Newtonian plateau was lower for polymer/gas mixture and spread out over a wider range, the transition from Newtonian plateau to shear thinning occurred at a higher shear rate. Elkovitch et al. (19) also measured the viscosity variation of a PS/CO2 system by using a slit die to attach at the front of a single screw extruder. It was reported that a 56% viscosity reduction could be made by CO2 addition for PS. Their conditions of experimental temperature was 170??and the shear rate was limited under 100 1/s. After improving the mixing efficiency by using a twin-screw extruder, Lee et al. (20,21) extended the measured shear rate to 600 1/s. The results showed that the viscosity reduction for PS/CO2 was higher than PE/CO2, which may be due to the operation temperature was closer to the glass temperature of PS, and so it enhanced the efficiency of dissolution of CO2 in PS system. In the following research, Lee et al. (22) presented the methodology to correlate the viscosity for PS/CO2 system by using the generalized elastic fluid model. A total of eight material parameters were calculated by data regression, and also the solubility of gas in the polymer melt could be gained by pressure correlation. Kwag et al. (23) repeated the experiment of Gerhardt by using PS melt to replace PDMS, and the gases used were CO2, R134a and R152a. By method of viscoelastic scaling, the effects of concentration and pressure at different temperatures could be rectified. The tested shear rate was elevated to 2000 1/s, and the results revealed that the viscosity reduction for PS could be as high as nearly three orders of magnitude at 150??and 10wt% R152a content. This reported data for viscosity reduction was extremely higher compared to others (15~17,19~22), which might be due to the reason that the temperature chosen was much lower and the polymer still remained rigid in un-melt state. It was reported that for these three types of systems, similar effects of dissolved gas content on rheological behavior were observed to follow roughly the same tendency with the composition variation. By using a high pressure extrusion slit die rheometer, Royer et al. (24) measured the viscosity of the PS/CO2 system and presented that the viscosity of PS could be reduced as high as 80% by CO2 addition, but the proportion was dependent on both the operational conditions as well as the CO2 amount. By combining the traditional free volume theory with the thermodynamic model, the W-L-F equation was used to simplify the correlation for viscosity reduction of the mixture, and then only the physical properties of pure material were needed in calculation. Again, Royer et al. (25) extended their work to PP and LDPE(low density polyethylene), and proposed that the Arrhenius model could be used to correlate the temperature effect for melt viscosity of semi- crystalline materials. The highest shear rate they achieved was 500 1/s. To summarize, most of the literature studies on the rheological behavior of polymer/SCF systems were made by using a modified extrusion machine. The viscosity of the fluid and the applied shear rate were obtained after measuring the pressure drop and the flow rate inside either the slit die or the capillary die. But due to the constraint of the extruder that the flow rates were induced by screw rotation, the generated shear rates were always limited below the order of 1E3 1/s. In this present study, the fast movement of the screw on an injection machine was utilized to generate a much higher pressure and flow rate, so the experiment was extended to a highly Non-Newtonian region. The range of tested shear rates was achieved as high as an order of 1E4 1/s, hence detailed examination for rheological behavior at high shear rates could be made. A series of studies on the fundamental rheology of PP/CO2 mixture and the temperature correction for shear heating had been presented previously by our earlier papers (26,27). In the present study we extend the work to correlate the viscosity data by different models and make the Rabinowitsch correction for the non-isothermal condition, finally the complete data in true viscosity are reported both experimentally and theoretically.
Theoretical modeling For the fluid flow through a slit die, the stress at the wall is (28): The apparent shear rate is From the definition the apparent viscosity becomes where H is the slit height, ?P the pressure drop, L the length of the die, Q the volumetric flow rate , and W the die width. The Cross-Carreau model interprets well the shear-thinning behavior or so called ?pseudo- plasticity??for non-Newtonian fluid that can be formulated as below (Hieber34): where is the zero-shear viscosity or the Newtonian plateau in low shear rate region, is the stress that characterizes the critical shear stress level at the transition between Newtonian plateau and Power law region. The parameter-n is material constant related to the slope in the power law region, and parameter-a characterizes the breadth of the transition zone. When a=1-n, it becomes Cross model and a=2, the Carreau model. Essentially, the consideration for temperature effect on viscosity had been categorized into two different approaches based on the type of material or range of the temperature. For amorphous polymers at temperatures less than 100??above their glass transition temperature, the free volume is mainly affected by temperature variation, so the W-L-F equation that was based on the free volume concept clearly explained the temperature dependence for polymer viscosity and could be expressed as below: (30) where is the zero-shear viscosity at any temperature T, the empirical parameter corresponds to the zero-shear viscosity at the reference temperature Tr , T the temperature, and C1, C2 are constants, respectively 17.44 and 51.6, that reflected the temperature dependence of free volume fraction. For semi-crystalline polymer such as PP with a much lower Tg value of -10?? the melt temperature is always higher than Tg+100?? At such a temperatures that far above the glass transition point, the effect of the thermal energy is not only affecting the free volume but also overcomes the molecular interaction and induces the melt flows. Therefore, either the Arrhenius type model (31), or simply the Eyring equation (32) that represents an approximation of the W-L-F equation should be used: where B,D are material constants, D implies the activation energy for flow. After combining the Cross and Carreau models with the Eyring equation, the dependence of the viscosity on both the shear rate and the temperature could be expressed in the following forms: when the raw viscosity data at different shear rates and temperatures were obtained, the parameters could then be determined by non-linear regression of least squares method. Furthermore, to rectify the non-Newtonian deviation for polymer melt, the Rabinowitsch correction has to be adapted, and the true shear rate becomes (28): where is the true shear rate, and the second term in parenthesis is the slope of the flow curve that can be calculated from the shear stress-shear rate plot. Finally the true viscosity can be obtained by
Experimentation Equipment: A traditional 3.5 ounce injection machine with a maximum 1260 Kg/cm2 injection pressure and 100 ton clamping force had been modified by equipping an extra gas port on the barrel and also using a special designed screw. The CO2 came from the gas cylinder was pressurized by an ISCO 260D precision syringe pump, and then forced into the barrel. The screw was made specially with a diameter of 36 mm. The gas was introduced at a special zone of the screw to prevent reverse pressure occurrence. Otherwise, that might cause the melt to flow backwardly. A shut off valve was installed at the front of nozzle and was driven by a hydraulic system in manual mode. The valve was closed to avoid the leakage before melt injection, and it was opened when the injection stage started. The slit die with a flat-wall was adapted as a substitute for the traditional capillary die, to eliminate the errors that could be generated by shape difference from the curved surface. The dimensions of slit die were 0.15 m in length, 0.02 m in width, and 0.00075 m in height. The major reasons for using such a high L/H ratio die were first to achieve a fully developed flow, and second to avoid the entrance effect as measured positions on the die wall were far away from the entrance. Moreover, four measuring points could be sampled at one time. Four Kistler 6159A pressure transmitters that 30mm apart from each other were installed inside the slit die. The first one was located at 10 mm away from the die exit, particularly to inspect the unusual occurrence of exit-effect at that region. Three temperature transducers were placed between every two pressure transmitters to record the thermal history of the melt. The location and movement of the screw were measured by using the Daytronic Linear Velocity Displacement Transducer (LVDT). All the detected signals were converted into voltages and amplified by a Kistler 5041E Charge Amplifier, and then transferred to Data Acquisition software DAQ-2000 on a personal computer. Noticeably, the gain value had to be adjusted properly to obtain a good resolution. The whole equipment system is drawn in Figure 1.
Materials: The PP polymer pellet, PP-7633 (Mw= 380,000 and Mw/Mn=4) produced by Taiwan Polypropylene Co. was used in this study. The industrial grade CO2 gas was supplied from San Yan Gas Co. with purity of 99%.
Figure 1. Schematic diagram of the equipment that consists of the modified injection machine, the slit die, the gas supply and the data acquisition system.
Operation: Since the compressibility of gas was very sensitive with pressure variation during the batch injection execution, the CO2 flow rate might vary significantly between different shuts when minor system fluctuation took place, and thus the gas input could hardly be controlled at the same amount in precision level. It was taken into account that the injected gas amount was dominantly governed by (1) the procedure operation time, (2) the pressure of gas input, and (3) the back pressure for polymer feed, so when the process was proceeding under the quasi-steady state in automatic mode, which meant that these three controlling parameters were all set fixed and the fluctuation of the system instability was regarded as uniformly distributed, therefore the gas charged amount would be the same at different shuts. Three stages of temperature settings on the barrel were 185/200/210?? The temperature setting nearest the polymer entrance was set higher than the others to ensure that the pellet would be melted immediately while entering into the barrel. Another independent heating band was installed on the slit die and was set at 140??to prevent it from cooling. When the gas was forced into the barrel, the mixture might not be uniform initially or even existed in two phases. But as the temperature and pressure escalated during the transportation generated by screw rotation, the gas converted into supercritical state gradually and the mixing efficiency had been greatly improved. Finally, the uniform single-phase mixture would be formed. During the trials for adjustment on gas injection pressure, it was found that if the pressure was set too high, the system became unstable, and then the melt and the gas would separate into two phases. After several tests, the system was stabilized and the injected samples were composed of uniform micro-bubbles, so this pressure was selected as the optimum operational condition. During the injection stage by different settings of injection pressure, the melt viscosity can then be determined after measuring the pressure drop, the melt temperature and the associated volumetric flow rate in the die.
Results and discussion Pressure profile After tedious but simple procedures of the data calculation, the pressure variations at a specified injection pressure setting could be obtained and typically the pressure profiles at the pressure setting of 60% are shown in Figure 2 as an example. The pressure profiles show the tendency that the measurement at upper stream is always higher than that at down stream. There is a small jump on every pressure lines at the beginning of injection stage, which reflects the over-shoot phenomenon when the melt was suddenly stressed, and it becomes more apparent for the sensor that at the positions with a higher pressure. The slightly descent of P1, P2 curves is caused by the natural decay of the quartz element of the pressure sensor, which would become more significant by the smaller gain setting. However, the P3, P4 lines tend to be slightly ascent probably due to the shear-induced temperature raise occurs especially at final stage of each shut, but the differences between P3 and P4 are still remaining almost unvaried.
Figure 2. The pressure profiles at different sampling points for pure PP at a specified pressure setting of 60%. The pressure distribution inside the slit die for pure PP material at different settings are shown in Figure 3. The straight lines on the plot are obtained by linear regression and are representative for data at upstream, it means that the pressure gradients are reasonably constant at the flow channel that with a fixed cross section. It is also evident that as the injection pressure setting increases, the flow rate and the shear rate both get higher. But the data points near the die exit exhibit a distinct non-linear profile. This implies the exit-effect exists and the pressure drops rapidly to normal atmosphere when the melt flows out of the die. Meanwhile, as the pressure gradient increases with rise of shear rates, and also significant length of the flow channel, the extrapolated pressure at the die exit from straight-line region becomes negative in this experiment, so the conventional method of Bagley correction for adapting the true shear stress should be modified. In present study, the difference of pressure and the difference of axial distance at sampling points, P3 and P4, was used as the pressure drop and the effective flow length to calculate the pressure gradient and the shear stress that based on equation (1), thus possibly avoiding any error that could be derived from extrapolation.
Figure 3. Pressure distribution along axial distance of the slit die for pure PP at different injection pressure settings. The same procedures were repeated for PP/CO2 system, and the measured pressure data are presented in Figure 4. Similarly, the pressure profiles are straight lines at upstream region and the area near die exit also exhibits a non-linear relationship, but particularly there is a deflection between these two regions that can be clearly observed and be sketched qualitatively. The deflection was occurred as the pressure reduced to be insufficient to keep the gas soluble when gas-contained melt flows to a specified distance apart from die exit, then the gas phase separates and the bubble grows rapidly by diffusion. While the two-phase gas/melt solution forms, the gas phase is highly compressible and it could convert the pressure into elastic energy, so the pressure gradient becomes higher and the flow resistance is raised. The locations of gas separation are also found to move toward closer to die exit as shear rates get higher, which is consistent with Han?s result (11). When the two-phase fluid flows further toward to the die exit, the exit-effect then dominates and the pressure gradient drops dramatically, hence the deflection occurs. However, the detailed pressure variation in this area is still need for further quantitative study.
Figure 4.Pressure distribution along axial distance of the slit die for PP/CO2 mixture at different injection pressure settings.
Correction on the shear heating As different from the extruder, the injection machine offered a much higher pressure to achieve extreme high shear rates, but unavoidably, the performance of shearing itself would generate the heat within the melt, and thus it might increase the temperature sufficient enough to reduce the viscosity and enhance the screw movement. Both the temperature and the shear rate variations during the injection stage had to be corrected. After inspecting the temperature measurement during the injection procedure, all three transducers showed almost the same variation tendency, but the temperature at T1 was slightly lower (1~2?? than the other two, since it was cooled more at the die end by natural convection. The location of T3 was exactly at the middle of sampling points- P3 and P4, so it was representative and was adapted as the melt temperature. As an example, the time series relationship of screw location and the melt temperature at pressure setting of 60% are depicted in Figure 5. It shows that firstly, the initial drop of LVDT location was due to compressibility of the melt, which is consistent with initial rapid move of the screw. Secondly, the location profile was not simply straight during the injection procedure and could be more suitably expressed by a second order polynomial. Actually the location profile described the variation of screw position, and its slope illustrated the speed of the screw movement, and further the slope change implied the acceleration of screw motion. Then by the consequence with the LVDT location, the velocity of screw, the flow rate and the shear rate of melt were calculated. The plot reveals that the shear rate changes with the temperature rises during the shut, therefore, the correction on shear heating has to be made to turn the measured viscosity into the same temperature base.
Figure 5. The relationship of LVDT location and the temperature variation during the injection stage for pure PP at pressure setting of 60%.
Apparent viscosity The measured data for apparent viscosity related to temperature and shear rate are displayed three dimensionally in Figure 6 for PP and in Figure 7 for PP/CO2. By these plots, the dependence of viscosity on both the shear rate and the temperature can be observed simultaneously. The surfaces on plots represent the result of theoretical calculation by equation (9) and (10) within the experiment range. All the parameters are estimated by nonlinear regression that using the Levenberg-Marquardt algorithm (33) and the best-fit values are shown in Table 1. From the table, as the parameter D is related to the activation energy for flow, the lower D value of PP/CO2 than pure PP implying the free volume has been changed after CO2 addition, and so the zero shear viscosity would be changed explicitly. The values of parameter n are very close for both materials by each model, which indicates the viscosity profiles would be parallel at high shear regions. There are some minor discrepancies for the ?* due to the numerical convergence calculation, but it would not affect the tendency of the viscosity curves significantly. The root-mean square deviations (RMSDEV) of the experimental data for both systems are also listed in Table 1. The small differences between experimental data and calculated values shown on the plot reveal that most of the deviations of predicted values are reasonable and also acceptable. However, as the measurement can not examine the data for Newtonian plateau at very low shear rates, the validation for both models seems to be approximately close within the testing range of the shear rates and the temperatures.
(a) Cross-Eyring model
(b) Carreau-Eyring model
Figure 6. Measured viscosity data with respect to the shear rate and the temperature for PP in three-dimensional coordination, and the regression surface from (a)Cross-Eyring model (b)Carreau-Eyring model.
Table 1. Parameters based on the best fit of eqs (9) and (10)
(a) Cross-Eyring model
(b) Carreau-Eyring model
Figure 7. Measured viscosity data with respect to the shear rate and the temperature for PP/CO2 in three-dimensional coordination, and the regression surface from (a)Cross-Eyring model (b)Carreau-Eyring model. For clear depiction, the data is then displayed two dimensionally on the viscosity-shear rate plane in Figure 8 for PP and PP/CO2 melts. From Figure 8(a), it is found that even the operational temperature settings are all the same during the whole experiment, the measured data still show the trend that the melt temperature rises at higher shear rates, which is the evidence for the effect of shear heating. From Figure 8(b), It is also evident that the viscous heating still exists after CO2 addition. Since the procedures were not conducted under the constant temperature, the numerical calculation had to been conducted to shift all the experiment data into the same base then the substantial consequence that SCF content acts on PP could be clarified. Comparing the regression results, all the viscosity profiles show the similar shear-thinning behavior. However, the lower limit shown on plot was beyond the experiment range and was obtained by extrapolation for presenting the Newtonian plateau at low shear rates.
(a) PP
(b) PP/CO2
Figure 8. The apparent viscosity for (a)PP and (b)PP/CO2 , and the regression calculation by Cross and Carreau models.
As all the viscosity profiles are similar in shape under the same rheological model for both systems, when the temperature factor was scaled out on the viscosity dependence and isolated the shear-rate effect along, then the temperature invariant master curve can be expressed in terms of reduced variables - and (34). After shifting the viscosity data from different temperatures, the master curves for PP and all experimental points are depicted in Figure 9. As illustrated in this figure, the distribution of all data is closely collapsed to the master curve. However, the Carreau model shows a steeper change at the transition area and the slope of profile becomes smaller at high sheared region which possibly implying the approach to the second Newtonian plateau.On the other hand, by the Cross model, the profiles keep a constant slope at high sheared regions. Usually the Carreau model gives a better description for narrow molecular weight distribution (MWD) materials, and the Cross model might be more appropriate for the wider MWD ones (34). As the PP we used presently is wide MWD (Mw/Mn=4), so the Cross model would be utilized in the following discussion for true viscosity.
Figure 9. The comparison of master curves by Cross and Carreau models for both systems.
The Rabinowitsch correction and the true viscosity As equation (2) for calculating the apparent shear rate only holds for Non-Newtonian fluids with a shear rate independent viscosity, it does not hold for polymer melts. The true shear rate for PP and PP/CO2 has to be modified by using the slope of the flow curve to correct the degree of deviation from Non-Newtonian behavior. The flow curves were determined by the regression modeling and are plotted in Figure 10. The experiment data are presented for reference. From this plot, the slope of flow curve is calculated and then the true shear rate and the true viscosity can be determined by using equation (11) and (12).
Figure 10. The shear stress and the shear rate relationship for both systems at various temperatures.
The viscosity curves for PP at 200 ??are depicted in Figure 11 for an example, to present the influence of Rabinowitsch correction. It shows that the deviation between the apparent viscosity and the true viscosity is getting higher as the shear rate increases. However, the deviation is not a constant value but a function of the material, the temperature and the shear rate.
Figure 11. Comparison of the apparent viscosity and the true viscosity for both systems at 200??/p>
The true viscosity that described by Cross model for both systems at various temperatures are depicted in Figure 12. It completely shows that the shear-thinning behavior at various temperatures for PP melt with and without CO2 addition. The slope of the profiles implies the sensitivity of the viscosity variation with the shear rate change. Under the same temperature, the transition of the nonlinear region for PP has extended to higher shear rates after CO2 adding, which is agreed with Khan?s result (18). At the transition zone, all the viscosity variation of PP with shear rate change shows less sensitive at higher temperatures and with CO2 constituent, which has to be explained by considering functions that all the shear stress, the temperature and the CO2 content act on molecule structure. As the shear stress increases, the density of entanglement of molecular chains has been reduced. When the temperature rises, the molecules gain more kinetic energy so motion becomes easier. With CO2 addition, the system free volume is increased and the attraction force between molecules is decreased. So it means that increasing each of three terms is favored to enhance the melt flow and reduce the viscosity. Actually the stress term and the energy term are competitive to each other. At lower temperatures, the molecule was frozen more, and the contribution from shear stress is relatively higher, so the viscosity variation with shear rate changes is more obvious. But at higher temperatures, the molecules tend to move freely, then the contribution from shear stress becomes relatively smaller, so the shear-thinning behavior is less sensitive. For each profile under the same temperature, the slope shows an increasing tendency as shear rate rises, which means that the shear stress term has a more important responsibility at higher sheared range, and finally it approaches to a straight line at high sheared region. Equivalently, the influence of temperature becomes minor at high sheared region when the polymer molecules are highly oriented. At region of extremely high shear rates for both systems, the viscosity profiles are almost parallel with a certain difference. It indicates that the SCF content contributes a fixed amount to reduce the viscosity when molecule chains have been almost completely disentangled.
After transforming and in terms of reduced variables again, the experiment data and the master curves that correlated by Cross model are presented in Figure 13, where the solid line and the dash line represent the true viscosity and the apparent viscosity respectively. The consistency of data distribution with the master curve indicates that the viscosity change of PP melt after CO2 addition can be regarded as mainly reflecting through the change of zero shear viscosity without influencing the other material constants, which still can be regarded as a " thermorheological simple melt ".
Figure 12. The true viscosity at various temperatures that correlated by Cross model for both systems.
Figure 13. The master curves of apparent viscosity and true viscosity that correlated by Cross model for both systems.
The deviation between true viscosity and apparent viscosity for PP and PP/CO2 is depicted in Figure 14. The negative sign means that at a specified shear rate the true viscosity is always smaller than that of apparent viscosity. The deviation curve at a specified temperature shows a special U-shape profile, and it is smaller at lower shear rates as the fluid is approaching to Newtonian fluid. But when the shear rate increases, the true viscosity- which is the slope of tangent of the shear stress-shear rate curve, increasing much rapidly than that of the secant- which is the apparent viscosity, so the deviation becomes higher gradually. As the shear rate increases further beyond a critical value, the change of slope of the tangent is almost minor, but the secant is getting closer to the tangent and the deviation is becoming smaller, so it causes a unique U-shape curve. The correlation of stress and shear rate for PP at 200 ?? is presented as an example in Figure 15 for a better understanding. Furthermore, both the addition of CO2 and the increase of the temperature would move the U-shape profiles to higher sheared zone as the Newtonian plateau has been extended to higher sheared range relatively.
Figure 14. The deviation between the apparent viscosity and the true viscosity for both systems.
Figure 15. The shear stress and the shear rate relationship for PP at 200 ??.
Viscosity reduction After the addition of CO2, the gas content becomes an extra factor that influences the viscosity of polymer, and it is now competitive to both original terms - the shear stress and the temperature. There are two mechanisms that CO2 contributes to reduce the viscosity. Firstly, increase in the system free volume to loosen the molecular attraction and secondly, reduction in the density of molecular entanglement to decrease the flow resistance. But actually the extent of viscosity reduction is determined by whatever dominant mechanism is at different stages, because both factors exist at low shear rates, but density of entanglement decreases as shear rate increases, and only free volume term remains at extremely high shear rates. The term of Viscosity Reduction had been defined as below for comparing the viscosity change after addition of CO2, and it represents the contribution from CO2 content: where , denotes the viscosity of pure PP and PP/CO2 respectively. The viscosity reduction below shear rates of 1000 1/s at constant temperature for both systems is shown in Figure 16. It is found that the viscosity reductions are the most evident at low shear rates for all temperatures. Similar observations that had been reported for PS and PE in literature (20) were presented on the same plot for comparison. The R-value is higher as temperature is lower at specified shear rate. For example, the maximum viscosity reduction can achieve 63% at 180?? but when temperature increases, the maximum viscosity reduction decreases to 34% at 220?? Alternatively, the viscosity reduction at constant temperature is also decreased as shear rates increase, but it behaves in different trends at different shear ranges. At low shear rates, the value of viscosity reduction is very high, but the decreasing tendency is also very sharp. As the shear rate increases, the trend of decreasing then is slower, and finally the R-value achieves a stable value at extremely high shear rates.
Figure 16. The viscosity reduction for pure PP by CO2 addition at different temperatures. For explicit comparison of the viscosity changes in the whole range of shear rates, the viscosity reduction is then plotted on the semi-log coordination in Figure 17. As in region I of the plot, due to the great contribution from SCF, the magnitude of viscosity reduction is very dramatic at low shear region. However, as the orientation of molecules has been enhanced and also the molecular disentanglement starts when the shear rate rises further, as in region II and III, the viscosity reduction drops rapidly because the SCF contribution meets the competition from stress term, so it becomes less important. However, roughly the slope change is positive in region II but negative in region III, which reflects that the rate of contribution from stress term is increasing in region II and then decreasing in region III. When shear rates get even higher, as in region IV, the shear stress term then becomes the dominant factor, and the contribution from SCF becomes relatively minor, hence the viscosity reduction value decreases further but with a smooth slope change. At the region of extremely high shear rates, as in region V, the value of viscosity reduction nearly approaches to a stable and a final fixed value, which implies the limited SCF influence remained whenever the molecule chains have been almost completely oriented. Moreover, the viscosity reduction is decreasing as temperature increases at a specified shear rate, because SCF contributes relatively more at a lower temperature when the molecules are frozen that they are hardly be able to move. When the temperature rises, the molecular motions are much more active, so the contribution from SCF plays a less important role and then the viscosity reduction decreases.
Figure 17. The viscosity reduction of pure PP by CO2 addition in semi-log coordination.
Conclusions The additional gas input port had been equipped on a traditional injection machine to make the investigation on rheological behaviors for PP/CO2 mixture at high shear rates. By measuring the pressure, the temperature and the flow rate of the melt that flowed through the slit die which was attached at the front of the nozzle, the viscosities were obtained and compared for PP materials both with and without CO2 addition. The experiment had been extended to a highly Non-Newtonian range and the order of shear rates achieved was as high as 1E4 1/s, and the shear heating induced temperature variations at high shear rates were also considered and corrected accordingly. It was observed that the pressure profile for pure PP melt within the slit die could be represented by a straight line at the region far above the die exit, and it showed a non-linear profile at the die exit as the consequence of exit-effect. A special deflection was found for PP/CO2 mixture at the region near the die exit, which exhibited the influence of gas separation. Theoretically, Cross model and Carreau model for expression the shear-thinning behavior are combined with the Eyring equation for describing the temperature dependence of zero shear viscosity, to correlate the viscosity for both systems. The results showed that the viscosity of PP melt was strongly dependent on CO2 addition. The viscosity of PP was effectively reduced as a result of increase of the system free volume and decrease of the density of molecular entanglement. And after Rabinowitsch correction, the true viscosity data were obtained and compared. By scaling out the temperature and the SCF effects, then the master curve could well represent the distribution of all experimental data. It implies that viscosity variation could be superimposed for both PP and PP/CO2 system even though the activation energy for flow is different from each other. The viscosity reduction was most apparent at low temperatures and low shear rates. The CO2 contributions were similar to the effects derived either from temperature rise or shear rate increase, but as the shear rate or temperature increased, the SCF contribution diminished, and finally the viscosity reduction achieved to a stable value at extremely high shear rates. Moreover, the ultimate reduction value was lower for higher temperatures. This paper presents a procedure to verify the influence of the CO2 content and the shear induced temperature variation on pure polymer viscosity at different shear rates, both by experimentally measuring and theoretically modeling. It could be utilized as a fundamental for simulation of the SCF-added plastic foam injection process.
Nomenclature:
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