1. IntroductionSince their origin in the 1930s, cellular plastics orpolymeric foams have received wide success inindustrial and consumer applications due to the lowmaterial costs, high strength-to-weight ratios, widerange of properties, and ease of processing. More-over, these materials are particularly attractivesince they can be produced with average cell sizesranging from few microns to hundreds of microns.For any given polymer, the use of different blowingagents and process conditions can yield ‘new mate-rials’ with different densities, structures, and prop-erties.Foaming consists of generating tiny gas bubbles inthe polymer melt phase in order to produce light-weight materials without sacrificing mechanical

and physical properties of the polymer. Gas bub-bles can be generated by means of physical orchemical blowing agents. The final foam productsusually possess better insulation properties, as wellas higher degrees of impact resistance with respectto the starting material, thanks to the presence ofthe gas bubbles in the polymer melt [1].There are many types of polymer foamingprocesses, such as foam extrusion, foam injectionmolding, compression molding, and micro-foaming[2, 3]. The final foam density depends on the origi-nal gas loading, the gas losses to the environment,and the foam expansion at quenching. The cell sizeand the cell size distribution depend on the inten-sity and kinetics of nucleation, on the characteris-tics of the bubble growth processes following

84

*Corresponding author, e-mail: icoccorullo@unisa.it© BME-PT and GTE

Theoretical and experimental study of foaming process withchain extended recycled PET

I. Coccorullo*, L. Di Maio, S. Montesano, L. Incarnato

Department of Chemical and Food Engineering, University of Salerno, via Ponte don Melillo,I-84084 Fisciano (Salerno), Italy

Received 31 October 2008; accepted in revised form 30 December 2008

Abstract. The theoretical and experimental study of a thermoplastic polymer foaming process is presented. Industrialscraps of PET were used for the production of foamed sheets. The process was performed by making use of a chemicalblowing agent (CBA) in the extrusion process. Due to the low intrinsic viscosity of the recycled PET, a chain extender wasalso used in order to increase the molecular weight of the polymer matrix. Pyromellitic dianhydride (PMDA) and Hydro-cerol CT 534 were chosen as chain extender and CBA, respectively. The reactive extrusion and foaming were performed ina two step process.Rheological characterization was carried out on PET samples previously treated with PMDA, as well as the morphologicalstudy was performed to define the cellular structure of the foams produced. Moreover, in order to predict the morphologyof the foam, a non isothermal model was developed by taking into account both mass transfer phenomenon and viscousforces effect. Model results were compared with experimental data obtained analyzing the foamed samples. The model wasvalidated in relation to working conditions, chemical blowing agent percentage and initial rheological properties of recy-cled polymer. A pretty good agreement between experimental and calculated data was achieved.

Keywords: processing technologies, modeling and simulations, recycling, industrial applications

eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96Available online at www.expresspolymlett.comDOI: 10.3144/expresspolymlett.2009.12

nucleation, and on the degree of cell wall collaps-ing, or cell coalescence, during expansion. Sincethe performance of foamed polymer is stronglyrelated to many aspects of bubble growth, it is cru-cial to understand and control the bubble growthduring the melt processing [1].In the last few years the production of poly(ethyl-ene terephthalate) (PET) foamed items, particularlysheets for insulating applications, is encountering arising interest. Moreover, by the contrast to thecommonly used thermoplastic resins, attention waspaid to recycled materials [4, 5]. In order to increasethe polymer viscosity and to enhance the foamabil-ity of recycled PET, various techniques have beeninvestigated, including chain extension by reactiveextrusion [4–10].The results obtained with this technique are encour-aging since it allows to perform in a single step therheological upgrading of recycled polymer andfoaming process.However, in recent years the quality control require-ments for plastic foamed products have becomeincreasingly stringent. Therefore, researchers haveattempted to optimize the foaming processes inorder to produce high quality final products.One of the most used methods for the optimizationof the manufacturing process, as well as final prod-uct quality is numerical modeling: a large numberof mathematical models for bubble growth werepresented in the literature [11–21].Some models have been written for bubble growthassumed to be governed by mass transfer alone,while others assumed momentum transfer alone.Using an integral method, the combination of thesephenomena was presented by some authors. Exten-sive reviews and references can be found in amonograph edited by Lee and Ramesh [22].The goal of this work is twofold:– starting from preliminary results obtained in a

previous work [7], the first goal of this work is toimprove the process of extrusion foaming bychemical blowing agent (CBA) in order to pro-duce high density foams from PET industrialscraps with a very low viscosity;

– the second goal of this work is to develop a sim-ple and useful tool which can help the companiesin choosing foaming conditions without per-forming complicated laboratory tests. With thisaim, according to literature indications [11, 14,16], the growth of a spherical bubble in a poly-

meric liquid has been theoretically studied bytaking into account both mass transfer phenome-non and viscous forces effect. Moreover, withthe aim of predicting the morphology of the finalfoam, a non isothermal model was developed.Model results were compared with experimentaldata obtained analyzing foamed sheets producedin laboratory starting from industrial scraps ofPET and using a chemical blowing agent. Themodel was validated in relation to working con-ditions, chemical blowing agent percentage andinitial rheological properties of recycled poly-mer.

2. Experimental

2.1. Materials

PET industrial scraps of low intrinsic viscosity,coming from the fibre production of a nationalcompany (Montefibre, Italy) were used. The chainextender used in this work is the Pyromellitic dian-hydride (PMDA) purchased by Aldrich. The chem-ical modification, in the proportion required for theaim of extrusion foaming, is achieved with verylow content of PMDA in PET; specifically threelevels of PMDA contents were analyzed: 0.25, 0.50and 0.75 weight% which proved to be the rightcompromise to tailor the required rheological mod-ification and suitable foaming processability ofPET. As far as the foam production is concerned,the choice was directed to a chemical foamingagent based process. In particular HydrocerolCT 534, kindly supplied by Clariant, was used as achemical foaming agent and specifically two levelsof Hydrocerol contents were analyzed: 0.30 and0.50 weight%. It was provided in powder form, andit is classified as an endothermic foaming agent,recommended for PET foaming, based on a mixtureof both organic and inorganic foaming substances.The gas yielding during the process is reported asnon toxic, presumably a blend of N2, CO2 and O2

with a very low level of water.

2.2. Reactive and foaming processes

The reactive processing of PET with the PMDAand the foaming extrusion process were both per-formed with a Brabender single screw extruder(D = 20 mm, L/D = 20). The operation was accom-plished in two steps.

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Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

The main operative conditions for chemical modifi-cation and foaming process are reported in Table 1.The recycled PET was tailored by the chain exten-sion reaction with the PMDA. The modified poly-mers were then used for the foam production.

2.2.1. Reactive processing

The reactive processing of PET with the PMDAwas realized by making use of the mentionedextruder equipped with a static mixer to allow therequired residence time for the reaction betweenPET and PMDA. The temperature profile used forthe extrusion process was the following: extrudertemperature (2 zones) 280°C; mixer temperature290°C; die temperature 270°C. In Table 1, theworking conditions for reactive process arereported.Modified PET was characterized in terms of rheo-logical properties (flow curves, melt strength andbreaking stretching ratio (BSR)), mechanical prop-erties (tensile and flexural properties) and densities.

Rheological properties

Rheological behavior of the modified PET wascarefully analyzed in this work because this param-eter strongly affects the foam morphology.The dynamic flow properties of the polymer matrixproduced by the chain extension process weremeasured with a Rheometrics Dynamic Spectrome-ter Mod. RDS-II (Rheometrics, Inc.) using a paral-lel plates geometry (plate radius = 25 mm; gap =2 mm). Frequency sweep tests (ω = 0.1÷100 rad/swere made at 280°C at a constant strain amplitude(10% strain) under a nitrogen gas purge in order to

minimize thermo-oxidative degradation phenom-ena.Rheological measurement in shear flow were per-formed using a Capillary Extrusion Rheometer(Bohlin Instruments) with a die radius of 1 mm anda 16:1 length/diameter, equipped with a twin borefor the Bagley correction. Viscosity measurementswere performed at 280°C within a shear rate rangeof 20÷10 000 s–1. As the shear rate at the wall isgreater for pseudoplastic than for Newtonian fluidsat a given volumetric flow rate, the Rabinowitschcorrections were applied in all cases. The CapillaryExtrusion Rheometer is equipped with a tensilemodule. The measurements were performed using a1 mm diameter capillary die (L/D = 20) with thetensile module situated about 20 cm from the extru-sion die. An extrusion temperature of 280°C and awall shear rate of 125 s–1 were used. The testsallowed the determination of the melt strength andthe breaking stretching ratio (BSR). The samplesfor testing were dried at 120°C in a vacuum ovenfor 12 h.

Mechanical properties and densities

The tensile properties were analyzed according tothe standard ASTM D-638, the flexural ones wereanalyzed according to the standard ASTM D-790and the densities were measured according to thestandard ASTM D-1622.

2.2.2. Foaming process

The second step of processing consisted in the foamproduction by extruding the modified PET with thechemical blowing agent (CBA). Dry blends oftreated PET and CBA powder were fed to the previ-ously described extruder apparatus, which wasoperated without the static mixer. In Table 1 theworking conditions for the processes of polymerfoaming are reported. Further details on reactiveprocess and foaming can be found elsewhere [7].Foam produced was characterized in terms of rheo-logical properties (flow curves, melt strength andBSR), mechanical properties (tensile and flexuralproperties), densities and finally in terms of cellsize and cell size distribution by means of scanningelectronic microscopy.

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Table 1. Operating conditions for chemical modificationand foaming process

Reactive extrusion processExtruder temperature (hopper, barrel) [°C] 280, 280Static mixer temperature [°C] 290Die temperature [°C] 270Screw speed [revolution per minute] 040

Foam extrusion processExtruder temperature (hopper, barrel) [°C] 270, 280Die temperature [°C] 280Extrusion die: slit die [mm2] 30×1Screw speed [revolution per minute] 040

Cell size and cell distributionCell size and cell distribution was evaluated bymeans of electronic scanning microscopy (SEM).In order to evaluate cell size and cell distributionfrom the SEM micrographs, a software for imageanalysis was developed and implemented in Lab-view (National Instruments). This software locates,counts, and measures objects in a rectangularsearch area. The software uses a threshold on thepixel intensities to segment the objects from theirbackground. Optional filters give the capability toignore the objects smaller or larger than givensizes. Other options allow rejecting the objectstouching the borders of the search area and ignoringthe holes that the segmentation process may createin the objects. The segmented objects are thenlocated and measured. The software can also over-lay on the image returned the position of the searcharea, the centers and bounding boxes of the objectsdetected.

3. Experimental results

3.1. Characterization of modified PET

Modified PET was characterized in terms of rheo-logical properties (flow curves, melt strength andBSR), mechanical properties (tensile and flexuralproperties) and densities. In Table 2 main experi-mental results obtained analyzing modified PETsamples were reported.

3.1.1. Rheological properties

Rheological behavior of the modified PET wascarefully analyzed in this work because this param-eter strongly affects the foam morphology.A significant increase in viscosity due to the use ofPMDA as chain extender in PET scraps (PET) isevident from the flow curves reported in Figure 1.These samples also exhibit a pronounced shearthinning behavior particularly the blend PET+PMDA 0.75%.

Values of zero shear viscosity, obtained analyzingrheological data, are reported in Table 2 for unmod-ified and modified PET samples.Moreover, in order to verify if the modified PETpossesses melt properties suitable for foamingprocess, melt strength measurements were per-formed and the results being reported in Table 2.As it can be seen in Table 2, a sharp increase inmelt strength is encountered with increasing PMDAcontent. Both the effects, the shear thinning behav-iour and melt strength improvement, can beascribed to the structural changes occurring duringthe chain extension process, i.e. the increase in Mw,the broadening of Mw/Mn and branching phenom-ena accomplished during the reactive extrusion.Actually, too large values of the MS tend to inhibitthe bubble growth during the foaming process. Asreported later, the parameters so obtained allow inall cases the production of foams, although withsome differences. However, the sample treatedwith 0.50% of PMDA appears as the best accom-plishment between the two parameters.Since the polymer matrix was produced by a chainextension process, we considered the viscositychanging with the chain extender content using apolynomial fittings curve to interpolate the experi-mental data of η0 vs. %PMDA [11] using Equa-tion (1):

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Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

Table 2. Main properties of the modified PET samples

Code %PMDAηη0 [Pa·s]

(T=280°C)Melt strength

[10–2 N]BSR

Density[kg/m3]

ηη[dl/g]

PET 0 0108 not meas. not meas. 1410 0.49PET_PMDA025 0.25 0543 0.005 080 1414 0.59PET_PMDA050 0.50 1275 0.012 120 1425 0.67PET_PMDA075 0.75 3355 0.054 092 1435 0.77

Figure 1. Flow curves for unmodified and modified PETsamples (T=280°C)

η0 (%PMDA) =

6577 (%PMDA)2 – 742.64 (%PMDA) + 160 (1)

Viscosity is related to temperature by an Arrheniusexpression [23] and its variation with thermal pro-file is given by Equation (2):

(2)

where Ea is an activation energy for viscous flow(94 000 J/mol [23]), η0 and η0Tr are the zero shearviscosity corresponding to T and Tr, respectively.The effectiveness of the foaming process isstrongly dependent on the viscosity of the polymermatrix and, consequently, on concentration of thechain extender. With an amount of PMDA lowerthan 0.5% no foam can be obtained.

3.2. Characterization of foam

Foam produced was characterized in terms of rheo-logical properties (flow curves, melt strength andBSR), mechanical properties (tensile and flexuralproperties), densities and finally in terms of cellsize and cell size distribution by means of scanningelectronic microscopy. In Table 3 main experimen-tal results obtained analyzing foamed samples werereported.Data reported in Table 3 show that without signifi-cantly sacrifice the mechanical and physical prop-erties (see results of tensile modulus and strength)it is possible to produce lightweight materials.

3.2.1. Cell size and cell distribution

The foamed strips obtained have a closed-cellstructure (see SEM micrographs). Closed-cellfoams are most suitable for thermal insulation andare produced when the cell membranes are suffi-ciently strong to withstand rupture at the maximumfoam rise.

Cell size and cell distribution was evaluated bymeans of electronic scanning microscopy (SEM).SEM micrographs of the cross section are reportedin Figures 2–4 for the samples analyzed in thiswork.

⎟⎟

⎠

⎞⎜⎜

⎝

⎛−=

η

η

rg

a

T

T

TTR

E

r

11ln

0

0

88

Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

Figure 2. SEM micrograph PET_PMDA050_CBA05

Table 3. Main properties of the foamed samples

Code %PMDA %CBADensity[kg/m3]

Tensile modulus[MPa]

Tensile strength[MPa]

PET 0 0 1410 1810 55.1PET_PMDA050_CBA05 0.50 0.50 0835 1240 23.4PET_PMDA075_CBA03 0.75 0.30 1165 1365 29.5PET_PMDA075_CBA05 0.75 0.50 0900 1304 23.8

Figure 3. SEM micrograph PET_PMDA075_CBA03

Figure 4. SEM micrograph PET_PMDA075_CBA05

Bubble dimensions, as evaluated by the imageanalysis software, are almost constant in the sam-ple, confirming the assumption that temperature isconstant along thickness direction.The cell size and cell distribution, reported inTable 4, are strongly dependent, during the foam-ing process, on the concentration of the chainextender and, consequently, on the high viscosityof the polymer matrix.

4. Modeling

4.1. Bubble growth dynamics (Theoreticalbackground)

Consider a polymer melt that has a dissolved gasconcentration c0 in equilibrium with the gas atsome elevated pressure PB0. With the release ofpressure at t = 0, the solution becomes supersatu-rated, and nucleation and bubble growth begin. Asthe bubble growth proceeds, the pressure inside thebubble and the dissolved gas concentration at thebubble surface decrease. With time, gas diffusesinto the bubble and a concentration gradient propa-gates radially in the polymer melt. A schematic of

the bubble growth is shown in Figure 5. The radiusand the dissolved gas concentration are denoted byR(t) and c(r,t).In analyzing the bubbles growth process, the fol-lowing assumptions can be made:1. The bubble is spherically symmetric when it

nucleates and remains so for the entire period ofgrowth.

2. The gas pressure in the bubble PB(t) is related tothe dissolved gas concentration at the bubble sur-face c(R,t) by the Henry law: c(R,t) = KHPB(t).

3. There are no chemical reactions during bubblegrowth.

4. Gravitational effects and latent heat of solutionare neglected.

5. Inertial effects are neglected and the fluid isassumed to be incompressible and Newtonian.

6. The surface tension at the gas-liquid interfacehas a constant value σ.

7. The effect of foam densities on thermal conduc-tivity of gas-filled polymeric bubble system isneglected.

The material properties such as polymer structure,molecular weight and its distribution, crystallinityand others are independent of the dissolved gasconcentration and are ignored.The neglect of inertia and the assumption of New-tonian behavior is imposed because the fluids arevery viscous and the initial bubble growth rates arevery small. Nevertheless, Amon and Denson [13]studied heat transfer analysis in polymer-gas sys-tems in great detail. They found from reliableempirical correlations that the effective thermalconductivity of gas-filled polymeric bubble systemchanges by no more than a few percentage pointsover the whole range of foam densities. Moreover,as for thermoplastic foam extrusion, growth occursin the molten-to-solid transition state. The polymeris cooled from 280°C (die temperature) to 25°C(ambient temperature) in a relatively short time:since in these circumstances all physical propertiesof the system undergo a rapid change, a transientheat transfer problem is considered here.

4.2. Governing equations for the bubblegrowth

In view of the above restrictions, the equation ofmotion, integral mass (gas) balance over the bubbleand differential mass (dissolved gas) balance in the

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Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

Figure 5. Schematic of single bubble growth

Table 4. The cell size and cell distribution for samples ana-lyzed in this work

SamplesN bubble[N/mm3]

Cell radius[μμm]

PET_PMDA050_CBA05 ~110 44 ± 15PET_PMDA075_CBA03 ~330 31 ± 10PET_PMDA075_CBA05 ~290 37 ± 15

surroundings mother phase take the followingforms [14]. Equation of motion is given by Equa-tion (3):

(3)

The initial condition for the above equation is:R(0) = Ri. Here Ri is the initial radius of the bubble,PC the pressure in the continuous phase, σ surfacetension and η melt viscosity.

Integral mass (gas) balance over the bubble

A differential mass balance in a binary systemassuming spherical symmetry, constant density anddiffusion coefficient (D) is of the form of Equa-tion (4):

(4)

where c is the dissolved gas concentration in themelt and D is the binary diffusion coefficient. Theboundary and initial conditions for Equation (4) aregiven by Equation (5):

(5)

At a distance far from the bubble surface, the solu-tion is not affected by the growing bubble and thedissolved gas concentration remains c∞, the same asbefore the onset of nucleation. The quantity cR isthe dissolved gas concentration at the bubble sur-face. It is related to the gas pressure in the bubblethrough the solubility coefficient KH. The quantityci(r) is the initial concentration profile in the melt.The mass balance on the bubble requires that therate of mass added to the bubble equals the rate thatmass diffuses in through the bubble surface. Thus,a simple mass balance at the bubble surface relatesthe bubble pressure to the concentration gradient atthe surface (see Equation (6)):

(6)

The initial condition for the above equation isPB(0) =PB0. Here PB0 is the initial bubble pressure,

Z2 the compressibility factor of the gas inside thebubble, T temperature and Rg universal gas con-stant.

4.2.1. Dimensionless form of the governingequations

To facilitate the subsequent analysis, the followingdimensionless variables and groups can be definedby Equations (7)–(15):

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

In defining the above dimensionless quantities, wepicked the critical bubble radius (Equation (16)):

(16)

and the critical momentum transfer time (Equa-tion (17)):

(17)

as our characteristic bubble radius and bubblegrowth time, respectively.

,4

0 CB

CPP

t−

η=

CB

CPP

R−

σ=0

2

RTKN Hsi =

cB

Cpi

PP

PN

−=

0

)( 0

2

cB

PePPD

N−η

σ=

20

3

)(3

16

cBB

GPPTk

N−

πσ=

c

at

tt =

C

aR

RR =

C

aR

rr =

cB

cBBa

PP

PPP

−

−=

0

CH

CHa

PKc

PKcc

−

−=

∞

Rrg

B

r

cDR

TRZ

RP

t=

π=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ π

d

d4

3

4

d

d 2

2

3

∞=∞==

=

ctc

tPKtctRc

rcrc

BHR

i

),(

)()(),(

)()0,(

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂

∂

∂=∂

∂+∂

∂

rr

rrD

r

cv

t

cr

2

2

1

η

σ−η

−=24d

dR

PP

t

R CB

90

Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

In terms of the dimensionless variables, the equa-tions governing the bubble growth dynamics takesthe following forms (see Equations (18)–(20)):

(18)

(19)

(20)

The corresponding initial and boundary conditionsare given by Equations (21)–(25):

Ra(0) = Rai (21)

PBa(0) = PBai (22)

ca(ra,0) = cai(ra) (23)

ca(Ra,ta) = PBa (24)

ca(∞,ta) = 1 (25)

Since the critical cluster represents an equilibriumstate, this specification of the initial conditions willnot produce bubble growth. To achieve the latter,we must perturb one or more of these variablesfrom the equilibrium state. The bubble growth is astrong function of the value of the initial radius,arbitrary choice of it can lead to considerable error[11].

4.2.2. Initial conditions for bubble growth

In order to calculate the initial conditions for bub-ble growth, the approach used follows from Shafiet al. [11]. Following this procedure, we get the ini-tial conditions for bubble growth (see Equa-tions (26) and (27)):

(26)

(27)

where A is defined by Equation (28):

(28)

The methodology for handling the transportprocesses around a single expanding bubble is validfor a bubble growing in an infinite expanse of liq-uid with no dissolved gas limitations. In actualfoaming, there is a finite amount of dissolved gasthat is continuously depleted by the simultaneousgrowth and nucleation of bubbles.In order to extend the analysis in a finite amount ofdissolved gas, in this work, the procedure presentedby Shafi et al. [11] was adopted (see Figure 5).Shafi et al. applying the integral method to thepresent problem introduce an undetermined func-tion of time, Vcb. Physically it represents the vol-ume of the melt between the bubble surface and theradial position where the dissolved gas concentra-tion approaches the initial dissolved gas concentra-tion c0. Moreover, they define two new variables: x,which represents the melt volume between the bub-ble surface and radial position r normalized to thevolume of concentration boundary region Vcb andalso a new concentration variable C as in Equa-tions (29) and (30):

(29)

(30)

Equations (29) and (30) transform a moving bound-ary problem with variable boundary conditions to afixed boundary problem with constant boundaryconditions. C is always 0 at the bubble surface(x = 0), and is 1 at the far end of the concentrationboundary (x = 1) and it can be assumed as a func-tion of x only. In view of Equations (29) and (30)and defining additional dimensionless variablesand groups as shown in Equations (31) and (32):

(31)BH

BHRRa

PKc

PKcc

−

−=0

R

R

cc

ccC

−

−=0

cbV

Rrx

33

3

4 −π=

14

31

3

1

2

1

−

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟

⎠

⎞⎜⎜

⎝

⎛ π+=GN

A

si

PepiB

N

NNAAP

)1)(1(1)0(

++−=

si

Pea

N

NAAAR

3

)1()1()0(

2+++=

⎟⎟

⎠

⎞⎜⎜

⎝

⎛

∂

∂

∂

∂=∂

∂+

∂

∂

a

aa

aPeaa

a

a

a

a

a

a

a

r

cr

rNrr

c

t

R

r

R

r

c 2

22

2 1

d

d

a

a

a

piBa

Rra

a

aPe

si

a

Ba

t

R

R

NP

r

c

RN

NZ

t

P

aad

d)(313

d

d

2 +−

∂

∂

=

=

1d

d−= aBa

a

a RPt

R

91

Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

(32)

the equations governing the bubble growth dynam-ics in terms of dimensionless quantities can berewritten by Equations (33)–(35):

(33)

(34)

(35)

With the initial conditions given by Equations (36)and (37):

(36)

(37)

4.3. Model formulation

In order to calculate the evolution of the bubblessize in the foam sheet starting from material proper-ties and working conditions, the model abovedescribed was implemented in a simulation codedeveloped in Labview (National Instruments).With this aim Equations (33)–(35) must be solvedwith the initial conditions given by Equations (36)and (37). Moreover, as for thermoplastic foamextrusion, growth occurs in the molten-to-solidtransition state. The polymer is cooled from 280°C(die temperature) to 25°C (ambient temperature).Rheological property variation certainly changesthe isothermal growth scenario and hence, a tran-sient heat transfer problem is considered here. Thepolymer is cooled by means of two cooling fans, in

this case, the energy equation combined withFourier's law of heat conduction, is given by Equa-tion (38):

(38)

where ρP, Cp,P and kp are density, specific heat andthermal conductivity, respectively.The initial and boundary conditions are then givenby Equation (39):

(39)

where δ is the half-thickness of the foam sheet, T0

is the initial temperature of the polymer (die tem-perature), TAIR is the ambient temperature and h isthe heat transfer coefficient.

δ=−=∂

∂

==∂

∂==

xTThx

T

xx

T

ttTT

AIR ),(

0,0

, 00

2

2

, x

T

C

k

t

T

PpP

P

∂

∂

ρ=

∂

∂

si

PepiR

N

NNAAc

)1)(1(1)0(

++−=

si

Pea

N

NAAAR

3

)1()1()0(

2+++=

∫ −−

+−+=

1

0

3

d)1()1(

)1()(

xCcN

NRNcV

Rasi

piapiRacba

a

a

a

piaR

xcba

aRa

Pe

si

a

Ra

t

R

R

Nc

x

c

V

Rc

N

ZN

t

c

d

d)(3

d

d)1(9

d

d

0

2 +−

−

=

=

1d

d−= aaR

a

a Rct

R

34

3

c

cbcba

R

VV

π=

92

Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

Figure 6. Flow chart describing the sequence of the calcu-lations in the model

A flow chart describing the sequence of the calcula-tions is reported in Figure 6. In Table 5, the mainvariables involved in the model are reported.

4.3.1. Solution methodology

The equations governing the bubble growthdynamics are highly nonlinear and stiff. Theseequations were solved using the Gear’s method.The nonlinear equations are solved by Brown’smethod. The equations were solved using a finitedifference scheme.It is worth mentioning that in the model adopted inthis work there are no involved adjustable parame-ters so that the model starting from data of materi-als properties and the operative conditions is able topredict bubble dimensions.

5. Model results

Model developed in this work following the litera-ture indications allows to calculate the evolution ofthe temperature, of the bubble pressure and radiusstarting from the operative conditions and materialproperties (Tables 1 and 6). Consistently withexperimental data, with an amount of chain exten-der lower that 0.5% according to the model theclusters are not sufficiently large compared to thecritical cluster in order to grow spontaneously to amacroscopic bubble and no foam can be obtained.In Figure 7, the calculated evolution of temperatureand bubble radius during the foaming process arereported for PET_PMDA050_CBA05 andPET_PMDA075_CBA05. Figures show that bub-bles growth takes about one second, after this timetemperature become too low and viscosity too high.

In Figure 8, the calculated evolution of bubblepressure and radius during the foaming process arereported for PET_PMDA050_CBA05 andPET_PMDA075_CBA05.

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Table 5. Main variables involved in the model adopted inthis work

σ surface tension D binary diffusion coeffi-cient

η melt viscosity Z2 compressibility factor ofthe gas

KH solubility coeffi-cient

Rg Universal gas constant

PB0 initial bubble pres-sure

c∞ initial gas concentration

Ri initial radius of thebubble

ci(r) initial gas concentrationprofile

R(t) bubble radius c(r,t) dissolved gas concentra-tion

PB(t) gas pressure in thebubble

c(R,t)=cR dissolved gas concentra-tion at the bubble sur-face

PC Pressure in the con-tinuous phase

Vcb volume of the melt between the bubble surface and theradial position where the dissolved gas concentrationapproaches the initial dissolved gas concentration c0

Figure 7. Temperature profile for the bubble growth simulation of extrusion. a – PET_PMDA050_CBA05;b – PET_PMDA075_CBA05

Table 6. Physical properties [23] and operative conditionsused in the model

Physical properties Operative conditionsPET specific heat Cp 1130 J/(kg·K)Thermal conductivity K 0.218 W/(m·K)Activation energy for viscous flow Ea 94 000 J/molRheological reference temperature 553 KSurface tension σ 0.0446 N/mDiffusivity 3·10–12 m2/sDie pressure 1.5·106 PaAmbient pressure 1.01·105 PaDie temperature T0 543 K

The bubble pressure start from a maximum anddecreases to a value close to the ambient pressure.The evolution of the bubble radius for the samplesanalyzed in this work was compared in Figure 9.As it can be seen from the figure, the radius of thebubbles in the sample coded asPET_PMDA050_CBA05 is bigger than the one ofthe bubbles in PET_PMDA075_CBA05. From fig-ure the effect of the PMDA content is evident, infact, the bubble radius increases on decreasing ofthe PMDA content: this is mainly due to the highermelt strength (shown by thePET_PMDA075_CBA05) which limits the growthof the bubbles.The comparison between experimental results andmodel prediction for the bubble radius is reportedin Figure 10. Because at the moment only fewexperimental data are available, literature data [25,26] are also reported in figure. Moreover, the modeldescribed in this work was adopted in order to cal-culate the evolution of the bubble radius in litera-ture experimental conditions and results were alsoreported in figure. The satisfactorily agreement

between literature experimental data and modelpredictions is a further validation of the modeladopted in this work.In order to underline results achieved in this work,the comparison between experimental results andmodel prediction for the bubble radius forPET_PMDA050_CBA05,PET_PMDA075_CBA03,PET_PMDA075_CBA05 is reported in Table 7.Comparison shows that model seems to be able topredict experimental data of bubble radius, even if,at the moment only few experimental data areavailable.

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Figure 8. Pressure profile for the bubble growth simulation of extrusion foaming, a – PET_PMDA050_CBA05;b – PET_PMDA075_CBA05

Figure 9. Evolution of the bubble radius forPET_PMDA050_CBA05 andPET_PMDA075_CBA05

Table 7. Comparison between experimental results andmodel prediction for the bubble radius

SamplesExperimental

cell radius [μμm]Calculated

cell radius [μμm]PET_PMDA050_CBA05 44 ± 15 49PET_PMDA075_CBA03 31 ± 10 33PET_PMDA075_CBA05 37 ± 15 33

Figure 10. Comparison between experimental results andmodel prediction for the bubble radius (litera-ture data are also reported in figure)

The comparison between experimental data andmodel prediction shown in Figure 10 is satisfacto-rily, however, better results of prediction of theevolution of the bubble radius during foamingprocess could be achieved by means of a better rhe-ological description, that is adopting more complexmodels which better describe viscoelastic proper-ties of the material.

5. Conclusions

In this work, the process of extrusion foaming bychemical blowing agent (CBA) was improved inorder to produce high density foams from PETindustrial scraps with a very low viscosity. Due tothe low intrinsic viscosity of the recycled PET(IV = 0.48 dl/g), a chain extender was also used inorder to increase the molecular weight of the poly-mer matrix. The reactive processing of PET and thefoaming extrusion process were both performedwith a Brabender single screw extruder. The opera-tion was accomplished in two steps. The chemicalmodification, in the proportion required for the aimof extrusion foaming, is achieved with very lowcontent of PMDA in PET; specifically three levelsof PMDA contents were analyzed: 0.25, 0.50 and0.75 weight% which resulted to be the right com-promise to tailor the required rheological modifica-tion and suitable foaming processability of PET. Asfar as the foam production is concerned, the choicewas directed to a chemical foaming agent basedprocess. In particular Hydrocerol CT 534 was usedas a chemical foaming agent and specifically twolevels of Hydrocerol contents were analyzed: 0.30and 0.50 weight%.Modified PET was characterized in terms of rheo-logical properties (flow curves, melt strength andBSR), mechanical properties (tensile and flexuralproperties) and densities. Foam produced was char-acterized in terms of rheological properties (flowcurves, melt strength and BSR), mechanical prop-erties (tensile and flexural properties), densities andfinally in terms of cell size and cell size distributionby means of scanning electronic microscopy.Finally, the growth of a spherical bubble in a poly-meric liquid has been theoretically studied by tak-ing into account both mass transfer phenomenonand viscous forces effect.Model results were compared with experimentaldata obtained analyzing foamed sheets produced in

laboratory starting from industrial scraps of PET.As for thermoplastic foam extrusion, growth occursin the molten-to-solid transition state. Rheologicalproperty variation certainly changes the isothermalgrowth scenario and hence, a transient heat transferproblem is considered and a non isothermal modelfor bubble growth was developed.The model was validated in relation to workingconditions, chemical blowing agent percentage andinitial rheological properties of recycled polymer.A good agreement between experimental and cal-culated data was achieved, even if, at the momentonly preliminary experimental data are available.In order to achieve a better understanding of thefoaming process, future work will consider an addi-tional validation by comparing model results with awider set of experimental data and the analysis ofthe bubble nucleation.

References[1] Lee C. H., Lee K-J., Jeong H. G., Kim S. W.: Growth

of gas bubbles in the foam extrusion process.Advances in Polymer Technology, 19, 97–112 (2000).DOI: 10.1002/(SICI)1098-2329(200022)19:2<97::

AID-ADV3>3.0.CO;2-B[2] Kumar V., Suh N. P.: Process for making microcellu-

lar thermoplastic parts. Polymer Engineering and Sci-ence, 30, 1323–1329 (1990).DOI: 10.1002/pen.760302010

[3] Baldwin D. F., Suh N. P., Park C. B., Cha S. W.:Supermicrocellular foamed materials, U.S. Patent5334356, USA (1994).

[4] Xanthos M., Dey S.: Foam extrusion of polyethyleneterephthalate (PET). in ‘Foam extrusion: Principlesand practice’ (ed.: Lee S. T.) Technomic, Lancaster,307–336 (2000).

[5] Branch G. L., Wardle T.: Manufacture of fully recy-clable foamed polymer from recycled material. Inter-national Patent PCT/US2004/015245 (2004).

[6] Incarnato L., Scarfato P., Di Maio L., Acierno D.:Structure and rheology of recycled PET modified byreactive extrusion. Polymer, 41, 6825–6831 (2000).DOI: 10.1016/S0032-3861(00)00032-X

[7] Di Maio L., Coccorullo I., Montesano S., Incarnato L.:Chain extension and foaming of recycled PET inextrusion equipment. Macromolecular Symposia, 228,185–200 (2005).DOI: 10.1002/masy.200551017

[8] Awaja F., Dumitru P.: Statistical models for optimisa-tion of properties of bottles produced using blends ofreactive extruded recycled PET and virgin PET. Euro-pean Polymer Journal, 41, 2097–2106 (2005).DOI: 10.1016/j.eurpolymj.2005.04.010

95

Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96

[9] Japon S., Boogh L., Leterrier Y., Manson J. A. E.:Reactive processing of poly(ethylene terephthalate)modified with multifunctional epoxy-based additives.Polymer, 41, 5809–5818 (2000).DOI: 10.1016/S0032-3861(99)00768-5

[10] Awaja F., Pavel D.: Injection stretch blow mouldingprocess of reactive extruded recycled PET and virginPET blends. European Polymer Journal, 41, 2614–2634 (2005).DOI: 10.1016/j.eurpolymj.2005.05.036

[11] Shafi M. A., Lee J. G., Flumerfelt R. W.: Prediction ofcellular structure in free expansion polymer foam pro-cessing. Polymer Engineering and Science, 36, 1950–1959 (1996).DOI: 10.1002/pen.10591

[12] Venerus D. C.: Diffusion-induced bubble growth inviscous liquids of finite and infinite extent. PolymerEngineering and Science, 41, 1390–1398 (2001).DOI: 10.1002/pen.10839

[13] Amon M., Denson C. D.: A study of the dynamics offoam growth: Analysis of the growth of closely spacedspherical bubbles. Polymer Engineering and Science,24, 1026–1034 (1984).DOI: 10.1002/pen.760241306

[14] Favelukis M., Zhang Z., Pai V.: On the growth of anon-ideal gas bubble in a solvent-polymer solution.Polymer Engineering and Science, 40, 1350–1359(2000).DOI: 10.1002/pen.11264

[15] Ramesh N. S., Rasmussen D. H., Campbell G. A.: Theheterogeneous nucleation of microcellular foamsassisted by the survival of microvoids in polymerscontaining low glass transition particles. Part I: Math-ematical modeling and numerical simulation. PolymerEngineering and Science, 34, 1685–1697 (1994).DOI: 10.1002/pen.760342206

[16] Patel R. D.: Bubble growth in a viscous Newtonianliquid. Chemical Engineering Science, 35, 2352–2356(1980).

[17] Joshi K., Lee J. G., Shafi M. A., Flumerfelt R. W.:Prediction of cellular structure in free expansion ofviscoelastic media. Journal of Applied Polymer Sci-ence, 67, 1353–1368 (1998).DOI: 10.1002/(SICI)1097-4628(19980222)67:

8<1353::AID-APP2>3.0.CO;2-D[18] Yue P., Feng J. J., Bertelo C. A., Hu H. H.: An arbi-

trary Lagrangian-Eulerian method for simulating bub-ble growth in polymer foaming. Journal ofComputational Physics, 226, 2229–2249 (2007).DOI: 10.1016/j.jcp.2007.07.007

[19] Otsuki Y., Kanai T.: Numerical simulation of bubblegrowth in viscoelastic fluid with diffusion of dissolvedfoaming agent. Polymer Engineering and Science, 45,1277–1287, (2005).DOI: 10.1002/pen.20395

[20] Everitt S. L., Harlen O. G., Wilson H. J.: Competitionand interaction of polydisperse bubbles in polymerfoams. Journal of Non-Newtonian Fluid Mechanics,137, 60–71 (2006).DOI: 10.1016/j.jnnfm.2006.03.005

[21] Favelukis M.: Dynamics of foam growth: Bubblegrowth in a limited amount of liquid. Polymer Engi-neering and Science, 44, 1900–1906 (2004).DOI: 10.1002/pen.20192

[22] Lee J. G., Ramesh N. S.: Polymeric foams: Mecha-nisms and materials. CRC Press, New York (2004).

[23] Van Krevelen D. W.: Properties of polymers. Elsevier,New York (1990).

[24] Amon M., Denson C. D.: A study of the dynamics offoam growth: Simplified analysis and experimentalresults for bulk density in structural foam molding.Polymer Engineering and Science, 26, 255–267(1986).DOI: 10.1002/pen.760260311

[25] Han C. D., Yoo H. J.: Studies on structural foam pro-cessing. 4. Bubble growth during mold filling. Poly-mer Engineering and Science, 21, 518–533 (1981).

[26] Xu D., Pop-Iliev R., Park C. B., Fenton R. G., JiangH.: Fundamental study of CBA-blown bubble growthand collapse under atmospheric pressure. Journal ofCellular Plastics, 41, 519–538 (2005).DOI: 10.1177/0021955X05059031

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Coccorullo et al. – eXPRESS Polymer Letters Vol.3, No.2 (2009) 84–96