PVT data first gained prominence when it was used to model compressibility in computer simulations of the packing phase of the injection molding process[1]. Plastics are compressible at the high pressures used in the injection molding process. During the packing phase, most of the flow results from compressibility. This effect is modeled using the PVT data. Further, after freeze off, the part begins to shrink. If the plastic is semi-crystalline, the shrinkage is primarily due to crystallization. PVT data has been used to model the volumetric shrinkage of the plastic which is then translated into linear dimensional changes. However, there have been several limitations in this step. For reasons described below, the traditional PVT data does not describe the true characteristics of the injection molded part and limits the ability of these simulations to correctly predict the shrinkage of semi-crystalline injection molded products.

Traditional measurements of PVT have used essentially equilibrium methods; the specimen is equilibrated or is in a state of quasi-equilibrium at each test temperature prior to taking measurements. Several modes of measurement have been used [2]. These are outlined below:

1) Isothermal cooling measurements:
Starting from the melt, the polymer is equilibrated at the test temperature before subjecting it to a compression cycle [3]. It is then cooled to successively lower temperatures and the compression process repeated to develop an equilibrium equation of state for the material. This technique has been in widespread use but suffers from severe drawbacks. By taking measurements while cooling the polymer, the technique is intended to capture the correct crystallization behavior of the plastic. We find from our experiments that this is not the case. The process of performing compression cycles provides the driving force needed for nucleation. Consequently, the plastic crystallizes close to its melting temperature, missing completely the supercooling effect which is so characteristic of the crystallization behavior of semi-crystalline polymers. Compare the melting transition in Figure 2 to the isothermal cooling transition in Figure 4. Most importantly, it is not possible to replicate the unique “skin-core-skin” crystalline morphology seen in injection molded products within a PVT apparatus. The PVT data of the solid state is then an artifact of the measurement and bears no resemblance to that of the injection molded part.

2) Isobaric cooling measurements:
The plastic is heated to its melt state and then solidified under a constant pressure [2]. The process is repeated at other pressures to develop a complete equation of state. This is also a quasi-steady state measurement conducted at very low cooling rates. Since the specimen is not being subject to the compression cycles, it does need the thermal driving force to crystallize. The supercooling behavior is correctly observed resulting in transition temperature shifts that correspond well with those seen by DSC. The pressure dependency of the transition is also captured correctly. However, it still suffers from the same drawback as the isothermal cooling mode: the solid state morphology does not represent that of the injection molded part. Moreover, several morphologies can be obtained depending on the pressure at which the polymer is solidified [6].

3) Isothermal heating measurements:
Here, the polymer is taken through a step-wise heating process with a compression cycle being performed at each equilibrated test temperature [2]. While well suited to general polymer characterization, the technique has a drawback in our situation in that it captures the behavior of the polymer as it melts, rather than as it cools. However, provided that the test utilizes an injection molded test specimen, the technique does capture the true solid state PVT behavior of the injection molded part. It should be pointed out that all three techniques have equivalent in their ability to characterize the melt state PVT behavior.

In this paper we present a hybrid scheme whereby we are able to circumvent the problems faced by the above techniques using a combination of PVT and DSC measurements. The solution is specific to the characterization of the PVT behavior of semi-crystalline injection-molded plastics.

Principle

DSC measurements are made on an injection-molded specimen at the same heating rates as those seen in the PVT measurement. These are used in the analysis to calibrate the results from one apparatus against the other. This calibration is necessary to ensure that there is correspondence between the volume change upon crystallization observed by the PVT apparatus and the heat evolution occurring during this process as observed by the DSC. PVT measurements are then performed on the injection-molded specimen as follows: isothermal heating measurements are first performed in the solid state over a wide temperature range. The specimen is then melted at a low pressure and its melting behavior is recorded. A series of isobaric cooling measurements are performed at several pressures well into the solid state. The purpose of these steps is to uniquely measure the solid state volumetric expansion coefficient and compressibility of the injection molded specimen, to characterize the melt state PVT behavior and to determine the slow cooling rate crystallization behavior of the polymer at different pressures.

Next, high cooling rate DSC measurements are performed to characterize the rate dependency of the crystallization transition. The purpose of this experiment is to capture a characteristic high cooling rate crystallization temperature and its corresponding crystallization kinetics. The hybrid PVT model is then constructed from the data gathered by piecing together the measured solid state PVT data of the injection molded part with the measured melt state PVT properties. The transition from melt to solid is constructed by transposing high cooling rate DSC kinetics. The pressure dependence of the transition temperature is obtained from the isobaric cooling experiments.

Apparatus

A Gnomix Research PVT apparatus [4,5] was used for the high pressure dilatometry work. The apparatus is fully computerized and capable of automated operation. It utilizes mercury as the confining fluid. A Perkin Elmer DSC7 was used for the high and low cooling rate crystallization studies. The apparatus was calibrated using indium and zinc standards. Volatile sample pans made from aluminum were used to hold the specimens.

Materials and Methods

The test material was a commercial grade unfilled nylon 66 polymer. The material was injection molded into test parts which were then razor cut to the appropriate size.

A 7 mg specimen was loaded into the DSC and melted at 3°C/min. It was subsequently cooled at 3°C/min. 20°C/min, 40°C/min and 100°C/min. The resulting heat flow curves are shown in Figure 1. Note that the curves are not normalized for rate. The peak analysis is shown in Table 1. The dramatic shift in transition is noteworthy.

For the PVT measurements, 1.03 gm of the test specimen was loaded into the dilatometer. The specimen was subject to isothermal heating measurements at 10 °C intervals over a range of 30 to 150°C and a pressure range of 10 to 200 MPa. The specimen was then melted at 10 MPa (see Figure 2). Isothermal cooling measurements were then performed at 10 MPa, 40 MPa, and 80 MPa. The resulting data are shown in Figure 3.

In a separate experiment, conventional isothermal cooling measurements were conducted to provide a baseline for comparison. These results are presented in Figure 4.

Data Analysis and Results

A Tait model was fit to the solid state of the PVT data derived from the isothermal heating measurements. In a similar manner, a Tait model was fit to the melt state region of the isobaric cooling measurements. In both cases, data used for the fit excluded measurements in the transition region, since the transition data was taken at low cooling rates.

Before transposing data from the DSC to the PVT, an attempt was made to correlate results from the two instruments. A partial areas analysis was performed on the 3°C/min fusion peak observed on the DSC. The corresponding conversion vs temperature data are shown in Table 2. The total volume change upon fusion was taken from the PVT data. This volume change was factored over the fusion conversion data to obtain the calculated volume change at each temperature as shown in Table. 2. The following equation was used:
v(T) = vs(Te) + {vm(Te) - vs(Te)}*a(T)

where

v(T) = specific volume at temperature T
vs(Te) = specific volume of the solid polymer at the end temperature of crystallization, Te
vm(Te) = extrapolated specific volume of the polymer if it were molten at the end temperature of crystallization, Te
a(T) = Degree of crystallization at temperature T

The value of vm(Te) was obtained by extrapolating the melt state Tait model to the crystallization end temperature. This step serves to eliminate from the equation, volume changes due to thermal contraction that have occurred over the temperature range of the crystallization. Figure 5 shows a plot of the calculated volume against that actually measured by the PVT apparatus. The DSC peak is also shown. It can be seen that the calculated points match the measured PVT data well. A similar calculation (not shown) was performed to correlate DSC crystallization peaks to PVT crystallization transitions with equally good results.

With this correspondence, we conclude that the heat released due to crystallization as measured by the DSC correlates well to the volume change during crystallization as measured by the PVT apparatus. It is reasonable to assume that this correlation should hold at other heating and cooling rates. A partial areas analysis of the high cooling rate DSC data was transposed to PVT data using the total volume change occurring due to crystallization. The starting point of the transition was taken to be at the crystallization onset temperature observed from the DSC. Similarly, the crystallization end temperature was also taken from the DSC.

We observed from the isobaric cooling PVT data, that the crystallization onset temperature varied linearly with pressure over the 10 to 80 MPa pressure range that we covered. This was in agreement with the findings of He and Zoller [6]. Following their work, we did not perform measurements at higher pressures due to the possibility of alternate crystal morphologies being developed. In our analysis, we assumed that the linear pressure dependency would apply at high cooling rates as well. Accordingly, the crystallization transition onset temperature at high pressures was shifted using this pressure dependency function. For each pressure, transition volumes were calculated between the crystallization onset temperature and the crystallization end temperature. The resulting data are shown in a composite plot (Figure 5) consisting of solid state isothermal heating measurements on the injection molded part, calculated transition volumes from DSC and melt state data from isobaric cooling measurements. For purposes of comparison, the solid state PVT curves from conventional isobaric cooling measurements are also shown. Note that these data are significantly lower in the solid state compared to that of the injection molded part, implying that the slow cooling rates of the instrument impart a higher crystallinity and a different morphology than that imparted by the injection molding process.

Discussion

The hybrid technique permits us to examine several aspects of the PVT behavior of plastics. We observe the effect of super-cooling on the crystallization temperature. Without considering the effect of cooling rate, the super-cooling effect results in a crystallization temperature of 238°C which is 30°C below the melting temperature, Tm, of 265°C. This correlates well with independent measurements by DSC. The introduction of high cooling rate effects further depresses the crystallization temperature to 210°C. For the nylon that we tested, the total shift in temperature amounted to about 55°C at a cooling rate of 100°C/min. We also noted that the temperature range over which the polymer crystallized was wider at high cooling rates so that at 100°C/min, the crystallization effect was apparent until 160°C. Consequently, the PVT curves in the transition are not sharp as typically seen in conventional data, but instead transition gradually into the solid state.

In modeling the crystallization at higher pressures, we have assumed that the kinetics are not a function of pressure. This assumption should be validated through high pressure DSC measurements but this could not be carried out in our study. The assumption however, permits us to provide a good first approximation of the volume change upon crystallization at high pressures and high cooling rates. The ability to make this calculation is based on our ability to accurately characterize the change in the crystallization onset temperature with pressure. The isobaric measurements provide us with a precise means to make this measurement. In contrast to the isothermal compression methods, the errors due to pressure induced crystallization are avoided because the pressure is kept constant during the crystallization process.

In modeling the solid state behavior, we note the depression in ambient specific volume of the isobaric cooled (or isothermal cooled) specimen, 0.9402 cm3/g at 32°C and 0 MPa, as compared to the isothermal heating (or hybrid) measurement of 0.9689 cm3/g. This difference amounted to a 3% lowering in specific volume. Further, since the specimen solidified in the apparatus does not possess the skin-core-skin morphology, we observed that the thermal expansion coefficients were also higher. The compressibility remained relatively unchanged. This difference could account, in part, for the overprediction of shrinkage by the CAE programs [7].

Plastics in injection molded parts cool very quickly. While the skin layer will freeze at a very high cooling rate, the bulk of the polymer will cool at a lower rate (in the 100 to 500°C/min range). We based our choice of cooling rate of 100°C/min on the point that we seek to develop a representative PVT model for the bulk of the polymer. Further, this rate represents a realistic upper limit to the measurement capability of the DSC. Thermal lag effects, which are already quite noticeable at 50°C/min, could become significant at very high cooling rates making it difficult to assess how much of the shift is due to the delayed nucleation vs. thermal lag of the DSC apparatus. It would be attractive to consider using Jaentsch-Kreigl’s scheme [8] for correction of thermal lag effects to see how we could improve the quality of the data. It should be noted however, that the application of such a correction will only define the ‘actual’ cooling rate of the DSC experiment. Since the DSC data are used solely to provide a representative transition from the melt to the solid state, the impact of this approximation is diminished. It has no bearing on solid state PVT data and the final solid state behavioral characteristics of the injection molded part since these are taken from actual PVT experiments. This would not be the case if a crystallization kinetics model was used to calculate the solid state PVT data where a precise characterization of the model would be vital. Further, the present uncertainty about the universal acceptability of such models [9] would make such a kinetics based scheme less robust.

Conclusions

Molding simulation programs have been hampered in their ability to predict shrinkage of semi-crystalline plastics. The inability of conventionally generated PVT data to properly

represent the crystallization phenomenon has been a factor. We have defined an elegant scheme to assemble a representative PVT model for injection molded parts. This model is created from experimental data that can be generated with currently available technology. It does not rely upon crystallization kinetics models which are as yet, not universally proven. It will permit us to use the PVT models currently available with the major mold analysis programs without modification. In future, with advances in the modeling of crystallization kinetics, it may be possible to better model the transition from melt to solid based on the original data.

Acknowledgements

We acknowledge the contributions of Craig Montoya who performed the PVT measurements and Michael Tylenda who performed the DSC measurements. Thanks also to Dr. Paul Zoller, University of Colorado, Dr. Gibson Batch of 3M and to Dr. Charles Tucker of the University of Illinois for their valuable comments.

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