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An extrusion system for the processing of microcellular polymer sheets: shaping and cell growth control.


Microcellular plastics are innovative cellular polymeric materials receiving increasing interest in both academic research and industrial application. This is due largely to their unique cell morphology and enhanced properties. In this paper, a new processing system for the extrusion of microcellular polymer sheets is presented (1). This innovative microcellular processing system was recently patented (2). The detailed design of a shaping and cell growth control system is discussed in the context of the overall extrusion system design with particular emphasis on the system level functional requirements of cell nucleation, cell growth, and shaping. After a brief introduction to microcellular technology and processing, an overview of the extrusion system design is presented. Next, the basic design concepts and strategy underlying the shaping and cell growth control device are discussed. These concepts are used to develop a process design model that is briefly reviewed. A detailed discussion of the design model is presented by Baldwin (3). Based on preliminary results presented in this work, the design model provides reasonable estimates of the critical design parameters with respect to the system process variables. Finally, two shaping/cell growth control devices (or dies) are presented along with critical experiments that verify the feasibility of shaping a nucleated polymer/gas solution flow. Moreover, these critical experiments verify the new microcellular extrusion system.

In general, microcellular processing consists of first forming a polymer/gas solution followed by the inducement of a rapid thermodynamic instability, which simultaneously nucleates a very large number of microvoids (2, 4-9). A scanning electron microscope (SEM) micrograph of a typical microcellular polymer cross section is shown in Fig. 1. The sample shown has an average cell diameter (or cell size) of 10 [[micro]meter] and a cell density of [10.sup.9] cells/[cm.sup.3], which translates into a specific gravity of approximately 0.5. Notice the uniform cell structure across the core, which is typical of these materials. After microcellular processing, transparent polymers become an opaque white and have a glossy surface finish. The glossy surface finish is due to a characteristic unfoamed surface layer, typically one to five cell diameters in thickness (4, 10, 11).

Microcellular plastics are characterized by cell sizes in the range of 0.1 to 10 [[micro]meter], cell densities in the range of [10.sup.9] to [10.sup.15] cells/[cm.sup.3], and specific density reductions in the range of 5 to 98%. Typically, microcellular plastics exhibit comparable and/or superior properties to structural foams and, in some cases, to the neat or unfoamed polymer (12).

The first stage of microcellular polymer processing involves dissolving an inert gas, such as nitrogen or carbon dioxide, under high pressure (i.e., the saturation pressure) into a polymer matrix to create a solution having a high gas concentration (typically 3 to 20% gas by weight). The next phase of microcellular processing is the rapid nucleation of billions of microvoids. Rapid nucleation promotes the even distribution of the dissolved gas, precipitating from the polymer matrix, over a multitude of cells. Nucleation is initiated by inducing a large thermodynamic instability. The thermodynamic instability is accomplished by quickly changing the solubility of gas in the polymer matrix, which is typically achieved by changing the temperature or pressure. The thermodynamic state must change quickly because of the competing phenomena of cell nucleation and cell growth. Without a rapid thermodynamic state change, the nucleation of cells occurs over a finite time, and the gas in solution will preferentially diffuse to cells that have already nucleated, rather than nucleating additional voids (3, 13). Thus, the overall cell density is reduced compared with rapid thermodynamic state changes. In general, gradual thermodynamic state changes result in large cells and non-uniform cell size distributions, which is the case for most conventional foam processing. To promote the large cell densities characteristic of microcellular polymers, homogeneous cell nucleation is preferred over heterogeneous cell nucleation, but is not always possible. This follows since cells will preferentially nucleate at the limited number of high energy interfaces such as additive particles, crystalline phases, contaminants, and pigments. This in turn limits the ultimate nucleation cell density compared with homogeneous nucleation.

The final phase of microcellular processing is the growth of stable nuclei. To allow growth of nucleated microvoids and to decrease the bulk density of the material, the polymer/gas solution is typically heated to near its glass-transition temperature. This lowers the polymer's flow strength and allows the cells to grow as gas diffuses into the cells. The temperature of the foaming process (i.e., the foaming temperature) can be used to control the rate of cell growth. Higher temperatures enhance cell growth because of the lower flow strength of the polymer and because of the higher gas diffusivity. Cell growth subsides when the system temperature is lowered to a critical value such that the polymer matrix is stiff enough to suppress further expansion and/or the gas has completely diffused out of solution.

Microcellular polymer processing differs considerably from conventional foam processing, and indeed conventional processes cannot be used to produce microcellular structures (3). In general, microcellular processing requires large concentrations of inert gas such as carbon dioxide or nitrogen. Concentrations can be ten times that of conventional foam processing. Conventional processes are not capable of achieving such high inert gas concentrations in single-phase polymer/gas solutions. In addition, microcellular processing requires the nucleation of at least three orders of magnitude more cells compared with conventional foams. This requires nucleation rates beyond the capability of conventional processes (3). Finally, microcellular processing requires the controlled growth of cells having an average final size 100 times smaller than conventional foams. At this scale, the growth of cells can occur in less than one hundredth of a second, which requires cell growth control techniques beyond that of conventional foam processing.

The first continuous microcellular polymer extrusion processing concepts were proposed by Waldman et al. (10) and further disclosed by Martini-Vvedensky et al. (4), while a similar process was patented by Hardenbrook et al. of the Eastman Kodak Company (11). The patent of Hardenbrook et al. describes a process where a web (i.e., a sheet) of plastic material, Impregnated with an Inert gas, is quenched using a complex die arrangement to form a saturated web of unfoamed material. Next, the surface gas is diffused out of the web in a controlled manner to promote an integral skin. The saturated web is then reheated at a station external to the extruder to induce foaming. During the foaming step, the temperature and duration of the foaming process are controlled to produce the desired cell morphology. The process is designed to produce a foamed plastic web with an Integral unmodified skin.

The significant limitation of this process is that only thin profiles (on the order of 0.020 inches in thickness) can be processed, owing to the limits of thermal cycling in producing thick-walled microcellular webs. Yet another complication with this process is the use of potentially invasive lubricants and coolants in the die system, which can degrade the sheet properties and surface finish. In addition, the die configuration used in the Kodak process is quite complicated and expensive. In contrast, the process developed in this work uses a relatively simple die arrangement having considerably lower capital costs. Moreover, the process developed here decouples cell nucleation, cell growth, and sheet shaping. A final difference between the process developed here and the Kodak process is that a staged pressure cycle is used to control microcellular processing in this work while the Kodak process uses a thermal cycle. In general, pressure cycles are easier to control than thermal cycles.


The continuous processing of microcellular polymers discussed In this work is based on three subprocesses, which include the processing of the polymer matrix, the processing of the microcellular structure, and the processing the net shape.(*) The creation of a microcellular structure is achieved by dissolving large gas concentrations into a polymer matrix and subjecting the saturated system to a rapid thermodynamic state change. This creates an unstable or supersaturated matrix that drives the nucleation of billions of microcells. Stable cells then grow as gas diffuses into the cells reducing the bulk density of the material. Based on these fundamental processing requirements, a hierarchical design strategy is used to synthesize the overall production system such that each of the processing functions is independently satisfied by a unique design parameter or process variable.

A schematic of the microcellular sheet extrusion system is shown in Fig. 2. The basic concept of this design is the use of a single-screw plasticating extruder to process the polymer matrix, a staged pressure loss to produce a microcellular structure, and a foaming/shaping die to produce the net shape. The plasticating extruder is used to melt and pump the pellets so the polymer is suitable for downstream processing. The polymer processing is accomplished in the first stage of a two-stage extruder. At the beginning of the second extruder stage, the polymer/gas solution formation system begins. Here, a metered amount of gas or supercritical fluid is injected into the polymer melt and mixed to form a single-phase solution using a technique presented previously (14). The solution formation system supplies a single-phase solution at the exit of the breaker plate/flow stabilizer. Next, the single-phase solution flows into the foaming die system. The foaming die accomplishes the nucleation and cell growth functions of the microcellular processing system and the shaping function of the sheet processing system. A microcellular sheet then exits the foaming die and can be post-processed to achieve an appropriate molecular orientation, surface finish, etc.

The three critical processing functions of the foaming die are continuous nucleation, cell growth control, and shaping. In general, cell nucleation must be accomplished independently of cell growth and shaping, and cell growth must be accomplished independently of sheet shaping. To this end, the concept of shaping a nucleated polymer/gas solution flow is presented and experimentally verified. As an integral part of this development, first-order process models were developed to aid in the design process. Preliminary results indicate these models adequately quantify the limited experimental results supporting their relevance in microcellular foaming die design. Moreover, the results of the critical experiments verify the overall performance of the microcellular extrusion system.


The basic premise of the foaming die design is to devise a way of handling and shaping a nucleated polymer/gas solution using cell growth control such that the nucleated cell density is not diminished (i.e., the process functions do not become coupled). In other words, the design must maintain the functional independence of cell nucleation, cell growth, and shaping.(**) The design strategy utilized in this work is a staged pressure change, as shown in Fig. 3, and precise temperature control. Microcellular nucleation is achieved using a rapid pressure loss. This is typically accomplished using a nozzle (13, 14), although new methods are presented by Baldwin (3). Next, primary shaping of the nucleated polymer/gas solution is performed under pressure, [P.sub.s], to prevent premature cell growth and loss of nucleated cell density. Finally, the pressure of the nucleated solution is decreased further to promote uniform cell growth and density reduction.

This design can be conveniently presented using a matrix equation representation presented by Suh (15). Here, the functional requirements, design parameters, and process variables are represented using vectors. Design matrices then map the interactions between the functional requirements, design parameters, and process variables. In the design matrices, Xs denote a strong interaction while Os denote a relatively weak interaction over the design range of interest.

Since cell nucleation, cell growth, and shaping are intimately related in continuous microcellular processing, it is helpful to consider these functional requirements in a single design equation. Looking at these requirements in a single design matrix provides a useful frame of reference for the design of a shaping and cell growth control device. The overall design equation for these requirements is given by

[Mathematical Expression Omitted]

The decoupled or upper triangular nature of Eq 1 follows from the physical link of these functions by the polymer/gas solution flow which allows pressure changes to be transmitted throughout the flow. In general, the solution pressure links shaping to cell growth and cell growth to nucleation. To satisfy the functional independence of Eq 1, the shaping elements must be specified first, followed by the staged expansion pressure, and finally specification of the rapid pressure loss. The physical coupling of Eq 1 can be interpreted as follows. Specification changes in the shaping die can change the flow resistance, which alters the inlet pressure of the shaping die. This in turn influences cell nucleation and cell growth by changing the upstream pressures. To achieve the proper cell growth, the shaping pressure can be adjusted independently of the shaping operation. Similarly, changes in the shaping pressure will influence cell nucleation by changing the upstream nucleation pressure, [Delta][P.sub.nuc] [approximately equal to] [P.sub.n] - [P.sub.s]. The cell nucleation requirement can then be satisfied by adjusting the magnitude of the rapid pressure loss parameter, [P.sub.n], without influencing the cell growth or shaping requirements.

To maintain functional independence from cell nucleation and shaping, the cell growth requirement of Eq 1 is expanded into three subordinate requirements. These functional requirements include controlling cell growth before shaping, controlling cell growth after shaping, and stabilizing the growing cells. The design parameters chosen to satisfy these requirements are the nucleated solution pressure during shaping, [P.sub.s], a mechanical constraint, and the die temperature, [T.sub.die]. The basic concept is sketched in Fig. 4, and the design equations are presented in Eqs 2 and 3.

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

As implied in Fig. 4, the geometry/shaping functional requirement of Eq 1 is expanded into two subordinate functional requirements. The design equations, Eqs 4 and 5, present the basic strategy for satisfying the shaping requirement. Notice that the shaping requirement is satisfied in two stages. The initial shaping is performed by the die, while the final dimensions are fixed by a physical constraint. In Fig. 4, the constraint is shown as a conveyor assembly although other conventional foam equipment (e.g., lubricated dies) can be used. The cross-sectional dimensions of the physical constraint fix the final dimension of the sheet while the chilled rolls control the surface temperature and provide for the postshaping cell growth control.

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

A critical aspect of the design presented in Eqs 1 through 5 is the ability to control the shaping and cell growth functions independently of cell nucleation. This is exceedingly challenging in microcellular processing due to the minute cells involved in the process and the extraordinarily large number of cells nucleated in these materials. The ability to achieve functional independence centers around three functional requirements: the control of preshaping cell growth, the stabilization of the growing cells, and the initial shaping requirement.

The need for preshaping cell growth control stems from the affinity of nucleated cells to agglomerate and coalesce during shaping operations. This follows since the agglomeration of cells is promoted by the compression, extension, and shear flow associated with shaping operations. The coalescence of cells leads to a deterioration of the nucleated cell density and couples cell nucleation, cell growth, and shaping. Cell coalescence occurs when adjacent cells agglomerate, at which point the cells merge into a single cell. The coalescence of cells is driven by the system free energy, which must decrease for this spontaneous process. For coalescing cells of similar size, the free energy decreases due to surface energy contributions (i.e., a decrease in the surface area). If the agglomerated cells are of sufficiently different sizes, then coalescence is driven by a rupture of the membranes common to the agglomerated cells. The rupture of the cell membranes occurs due to the differential gas pressure between cells of different size. To minimize the effects of coalescence during shaping, the agglomeration of the cells must be minimized, which can be achieved by increasing the mean interfacial distance between adjacent cells. Based on the theory of mixing for highly viscous fluids, the mean interfacial distance is quantified using the striation thickness, s. By definition, the striation thickness is the average distance between interfaces of the same component in the mixture and is given by Eq 6 where A/V is the interfacial area per unit volume. To increase the striation thickness and minimize cell coalescence, the interfacial area of the gas phase can be minimized. The concept implemented in the extrusion system is to minimize the gas phase volume (i.e., the cell size) through the use of high foaming die pressures during shaping (see Eq 2).

s [equivalent] 2 / A/V (6)

The preshaping cell growth control is also important in reducing the effects of shear on the nucleated polymer/gas solution flow. In general, viscous, non-Newtonian flow generates large shear stresses and shear rates near the boundary walls (16). The shear thinning behavior of the non-Newtonian flow localizes the shear effects to the wall (i.e., much like boundary layer flow), while the core regions experience relatively little shear effects (i.e., plug flow). Cells within the shear field are elongated, forming needlelike structures. The elongation of the cells near the boundary can lead to dispersive mixing (17). When a cell is highly stretched, its surface becomes unstable resulting in the formation of one or more new cells and increasing the number of cells in a given volume (i.e., the cell density). However, the shear flow at the boundary can also lead to the coalescence of cells. The shear deformation of the cells increases the surface to volume ratio of affected cells decreasing the striation thickness. This decreases the interfacial distance between cells promoting agglomeration and cell coalescence. It is clear that the boundary shear field generates competing mechanisms that can affect the cell density: dispersive mixing which increases the number of cells and cell coalescence which decreases the number of cells. In the current design, no attempt is made to reduce the dispersive mixing aspects of the shear flow. Instead, the design provides for minimization of cell coalescence so as to decouple cell nucleation, cell growth, and shaping. Ultimately, the critical experiments will give some indication whether the dispersive mixing aspects of shear flows must be addressed in the design of foaming dies. In general, dispersive mixing effects will influence the cell morphology along the surface of the extrudate.

To understand the rationale underlying the shaping pressure design parameter that satisfies the preshaping cell growth requirement, consider the following: Relatively large shaping pressures, [P.sub.s], maintain relatively small cells in the nucleated polymer/gas solution. Provided that the cells are small enough during shaping (i.e., die flow), the cells will not tend to agglomerate, and the effects of cell coalescence and boundary shear flow will be minimized. For nucleated solutions having equal cell densities, smaller cell sizes imply larger interfacial distances between adjacent cells. This reduces the probability that adjacent cells will come in contact leading to coalescence and cell density deterioration.

The use of the shaping pressure to maintain relatively small cells in the nucleated solution can be understood with the aid of Fig. 5. In equilibrium, the gas phase pressure in the cells, [P.sub.g], is a function of the solution pressure surrounding the cells, P, and the surface energy, [[Gamma].sub.bp], where from Laplace's equation, [P.sub.g] = P + 2[[Gamma].sub.bp]/R. Likewise, the specific volume of the gas, [v.sub.g], varies inversely with the gas phase pressure based on the ideal gas law [ILLUSTRATION FOR FIGURE 5 OMITTED]. Therefore, as the solution pressure or shaping pressure is increased, the gas phase pressure increases and the specific volume of the gas decreases leading to smaller cell sizes.

A final cell growth control requirement that deserves mention is that of cell growth stabilization (see Eqs 2 and 3). The importance of cell growth stabilization follows from the tendency of the nucleated solution flow to experience unstable cell growth and overexpansion of the cells, particularly when exiting the foaming die. When cell growth occurs without constraint, it becomes unstable and can lead to cell wall rupture and a deterioration of the cell density. This problem is pronounced at the elevated temperatures of melt processing due to the low melt strength of the polymer matrix, the relatively high specific volume of the gas phase, and the low surface tension of the polymer/cell interface. One might expect that the overexpansion of cells is pronounced at the surfaces of the foaming sheet, which is typically the case in microcellular sheet extrusion. To minimize the over-expansion of cells, lower temperatures can be employed (see Eqs 2 and 3), which increase the melt strength or stiffness of the viscoelastic matrix, decrease the specific volume of the gas phase, and increase the surface tension. In Fig. 4, this is accomplished by cooling the die lips of the foaming die to a temperature substantially lower than typical melt extrusion temperatures for the neat polymer.


To satisfy the preshaping cell growth control requirement of Eq 2, it is necessary to design a shaping and cell growth control die that can maintain the required shaping pressures. Therefore, the design of a shaping and cell growth die requires knowledge of the pressure loss effects of nucleated polymer/gas solutions. In general, the flow of a nucleated polymer/gas solution is complex and involves a heterogeneous system consisting of a polymer melt with dispersed cells having relatively large center-to-center spacing compared with the average cell diameters [ILLUSTRATION FOR FIGURE 5 OMITTED]. The pressure loss in the flow results from frictional effects at the die walls. As the pressure decreases along the die channel, the nucleated cells grow resulting in an increase in (i) the specific volume (or decrease in density) of the two-phase system and (ii) the volumetric flow rate. Cell growth is driven by the pressure within the cells and diffusion of solution gas into the cells. Gas diffusion into the cells results from the decrease in solubility as the solution pressure decreases along the die channel. As the heterogeneous system expands, there is less polymer across any given area of the flow channel to support the shear stresses generated by the wall friction. This implies that the expanding solution has a lower apparent viscosity. The apparent viscosity also tends to decrease because of shear thinning as the volumetric flow rate increases. In this section, a brief overview of the design model is presented. A detailed presentation of the model including assumptions and derivations is presented elsewhere (1, 3).

The pressure of a nucleated polymer/gas solution along a die can be estimated using Eqs 7 through 9. The model accounts for the fact that gas diffuses into the cells as the solution pressure decreases along the die length such that cell growth during the die flow is driven by both the gas pressure in the cells and the diffusion of gas into the cells. The model estimates the pressure loss and volumetric flow rate along a die using the power law approximation for non-Newtonian viscous flow of a bulk nucleated polymer/gas solution. Flow is assumed steady and fully developed though a constant cross-section slit. The gas phase, approximated as ideal, is assumed to be in quasi-static equilibrium at any point along the flow channel, and gas diffusion is approximated as instantaneous.

The pressure drop along the die is given by Eq 7 and used to estimate the slit inlet shaping pressure, [P.sub.s].

[Mathematical Expression Omitted]

In Eq 7, the local gas phase specific volume, [v.sub.g/p], is estimated from an instantaneous mass balance for the gas and the ideal gas approximation.

[v.sub.g/p] = ([c.sub.[infinity]] - [K.sub.s](T)[P.sub.g](P)) RT/[P.sub.g](P) (8)

The local gas phase pressure, [P.sub.g], is estimated from Laplace's equation and an instantaneous average cell size approximation based on the nucleated cell density.

[P.sub.g] = P + 2[[Gamma].sub.bp](T) [[3[[Rho].sub.p]/4[Pi][[Rho].sub.c] RT/[P.sub.g]([c.sub.[infinity]] - [K.sub.s](T)[P.sub.g]].sup.-1/3] (9)

Pressure loss and flow rate estimates typical of nucleated solution flows during shaping and cell growth operations are presented in Fig. 6. The model parameters used in Eqs 7 through 9 were as follows: constituents = polystyrene/C[O.sub.2] system, T = 150 [degrees] C, [[Rho].sub.p] = 1.04 g/[cm.sup.3], [[Gamma].sub.bp] = 0.0314 N/m (18), [[Rho].sub.c] = 1.5 x [10.sup.9] cells/[cm.sup.3], [K.sub.s] = 0.0039 kg(C[O.sub.2])/kg(PS)MPa (14), [c.sub.[infinity]] = 0.05, [Mathematical Expression Omitted], n = 0.29, and m = 40,750 Pa [s.sup.n]. The slit dimensions used were B = 0.32 mm, W = 25.4 mm, and L = 20.3 mm. Equations 7 through 9 were solved using a finite difference technique having N = 20 elements (i.e., [Delta]z = 1.02 mm) and a boundary condition of [P.sub.exit] = 0.965 MPa (140 psi). This boundary condition is based on the findings of Han et al. (19) and Han and Villamizar (20). Han and co-workers measured pressure profiles of polymer foam flows through various die geometries. These measurements revealed exit pressure losses equal to approximately 10% of the die entrance pressures.

Equations 7 through 9 can also be used to estimate the average cell sizes during shaping operations. For the conditions of Fig. 6, which predicts a shaping pressure, [P.sub.s], of 11.5 MPa (1670 psi), the model estimates an average cell radius of 2 [[micro]meter] at the entrance of the foaming die. Based on the cell morphology and geometry for a nucleated cell density on the order of [10.sup.9] cells/[cm.sup.3], an initial shaping cell size on the order of 2 [[micro]meter] should be sufficient to prevent degradation of the nucleated cell density and therefore satisfy the preshaping cell growth control functional requirement of Eq 2.


Shaping and Cell Growth of a Thick Filament

To verify the concept of shaping a nucleated polymer/gas solution flow, a relatively simple geometry was selected capable of producing large diameter filaments. The predictions of Fig. 6 in conjunction with the estimates of Baldwin (3) indicate that shaping pressures on the order of 6.9 to 14 MPa (1000 to 2000 psi) are required to satisfy the preshaping cell growth control requirement. Using this pressure range as an acceptable design parameter range, a nucleated flow analysis was performed for tube flow following the same lines as that for Fig. 6. Based on this analysis, the shaping and cell growth control die design of Fig. 7 was manufactured. The foaming die design consists of a nozzle nucleation device and a filament shaping die. The staged nozzle configuration provides for the necessary staged pressure loss to maintain functional independence of the nucleation, cell growth, and shaping requirements.

A critical experiment was run to verify the concept of shaping a nucleated solution flow using the extrusion system configuration of Fig. 8 and the foaming die of Fig. 7. The process parameters for the experiment were: material = Novacor 101 PS, nozzle diameter = 0.533 mm, nozzle length = 6.35 mm, filament die diameter = 1.04 mm, filament die length = 12.7 mm, flow rate = 23 g/min, die temperature = 149 [degrees] C, estimated gas concentration = 6%, nucleation pressure = 28.28 MPa (4100 psi), shaping pressure = 6.89 MPa (1000 psi). The critical experiment was successful in demonstrating the feasibility of continuous shaping of a nucleated polymer/gas solution. A typical scanning electron microscope micrograph of the microcellular polystyrene thick filament is shown in Fig. 9 exhibiting an average cell size of 10 [[micro]meter] and an average cell density of [10.sup.9] cells/[cm.sup.3]. The repeatability of these results was also experimentally verified.

Shaping and Cell Growth of a Planar Sheet

To further verify the concept of shaping a nucleated polymer/gas solution flow and to demonstrate continuous microcellular sheet extrusion, a planar sheet foaming die was used. The die design was based on the analysis of Fig. 6, which resulted in the configuration shown in Fig. 10. This design consisted of a nozzle nucleation device and a planar sheet foaming die. In this case, the nozzle provided the rapid pressure loss for controlling cell nucleation and the die provided the initial sheet shaping and the shaping pressure control. The foaming die design of Fig. 10 also included a technique for stabilizing cell growth. Cell growth stabilization is satisfied by maintaining accurate temperature control of the die lips using the cooling ports located near the upper and lower die lips.

A critical experiment was run to verify the planar sheet processing system using the extrusion system configuration of Fig. 8 with the foaming sheet die of Fig. 10. The process parameters for the experiment were: material = Novacor 103 PS, nozzle diameter = 0.533 mm, nozzle length = 6.35 mm, slit height = 0.635 mm, slit length = 20.32 mm, slit width = 25.4 mm, flow rate = 26 g/min, die temperature = 150 [degrees] C, estimated gas concentration = 5%, nucleation pressure = 32.40 MPa (4700 psi), shaping pressure = 9.65 MPa (1400 psi). The cooling port fluid used was low pressure carbon dioxide. The critical experiment was successful in demonstrating the feasibility of continuous shaping of a nucleated polymer/gas solution. A typical scanning electron microscope micrograph of the microcellular polystyrene sheet is shown in Fig. 11 exhibiting an average cell size of 11 [[micro]meter] and an average cell density of 1.5 x [10.sup.9] cells/[cm.sup.3]. The repeatability of these results was also experimentally verified.

Finally, it was interesting to compare the flow rate results of this foaming die configuration with the design model predictions. For comparison, Fig. 6 is calculated for the same flow parameters as the planar sheet extrusion experiment presented above. Notice that the shaping pressure achieved by the foaming die, [P.sub.s] = 9.65 MPa (1400 psi), was in reasonable agreement with the predicted value of 11.5 MPa (1670 psi). It is also interesting to note that predictions based on a neat polymer flow overpredicted the actual pressure loss by 66%. Thus, the pressure loss estimates from the nucleated solution flow models appeared to capture the major physics of the shaping and cell growth processes to provide reasonable estimates for foaming die designs.


In this paper, the shaping and cell growth control functions of a microcellular sheet extrusion system were presented and experimentally verified. The principle of the basic design was to shape a nucleated polymer/gas solution flow under pressure and close temperature control. In this way, the initial cell growth was controlled so as to prevent degradation of the nucleated cell density during shaping. Two foaming die designs for satisfying the initial shaping and cell growth requirements were presented. Critical experiments were then performed which verified the concept of shaping a nucleated polymer/gas solution. Moreover, these experiments demonstrated the feasibility of the overall microcellular polymer sheet extrusion system design.

The feasibility of shaping a nucleated polymer/gas solution represents a significant advancement for microcellular plastics process technology. Through proper design of the foaming die, nucleated solution flows can be shaped to arbitrary dimensions while maintaining the functional independence of cell nucleation, cell growth, and shaping. To maintain functional independence, stringent pressure and temperature design specifications, which supersede those of conventional foam processing, must be met by the foaming die design. As a means of aiding the design process, a model was developed for predicting pressure losses and flow rates of nucleated polymer/gas solutions. A comparison of the model predictions and the actual foaming die design performance showed good agreement for limited data. Moreover, this relatively simple model captures the major physics of the complicated two-phase flow field and provides a sound base from which scale-up of the foaming die concept to industrial levels can be achieved.


The authors would like to thank Dr. Bruce M. Kramer and Dr. Maria Burka for their interest in this work and the National Science Foundation, Grant Number CTS-9114738, for supporting this research. This work was performed at the MIT-Industry Microcellular Plastics Research Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts.


A = Interfacial area of polymer/gas mixture ([m.sup.2]).

B = Half slit height (m).

[c.sub.[infinity]] = Initial equilibrium gas concentration (kg(gas)/kg(polymer).

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

[K.sub.s] = Henry's law constant [kg(gas)/kg(polymer)Pa].

L = Flow channel length (m).

m = Factor in power law constitutive equation for the neat polymer (Pa [s.sup.n]).

[Mathematical Expression Omitted] = Polymer mass flow rate (kg/s).

n = Exponent in power law constitutive equation for the neat polymer.

[p.sub.[infinity]] = Pressure of the polymer far from the cells (Pa).

[P.sub.b] = Barrel pressure at the gas injection port (Pa).

[P.sub.barrel] = Pressure at the barrel venting port (Pa).

[P.sub.exit] = Pressure at the foaming die exit (Pa).

[P.sub.g] = Pressure of the gas phase in the cells (Pa).

[P.sub.head] = Pressure at the head of the screw (Pa).

[P.sub.n] = Pressure at the nucleation device (Pa).

[P.sub.s] = Shaping pressure at the foaming die inlet (Pa).

[Delta]P = Pressure loss along the flow channel ([P.sub.inlet] - [P.sub.outlet]) (Pa).

[Delta][P.sub.nuc] = Effective pressure change driving nucleation (Pa).

R = Average cell radius (m).

R = Universal gas constant/molecular weight of the gas (J/kg K).

s = Striation thickness (m).

T = Absolute temperature (K).

[T.sub.die] = Temperature of the die or the die lips (K).

[T.sub.exit] = Flow temperature at die exit (K).

[] = Final temperature of adiabatic expansion (K).

[T.sub.n] = Temperature at nucleation (K).

[T.sub.s] = Temperature at shaping (K).

[v.sub.g/p] = Specific volume of the gas phase relative to the polymer mass ([m.sup.3]/kg).

V = Volume of mixture ([m.sup.3]).

W = Width of the slit (m).

[Delta]z = Incremental distance along the flow channel (L/N) (m).

[[Rho].sub.p] = Density of polymer (kg/[m.sup.3]).

[[Rho].sub.c] = Density of nucleated cells (cells/[m.sup.3]).

* A detailed presentation of the microcellular sheet extrusion system design is presented by Baldwin (3) and will be the subject of a future article.

** This is consistent with the axiomatic design approach developed by Suh (15).


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Author:Baldwin, Daniel F.; Park, Chul B.; Suh, Nam P.
Publication:Polymer Engineering and Science
Date:May 1, 1996
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