a study of strain-induced nucleation in thermoplastic foam extrusion

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2004 40: 27Journal of Cellular PlasticsJacques Tatibouët and Richard Gendron

A Study of Strain-Induced Nucleation in Thermoplastic Foam Extrusion

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+ [27.1

A Study of Strain-inducedNucleation in Thermoplastic

Foam Extrusion*

JACQUES TATIBOUETyAND RICHARD GENDRON

Industrial Materials Institute

National Research Council of Canada

75 De Mortagne Blvd., Boucherville, Quebec, Canada J4B 6Y4

ABSTRACT: The conditions that induce the phase separation and the bubblenucleation for the thermoplastic foam extrusion process in which physicalfoaming agents (PFA) are involved are obviously linked to the solubilityparameters: temperature, PFA content, and pressure. However, it has beenreported that flow or shear can significantly modify these degassing conditions.An in-line detection method based on ultrasonic sensors was used to investigatethe influence of the flow on the foaming conditions of polystyrene/HFC134amixtures, for PS resins of various melt flow rates. An increase of the apparentdegassing pressure at low melt temperature was observed for high viscosityresins. Deviations from solubility data have been attributed to the combinedeffects of elongational and shear stresses.

KEY WORDS: solubility, foam extrusion, nucleation, ultrasounds, elasticity.

INTRODUCTION

The mechanisms underlying nucleation for thermoplastic foamextrusion based on physical foaming agents (PFA) has been the

object of many studies [1]. Among these studies, different experimentalpathways have been investigated. Part of these works have been

*This revised paper was presented in its original form at the 61th Annual TechnicalConference (ANTEC ’03), Nashville, TN, May 4–8, 2003, and the copyright is held by theSociety of Plastics Engineers.yAuthor to whom correspondence should be addressed.E-mail: [email protected]

JOURNAL OF CELLULAR PLASTICS Volume 40 — January 2004 27

0021-955X/04/01 0027–18 $10.00/0 DOI: 10.1177/0021955X04040281� 2004 Sage Publications

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conducted under static, no flow, conditions, i.e., in solid-state foaming,or through depressurization in an autoclave. However, it is believed thatthe shear conditions that prevail in the extruder as well as in theshaping die can enhance the nucleation, which makes the link betweensolubility test and degassing during the extrusion not an easy one toestablish. For these reasons, other works have been performed underflow condition, i.e., by monitoring the bubble initiation in a slit die, andthrough cell count on extruded foam products.

Pioneering in-line study by Han and Han [2] suggested that nucleationcan be induced either by flow and/or shear stress and that flow-inducednucleation is the dominant mechanism near the center of the flow, whileshear stresses dominate near the die wall. As a conclusion of more recentexperiments, Chen et al. [3] proposed a model where nucleation sitesare stretched under shear; nuclei are then easier to expand owing tolarger surface area and nonspherical shape. Investigation by Park et al.[4] has underlined the importance of pressure drop rate and pressureprofile in the die. Timescale thus would play an important role in bubblenucleation, since this latter competes with diffusion of PFA moleculestoward existing bubbles. The role of shear stress in heterogeneousnucleation was also pointed out by Lee [5], and a very simple physicalmodel called the cavity model was introduced to explain the observations,where increase of the shear through a higher feed rate magnifiedthe nucleation density. However, despite these numerous studies, anadequate description of the mechanisms for homogeneous as well asheterogeneous nucleation still needs to be elaborated.

As one of the many techniques available for process study, an in-lineultrasonic characterization technique has allowed monitoring thecritical steps of the foam extrusion process [6]. Sound velocity andattenuation are very sensitive parameters not only to the presence ofbubbles, but also to the composition of the polymer/blowing agentmixture and to the dynamic of phase separation [7].

Degassing pressure, defined as the pressure at which phase separationbetween PFA and polymer matrix is observed, has been determined fornumerous polymer/PFA systems, under various conditions. Preliminaryexperiments have shown that in the case of studies conducted understatic conditions (no flow), the degassing pressures were much lowerthan those observed during extrusion experiments [8]. While staticresults appear to be closer to solubility data, the effect of flow inducespremature nucleation under higher pressures. Moreover, these largedeviations from solubility results were observed especially at lowtemperatures. For a given blowing agent content, the curves wheredegassing pressures are plotted as a function of temperature exhibited

28 J. TATIBOUET AND R. GENDRON

+ [27.11.2003–11:38am] [27–44] [Page No. 28] FIRST PROOFS I:/Sage/Cel/Cel40-1/CEL-40281.3d (CEL) Paper: CEL-40281 Keyword



a parabolic shape [6]. This parabolic shape was repeatedly obtained forsystems based on a PS matrix, with various PFAs such as HFC-134a,CO2, and HCFC-142b [6–10].

Even for mixtures with added nucleating agent such as talc ortitanium dioxide, these curves kept their parabolic shape, but wereshifted upward towards higher pressures [7]. Schematic features ofthese curves are presented on Figure 1. Deviations at low temperaturesor in the presence of nucleating agents still need to be explained in termsof thermodynamics (solubility) and mechanics (rheology). In this work,homogeneous nucleation will be explored.

EXPERIMENTAL METHODS

Foam extrusion was carried out on a Leistritz 50mm counter-rotatingtwin screw extruder equipped with an instrumented slit die (pressure,temperature, and ultrasonic probes) as described in [11]. The geometryof the slit die (140� 40� 5mm3) allows steady and fully developed flowconditions at the locations of the probes. A gear pump was placed afterthe instrumented slit die to allow controlling the pressure inside the slit.An increase of the speed of the gear pump would decrease the volume ofpolymer comprised in the last pumping zone of the starved-fed extruder,

T (°C)

Deg

assi

ng

pre

ssu

re (

MP

a)Addition of

nucleating agent

Given PFA content,no nucleating agent

Increase ofPFA content

Figure 1. Schematic evolution of degassing pressure curve when physical foaming agent

content is increased, or with addition of nucleating agent.

Thermoplastic Foam Extrusion 29




lowering then the flow rate and the pressure in the instrumentedchannel. The physical foaming agent used was HFC-134a, and it wasinjected into the extruder barrel using a preparative chromatographypump to maintain a constant concentration of blowing agent, set at6%wt. The nominal resin flow rate was 10 kg/h. Five different linearpolystyrene resins were investigated, and their characteristics are givenin Table 1. No nucleating agent has been used.

Measurements of the degassing conditions were carried out as follows(see Figure 2). First, a steady flow of the homogeneous mixture wasestablished at different but fixed temperatures. The pressure was highenough to prevent bubble nucleation in the die. The melt temperaturewas kept constant to within a degree. Then, in a second step, thepressure in the die was lowered rapidly at approximately 200 kPa/s byincreasing steadily the speed of the gear pump. During these operations,the pressure and the ultrasonic parameters (attenuation and soundvelocity) were continuously monitored. The pressure measurementsprovided data to calculate the shear stress in the flow channel, while theultrasonic data provided the information on the onset of bubblenucleation as that has been reported elsewhere [6].

Rheological characterization was also performed off-line on the neatPS resins. Dynamic viscosity, as well as loss and storage moduli, weredetermined at 180�C using the Rheometrics Mechanical Spectrometer(RMS) with small parallel plates on disk molded samples. Frequencysweeps were conducted from 0.1 to 100.0 rad/s.

RESULTS

Results for the degassing experiments, in terms of degassing pressureas a function of melt temperature, are shown in Figure 3, alongwith solubility data excerpt from [12,13]. A good agreement is observedbetween in-line results and data from literature, for a group oftwo resins of low viscosity (11.5 and 20.3-MFI resins). Degassing

Table 1. Rheological characterization of the resins.

Resin MFI(dg/min)

�0(kPa s)

J0e �105

(kPa�1)

�m (s)

155�C 165�C 175�C

1.6 172.0 13.6 500 200 1002.3 128.9 13.4 325 135 655.3 41.7 15.6 100 40 2011.5 23.5 9.6 35 15 720.3 9.8 8.6 6 3 1





pressures for these resins fall within the experimental errors that can beassociated to equilibrium measurements of solubility. The three moreviscous resins form a second group, with higher degassing pressuresby at least 0.7MPa. Trends for the two groups are parallel fortemperatures higher than 160�C, i.e., degassing pressures decreasewith decreasing temperature, which is consistent with solubilitybehavior. However at lower temperature, below 160�C, an upwardtendency is observed, with the magnitude being proportional to theviscosity of the resin. The most viscous PS (MFI of 1.6) exhibits adegassing pressure above 7.0MPa at 153�C, which is roughly 2.7MPahigher than the solubility data.

1020

1040

1060

1080

Vel

oci

ty (

m/s

)

0.0

40.0

Att

enu

atio

n (

dB

/cm

)

0

2.5

5.0

10.0

12.5

Pre

ssu

re (

MP

a)

40 80 120 160 200

Time (s)

20.0

Figure 2. Evolution of velocity, attenuation and pressure during typical degassing

experiments. Arrow indicates the degassing conditions.





Results from the dynamic rheological characterization, performed at180�C, are listed in Table 1. The steady-state compliance J0

e can bedefined as the amount of strain recovery or recoil that occurs after thestress is removed. Its value was derived from the relationship [14]:

J0e ¼

G0

�20!2

ð1Þ

where G0 is the elastic modulus, �0 the zero-shear viscosity and ! thefrequency. The modulus value was, in that case, extrapolated at thelower limit of frequency. The steady-state compliance is strongly relatedto elastic properties of the materials but also to molecular weight andmolecular weight distribution.

DISCUSSION

Nucleation and Thermodynamics

First, a clear definition of nucleation is needed. The occurrenceof nucleation is associated with the smallest size of the cluster of thePFA molecules that could initiate bubble growth, yielding a permanenttwo-phase system. The minimum needed for the cluster radius is usually

4

5

6

7

8

Deg

assi

ng

pre

ssu

re (

MP

a)

150 155 160 165 170 175

Temperature (°C)

20.311.55.32.31.6

Figure 3. Degassing pressure as a function of the temperature for resins of various MFIs.

Resins are identified with their respective MFI-value. This nomenclature will be kept

for the other figures. HFC 134a content: 6wt%. Dotted lines: equilibrium solubility datafrom [12,13].





obtained through the derivative of the Gibbs energy, which opposes thevolume free energy (volume effect) to the interfacial energy (surfaceeffect), as illustrated in Figure 4 [15].

The excess energy associated to the production of a gas bubble in apolymer through a reversible thermodynamic process is equal to:

�Ghom ¼ �Vb�Pþ Abp�bp ð2Þ

where Vb is the volume of the nucleus, �P is the gas pressure in thebubble nucleus, Abp is the surface area of the bubble and �bp is the surfaceenergy of the polymer–bubble interface. In the case of a spherical nucleuswith radius r, the maximum free energy is associated to a critical radiusr�above which the growth of the bubble leads to a reduction of freeenergy. Differentiation of Equation (2) gives the critical radius r�,

r� ¼ 2�bp=�P ð3Þ

and the free energy for the homogeneous nucleation of a critical nucleus:

�G�hom ¼

16�

3�P2�3bp ð4Þ

The size of the critical cluster, which can be approximated in the10nm-range [16], is such, in comparison with the size-domain of the PSmacromolecules, that a deformation of the resin matrix should be

InterfacialEnergy � r2

VolumeFree Energy � r3 DP

0

∆G

r

∆G*

r*

Nucleation &bubble growth

∆G

Figure 4. Homogeneous nucleation: evolution of the Gibbs free energy associated to

nucleation and growth of the bubbles.





anticipated in the initial stage of nucleation. Microscale rheology shouldbe that of interest, which scales with the entanglement network, and notthe bulk rheology that is additionally sensitive to chain ends andmolecular weight. Strain magnitude and strain rate encountered duringnucleation would also correspond to very small times, thus highfrequencies, with small strains falling within the linear viscoelasticitydomain. Also, the mode of deformation prevailing will be that in tension/compression, with little shear induced.

Degassing Pressures and Tensile Stress

Our first concern is to find the appropriate criteria that could explainthe splitting of the resins into two groups for the degassing pressures athigh temperature. Examination of the rheological data in Table 1indicates that the steady-state compliance fits nicely with the pressureresults. A rather poor elastic recovery is associated with the two low-viscosity resins that exhibit degassing pressures close to the solubilitydata, while larger J0

e results were obtained for the other three resinswhose degassing pressures are shifted to higher values by approximatelythe same magnitude.

Elastic recovery is generally related to the extrudate swell – not to beconfounded with cellular expansion – of most extruded viscoelasticmaterials. Low-stress condition may induce little swell, while swellincrease is observed with higher stresses [17]. Short dies yield largeswell, while longer dies lead to an asymptotic value of the swell. Thisswelling behavior can be associated with the very simple illustrationthat swelling results from a tensile stress maintained on the polymerwithin the die [17]. This tensile stress originates from the extensionaldeformation occurring at the inlet of the die. The stress may relax in thedie according to the Weissenberg Number, We, which can be defined asthe ratio of the longest relaxation time to that of the residence timewithin the die (reciprocal of the deformation rate). The remaining of thetensile stress finally relaxed completely after it exits the die, which leadsto the swelling of the extrudate. Thus, for short dies, or at a distanceclose to the entrance, the remaining tensile stress, that is not inequilibrium yet, may be pretty large.

At some point during the flow in the die, if the die is long enough, thetensile stress will reach an equilibrium that corresponds to the firstnormal stress difference N1 induced by the shear [14]:

N1 ¼ �11 � �22 ¼ 2Joe�

212 ð5Þ





This tensile stress in equilibrium will last till the exit, and correspondsto what is usually referred as the exit pressure, as illustrated in Figure 5.It has already been proposed to use this exit pressure for thedetermination of the first normal stress difference under high shearrate conditions [18]. The entrance pressure, also defined in the samefigure, corresponds to the stress induced through the extensionaldeformation. As suggested by Cogswell, determination of this entrancepressure can provide valuable information on the extensional rheologi-cal behavior of the fluid [19].

As illustrated in Figure 6, the high viscosity resins have experiencedhigher shear stresses, since all the experiments have been conducted ata set throughput, i.e., fixed shear rate (roughly 15 s�1). Assumingthat under the high temperature conditions the tensile stress hasrelaxed and reached equilibrium, the normal stress can be calculatedusing Equation (5), which gives roughly a few negligible kPa forthe 20.3MFI-resin, but a significant 800 kPa for the high viscosity1.6MFI-resin. That means that along the h11i axis (flow direction), thetensile stress still acting on the polymer and against the hydrostaticpressure is 800 kPa, which corresponds to the difference observed in thedegassing pressures between the two resins groups at high temperature.

As the temperature is lowered, the relaxation times of the polymersincrease, and the situation where the tensile stress has not reached the

Pre

ssu

re (

MP

a)6.0

4.0

2.0

Distance within the slit die-4 -2 0 2 4 6 8 10

P exit

ΦP entrance

0.0

Tensile deformation

Relaxation

Equilibrium

Elasticrecovery(swell)

Die

en

tran

ce

Die

exit

Slope� shearstress

Pre

ssu

re (

MP

a)6.0

4.0

2.0

Distance within the slit die-4 -2 0 2 4 6 8 10

P exit

∆P entrance

0.0

Tensile deformation

Relaxation

Equilibrium

Elasticrecovery(swell)

Die

en

tran

ce

Die

exit

Slope� shearstress

Figure 5. Evolution of the pressure in a slit die.





equilibrium may be gradually encountered. A crude estimate of themaximum relaxation times �m obtained from the dynamic rheologicalmeasurements on the neat resins at 180�C (which correspondsapproximately to the plasticized PS at 155�C [20]) is listed in Table 1.The relaxation time spectrum H(�) was obtained from a numericalroutine based on the loss and storage moduli, as detailed in [21]. Themaximum relaxation times at 165 and 175�C were estimated using theW-L-F equation that relates viscosity (or relaxation times) to tempera-ture for amorphous polymers. It is quite obvious that the very longrelaxation times that prevail for the 1.6MFI-resin at 155�C will prohibitany relaxation of the stretched state that has originated from theextensional deformation at the die entrance.

Our results can be coupled to other findings published in theliterature. As reported by Han and Han [2], the first bubbles toappear were located in the center of the flow. The onset of nucleationwould follow a parabolic degassing profile with highest degassingpressures located at the centerline of the flow, as illustrated inFigure 7. It is known that the amount of stretching in a flow inside adie is at its maximum along the centerline [22]. So the influence oftensile deformation on degassing, as we have shown, may explain theobservations of Han and Han. Moreover, the anisotropic nature of thestresses acting at the nucleation onset and during the bubble growth

4

4

5

6

7

8

0 10 20 30 40 50

20.311.55.32.31.6

Deg

assi

ng

Pre

ssu

re (

MP

a)

Shear stress (kPa)

Figure 6. Degassing pressure as a function of apparent shear stress.





could be linked to the elliptical shape of the bubbles (less resistance togrowth in the machine direction), observed during their flow in the slitdie. As suggested by Chen et al. [3], the elliptical shape of the nucleiwould even ease the foaming process.

Ultrasonic Velocities

Ultrasonic properties as measured in-line can also be linked to therheological characteristics of the melt, under shear and/or extensionalfield. But first, Figure 8 illustrates typical results from temperaturesweeps in a static (no flow) mode for the ultrasonic velocity for the 20.3and 1.6-MFI resins, subjected to a hydrostatic pressure of 10MPa.Under these conditions, ultrasounds are not sensitive to molecularweight and molecular weight distribution but only to local segmentinteractions.

However, when looking at the results obtained during the degassingtrials, one can see that the ultrasonic velocity is sensitive to the flowingconditions, which vary according to the rheological behavior of eachresin. The ultrasonic velocity measured at 7.6MPa is presentedin Figure 9 as a function of the temperature for the homogeneousphase. At low temperature, velocity decreases when resin viscosityincreases. Under flow conditions, ultrasonic velocity probes also thelocal arrangements of the chains induced by the stresses (entanglement,

0.25

0.50

0.75

-0.2 -0.1 0 0 .1 0.2y (cm)

Shear (wall)

Tensile

Syy

(MP

a)

0.25

0.50

0.75

-0.2 -0.1 0 0 .1 0.2y (cm)

Shear (wall)

Tensile

Syy

(MP

a)

Figure 7. Degassing pressure as a function of the axial position in a slit die for a mixture

of PS with 4wt.% of R-11. From data of [2].





conformation,. . .). This is confirmed when plotting velocity measured at152�C as a function of the apparent shear stress (Figure 10). Thevelocity is sensitive to the effective stress and to the associated shear-thinning effect. Higher shear stresses are experienced by the moreviscous mixtures and therefore induced local arrangement such asmolecular alignment and disentanglement.

1080

1090

1100

1110

1120

1130

1140

1150

1160

1170

1180

Co

rrec

ted

vel

oci

ty a

t 7.

6MP

a (m

/s)

145 150 155 160 165 170 175

Temperature (°C)

20.3

5.32.31.6

11.5

Figure 9. Velocity measured in the homogeneous phase at 7.6MPa as a function of

temperature.

1100

1200

1300

1400

1500

1600

1700

1800

Vel

oci

ty (

m/s

)

150 160 170 180 190 200 210 220 230

Temperature (°C)

1.620.3

Figure 8. Velocity as a function of temperature, measured in static conditions at 10MPa

for the 20.3 and 1.6-MFI resins.





In Figure 11(a), we attempt to correlate the variation of the ultrasonicvelocity with an estimated efficient pressure (or stress) that wouldprevail in the machine direction, as schematically illustrated inFigure 11(b). The ultrasonic velocities were measured at constantpressure (7.6MPa) prior the degassing ramp for the tests performedat 155�C, while the efficient pressure, reported on the x-axis ofFigure 11(a), was computed according, the following equation:

Pefficient ¼ Phydrostatic � Tensile Stress ¼ Pmeasured � ðPdegassing � PsolubilityÞ

ð6Þ

The measured pressure is the hydrostatic pressure maintainedbefore the pressure ramp decrease (7.6MPa). Making the assumptionthat deviation from equilibrium solubility data resulted from thetensile stress, we estimated this last one by the difference betweenthe measured degassing pressure and the solubility data. Thisefficient pressure is the scaling parameter, and the linear dependencyof the ultrasonic velocity with respect to this efficient pressureleads to a slope of 7.8m/sMPa, which is in close agreement to thepressure dependency of the ultrasonic velocity for PS in the moltenstate (roughly 6.3–9.3m/sMPa). In summary, the ultrasonic velocityprobes the molecular conformation or packing, which results from thesum of the various stresses acting on the flowing melt. Althoughmeasured under the same temperature and hydrostatic pressure

1130

1140

1150

1160

Vel

oci

ty (

m/s

)

20 25 30 35 40 45 50

Shear Stress (kPa)

Figure 10. Velocity measured at 152�C as a function of the apparent shear stress.





conditions, the ultrasonic velocity remains sensitive to the degree ofstretching induced at the die entrance and the shear stress prevailingin the die.

On the contrary, in Figure 12 the ultrasonic velocity is measuredat the very moment when degassing has occurred, as a function ofthe melt temperature for the five resins, a master curve is almostobtained, with little scattering in each group of data points. This isquite remarkable, since it is known that the ultrasonic velocity is

1130

1140

1150

1160V

elo

city

at

7.6

MP

a (m

/s)

4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

Efficient Pressure (MPa)

P hydrostatic

centerline(machine direction)Tensile stress

20.311.55.32.31.6

(a)

(b)

Figure 11. Velocity measured at 7.6MPa and 155�C as a function of the efficient pressure

Peff, defined as: Peff¼Phydrostatic�Tensile stress¼Phydrostatic� (Pdegassing�Psolubility).





sensitive to both temperature and pressure. While the temperaturewas kept constant and close to 155�C, the pressure at the degassingpoint, as reported previously in Figure 3, spanned between 4.0 and7.2MPa for the various resins.

Moreover, the ultrasonic velocity for the set of results at 155�C isapproximately 1125–1135m/s. This would match closely the resultsdisplayed in Figure 11 for the ultrasonic velocity extrapolated at4.0–4.5MPa, i.e., the pressure for solubility equilibrium of a mixture ofPS with 6wt.% of HFC-134a at 155�C. Since the ultrasonic velocity v isdefined by:

v¼ ðL0VspÞ1=2

ð7Þ

this suggests that both elasticity (L0 is the elastic modulus) and freevolume (through the specific volume Vsp) could be brought into a singlecharacteristic to define the molten state required for the equilibriumcondition that would satisfy both solubility and rheology.

CONCLUSIONS

A tentative explanation has been provided for the unexpected increasein the degassing pressures observed at low temperature for some PSresins. Even if degassing measurements could be associated to solubilityresults, the tests performed on the extrusion line accounts for the lower

1100

1110

1120

1130

1140

1150

1160

1170

1180

Deg

assi

ng

Vel

oci

ty (

m/s

)

145 150 155 160 165 170 175

Temperature (°C)

20.3

5.32.31.6

11.5

Figure 12. Velocity measured at the degassing conditions as a function of temperature.





stress imposed on the melt/PFA system, through the tensile deformationexperienced at the die entrance. The solubility conditions are then not atequilibrium, but remain very sensitive to the elastic recovery and overallrheological behavior experienced at the die level. This also includesrelaxation times, through the Weissenberg Number. Although foamingis usually performed outside the die, the degassing results suggest thatpremature nucleation could be accidentally induced prior the die exit.Moreover, even if the melt undergoes rapidly elastic recovery outside thedie, nucleation could still be influenced by the elastic component: onehas to take into consideration the time scale for elastic recovery, versusthe diffusion rate of the PFA molecules. These thoughts would need tobe expanded to other resins taking into account their respectiveelasticity.

Heterogeneous nucleation should also be investigated, where thepresence of nucleating agent particles could modify locally the elasticity(interaction of the long molecules with the particle surface). This couldinduce premature nucleation with smaller clusters needed. Also, asreported previously, higher nucleation densities were associated withhigher degassing pressures [7].

Following that last observation, a third valuable area of investigationwould consist of evaluating the impact of induced local stresses that

108

109

1010

104 105

Cel

l den

sity

(#/

cc)

σ12

2

Figure 13. Cell density as a function of one component of the elastic stress (Equation (5)),

from data of [4].





could initiate premature nucleation (higher degassing pressures) on theexpected increased nucleation density. The reported results of Parket al., who explained the enhanced nucleation density through anincreased pressure drop rate [4], would also nicely fit the mechanismproposed in our paper, with the scaling parameter being based on theshear stress (Equation (5)), as illustrated in Figure 13.


+ [27.11.

REFERENCES

1. Lee, S.-T. (2000). Foam Nucleation in Gas-Dispersed Polymeric Systems,In: Foam extrusion: Principles and Practice, Chap. 4, pp. 81–124, TechnomicPublishing Co., Lancaster, PA.

2. Han, J.H. and Han, C.D. (1988). A Study of Bubble Nucleation in a Mixtureof Molten Polymer and Volatile Liquid in a Shear Flow Field, Polym. Eng.Sci., 28(24): 1616–1627.

3. Chen, L., Wang, X., Straff, R. and Blizard, K. (2002). Shear StressNucleation in Microcellular Foaming Process, Polym. Eng. Sci., 42(6):1151–1158.

4. Park, C.B., Baldwin, D.F., Suh, N.P. (1995). Effect of the Pressure DropRate on Cell Nucleation in Continuous Processing of MicrocellularPolymers, Polym. Eng. Sci., 35(5): 432–440.

5. Lee, S-T. (1993). Shear Effects on Thermoplastic Foam Nucleation, Polym.Eng. Sci., 33(7): 418–422.

6. Sahnoune, A., Tatibouet, J., Gendron, R., Hamel, A. and Piche, L. (2001).Application of Ultrasonic Sensors in the Study of Physical Foaming Agentsfor Foam Extrusion, J. Cell. Plast., 37(5): 429–454.

7. Tatibouet, J., Gendron, R., Hamel, A. and Sahnoune, A. (2002). Effect ofDifferent Nucleating Agents on the Degassing Conditions as Measured byUltrasonic Sensors, J. Cell. Plast., 38(3): 203–218.

8. Sahnoune, A., Piche, L., Hamel, A., Gendron, R. and Daigneault, L.E.(1997). Ultrasonic Monitoring of Foaming in Polymers, In: Proc. SPEANTEC Tech. Papers, pp. 2259–2262.

9. Gendron, R., Huneault, M., Tatibouet, J. and Vachon, C. (2002). FoamExtrusion of Polystyrene Blown with HFC-134a, Cell. Polym., 21(5):315–341.

10. Vachon, C. and Gendron, R. (2003). Foaming Polystyrene with Mixtures ofCarbon Dioxide and HFC-134a, Cell. Polym., 22(2): 75–87.

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a study of strain-induced nucleation in thermoplastic foam extrusion

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