COMMUNICATION
`
`DOI: 10.1002/adem.200900129
`
`Heat Transfer in Polypropylene-Based Foams Produced
`Using Different Foaming Processes**
`
`By Marcelo Antunes,* Jose´ Ignacio Velasco, Vera Realinho, Antonio B. Martı´nez,
`Miguel-A´ ngel Rodrı´guez-Pe´rez and Jose´ Antonio de Saja
`
`It is well known that the thermal conductivity of cellular
`materials is a strong function of density and structure.
`Characteristics such as the average cell size and cell
`anisotropy, density distribution, etc., have a significant
`influence on the heat
`transfer mechanisms and, as a
`consequence, on the values of
`the thermal properties.
`Polypropylene (PP) foams are commercially produced using
`one of the following four processes:[1] 1) direct extrusion,
`where a foam is directly obtained by decompressing at the exit
`of an extrusion die, normally using a physical blowing agent
`(PBA) such as CO2 or n-butane.[2] A cast-sheet extrusion
`process combined with the later expansion of the extruded
`sheet by thermal decomposition of a chemical blowing agent
`(CBA) in specially designed ovens may also be used, resulting
`in foams with slightly different cell structures and densities,
`and, thus, different properties.[3] 2) Injection moulding, where
`polymer expansion is carefully adjusted by controlling CBA
`thermal decomposition inside a closed injection mould.
`3) Compression molding, where the material is foamed inside
`a hot-plate press or modified oven by simultaneously
`applying temperature and pressure in order to gradually
`crosslink, where required, and foam the material.[4] This third
`type of polyolefin foam is usually obtained using exothermic
`CBAs, such as azodicarbonamide (ADC). 4) Batch foaming,
`where the material is foamed inside an autoclave reactor by a
`high-pressure gas dissolution process.[5] These foaming
`processes, each with its own particularities, can be used to
`obtain a wide range of polyolefin-based foams, with densities
`3 to 400–600 kg m
`3 in high-density
`from as low as 20 kg m
`
`[*] Prof. M. Antunes, Prof. J. I. Velasco, Prof. V. Realinho,
`Prof. A. B. Martı´nez
`Centre Calala` del Pla`stic, Departament de Cie`ncia dels
`Materials i Enginyeria Metal lu´rgica
`Universitat Polite`cnica de Catalunya, C/Colom 114, E-08222,
`Terrassa, Barcelona (Spain)
`E-mail: marcelo.antunes@upc.edu
`Prof. M.-A. Rodrı´guez-Pe´rez, Prof. J. A. de Saja
`Cellular Materials Group (CellMat), Condensed Matter
`Physics Department
`University of Valladolid, 47011 Valladolid (Spain)
`[**] Financial assistance from the Spanish Ministry of Science and
`Education
`(nos. MAT2007-62956, MAT-2006-11614-
`C03-01), the Junta of Castile and Leon (no. VA047A07) and
`the FEDER program is gratefully acknowledged.
`
`foams, different cell structures from open-cell foams with
`improved acoustic absorption to closed-cell ones for structural
`applications, etc.
`Generally speaking, foams produced using the compres-
`sion-molding technique show a small average cell size and a
`cellular structure that changes along the block thickness, with
`the cells being smaller close to the surface.[6] As with
`oven-expanded cast-sheet extruded or injection-molded foams,
`these foams have solid residues from the thermal decomposi-
`tion of CBA. Foams produced by extrusion using a PBA, such as
`CO2, although free of the solid residues inherent to CBA
`decomposition, tend to show a rather anisotropic cell structure,
`the cells being elongated in the extrusion flow direction.[7] In
`contrast, foams produced from a high-pressure gas dissolution
`process typically have a homogeneous cell structure with
`isotropic cells,
`their geometry varying from spherical
`to
`polygonal depending on the final degree of expansion.[8]
`Previous works on PP foamed using an extrusion process
`and different nucleating and blowing agents focused on the
`cell-nucleating behavior and final cell density.[9,10] The
`volume-expansion behavior and final foam density have also
`been extensively studied,[11,12] as well as the effect of cell
`nucleation on the cell-growth behavior, particularly hetero-
`geneous nucleation using talc.[13] The fundamental expansion
`mechanisms of gas loss and melt stiffening for PP foam
`processing have also been identified.[14] Regarding the study of
`the thermal conductivity of poyolefin-based foams measured
`by transient methods such as the transient plane source (TPS)
`method, a couple of works have focused on the possibility of
`using it as a technique for measuring the thermal conductivity
`in closed-cell low-density polyethylene (LDPE) foams.[15,16]
`In this paper, several PP-based foams, produced from four
`different
`foaming processes using chemical or physical
`blowing agents and with densities ranging from 20 to
`3 are studied and compared, focusing on how their
`610 kg m
`different degrees of expansion and cellular structures,
`characterized in terms of the open-cell content, average cell
`size and cell anisotropy, among others, may affect their
`thermal behavior and thermal conductivities, and particularly
`how the relative density alters the theoretical model used for
`characterizing the thermal conductivity.
`
`The Transient Plane Source (TPS) Method
`
`The TPS method is a transitory method that allows
`determination of the thermal conductivity of samples over
`
`ADVANCED ENGINEERING MATERIALS 2009, 11, No. 10
`
`ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
`
`811
`
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`BOREALIS EXHIBIT 1056
`
`

`
`M. Antunes et al./Heat Transfer in Polypropylene-Based Foams Produced Using Different . . .
`
`only one variable, t, defined as:
`Þ1=2; u ¼ a2=k
`t ¼ t=uð
`
`(3)
`
`Where t is the measurement time from the start of the transient
`heating, u is the characteristic time, which depends both on
`sensor and sample parameters, a is the sensor radius and k is the
`thermal diffusivity of the sample.
`The thermal conductivity can be obtained by fitting the
`experimental data to the straight line given by Equation (2)
`and the thermal diffusivity is calculated from Equation (3),
`taking into account the t value determined in the previous fit.
`
`Experimental
`
`Materials and Compounding
`the materials.
`A PP-based matrix was used for all
`Specifically a high-melt-strength grade (PP-HMS) with the
`commercial name Daploy WB130HMS (50.0 phr), manufac-
`tured by Borealis, and an extrusion-grade PP, Isplen 050 G1E
`(50.0 phr), manufactured by Repsol, were melt-compounded
`using a co-rotating twin-screw extruder (Collin Kneter
`25X36D). In the case of the CO2 dissolution foams, a recycled
`PP (50.0 phr) was used instead of Isplen 050 G1E. Also, for the
`chemically foamed materials, ADC was added in situ in the
`form of powder
`in different amounts, depending on
`the desired final foam density. At the exit of the die, all the
`extrudates were water-cooled and pelletized.
`
`Foaming Process
`In order to compare the thermal conductivities of the
`different foamed materials with the unfoamed ones, cubic
`samples of the latter, with sides of approximately 34 mm, were
`directly cut from compression-molded discs (8.5 mm thick
`and 74 mm diameter), prepared in a hot-plate press (IQA-
`P-LAP PL-15) from the pelletized extrudates.
`Four different foaming processes were considered: extru-
`sion,
`injection molding, compression molding and batch
`foaming using gas dissolution.
`Three different extrusion-produced foams were character-
`3. In the
`ized, with densities ranging from 0.055 to 0.262 g cm
`case of the materials referred to as PPEx-3 and PPEx-1, a PBA
`was used as blowing agent, the nature of which affecting the
`final foam density. These foams were obtained from directly
`placing the previously twin-screw extrusion-compounded
`pellets in the feeder of a foaming extruder, designed to allow
`the introduction of PBAs, such as CO2 or n-butane, through
`the barrel without polymer escape. The PBA mixes with the
`melt polymer inside the extruder, the steady increase in
`pressure inside the machine promoting the expansion of the
`polymer/gas blend by decompression at the exit of the
`extrusion die. Due to the rather high temperatures required,
`foams produced using this process tend to have big cells, the
`final density depending mainly on the type and amount of
`PBA used.
`3),
`In the case of PPEx-2 (0.236 g cm
`the foam was
`produced by a cast-extrusion process combined with the
`
`1). It is based on the
`1 K
`a very wide range (0.02–200 W m
`analysis of the transient term within the heat conduction
`equation that relates change in temperature to time. It has been
`proved that this method can be used to measure the properties
`of small samples and/or inhomogeneous materials (with a
`non-constant density distribution) by carrying out
`local
`measurements that mask out the density distribution.[17]
`Nevertheless, the measurement can be local or bulk according
`to the experimental parameters.[18] By using this technique
`combined with the computed tomography, different types of
`cellular materials have been analyzed in recent years, from
`polymer to metal foams.[15,19,20]
`The transient source element is a round planar heat source,
`working simultaneously as heating device and temperature
`sensor. This element consists of an electrical conducting
`pattern of thin nickel foil (10 m m thick) in the form of a double
`spiral (see Fig. 1a), embedded between two insulating layers
`(each 70 m m thick) made of Kapton. The heating element is
`placed in contact with two samples surfaces as depicted in
`Figure 1b. Two samples of similar characteristics are
`preferable for this purpose.
`To perform the experiment, a constant electric power is
`supplied to the hot-disk sensor during a selectable time t. The
`increase in temperature DT(t) can be related to the variation in
`the sensor resistance R(t) by the equation:
`RðtÞ ¼R 0 1 þ aDTðtÞ
`½
`Š
`(1)
`Where R0 is the initial resistance (at t¼ 0) and a is the
`temperature coefficient of resistance of the nickel foil.
`Assuming an infinite sample and a 2D source consisting of
`concentric heating rings situated in a plane (see Fig. 1b), the
`temperature rise at a particular point and time can be
`calculated by solving the equation for heat conduction.[21,22] In
`the case of TPS sensor geometry, the heat source is assumed to
`be a series of rings disposed as described above and, therefore,
`the spatial average DT tð Þ can be obtained using the following
`equation:
`DTðtÞ ¼P 0ðp3=2a lÞ1DðtÞ
`Where P0 is a Bessel function, D(t) is a geometric function
`characteristic of the number n of concentric rings, and DTðtÞ is
`the temperature increase of the sensor expressed in terms of
`
`(2)
`
`COMMUNICATION
`
`Fig. 1. Schematics of the a) transient plane source element and b) experimental set-up.
`
`812
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`
`ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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`ADVANCED ENGINEERING MATERIALS 2009, 11, No. 10
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`

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`COMMUNICATION
`
`M. Antunes et al./Heat Transfer in Polypropylene-Based Foams Produced Using Different . . .
`
`later free expansion of the sheet inside an oven by promoting
`the thermal decomposition of ADC.
`3) was
`A high-density injection-molded foam (0.610 g cm
`also considered. In this process, the extrusion-compounded
`pelletized material containing ADC was placed in the feeder
`of an injection molding machine. Control of both the
`temperatures and the injection pressures allows careful
`regulation of the decomposition of ADC and, thus,
`the
`expansion of the material, cooled by direct contact with the
`walls of the closed mold.
`The third type of
`foaming process considered was
`compression molding using ADC as blowing agent. Due to
`the fact
`that
`the process is done in a hot-plate press
`(IQAP-LAP PL-15), previously to its foaming the pelletized
`material had to be compression-molded into discs, using
`the same process as with the unfoamed discs. These discs were
`heated at 180 8C applying a pressure of 40 bar and varying the
`foaming time from 15 to 20 min. This process allows control of
`both the nucleation of the gas bubbles and their growth by
`varying the foaming time, resulting in different foaming agent
`gas yields, and allowing cell growth by decompression.[23,24]
`Finally, several foams prepared by a batch-foaming process
`using a gas dissolution process with CO2 as PBA were
`analyzed. Rather than mixing the gas with the polymer in the
`melt, batch-expanded foams were obtained by saturating
`compression-molded PP discs with CO2 in a high-pressure
`chamber, the saturated sample being foamed by a sudden
`pressure drop (DP) and/or temperature increase. Pressurized
`at 160 bar and 155 8C for 30 min, the CO2 saturated discs were
`cooled to 135 8C and foamed by sudden decompression from
`140 bar to a range of residual pressures varying from 30 to
`100 bar, i.e., applying a DP of 40 to 110 bar.
`
`Testing Procedure
`the extrusion-
`the solid discs and of
`The density of
`produced, injection-molded, compression-molded and gas-
`dissolution foams was measured according to standard
`procedures (ISO-845).
`In order to obtain the open-cell content of each specimen
`expressed as the percentage of the calculated volume (Ov),
`both the geometric volume (V) and the displacement volume
`(Vp) of each foamed sample were determined, the later by
`means of an air pycnometer. The open-cell content was
`determined as follows:
`
`Ovð%Þ ¼ V Vp Vs
`
`V
`
` 100
`
`(4)
`
`Where Vs takes into account the volume occupied by the surface
`cells opened during specimen preparation. All open-cell
`content and correction calculation procedures are described
`in ISO-4590.
`The cellular structure of the foams was observed using a
`Jeol JSM-5610 scanning electron microscope (SEM). Samples
`were fractured at low temperature and made conductive by
`sputtering deposition of a thin layer of gold. Low-
`magnification micrographs were analyzed using the intercept
`
`counting method,[25] in order to obtain both the average cell
`size (f) as well as cell density. Considering that in this study
`several foaming processes were considered, each with its
`particularities, two different cell sizes were determined from
`cellular structure analysis: fVD, with VD stating for vertical
`direction, in this case being the cell size in the preferential
`direction of foaming, and fWD, being the cell size measured
`perpendicularly to the previously stated direction (width
`direction). The aspect ratio (AR), defined as the ratio between
`the highest (fVD) and smallest (fWD) characteristic cell sizes,
`was assessed for the different foams using a representative cell
`population.
`A commercial thermal constant analyzer (model Hot Disk)
`based on the TPS method was used to measure the effective
`thermal conductivity (l). Experiments were performed with a
`sensor radius of 3.2 mm. The power output and measured time
`were selected according to each sample thermal characteristics
`and varied between 0.005–0.015 W and 15–80 s, respectively.
`Experiments were carried out at room temperature.
`Five repeated experiments were performed for each
`experimental set-up. The calculations of the thermal properties
`were performed according to equations
`reported else-
`where,[21,22] using the Hot Disk software v.5.6, which computes
`the equation in an external processor. The values reported in
`this work are the average of these five experiments.
`
`Results and Discussion
`
`Foaming Behavior
`The expansion ratio (ER) and open-cell content (Ov) are
`presented in Table 1 together with the cellular structure
`characterization results, except for the nitrogen dissolution
`foams. Cellular stucture parameters of the compression-
`molded foams were obtained as the average of several SEM
`micrographs of two different samples foamed using the same
`foaming parameters.
`As can be seen, extrusion is a process that allows a wide
`3;
`range of foam densities (from 0.262 to as low as 0.055 g cm
`i.e., expansion ratios of 3.5 to 17), mainly by varying the
`amount of PBA used, the foams being inherently of the
`closed-cell type. On the contrary, injection-molded foams,
`such as the one considered here, although closed-cell
`in
`nature, are rather limited to high density values (expansion
`ratios of 1.5–2), thus reducing their applicability to structural
`applications. Foams produced using CBA thermal decom-
`position by compression molding, although limited when
`compared to some of the extrusion-produced ones due to the
`solid residues generated during CBA decomposition, may
`show a wide range of densities and cellular structures, from
`inherently closed-cell ones, such as the ones analyzed here, to
`open-celled. The carbon dioxide dissolution foams analyzed
`in this study present a very wide range of expansion ratios and
`open cell contents, from relatively low ER values of 3–4 and
`somewhat closed-cell structures, to ER values as high as 15 for
`foams that are totally open-celled; these variations were
`achieved by simply varying the applied gas pressure drop.
`
`ADVANCED ENGINEERING MATERIALS 2009, 11, No. 10
`
`ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
`
`http://www.aem-journal.com
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`

`
`M. Antunes et al./Heat Transfer in Polypropylene-Based Foams Produced Using Different . . .
`
`Table 1. Cellular structure characterization results.
`
`Material code
`
`Foaming process
`
`PPEx-1
`PPEx-2
`PPEx-3
`PPInj
`PPCom
`
`Extrusion
`
`Injection
`Compression molding
`
`PPAut
`
`CO2 dissolution
`
`3]
`
`Foam density [g cm
`0.262  0.008
`0.236  0.012
`0.055  0.003
`0.610  0.004
`0.444  0.013
`0.422  0.012
`0.346  0.018
`0.311  0.009
`0.268  0.006
`0.261  0.013
`0.318  0.010
`0.261  0.013
`0.189  0.013
`0.131  0.007
`0.126  0.009
`0.082  0.008
`0.059  0.006
`
`ER[a]
`
`3.49
`3.88
`16.71
`1.50
`2.06
`2.17
`2.65
`2.94
`3.42
`3.51
`2.78
`3.39
`4.66
`6.75
`6.99
`10.73
`14.97
`
`Ov [%]
`8.4  0.7
`17.0 0.5
`3.0  0.3
`5.9  0.3
`0.0  0.9
`4.7  2.8
`12.4 3.8
`44.9 1.8
`45.0 2.3
`67.2 1.3
`80.3 5.6
`75.0 3.8
`90.0 3.0
`96.6 2.9
`
`fVD [mm]
`928.3  12.4
`1084.4 16.8
`1899.5 57.0
`219.0  6.6
`186.6  9.3
`194.4  6.6
`242.5  14.3
`110.1  5.5
`140.6  2.8
`392.5  19.6
`2439.3 48.8
`2574.5 38.6
`9200.5 100.5
`9308.5 186.2
`
`fWD [mm]
`666.2  23.5
`714.1  39.3
`1310.2 39.3
`223.8  9.0
`194.3  9.7
`174.5  1.0
`239.3  1.7
`98.8 4.9
`102.7  3.1
`152.9  7.8
`854.5  8.5
`896.9  9.0
`985.2  21.3
`991.5  29.7
`
`AR[b]
`
`1.39
`1.52
`1.45
`0.98
`0.96
`
`1.11
`
`1.01
`
`1.11
`1.37
`2.57
`2.85
`2.87
`9.34
`9.39
`
`3]
`
`Cell density [cells cm
`2.195 103
`2.183 103
`1.246 103
`5.106 104
`4.699 104
`4.709 104
`3.417 104
`1.867 105
`1.430 105
`HC[c]
`HC[c]
`HC[c]
`HC[c]
`HC[c]
`
`COMMUNICATION
`
`[a] ER: expansion ratio.
`[b] AR: aspect ratio.
`[c] HC: honeycomb-like cell structure.
`
`Cellular Structure
`The cellular structure characterization results, particularly
`values of the average cell size on both directions of foaming
`(fVD and fWD), cell density and aspect ratio (AR), are
`presented in Table 1 for all the thermal conductivity analyzed
`foams, except for the nitrogen dissolution foams.
`
`SEM pictures of some of the cell-characterized foams
`shown in Table 1 are presented in Figure 2. Extrusion-
`produced foams tend to show a rather high average cell size
`(>700 m m), including those with densities higher than 0.2 g
`3 (Fig. 2b), the cells being elongated in the extrusion flow
`cm
`direction, explaining the considerably higher fVD values when
`
`Fig. 2. SEM pictures of several of the foamed samples - Extrusion-produced: a) PPEx-3, b) PPEx-1; c) injection-moulded; compression-moulded: d) 15 min, e) 18 min and f) 20 min;
`and CO2 dissolution: g) DP¼ 110 bar, h) DP¼ 120 bar and i) DP¼ 140 bar. VD: Vertical direction of foaming; WD: Width direction.
`
`814
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`http://www.aem-journal.com
`
`ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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`ADVANCED ENGINEERING MATERIALS 2009, 11, No. 10
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`Page 4 of 7
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`

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`COMMUNICATION
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`M. Antunes et al./Heat Transfer in Polypropylene-Based Foams Produced Using Different . . .
`
`Table 2. Thermal conductivities obtained using the TPS method.
`
`Sample Group
`
`Solid sheet
`
`Extrusion
`
`Injection
`
`Compression molding
`
`CO2 dissolution foams
`
`N2 dissolution foams
`
`r [g cm
`
`3]
`
`l [W m
`
`1 K
`
`1]
`
`0.916
`0.883[a]
`0.262
`0.236
`0.055
`0.610
`0.610
`0.444
`0.422
`0.346
`0.311
`0.268
`0.261
`0.318
`0.261
`0.189
`0.131
`0.126
`0.082
`0.059
`0.032
`0.031
`0.025
`0.017
`
`0.276
`0.266[a]
`0.095
`0.091
`0.054
`0.181
`0.183
`0.133
`0.139
`0.122
`0.096
`0.091
`0.090
`0.111
`0.099
`0.078
`0.068
`0.067
`0.064
`0.059
`0.041
`0.044
`0.037
`0.037
`
`[a] Solid reference material for CO2 dissolution specimens
`
`compared to fWD. Injection-molded foams, due to their
`3), show a small cell size
`extremely high density (0.610 g cm
`( 220 mm), their main characteristic being the fact that the
`cells, which are much more isotropic than the ones observed
`for the extrusion-produced foams, get smaller closer to the
`skin (Fig. 2c). Compression-molded foams also showed a
`small cell size, comparable to that of the injection-moulded
`ones, but with densities almost three times lower (Fig. 2d–f).
`Finally, CO2 dissolution foams, depending on the applied
`pressure drop (DP), show, at the lowest values of DP, very
`small cell sizes (around 120 mm) giving density values
`comparable to those of
`the compression-molded foams
`(Fig. 2g), and at high values of DP (130 bar) a honeycomb-like
`cell structure, increasingly induced with only small increases
`in pressure drop, as seen in Figure 2h and i.
`
`Thermal Conductivity Measurements
`The thermal conductivities and densities of the character-
`ized samples are presented in Table 2. The standard deviation
`was lower than 5% for all the performed tests and both the
`density and the thermal conductivity have been normalized to
`those of the reference solid materials. The results for the
`different processing methods are plotted against the relative
`density in Figure 3. The data can be subdivided into two parts,
`as shown, in terms of the variation of thermal conductivity
`with relative density. The main heat transfer mechanisms for
`closed-cell cellular materials are conduction through the solid
`phase, conduction through the gas phase and radiation. It is
`well known that convection can be neglected for materials
`with cell sizes below approximately 3 mm.[26] For low relative
`
`Fig. 3. Normalized thermal conductivity versus relative density for the studied samples.
`
`(5)
`
`densities, conduction through the gas phase and radiation
`play the key role, while for high relative densities the main
`contribution is due to the solid phase, the contributions of gas
`conduction and the radiation being negligible. For cellular
`materials in which the solid phase is polymeric in nature, with
`
`1K1, the
`thermal conductivities ranging from 0.1 to 0.3 W m
`transition limit seems to be obtained at a relative density of
`approximately 0.2.
`In order to analyze the results in more detail, a first
`estimation of the conductivity values was obtained using the
`simple equation:
`lfoam ¼ lg þ ls ¼ lgasVgas þ jlsolVsol
`Where lg is the thermal conductivity due to the conduction in
`the gas phase, ls is the solid phase conduction term, lgas is the
`conductivity of the gas filling the cells, lsol is the conductivity of
`the solid matrix, Vgas and Vsol are the volume fractions of gas
`and solid, respectively, and j is a parameter (with values
`between 0 and 1) that accounts for the tortuosity of the cellular
`structure.[26] If j is 1,
`the above shown equation would
`correspond to a simple mixture rule.
`Figure 4 shows the experimental results plotted in
`combination with theoretical curves obtained using Equation
`(5) and values of j¼ 2/3 and 1. As can be appreciated, a value
`of j¼ 2/3, commonly used to predict the properties of low
`density foams,[27] clearly underestimates the conductivity
`data. However, a value of j¼ 1 fits with good accuracy the
`values of conductivity for the foams with relative densities
`higher than 0.2. This means that the mixtures rules can be used
`to predict the conductivity of high relative density foams.
`Paying attention to the results for relative densities lower
`than 0.2, it can be seen that Equation (5) underestimates the
`conductivity data. The reason behind this is that for these
`densities the contribution of radiation [neglected in Eq. (5)]
`starts to play a role. The structural characteristics, such as cell
`size and foam thickness, and optical properties of the polymer
`phase have a strong influence in this density range.
`Although a good agreement is observed in Figure 4 for
`j¼ 1, it is still interesting to compare the compliance of the
`
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`M. Antunes et al./Heat Transfer in Polypropylene-Based Foams Produced Using Different . . .
`
`have lower conductivities than those produced by extrusion;
`the reason should be related to a cellular structure with a
`higher capability for conducting heat flow. In general terms it
`can be said that although there are differences in conductivity
`observed between foams produced using different processes,
`these are much smaller than that observed in foams with
`different densities.
`
`Concluding Remarks
`
`The cellular structure and thermal conductivity of PP foams
`produced using different techniques were characterized. It
`was shown that the different production methods allow a
`wide range of densities and types of cellular structures. The
`results of the thermal conductivity prove that the most
`important characteristic that alters the heat
`transport
`is
`density, thermal conductivity increasing with density.
`It was found that differences between foams produced
`from different technologies are small for relative densities
`higher than 0.2. This fact can be explained considering that the
`conduction mechanism is the only significant heat transfer
`mechanism in this density range. Both the mixture rule as well
`as the Russell model can be used to predict the conductivity
`data above a relative density value of 0.2. Further and finer
`experiments are needed to demonstrate clear differences
`between the production methods (i.e., different cellular
`morphologies) in this density range.In the low density range,
`all of
`the proposed models underestimate the overall
`conductivity, since radiation starts playing an important role.
`In this density range, the effect of the processing method
`should be more significant and in fact a slight difference
`between foams produced by extrusion and those produced by
`gas dissolution with a higher cell size has been detected.
`Foams with a smaller cell size tended to be better insulating
`materials.
`
`Received: May 12, 2009
`Final Version: June 4, 2009
`Published online: August 21, 2009
`
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`Fig. 4. Experimental data and estimation of the thermal conductivities using Eq. (5).
`
`experimental data with other models used in literature. Since
`most of the samples produced had a relative density over 0.2,
`we will consider this range in which there is a minimum
`the radiation term. The series, parallel,[28]
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`density range, the foams produced by compression-molding
`
`Fig. 5. Experimental thermal conductivity data and theoretical models discussed.
`
`816
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`ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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`M. Antunes et al./Heat Transfer in Polypropylene-Based Foams Produced Using Different . . .
`
`COMMUNICATION
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`ADVANCED ENGINEERING MATERIALS 2009, 11, No. 10
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`http://www.aem-journal.com
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