# A microcellular processing study of poly(ethylene terephthalate) in the amorphous and semicrystalline states, part II, Cell growth and process design.

INTRODUCTIONThis paper is the second of a two part series presenting a comparison of the microcellular processing of amorphous and semicrystalline poly(ethylene terephthalate) (PET) (1, 2). The goal of the microcellular processing comparison is threefold: 1) to characterize the microcellular processing of an engineering thermoplastic in the amorphous and semicrystalline states so as to identify critical process parameters, 2) to discern the effects of crystallization and crystallinity on microcellular processing, and 3) to determine the physical phenomena that govern each of the microcellular processing functions. Specifically, this paper investigates the cell growth stage of microcellular processing with respect to four major process variables: saturation time, saturation pressure, foaming time, and foaming temperature. Moreover, a comprehensive process design strategy is presented based on the cell growth characterization and the microcell nucleation characterization presented in Part I of the series (2). The process design strategy emphasizes the significant differences between processing of amorphous and semicrystalline polymers and distinguishes the critical process parameters in a concise format.

Microcellular processing consists of first forming a polymer/gas solution followed by the inducement of a rapid thermodynamic instability that simultaneously nucleates a very large number of microcells (3-8). Characteristic cell morphologies are on the order of 10 microns having [10.sup.9] cells/[cm.sup.3]. After microcellular processing, transparent polymers are an opaque white and have a glossy surface finish. The glossy surface finish results from a characteristic unfoamed surface layer, typically one to five cell diameters in thickness (3,9). A comprehensive review of microcellular polymers and process technology is presented by Baldwin et al. (10-12).

The first paper of this series investigates microcellular nucleation of amorphous and semicrystalline polyester materials (2). The results presented give considerable insight into the mechanisms governing cell nucleation. The amorphous poly(ethylene terephthalate) (PET) and PET containing a nucleating agent (CPET) exhibited similar nucleation characteristics and nucleation mechanisms. At low saturation pressures, these materials appear to experience heterogeneous nucleation because of inherent flaws in the material. At higher pressures, both the amorphous PET and CPET showed a strong cell density dependence indicating the activation of additional nucleation sites and/or homogeneous nucleation contributions. Conversely, the semicrystalline PET and CPET showed similar nucleation mechanisms and a less pronounced cell density dependence on the saturation pressure. In general, the semicrystalline polymers exhibited considerably higher cell densities than the amorphous polymers (i.e., 10 to 1000 times higher), which is attributed to the significant contributions of heterogeneous nucleation in the amorphous/crystalline interfacial regions. Moreover, classical nucleation theory was not adequate to quantitatively predict the effects of saturation pressure for either the amorphous or the semicrystalline polyesters. The results presented in Part I also indicate that the foaming time had a relatively weak effect on cell nucleation for both the amorphous and semicrystalline polyesters. Foaming temperatures near the glass transition were found to influence the cell density of the amorphous polyesters, indicating some degree of thermally activated nucleation. Furthermore, classical nucleation theory was not adequate to predict the cell density dependence on foaming temperature. Similar to the amorphous polyesters above the glass transition temperature, nucleation in the semicrystalline materials was found to be independent of the foaming temperature.

EXPERIMENTATION

Two different PET resins were studied during the course of this investigation. The materials used were a PET homopolymer (PET) and a PET resin containing approximately 0.5% polyolefin as a nucleating agent (CPET) both manufactured by Unitika Co. Ltd. in the form of 0.4 mm thick extruded sheets. The sheets were experimentally processed in an as-received condition. The material characteristics of the as-received material are presented elsewhere (10, 13).

The microcellular processing experiments were carried out using the technique outlined in Part I (2). In summary, the polyester sheets were saturated with carbon dioxide under high pressure (the saturation pressure). Once the saturation time was reached, the samples were removed from pressure and foamed at an elevated temperature (the foaming temperature) for a fixed time period (the foaming time). Finally, the samples were quenched in a water bath to vitrify the microcellular structure.

Characterization of the foamed samples was accomplished using scanning electron microscope (SEM) micrographs to estimate an average cell size assuming a uniform cell structure, randomly distributed cells, and a planer cross section intersecting a single layer of cells.

RESULTS

This microcellular processing investigation of amorphous and semicrystalline polyesters centered around the cell growth processing stage. The study was performed with respect to four major process variables: gas saturation time, gas saturation pressure, foaming time, and foaming temperature. The resulting foams are considered to be amorphous if they have less than 10% crystallinity by mass, and semicrystalline if they have crystallinities greater than 10%. The crystallinities were measured using differential scanning calorimeter (DSC) analysis with a heat of fusion of 125.6 J/g at a scan rate of 20 [degrees] C/min. It is important to note that the samples used in this study were the identical samples used for the microcell nucleation study of Part I (2).

Figure I shows the effect of C[O.sub.2] saturation time on the cell size of the PET and CPET materials (see the results for Fig. 1 in Ref. 2 for a detailed description). The saturation time is reported as a dimensionless parameter, Dt/[l.sup.2] using a diffusivity of D = 8 x [10.sup.-9] [cm.sup.2]/s (10,13). In Fig. 1, crystallization of the amorphous materials begins at Dt/[l.sup.2] [approximately equal to] 0.6 and approaches a maximum at Dt/[l.sup.2] = 1.2 (11). Figure 2 shows the effect of C[O.sup.2] saturation pressure on the cell size of amorphous and semicrystalline PET and CPET (see the results for Fig. 2 in Ref. 2 for a detailed description). The polyester materials shown as data symbols 'PET' and 'CPET' were largely amorphous except at the highest saturation pressures where crystallization was prevalent. At the highest saturation pressure (5.51 MPa), the PET and CPET were 28% and 35% crystalline, respectively. The semicrystalline PET and CPET specimens in Fig. 2 were 32% and 33% crystalline, respectively. Figure 3 shows the effect of foaming time on the cell size of amorphous PET and CPET and semicrystalline CPET (see the results for Fig. 3 in Ref. 2 for a detailed description). In Fig. 3, the semicrystalline CPET samples were 33% crystalline. Finally, Fig. 4 shows the effect of foaming temperature on the cell size of amorphous and semicrystalline PET and CPET (see the results for Fig. 4 in Ref. 2 for a detailed description). The semicrystalline PET, semicrystalline CPET (data symbol CPET-800/10); and semicrystalline CPET (data symbol CPET-900/30) had crystallinities of 28%, 35%, and 34%, respectively.

The microcellular PET and CPET foams presented in Fig. 4 illustrated some interesting behavior that warrant additional discussion. The amorphous PET and CPET samples foamed at 50 [degrees] C, which is [approximately]20 [degrees] C below the neat polymer's glass transition temperature. In some cases, the amorphous PET and CPET samples were observed to foam at room-temperature, some 45 [degrees] C below the glass transition temperature. Such low temperature foaming is feasible because of the plasticizing effect of the dissolved C[O.sub.2] on the PET matrix, which can lower the glass transition temperature by as much as 75 [degrees] C (10, 13-15). On the other hand, the semicrystalline PET samples showed no detectable cell structures (i.e., within a measurement resolution of 0.3 [[micro]meter]) when foamed at or below 100 [degrees] C. Finally, the semicrystalline CPET samples showed no detectable cell structures when foamed at or below 80 [degrees] C.

DISCUSSION

The microcellular processing characterization presented in Figs. 1 through 4 shows some very interesting processing differences between the amorphous and semicrystalline polyesters. Moreover, the results suggest considerably different process design strategies for the amorphous and semicrystalline systems. In this section, the cell growth results will be analyzed with respect to the four major process variables, and the process design implications will be discussed. Moreover, a basic engineering analysis will be used to identify the dominant physical mechanisms underlying the cell growth effects exhibited by the amorphous and semicrystalline polymers.

To begin, consider the effects of the major processing variables on cell size and the mechanisms governing cell growth. Cell growth is controlled by the degree of supersaturation, rate of gas diffusion into the cells, the hydrostatic pressure or stress applied to the polymer matrix, the interfacial surface energy, and the viscoelastic properties of the polymer/gas solution. It is also important to acknowledge the influence of cell nucleation density on cell size. Cell density and cell size follow an inverse cubic relation for constant void fraction foams [derivable from Eqs 1 and 2 in (2)!. A factor of 1000 increase in the cell density decreases the cell size by a factor of 10 for comparable void fractions.

In general, the gas saturation time is an inappropriate process variable for controlling cell size. Saturation times should be selected as the minimum necessary to achieve an approximately uniform gas concentration thereby controlling the solution formation step. However, the results shown in Fig. 1 illustrate some important characteristics that must be integrated into the process design strategies.

Looking first at the amorphous materials (i.e., for Dt/[l.sup.2] [less than] 0.8), the data indicates a decreasing cell size with saturation pressure. Since, these materials had fully grown cells (i.e., a dodecahedron morphology) and similar void fractions, the decrease in cell size is attributed namely to the increase in cell density resulting from the increasing gas concentration during saturation (2).

At saturation times greater than Dt/[l.sup.2] [approximately equal to! 0.8, the PET and CPET experience significant crystallization. The crystallization results in a 100-fold decrease in cell size for the PET and 10-fold decrease in cell size for the CPET. In this case, the majority of the cell size decrease can be attributed to the increase in cell density associated with crystallization (2). However, the semicrystalline PET and CPET did not exhibit fully grown cells (i.e., a spherical geometry), and these microcellular foams have higher specific densities than the amorphous foams. This implies the cell growth mechanisms dominating in the semicrystalline polymers differ from that of the amorphous materials. In general, the amorphous foams experience diffusional controlled cell growth while the semicrystalline foams experience viscoelastic controlled cell growth. To better understand the differences between the cell growth mechanisms of the amorphous and semicrystalline polymers next consider the influence of the saturation pressure.

The cell size results of Fig. 2 show some stark contrasts between the amorphous and the semicrystalline PET and CPET resins. Previously, the saturation pressure was determined to be an effective process variable for controlling cell density (2). Therefore, to insure an uncoupled process, it is desirable to have a relatively independent cell size with varying saturation pressure. In Fig. 2, the semicrystalline PET and CPET show an independent cell size with saturation pressure illustrating the potential for a decoupled process. In contrast, the amorphous materials show a strong cell size dependence on saturation pressure.

To understand the growth mechanisms that govern the cell size results of Fig. 2, first consider the amorphous PET and CPET samples. These foams had fully grown cell structures with a characteristic dodecahedron geometry and similar void fractions. Therefore, the decreasing cell size is attributed primarily to the exponential increase in cell density of these amorphous foams.

In contrast, the semicrystalline PET and CPET microcellular foams showed no appreciable change in cell size with saturation pressure even though the cell density varies by a factor of 10 over this range. In addition, these microcellular foams did not exhibit fully grown cell structures. The lack of such cell structure indicates cell growth that is governed by the gas diffusion rate or the viscoelastic behavior of the semicrystalline materials. Using Eqs 1 and 2 and a diffusivity of D = 8.5 x [10.sup.-8] [cm.sup.2]/s [reported by Koros and Paul (15) for PET/C[O.sub.2] systems at 115 [degrees] C], the gas diffusion time necessary for diffusion limited cell growth can be estimated where the characteristic diffusion length is taken as l [approximately equal to] [D.sub.c]/2. The semicrystalline PET and CPET foams have cell sizes of 1.5 [[micro]meter] and 5 [[micro]meter] yielding estimated diffusion times of t [approximately equal to] 0.3 and 1.4 s, respectively. Since these materials were allowed to foam at 200 [degrees] C for 10 s, the cell growth characteristics shown in Fig. 2 are not likely the result of diffusion limited growth.

[Delta]c/[Delta]t = [Nabla] [center dot] (D[Nabla]c) (1)

t [approximately equal to] [l.sup.2] / D (2)

For the semicrystalline polymers, the cell growth characteristics are attributed to the viscoelastic behavior of the semicrystalline polymer matrix. In this case, the primary factor effecting cell growth is the time and temperature dependent relaxation modulus, which is a strong function of crystallinity (10, 13). This point is discussed further by Baldwin (10, 13).

The next process variable studied was the foaming time. In general, foaming time is a potential process variable for controlling the cell size because under some circumstances cell growth is governed by the rate of gas diffusion into the cells. The longer the gas is allowed to diffuse into the cells (i.e., the foaming time) the larger the cell size.

To understand the results of Fig. 3, it is useful to consider the possible kinetic mechanisms that contribute to the cell growth process for a varying foaming time that are 1) the rate of gas diffusion into the cells, 2) the flow/relaxation of the viscoelastic matrix, and 3) the coalescence of cells. To estimate the contribution of the gas diffusion rate, Eq 2 is used with D = 8.5 x [10.sup.-8] [cm.sup.2]/s [reported by Koros and Paul (15) at 115 [degrees] C]. For the amorphous PET, the estimated cell growth time is t [approximately equal to] [l.sup.2]/D = 89 s where l [approximately equal to! 55/2 [[micro]meter]. For the amorphous CPET, l [approximately equal to! 13/2 [[micro]meter], and the estimated growth time is 5 s. The semicrystalline CPET foams have a typical cell size of 7 [[micro]meter] yielding an estimated diffusion time of t [approximately equal to] 1.4 s. Thus, it is not surprising that the amorphous polyesters show an increasing cell size during the shorter foaming times due, in part, to limiting gas diffusion rates. In contrast, the estimated diffusion time of the semicrystalline CPET, would suggest that the foaming time has very little influence on cell growth, which is supported by the data of Fig. 3.

The initial increase in cell size with foaming time for the amorphous polyesters may also be impacted by the decrease in cell density over this range of foaming time (2). The initial decrease in cell density was attributed to relaxation of the cell structures through cell coalescence. Since the amorphous foams of Fig. 3 exhibited fully grown cell structures and similar void fractions, some degree of the cell size increase over the shorter foaming times is likely due to the relaxation of the cell structure and the system's natural tendency to seek a lower free energy state through cell coalescence. The conclusion is the foaming time is a relatively poor process variable for controlling cell growth and the cell size for both amorphous and semicrystalline polyesters for foaming times greater than 2 and 10 s, respectfully.

The foaming temperature is also a potential process variable for controlling cell growth and cell size during microcellular processing. The results of Fig. 4 show some very interesting contrasts between the cell growth characteristics of the amorphous and semicrystalline polyester resins. The first is the relatively independent cell size with changing foaming temperature for the amorphous PET and CPET. In contrast, the semicrystalline PET and CPET show a strong positive relationship between the foaming temperature and the cell size. These results suggest a process strategy for the semicrystalline polymers where the foaming temperature is used to control cell growth and the cell size. However, the foaming temperature cannot be used to control the cell size of the amorphous polymers.

At this point, it is worth exploring the mechanisms that govern cell growth and cell size for the data of Fig. 4 in more detail. In general, the foaming temperature can affect cell growth through the gas diffusion rate, the interfacial surface energy (i.e., surface tension), and the viscoelastic behavior of the polymer/gas matrix.

The amorphous PET and CPET foams processed above 50 [degrees] C showed a fully grown cell morphology (i.e., a dodecahedron geometry) and a nearly constant cell size. However, the amorphous foams processed at 50 [degrees] C did not show a fully grown cell structure, and the cell density of these materials is considerably lower than those processed above 50 [degrees] C. At the lower temperature, it is possible that both the gas diffusion rate and the viscoelastic behavior of the polymer/gas matrix are responsible for the cell growth characteristics. To estimate the extent of the gas diffusion rate contribution at the lower temperatures, an approximate gas diffusion time can be obtained from Eq 2 using a diffusivity of D = 8 x [10.sup.-9] [cm.sup.2]/s [at 20 [degrees] C from (13)]. Using characteristic diffusion distances of l [approximately equal to] 70/2 [[micro]meter] and l [approximately equal to] 20/2 [[micro]meter], the estimated gas diffusion times for the amorphous PET and CPET are 25 min and 2 min, respectively, compared to the 10 s foaming time (2). Therefore, it is likely that the amorphous foams experience primarily diffusion limited growth at the lower temperatures.

In contrast, the semicrystalline PET and CPET show a strong cell size dependence on foaming temperature over the range studied. The contributions of diffusion controlled cell growth can be estimated using Eq 2 with D = 8.5 x [10.sup.-8] [cm.sup.2]/s [reported by Koros and Paul (15) for PET/C[O.sub.2] systems at 115 [degrees] C]. For the PET surface cells, the estimated cell growth time is 10 s, while for the center cells, the estimated diffusion time is 0.1 s. For the CPET microcellular foams (samples CPET-800/10 and CPET-900/30), the estimated cell growth time is 2.9 s. These diffusion limited growth times are compared with the 10 and 30 s foaming times for these samples (2). Therefore, it seems that the gas diffusion kinetics are sufficiently rapid such that the growth phenomenon observed for the semicrystalline materials in Fig. 4 are not the result of diffusion limited growth rates.

Another factor that can contribute to the cell size effect for foaming temperature variations is the surface tension. To a first order approximation, the surface tension contribution to the equilibrium cell size for a spherical bubble is given by Eq 3, and the relative contribution is given by Eq 4 for a given saturation pressure.

[([D.sub.c]).sub.surface] [varies] 4[[Gamma].sub.bp](T)/[Delta]p (3)

[([D.sub.c2]/[D.sub.c1]).sub.surface] = [[Gamma].sub.bp]([T.sub.2])/[[Gamma].sub.bp]([T.sub.1]) (4)

Since -[([Delta][[Gamma].sub.bp]/[Delta]T).sub.p] is proportional to the entropy, it follows from the second law of thermodynamics that the surface tension must decrease with an increasing temperature. From Eq 4, this implies the surface tension effects tend to decrease the equilibrium cell size when the foaming temperature is increased. Using the PET surface tension data presented by Wu (16), the estimated surface tension contribution is a 22% decrease in equilibrium cell size when the foaming temperature increases from 100 [degrees] to 230 [degrees] C. It is clear then that the surface tension effects do not account for the cell growth mechanisms exhibited by the semicrystalline polymers in Fig. 4 (i.e., an increasing cell size with foaming temperature).

Therefore, the cell growth effects demonstrated by the semicrystalline polymers in Fig. 4 seem to result primarily from the viscoelastic behavior of the polymer/gas matrix. SEM micrographs of these microcellular polymers have been presented previously (10, 13, 17). These foams exhibited a spherical cell morphology indicating only partially grown cell structures, except at the highest processing temperatures where the cells were fully grown showing a dodecahedron morphology. In general, the viscoelastic behavior of the semicrystalline PET matrix is a strong function of temperature and time (18). Moreover, the modulus of semicrystalline PET is an order of magnitude larger than that of the amorphous PET, at temperatures above the glass transition (13, 14, 18). It is not surprising that the amorphous PET and CPET show little cell size dependence at the higher foaming temperatures. Whereas the higher modulus of the semicrystalline material implies a strong cell size dependence over the temperature range of interest. As the foaming temperature increases, the stiffness of the semicrystalline matrix relaxes, promoting larger strains and cell sizes for a given stress level. In this way, the cell growth of the semicrystalline materials is controlled by the viscoelastic nature of the polymer matrix, as opposed to being controlled by gas diffusion rate. For a more detailed discussion on this point see Baldwin (10) and Baldwin et al. (13).

To conclude this discussion, some final observations are in order. From the data of Figs, 1 through 4, it is clear that: 1) the amorphous CPET foams show a much finer cell structure than the amorphous PET, 2) the semicrystalline PET foams show a freer cell structure (in the center regions) than the semicrystalline CPET (i.e., the inverse behavior of the amorphous resins), and 3) the semicrystalline PET and CPET foams show finer cell morphologies than the amorphous materials.

PROCESS DESIGN IMPLICATIONS

The microcellular processing characterization presented in Part I (2) and Figs. 1 through 4 suggests a number of important process design implications. In this section, a unique process design analysis is presented that is based on two general conclusions drawn from the process characterization: 1) the crystallizable polymers studied have multiple processing windows covering unique process variable ranges and 2) different process design strategies must be derived within these processing windows to insure independent control of the process functions (i.e., solution formation, microcell nucleation, and cell growth). Moreover, this process design analysis underscores the significant processing differences of the amorphous and semicrystalline materials and identifies the critical process variables in a concise format. In general, the feasible processing windows for the amorphous and semicrystalline polyesters differ considerably. These differences must be integrated into the process design strategies for the respective materials so as to take advantage of their unique processing characteristics. Strictly speaking the process strategies presented below hold only for the amorphous and semicrystalline polyesters studied. However, it is expected that comparable process strategies apply for other crystallizable polymers that exhibit similar gas dissolution and crystallization behavior [e.g., poly(vinylidene fluoride)/poly(methyl methacrylate) blends, Chiou et al. (19)!.

The process design strategies derived are presented in the form of matrix equations where the matrix elements indicate the relative dependence of the major process functions (i.e., solution formation, microcell nucleation, and cell growth) on the process variables (i.e., saturation time, saturation pressure, foaming time, and foaming temperature). The matrix elements consist of an X indicating a relatively strong dependence, an [cross product! indicating a relatively weak dependence, and an 0 indicating a nearly independent behavior between the process function and the process variable. The process design representation is adopted from the design framework developed by Suh (20).

The data of Figs. 1 through 4 in Parts I (2) and II suggest a number of processing domains or windows for the polyester materials. For each separate processing window, an independent process design strategy is derived under the assumption that homogeneous foams are to be produced. In the case of the amorphous polymers, three processing windows are suggested by the data. The first applies for foaming temperatures near the glass transition (of the neat PET) and for higher saturation pressures (i.e., [greater than or equal to! 2.07 MPa or 300 psi). In this processing domain, the design strategy for the amorphous materials is given by Eq 5. Since Eq 5 can be rearranged into a triangular form, it is clear that at least one independent process variable exists for satisfying or controlling each of the process functions provided that the processing variables are set in a specific order. In the case of Eq 5, the foaming temperature should be selected first at a value near the glass transition temperature. Next, the saturation pressure should be selected to satisfy the required cell nucleation density. Finally, the saturation time and foaming time can be selected to achieve the required solution formation and cell growth (i.e., cell size) requirements, respectively. It is important to realize that the saturation time must be long enough to achieve a uniform gas concentration but short enough to minimize crystallization.

[Mathematical Expression Omitted]

Strictly speaking, Eq 5 is a redundant process design since it has more process variables than functional requirements. Rearranging Eq 5 and eliminating one of the redundant process variables yields a decoupled process design strategy given by Eq 6. Notice in Eq 6 that the matrix is triangular suggesting the specification of saturation pressure first to satisfy the cell growth requirement followed by specification of the saturation time and foaming time, to satisfy the solution formation and cell nucleation requirements, respectively. This is an alternate process control strategy than stated for Eq 5. However, non-redundant process design equations are sometimes misleading in that the effects of the redundant process variables are not explicitly stated. This can lead to a common misperception that these redundant process variables can be set arbitrarily. In fact, the redundant process variables must be specified prior to the process variables used to satisfy the functions. For the remaining process design strategies, the redundant form of the equations are presented so as to explicitly show the effect of the major process variables.

[Mathematical Expression Omitted]

For the amorphous polyesters at foaming temperatures above the glass transition and at higher saturation pressures, the results suggests the following process design strategy:

[Mathematical Expression Omitted]

Notice at the higher foaming temperatures, cell nucleation is independent of the foaming temperature, and therefore, the process strategies given for Eqs 5 and 6 apply except the foaming temperature can be selected arbitrarily above the glass transition without influencing any of the process functions.

A third process design strategy applies for the amorphous PET and CPET at relatively low saturation pressures and is given by Eq 8. In this case, the process variables studied were not sufficient to satisfy each of the process functions indicating an uncontrollable process. Notice that none of the process variables influence cell nucleation. At low saturation pressures, the amorphous PET and CPET experience predominant heterogeneous nucleation governed by the inherent flaws, inclusions, and/or process additives. In order to satisfy the cell nucleation function within this processing window, an additional process variable is needed. One potential process variable for controlling cell nucleation in this domain would be a specified concentration of second phase particles to act as heterogeneous nucleation sites.

[Mathematical Expression Omitted]

A significant implication of Eqs 5 through 8 for the amorphous materials is that only limited control over cell growth can be achieved once the saturation pressure has been selected. In general, the saturation pressure limits the ultimate size of the cells. Within this limit, the cell size can be moderately varied using the foaming time. However, in order to span the full size range, foaming times less than two s are needed, which are difficult to achieve, owing to limits in the heat transfer kinetics. Moreover, the relaxation of the cell structure through cell coalescence, limits the repeatability of cell growth control. Therefore, cell growth is a relatively difficult process function to satisfy for the amorphous polyesters within the scope of process variables studied.

At sufficiently high saturation pressures and over sufficiently long saturation times, the PET and CPET resins crystallize. Crystallization changes both the cell nucleation and cell growth mechanisms through its effects on interfacial energy and viscoelastic behavior, respectively. This results in a coupled foaming process as given by Eq 9, which holds during any processing window encompassing the crystallization process. During the crystallization process, solution formation and cell nucleation cannot be satisfied independently. This is the primary reason the process design strategies for the amorphous and semicrystalline must be specified independently.

[Mathematical Expression Omitted]

In contrast to the amorphous materials, the results for the semicrystalline PET and CPET suggest a single process design strategy given by Eq 10. The gas saturation pressure should be selected first to satisfy the cell nucleation function followed by the selection of the saturation time to satisfy the solution formation function. Finally, the foaming temperature should be selected to satisfy the cell growth function, and the foaming time can be selected arbitrarily without appreciably influencing the resulting cell morphologies.

[Mathematical Expression Omitted]

Controlling cell growth using the foaming temperature rather than the foaming time is an important difference between the processing of the semicrystalline polymers and amorphous polymers. Moreover, it is important to realize that although cell nucleation can be controlled for the semicrystalline polymers using the saturation pressure, the range of this control is significantly less than that of the amorphous foams. The somewhat limited cell nucleation control for the semicrystalline polymers results from the additional heterogeneous nucleation contributions at the amorphous/crystalline interfaces. Finally, notice that the process design strategy for the semicrystalline polymers is decoupled allowing for independent control over each of the process functions.

CONCLUSIONS

The findings of this study clearly illustrate significant differences in the microcellular processing characteristics of amorphous and semicrystalline polymers. Moreover, these differences in processing characteristics require the specification of independent process design strategies for the amorphous and semicrystalline polymers since the crystallization process was found to couple the solution formation and microcell nucleation requirements. The amorphous polyesters studied revealed three separate processing windows and process design strategies. Within these processing domains, the amorphous CPET exhibited primarily microcellular morphologies whereas the amorphous PET showed larger cell structures. In contrast, all of the semicrystalline polymers exhibited microcellular morphologies and showed a very broad processing window over the spectrum of the process variables studied suggesting a single process design strategy.

Furthermore, the results presented give considerable insight into the mechanisms that govern microcell nucleation (2) and cell growth during the microcellular processing of amorphous and semicrystalline polymers. The results from this two part study showed that the amorphous CPET experiences heterogeneous nucleation contributions resulting from the polyolefin additive, and the amorphous PET and CPET exhibited similar nucleation characteristics and mechanisms. At low saturation pressures, the amorphous materials appear to experience heterogeneous nucleation due to inherent flaws. At higher pressures, both the amorphous PET and CPET showed a strong cell density dependence indicating the activation of additional nucleation sites and/or homogeneous nucleation contributions. Conversely, the semicrystalline polymers showed similar nucleation mechanisms and a lesser cell density dependence on the saturation pressure. In general, the semicrystalline polymers exhibited considerably higher cell densities than the amorphous polymers, which is attributed to the significant contributions of heterogeneous nucleation in the amorphous/crystalline interfacial regions. Moreover, it was found that classical nucleation theory was not adequate to quantitatively predict the effects of saturation pressure on cell nucleation for the amorphous and semicrystalline polyesters.

The foaming time had a relatively weak influence on cell nucleation and cell growth for both the amorphous and semicrystalline polyesters. This contrasts the strong cell size dependence on foaming time reported for styrenic resins (2, 5, 21, 22).

For the amorphous polymers, foaming temperatures near the glass transition were found to influence the cell density, indicating thermally activated nucleation. Moreover, the cell density dependence on foaming temperature was found not to follow the quantitative trends predicted by classical nucleation theory. In contrast, the semicrystalline polymers exhibited a relatively independent cell density and a strong cell size dependence on foaming temperature. The foaming temperature dependence on the cell size is attributed to the viscoelastic behavior of the semicrystalline polymers.

NOMENCLATURE

D = Diffusivity of gas in a polymer matrix [[m.sup.2]/s].

[D.sub.c] = Average cell diameter or size [[[micro]meter]].

l = Half thickness or characteristic length over which gas diffuses [m].

[N.sub.f] = Cell density relative to foamed material [cells/[cm.sup.3]].

[Delta]p = Difference in the pressure of the gas in the cluster and the ambient nucleation pressure [Pa].

t = Time or characteristic time [s].

T = Absolute temperature [K].

[V.sub.f] = Volume fraction of voids or cells.

[[Gamma].sub.bp] = Surface energy of the polymer/bubble interface [N/m].

[[Rho].sub.c] = Cell density relative to unfoamed material [cells/[cm.sup.3]].

REFERENCES

1. A portion of this paper was presented at ANTEC 1994: D. F. Baldwin, C. B. Park, and N. P. Suh, SPE ANTEC Tech. Papers, 40, 1951 (1994).

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Author: | Baldwin, Daniel F.; Park, Chul B.; Suh, Nam P. |
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Publication: | Polymer Engineering and Science |

Date: | Jun 15, 1996 |

Words: | 5909 |

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