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THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMSM. Khairul Alam a & Benji Maruyama ba Department of Mechanical Engineering, Stocker Center, Ohio University, Athens, Ohiob AFRL Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Dayton,OhioPublished online: 24 Jun 2010.

To cite this article: M. Khairul Alam & Benji Maruyama (2004) THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS,Experimental Heat Transfer: A Journal of Thermal Energy Generation, Transport, Storage, and Conversion, 17:3, 227-241, DOI:10.1080/08916150490449055

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Experimental Heat Transfer, 17:227–241, 2004Copyright © Taylor & Francis Inc.ISSN: 0891-6152 print/1521-0480 onlineDOI: 10.1080/08916150490449055

THERMAL CONDUCTIVITY OF GRAPHITICCARBON FOAMS

M. Khairul AlamDepartment of Mechanical Engineering, Stocker Center, Ohio University,Athens, Ohio

Benji MaruyamaAFRL Materials and Manufacturing Directorate, Wright-Patterson Air ForceBase, Dayton, Ohio

Carbon foams are being developed as a new class of thermal management materials. Thesefoams are produced with a wide variety of thermo-mechanical properties; however, veryfew studies of the properties of carbon foams have been reported in literature. This articlereports on an experimental study that was conducted to determine the thermal conductivityof various forms of graphitic carbon foam by using the flash diffusivity and guarded hotplate method. To reduce errors introduced by porous specimen, the test samples werevacuum infiltrated with epoxy. The thermal diffusivity results from the flash diffusivityinstrument were used to determine the thermal conductivity of the samples. Some foamsamples were determined to have large variations in thermal properties within the sampleblock. A theoretical and numerical model has been used to examine the effect of thefiller epoxy on the experimental results and the influence of pore characteristics on thethermal conductivity of these foams. It was determined that accurate measurement ofthermal properties of graphitic foam samples requires careful selection of sample size andmeasurement technique.

INTRODUCTION

Carbon foam is a new class of material that has received special attention becauseof potential applications in several areas of thermal management. These foams are man-ufactured from a porous preform of pitch material. The process parameters can be variedto produce foam with a large range of thermal and mechanical properties. Because ofthe low density, and high intrinsic thermal conductivity of graphitized pitch-based car-bon, the specific thermal conductivity (i.e., thermal conductivity divided by density) ofsuch foams can be several times greater than copper. The open cell foams are also goodcandidates for heat exchanger applications.

Received 9 June 2003; accepted 29 October 2003.Address correspondence to M. Khairul Alam, Department of Mechanical Engineering, Stocker Center,

Ohio University, Athens, OH 45705-2979. E-mail: alam@ohio.eduThis work was supported by the U.S. Air Force through an IPA assignment, and by AFOSR contract

number F49620-03-1-1004. The authors would like thank UDRI researchers at Air Force Research Laboratory(AFRL, Dayton, OH); Dr. D. Anderson, Dr. W. Lee and Mr. B. Rice for their helpful contributions to thisstudy.

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NOMENCLATURE

d thickness of the specimen [m]Kb bulk thermal conductivity [W/mK]Ks solid (intrinsic) thermal conductivity

[W/mK]Kp thermal conductivity of pore material

[W/mK]n pore conduction factorP porosity of the porous materialq heat flux [W/m2]

R relative density, R = ρbρs

, [-]�T temperature difference between two

points on the slab [K]

Greek symbolsρb bulk density of pure foam [kg/m3]ρs intrinsic density of the solid in the foam

[kg/m3]α thermal diffusivity [m2/s]

Although the foam production process tends to vary, many processes start with acompacted, porous preform of pitch material. The pitch preform is then melted underhigh pressure of an inert gas. When the pitch material begins to flow above its softeningtemperature (typically 250◦C), the pressure is released to expand trapped gases in thevoids, thereby producing a foam from the pitch. The product is then stabilized at about150◦C, and carbonized at about 1000◦C. A heat treatment step is often used to graphitizethe foam at temperatures over 2000◦C. The foam material can have porosity varyingfrom 60 to 95%. Typical foam pores range from 50 to 500 microns in diameter. Most ofthese foams tend to have open cell structures.

Several factors influence the thermal properties of carbon foams. The nature andamount of porosity of the foam is a major factor in the determination of thermo-mechanical properties. Another important parameter is the degree of graphitization ofthe carbon in the foam. Depending on the precursor and heat treatment, the thermalconductivity of carbon ranges from ∼1 to 2000 W/mK. The graphitization index of agraphitic carbon is a measure of its degree of perfection. It is defined as the probabilityof finding two layers of graphene (a single layer of hexagonally arranged carbon atoms)with the same stacking as given by the crystallographic definition of graphite. Carbonfoams that are not graphitic exhibit very low thermal conductivities, and are excellentlightweight insulators that can survive high temperatures in a nonoxidizing environment.On the other hand, it is possible to produce foam with high graphitization index, resultingin high thermal and electrical conductivity. Highly graphitic foams can have bulk thermalconductivities >100 W/mK.

Carbon foams are a new class of material; therefore, very few studies of thermalproperties of foams have been reported in literature. Klett and Burchell reported on highthermal conductivity carbon foam produced at Oak Ridge National Laboratory (ORNL)[1]. This particular foam has a high graphitization index (over 0.9), and thermal conduc-tivity higher than 150 W/mK. Air Force Research Laboratory (AFRL, Dayton, OH) hasbeen investigating a foam that is produced in-house as shown in Figure 1 [2]. Severalother producers manufacture foam using different processes. Carbon foams are made byPOCO Graphite (Decatur, TX), MER Corp. (Tucson, AZ), and Touchstone Research Lab.(TRL, Triadelphia, WV).

The bulk properties of the foam depend on the intrinsic property of the solid phase inthe foam, the foam density, and the nature of the pores. Furthermore, the intrinsic thermalconductivity of the solid phase will depend upon the degree of alignment of the graphene

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THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS 229

Figure 1. Micrograph of a graphitic carbon foam.

planes induced by the foam blowing process, which varies within the microstructure of thefoam, i.e., very good alignment is observed in the ligament versus very poor alignmentin the nodes. The manufacturing process imparts all of these characteristics. Becauseof variations in the precursor pitch, the foaming process, and the foam density andmicrostructure, there is significant uncertainty about the thermo-mechanical propertiesof these foams. This uncertainty makes it difficult to transition these foams into theirintended applications. Such uncertainties are compounded by the fact that measurementof thermal properties of foams can be quite difficult.

The objectives of this study are: (a) to evaluate the flash diffusivity method fordetermination of thermal properties of graphitic foams; (b) to investigate foam infiltrationas a technique for improving the measurement of foam thermal properties; and (c) toevaluate the experimental results on the basis of analytical models.

The ASTM E1461 method [3] for measuring thermal diffusivity is to use the flashdiffusivity method, in which a burst of radiation energy is applied to one surface ofa sample, and the diffusivity is then deduced from the temperature-time history of theback surface of the sample. The analysis method is sensitive to the thickness of thesample across which the energy pulse traverses to produce the diffusivity signal. Errorsin foam property measurement can arise from the fact that neither the front nor the backsurface is a smooth plane. In addition, the radiant energy falling on carbon foam maybe scattered in many different directions, thereby penetrating the connected voids bymultiple reflections. Since the sample thickness in many instruments is usually restrictedto a few millimeters, this can produce a significant error in the measurement.

Although the laser flash method is designed for determination of the thermal diffu-sivity, it is often used to determine the thermal conductivity of the sample. This canbe done by determination of specific heat from comparison of the temperature riseof the sample with that of a known standard material and then using the followingequation:

K = αρCp (W/mK) (1)

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where ρ is the density of the specimen (kg/m3), Cp is the specific heat (J/kgK), and α

is the thermal diffusivity (m2/s). The specific heat can also be determined independentlyby other instruments or from known values of the sample for use in the above equation.

The guarded hot plate, the heat flux meter, and similar steady-state measurementinstruments are often used to determine thermal conductivity. The guarded hot plate isdescribed in ASTM C-177 [4] and can be used to measure samples with conductivitiesin the range of 0.1 to 16 W/mK. The guarded heat flow meter, which is very similar tothe guarded hot plate, is described in ASTM E1530 [5] and is prescribed for sampleswith conductivity in the range of 0.1 to 30 W/mK. In these two instruments, a sample inthe shape of a plate is subjected to a temperature gradient by a hot plate and the thermalconductivity is determined from the ratio of the heat flux to the temperature gradient.

For graphitic foam samples, there are several difficulties in measuring such samplesby instruments based on the hot plate. The contact between the foam and the thermo-couples, as well as the hot and cold plates, tends to be poor. If foams are subjectedto significant loads to improve thermal contact, there is a possibility of damaging theinternal pore structure because the foams do not have high strength. Any face sheets andthermal pastes used to improve the contact can add a significant resistance that must bedetermined because the graphitic foam has low thermal resistance. Thermal pastes thathave high thermal conductivity can also produce errors because the paste can infiltratethe foam and, when heated, can wick into the foam. For certain foams, this can leadto significant errors in the thermal conductivity. Finally, the thermal conductivity that ismeasured results from the combined effect of conduction, convection, and radiation. Foropen cell foams, the convection effect can influence the results depending on pore sizeand foam orientation with respect to the temperature gradient. An objective of this studyis to evaluate a foam infiltration method to make the flash diffusivity method independentof convection and uncertainties of interface contact.

The present study is a combination of analytical, numerical, and experimental meth-ods to study the flash diffusivity and the guarded hot plate/heat flow meter methods whenused with graphitic carbon foams. In this study, the goal is to reduce errors by infiltratingthe foam samples with a polymer of low conductivity such that it does not significantlyaffect the thermal conductivity of the bulk foam. The polymer does change the densityand the specific heat of the sample, however, these properties can be determined or cal-culated without difficulty. The results are then compared with values obtained by otherinvestigators and other instruments.

THEORY

Foams are a subset of composite materials since they are composed of gas porescontained within a solid. The most common method for the determination of compositeproperties is to use a rule of mixtures based on volume fractions. This has been used toestimate thermal conductivity of continuous fiber reinforced composites. However, whenthe thermal conduction in the cells is not isotropic, the thermal conductivity becomes atensor that has nonidentical components depending on the thermal conduction in specificdirections within the material. For the case of foams, the heat flow path is very tortuous;therefore the value cannot be obtained by rule of mixtures. The general practice is todetermine the bulk thermal conductivity in a specific direction as the ratio of the heatflux to the applied temperature gradient in that direction.

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THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS 231

Several models have been proposed to predict the thermal conductivity of foams.Many of the models were developed for low density insulating foams [6]. In this analysis,the relative density R will be used as one of the parameters. The relative density isdefined as:

R = ρb/ρs = 1 − P/100 (2)

where ρb is the bulk density of the pure foam, ρs is the intrinsic density of the solid inthe foam, and P is the porosity (%), or the percent void volume of the foam.

High porosity (above 90%) foam made of a poorly conducting solid conducts heatprimarily by conduction through gas in the pores; radiation and convection in the porescan also be significant [7]. As the relative density increases, conduction through the solidbecomes more important. For a foam made of highly conducting solids, the conductionthrough the solid tends to dominate, especially when the intrinsic thermal conductivityof the carbon is much higher than the pores. Since graphitic carbon is highly conducting,and most of the graphitic carbon foams examined in this study have much higher relativedensity than insulating foams, conduction by the solid carbon phase should dominate theenergy transport.

From thermodynamic consideration, the value of thermal conductivity of foam withnonconducting pores has a limiting value given by:

Kb ≤ Ks

[ρb

ρs

]= KsR (3)

where Kb is the bulk conductivity, Ks is the intrinsic conductivity of the solid phase,ρb is the bulk density, and ρs is the density of the solid phase. The maximum value, asshown in the above equation, is obtained by the rule of mixtures. In practice, however,the energy flow path is tortuous, and the true value is always less than the maximumpredicted by Eq. (2). Several authors have used an “inefficiency factor” or a “pore factor”to modify the above equation. A factor of 2/3 has been used to correct for the flow inpolymer foams [8]. A more rigorous approach was adopted by Bauer who consideredthe perturbation of a continuous medium by the presence of pores. By solving for thetemperature profile, the following differential equation can be derived for the change inthe bulk thermal conductivity Kb in the porous medium as a function of porosity in themedium [9]:

dKb

Kb

= − 1 − Kp/Kb

n + (1 − n)Kp/Kb

dV

V(4)

In the above equation, Kp is the conductivity of the pores and Kb is the thermalconductivity of the bulk material that changes as the porosity increases due to increasein the total pore volume V . The new constant ‘n’ that now has been introduced will betermed the ‘shape factor’. This factor has a maximum value of unity. This constant isobtained from the evaluation of boundary conditions at the pore surface, and thereforereflects the effect of the pore shape and the pore volume fraction on the thermal conduc-tion process. Integrating the above equation from V = 0 to the final porosity value, one

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obtains the following equation:

Kb − Kp

Ks − Kp

(Ks

Kb

)1−(n/3)

= 1 − (P/100) (5)

The bulk conductivity will always be an intermediate value between the intrinsicconductivity of the carbon (the solid part of the foam), and the conductivity of the pores(the insulating part of the foam). In addition, it is expected that, for graphitic carbonfoams, the bulk conductivity Kb will be much greater than the pore conductivity, i.e.,

Kp � Kb � Ks (6)

Equation (3) then reduces to the following:

Kb/Ks = (1 − P/100)1/n = R1/n (7)

Equation (7) is expected to be applicable for the graphitic carbon foam if the bulkthermal conductivity is much greater than the conductivity of the pore material. If thepores are filled with a low conductivity polymer (epoxy) to replace the air in the pores,Eq. (5) shows that the pore conductivity can still be neglected if the resulting bulk thermalconductivity is much higher than the conductivity of the epoxy. Therefore, bulk thermalconductivity of the filled composite foam can be assumed to be equal to Kb (of theunfilled foam) if the resulting value for the composite is at least an order of magnitudegreater than the filler conductivity (0.2 W/mK for a typical epoxy). This is the basis ofthe experimental study described below.

The filled “composite” foam has several advantages over the original foam in thelaser flash and the guarded hot plate methods. For the laser flash method, it providesa fully dense, well-defined plane for absorption of the laser pulse. Even though thepolymer may be transparent to the laser radiation, the infiltrated sample surface can beeasily coated with a graphite spray to prevent the radiation energy pulse from penetratingthe foam. The laser flash method provides the value of thermal diffusivity; the thermalconductivity is then calculated by determining density and specific heat. Since most of themass of filled foam is the epoxy, therefore, the specific heat and density are determinedprimarily by the epoxy filler; these property values for the epoxy are well known.

In the case of a guarded hot plate or guarded heat flow meter, the filled foam isadvantageous because it has greater structural integrity compared to the original foam.The sample can now be placed under compressive load to improve contact with the samplewithout fracturing the ligaments. Thermal paste that is used to improve the contact cannotwick into the sample. All convection effects are also eliminated. Therefore, the filled foamprovides a more accurate measurement of the true thermal conductivity. Since the hotplate and the heat flow meter measure the thermal conductivity directly, the change inspecific heat does not affect the measurement. Therefore, testing composite foam shouldbe preferable to testing porous foam in the hot plate system.

The infiltration of the foam changes the specific heat and density in a predictablemanner that can be measured or calculated; but it has negligible effect on the thermalconductivity of the graphitic foam sample. These advantages form the basis of this ex-perimental method.

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THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS 233

Equation (7) can be used to determine the conductivity of the bulk material onlywhen the other parameters are known. However, there are two unknowns in the equations:the pore factor ‘n’ and the intrinsic thermal conductivity of the solid (Ks). Carbon foam isa novel engineered material; its intrinsic thermal conductivity Ks is not known accurately.In this study, the bulk conductivity results will be used to estimate the range of valuesof the intrinsic thermal conductivity Ks .

EXPERIMENT

Experimental determination of the thermal conductivity was conducted using pri-marily two different measurement techniques: a flash diffusivity system and the guardedhot plate/heat flow meter. Some of the samples, e.g., POCO foams, were highly anisotropic.For purposes of comparison, the results reported here are for the direction of highest con-ductivity. This will be termed the vertical direction which is perpendicular to the planeof the sample blocks as received from the manufacturer.

Laser flash diffusivity instrument

The flash diffusivity technique is a standard instrument for the determination ofthermal diffusivity of a material. In this method, the front face of a sample is subjectedto a short pulse of energy from a lamp or a laser while recording the resulting temperaturerise at the back face of the sample. The magnitude of the temperature rise or the quantityof radiant energy is not required for determination of diffusivity. Only the shape of thecurve (as a function of time) is used to determine the diffusivity. The thermal diffusivityα can be obtained from the following equation:

α = 0.1388d2

t50(m2/s) (8)

where d is the sample thickness and t50 is the time for the temperature rise to reach 50%of its maximum value.

Several modifications have been proposed to improve the above formula. Cowanincluded the effect of heat loss from the sample by developing a theoretical relation-ship between cooling and heating parts of the curve [10]. Koski included an energy lossfactor in the analysis and provided a more extensive averaging method by using temper-ature ratios proposed by Taylor and Clark to determine the thermal diffusivity [11, 12].The laser flash instrument (Holomatrix Microflash) used in this study incorporates thesemodifications in the calculation of the thermal diffusivity.

After the thermal diffusivity has been determined, the thermal conductivity of thematerial can then be determined from Eq. (1). The specific heat and density are scalarquantities that can be determined by other standard methods, and for the foam specimen,these quantities can be calculated accurately by rule of mixtures. Therefore, the thermalconductivity can be determined accurately from an accurate determination of the thermaldiffusivity.

The primary advantages of using laser flash measurements are the following:(1) small sample size; (2) fast and highly automated measurement; and (3) the avoidanceof convection effects due to the quick response of the instrument. However, there are

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several issues that need to be considered in using the laser flash method for measuringfoams. For this measurement to be valid, the foam cell size must be much smaller thanthe diameter and thickness of the sample. When the sample thickness is large, there maybe significant thermal losses from the sides of the sample. This error can be quantifiedby comparing the theoretical and experimental heating curves. The laser flash instrumentused in this study (Holomatrix Microflash) has a software to estimate the heat loss.

A significant issue is the decoupling of the thermal signal within the foam-epoxycomposite. The foam conductivity is much higher compared to the epoxy. In some casesthis can lead to two different signals propagating with different speed separately throughthe foam and the epoxy. However, the foam forms a tortuous path through the epoxy;therefore it is assumed that the signal will not be decoupled. This is confirmed by carryingout a numerical simulation of the foam-epoxy heating process as described below.

Numerical simulation of the laser flash method

A finite element analysis was carried out to determine the response of a filledcomposite foam sample to a transient heat flux in the same manner as the flash diffusiv-ity experiment. To analyze the thermal field in the foam microstructure, the governingdifferential equation of transient heat conduction is solved with a heat flux ‘spike’ atone end face of the sample. The epoxy-filled foam is numerically modeled by a regulardistribution of spherical epoxy pores in a carbon foam matrix.

The transient heat conduction equation is applied to the model with the followingboundary conditions. An initial uniform temperature is applied throughout the foam-epoxy composite. In addition, a heat flux ‘spike’ is applied to the bottom surface ofthe sample at the beginning of the simulation and then the thermal energy is allowedto diffuse through the sample by conduction through the foam and the epoxy. All otherboundaries are kept insulated.

The solid model was analyzed by ALGOR FEM software to predict the temperatureand heat flux distribution in the filled composite foam. After the mesh has been generated,the boundary conditions were applied to the mesh. The temperature distribution at the topface was then determined by finding temperature values at several points on the top face,making certain that the points in the carbon foam and the epoxy pores were included.

It was determined that the temperature variation between the foam and the epoxywas less than 0.5%. A plot of a typical temperature history on the back face of a 5.5-mmthick sample is shown in Figure 2. It can be observed that the two temperature curvesat the back face for two points (corresponding to the epoxy and the foam) coincide witheach other. A typical experimental curve obtained from the laser flash test is in shownin Figure 3. The numerical and experimental curves are very similar as they reach thepeak. The drop-off after the peak in the experimental curve is due to the heat loss fromthe sample. The experimental curve is what is expected from a homogeneous material.Therefore, we can conclude that the temperature signal is not decoupled, and the thermaldiffusivity of the filled foam composite can be determined by the laser flash method.

Guarded hot plate and guarded heat flow meter

The guarded hot plate method and the very similar guarded heat flow meter willbe used to find the thermal conductivity directly. These two methods are both based

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THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS 235

Figure 2. Nondimensional temperature distribution in foam and epoxy at the top surface of a sample. Theepoxy temperature curve matches the foam temperature curve.

Figure 3. Heating curve from laser flash instrument. The dotted line is the analytical matching curve used todetermine the diffusivity.

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on a guarded hot plate system and require larger samples. The samples are typically10 cm × 10 cm (4′′ ×4′′) in cross section, and 1- to 2-cm thick. Two identical specimensare needed for the guarded hot plate whereas a single sample is used in the heat flowmeter. In the guarded hot plate, two samples are placed symmetrically above and belowa flat, electrically heated metering section that is surrounded laterally by a guard heatersection. Heat sinks are placed at the two ends of the sandwiched stack, and a steady-stateunidirectional heat flow is established across the two specimens. In the heat flow meter,a single sample is sandwiched by a hot plate and a heat flux sensor material. The thermalconductivity is calculated from the following equation:

Kb = q�T/d (9)

where Kb is the thermal conductivity of the specimen, q is the heat flux (W/m2), �T isthe average temperature difference across the two specimens, and ‘d’ is the thickness ofeach specimen.

EXPERIMENTAL RESULTS

Several samples from different sources of carbon foam were used in this study.Since this is a novel material, only a limited amount of material was available for testing.The foams were made by different laboratories using different precursors and processes,and had different levels of porosity. Samples identified with a letter ‘A’ were made in-house at the Air Force Research Laboratory (AFRL) using a patented process [13]. Sincethe foam specimen made in-house was too small for the guarded hot plate, three more setsof specimen were obtained from commercial manufacturers. A number of foam blockswere obtained from Touchstone Research Laboratory (Triadelphia, WV). This foam ismade from a coal-derived precursor. Each of the blocks was generally uniform in density(approx. 0.23 g/cc). The third set of specimen was manufactured by MER Corporation(Tucson, Arizona); the density of this sample was also approximately 0.3 g/cc. Finally,the fourth set of samples was from POCO Graphite, Inc. (Decatur, Texas). This foam, likethe AFRL foam, is made from synthetic pitch, but it is much denser (typically >0.5 g/cc).It was determined that there was a density gradient between the top and bottom of all ofthe POCO foam blocks. This produces large differences in thermal properties betweentop and bottom of the foam block. The POCO foam is made by a proprietary processdeveloped at the Oak Ridge National Laboratory (Oak Ridge, TN) [14].

Sample preparation

Table 1 lists the different foams, the source and sample ID, density, and the thermalconductivity values for the different foams. Since some of the foams were not isotropic,all tests were conducted to determine the thermal conductivity in a specific direction. Forthe POCO foams, this is the direction of the highest conductivity. One of the sampleswas not graphitized and this is noted in the table. Samples identified with ‘f’ in the IDnumber were tested by flash diffusivity (using laser flash) with an epoxy-filled sample.Samples identified by a ‘u’ in the ID number were tested as unfilled foams with the laserflash. Samples identified by an ‘h’ were tested by the guarded hot plate apparatus and/orthe guarded heat flow meter apparatus.

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THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS 237

Table 1. Thermal conductivity test results

AverageFilled/unfilled foam density K

Source Sample ID (test method) (g/cc) (W/mk) Comments

AFRL A1f Filled foam (laser flash) 0.24 15.18TRL T1f Filled foam (laser flash) 0.30 4.51AFRL A2f Filled foam (laser flash) 0.30 0.24 NongraphitizedMER M1f Filled foam (laser flash) 0.23 22.3AFRL A1u Unfilled foam (laser flash) 0.24 17.51TRL T1u Unfilled foam (laser flash) 0.30 3.88–7.54 Large variationMER M1u Unfilled foam (laser flash) 0.23 17.6POCO P1u Unfilled foam (laser flash) 0.59 134.6 Samples from top halfPOCO P2u Unfilled foam (laser flash) 0.65 174.9 Samples from bottom halfMER M1h Filled foam (hot plate) 0.23 23.1TRL T3h Filled foam (hot plate) 0.32 4.75POCO P3h Filled foam (hot plate) 0.62 148.6 Infiltration limited to surfaces

Several identical (or nearly identical) samples were selected for testing by differentmethods: as filled foam, unfilled foam, using laser flash, and the guarded hot plate. Dueto sample geometry differences and sample machining requirements, it was not practicalto test the same sample using both methods. However, the samples for the hot plateinstrument and the laser flash were obtained from the same block of material. At leastthree samples of each type of foam were tested by laser flash, and each sample was testedat least three times. POCO foam samples were not tested as filled foam in the laser flashsince the foam was too dense for complete infiltration by epoxy.

The preferred sample thickness for the laser flash is 5 to 6 mm since the ratio ofthe sample thickness to pore size should be much greater than unity. Thinner sampleswere also tested to determine the effect of thickness on the diffusivity and conductivityresults. The maximum thickness is limited by sample properties, sample holder size ofthe laser flash, and the laser radiation geometry. Flash diffusivity samples were machinedfrom specimen blocks that were typically one-inch cubes. Two laser flash samples wereobtained from each block. To produce samples filled with epoxy, the specimen block wasfirst infiltrated under vacuum with epoxy (EPONTM 828 with JeffamineTM D230). Afterthe epoxy was cured, the composite specimen was machined to produce two samples, onefrom the top and one from the bottom. The initial and final densities were noted—thesedensities were used to determine the specific heat Cb of the epoxy filled samples.

The samples were then coated with a thin layer of graphite (from a colloidalsuspension, 204 Dry Graphite Lube, Sherwin-Williams Company, Anaheim, CA) on thetwo faces to prevent penetration of laser radiation. One of the typical curves obtainedfrom the laser flash test was described and is shown in Figure 3. This plot is similar tothe numerical simulation in Figure 2; the drop-off after the peak is due to the heat lossfrom the sample in the experiment. The laser-flash instrument approximates the heatingcurve (including the heat loss) by a theoretical curve that is shown by the dotted linein Figure 3. It can be seen that the theoretical heating curve matches the experimentalcurve quite well. A minimum of three samples were tested, and each sample was testedthree times.

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238 ALAM ET AL.

Tests on guarded hot plate and heat flow meter

Both of these instruments use a hot plate and 4-inch square samples. The sampleswere machined from 1/2- to 1-inch thick plates. Thicker samples were used for the POCOfoam (20-mm thick plates) as compared to the TRL foam (10-mm thick plates) becauseof its high conductivity. The samples were carefully insulated to reduce heat loss to thesides. The specimen blocks were infiltrated with epoxy and then the 4′′ × 4′′ sampleswere machined from the blocks. All measurements with the hot plate systems are averagevalues for two samples. Because of variation of foam properties between two blocks ofsamples, and variation within the same block of materials, it was not possible to comparemultiple samples. It should be noted that the hot plate requires two samples, and the resultof the test gives the average value of the two samples.

As noted in Table 1, a sample of foam that had not been graphitized (T2f) wasalso tested for purposes of comparison.

The results are summarized below for the different types of carbon foams:

1. TRL carbon foam samples. These samples were generally quite uniform indensity, pore size, and pore shape as long as the sample size was significantlybigger than the pore sizes. Density and property variation between bulk sampleswere less than 4%.

The conductivity of the epoxy-filled samples varied from 4.34 to 4.77W/mK as measured by the laser flash instrument. The average value of 4.52W/mK compares quite well to the average value of 4.75 W/mK as measuredby the guarded hot plate (samples T4h). It should be noted that the guardedhot plate samples were slightly denser, so a higher conductivity value for thehot plate samples is to be expected. Therefore, it appears that these filled foamsamples can be used to determine the thermal conductivity of foams by flashdiffusivity and hot plate method.

The TRL samples (T1u), which were not filled by epoxy, did not produceconsistent results when tested by laser flash. The thermal conductivity resultsranged from 3.88 to 7.54 W/mK. This is probably due to the large pore sizeof the foam that makes it likely that the laser energy penetrated the foam to asignificant extent. For reasons stated earlier, it is difficult to measure these barefoam samples by guarded hot plate method.

2. POCO foam. The POCO samples are known to be much more graphitic than theother samples, and that property in combination with the high density resultedin very high thermal conductivity in these samples [1]. The average conductivitywas 154.76 W/mK by laser flash, and 148.62 W/mK by the guarded hot plate. Itshould be noted that the POCO samples were observed to have large differencesin the thermal conductivity along the vertical direction due to a different degreeof graphitization as well as density differences. The density differences fromtop to bottom were of the order of 10%, with lowest density at the top. Theconductivity difference from top to bottom was about 25% (134 vs. 174 W/mK);this is a very large difference within 1 inch of height. The gradient of densityand conductivity in the vertical direction was consistently seen in several othersamples and is due to the process by which the foam is synthesized [14].

It should be noted that the hot plate method is not appropriate for highconductivity materials, therefore this measurement may have significant errors.

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THERMAL CONDUCTIVITY OF GRAPHITIC CARBON FOAMS 239

However, the instrument used in this study was instrumented carefully to pro-duce accurate results even with high conductivity materials. Moreover, the con-ductivity of the POCO foam was independently confirmed by measurementscarried out at Oak Ridge National Laboratory (ORNL). The laser flash samplesof POCO foam did not require infiltration by epoxy because the foam is verydense. For the hot plate, the samples were subjected to the epoxy infiltrationprocess; only 3 to 4 mm of surface layers was filled by epoxy due to the highdensity of the foam. However, the hot plate measurement is not sensitive to thedegree of infiltration as shown by Eqs. (6) and (7).

3. MER samples. The epoxy-filled samples identified as M1f and M1h producedcomparable results by laser flash and guarded hot plate and heat flow meter. Thedifference between the laser flash and guarded heat flux meter measurement(22.3 vs. 23.1 W/mK) was 4%. However, the unfilled MER samples (M1u)produced very different results when compared with the laser flash and guardedhot plate. This foam had pore size of about 350 microns. It is very much possiblethat the sample thickness for highly porous foam with large pores needs to begreater than the maximum possible (6 mm) in the laser flash instrument.

4. AFRL. The AFRL samples had smaller pore size (but lower density). Thisfoam is produced in very small pieces, so a hot plate sample could not beobtained. The pore size was the smallest of all the foams tested in this study.This produced a 15% higher value when measured as unfilled foam. The smallpore size makes it difficult to infiltrate this foam—this may be a reason forthe discrepancy. The nongraphitized samples (T2f) exhibited very low thermalconductivity, 0.24 W/mK. The experimental value of 0.24 W/mK is close tothe value of the epoxy filler. From this experimental value and the derivationof Eq. (7) above, it can be seen that the determination of thermal conductivityusing foam-filled samples will not be valid for nongraphitic foams.

To determine the validity of using 6-mm thick samples, additional samples weremade that were thinner than 6 mm. It was observed that samples that are thinner than4 mm produced inconsistent results. The laser flash instrument used in this study is notdesigned for samples thicker than 6 mm because of increased heat losses from thickersamples. It is expected that thicker samples may provide better results; provided heatlosses to the sides can be reduced.

It can therefore be concluded that caution must be taken when measuring thermalconductivity of very low-density graphitic foams. The epoxy infiltration of the foam pro-duces composite samples that give thermal conductivity values that are very comparablein different instruments, using different measurement principles. The epoxy infiltration ofthe foam makes the foam samples much more amenable to hot plate testing by improvingthe strength and reducing errors due to penetration of foam by thermal paste.

The above results demonstrate that graphitized carbon samples have thermal con-ductivities ranging from approximately 4 to 150 W/mK. The factors that appear to de-termine the thermal conductivity are the source of the foam (precursor and process),and the relative density (or porosity) of the foam. These parameters are related to theconductivity Eq. (7) shown earlier:

Kb/Ks = (1 − P/100)1/n = R1/n

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240 ALAM ET AL.

where R is the relative density and P is the porosity (%). The pore factor ‘n’ includes theeffect of the pore geometry on the heat conduction process, however, other parametersmay influence the thermal conductivity. Recent studies have shown that the parameter‘n’ for carbon foams could be as high as 0.8 [15]. Based on this value of n = 0.8,and the bulk conductivity in Table 1, it can be estimated (from Eq. (7)) that the averageintrinsic conductivity Ks of the carbon in the graphitic foam ranges from 45 W/mK forthe TRL foam to 600 W/mK for the POCO foam. It should be noted that this estimateis an average value for the carbon in the foam; there are strong variations of thermalproperties within the foam microstructure.

CONCLUSIONS

The thermal conductivity of several different graphitic foams has been analyzed byusing different sample preparation methods and two different techniques. Based on theresults, it appears that the flash diffusivity method should be used with caution on foamssince the results may not be accurate when the pore size is large and/or the densityof the foam is very low. The accuracy probably can be improved by using a thickerspecimen with careful insulation of the sample from heat loss through the sides. Therequirement of a thicker sample may be problematic for commercial instruments withlimited sample thickness. The low-density foams were tested in the laser flash as filledfoams, after infiltration with a low conductivity material, and the results were comparableto the results obtained from hot plate and hot disk analyzer measurements. High-densityfoams are difficult to infiltrate and therefore they should be tested as unfilled foam in theflash diffusivity instrument.

The filled foams were very suitable for testing in a hot plate system because itproduced a smooth, solid interface in the hot plate system. The graphitic foams (withconductivity much greater than the polymer conductivity) can be tested with full orpartial infiltration by polymer since the filler does not affect the bulk conductivity of theoriginal foam. The results also demonstrate that graphitic foams have a wide range ofthermal conductivity due to differences in precursor, processing method, heat treatment,and degree of porosity.

REFERENCES

1. J. W. Klett and T. D Burchell, High Thermal Conductivity, Mesophase Pitch-Derived CarbonFoam, Eurocarbon 98: Science and Technology of Carbon, Published by French Carbon Group,Strasbourg, France, July 5–9, 1998.

2. D. P. Anderson, K. M. Kearns, J. W. Klett, and A. K. Roy, Microcellular Graphitic Car-bon Foams for Next Generation Structures and Thermal Management, IEEE 2000 AerospaceConference Proceedings, Big Sky MT, 2000.

3. ASTM International, E1461-01 Standard Test Method for Thermal Diffusivity of Solids by theFlash Method, Book of Standards, vol. 14.02, 2003.

4. ASTM International, C177-97 Standard Test Method for Steady-State Heat Flux Measurementsand Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus, Book ofStandards, vol. 04.06, 2003.

5. ASTM International, E1530-99 Standard Test Method for Evaluating the Resistance to ThermalTransmission of Thin Specimens of Materials by the Guarded Heat Flow Meter Technique,Book of Standards, vol. 14.02, 2003.

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6. L. R. Glicksman and M. A. Schuetz, A Basic Study of Heat Transfer through Foam Insulation,Journal of Cellular Plastics, pp. 114–121, 1984.

7. L. J. Gibson and M. F. Ashby, Cellular Solids, Cambridge University Press, 1988.8. N. C. Hilliard and A. Cunningham, Low Density Cellular Plastics, Chapman & Hall Publishers,

p. 108, London, 1994.9. T. H Bauer, A General Analytical Approach Toward the Thermal Conductivity of Porous

Media, Int. Journal of Heat and Mass Transfer, vol. 36, pp. 4181–4191, 1993.10. R. D. Cowan, Pulse method of determining thermal diffusivity, Journal of Applied Physics,

vol. 34(4), p. 1679, 1961.11. J. A. Koski, Improved Data Reduction Methods for Laser Pulse Diffusivity Determination with

the Use of Minicomputers, Proc. of the Eighth Symposium on Thermophysical Properties, vol.II, pp. 94–103, 1981.

12. L. M. Clark and R. E. Taylor, Radiation Loss in the Flash Method for Thermal Diffusivity,Journal of Applied Physics, vol. 46, p. 714, 1975.

13. K. Kearns, Process for preparing pitch foams, US Patent #US5868974, 1999.14. J. W. Klett, R. Hardy, E. Romine, C. Walls, and T. D. Burchell, High Thermal-Conductivity

Mesophase Pitch-Derived Carbon Foams: Effect of Precursor on Structure and Properties,Carbon, vol. 38(7), pp. 953–973, 2000.

15. A. M. Druma, M. K. Alam, and C. Druma, Numerical Analysis of Conduction in a Foam,Proc. of IMECE2002, ASME International Mechanical Engineering Congress & Exposition,November 17–22, New Orleans, Louisiana (IMECE2002-33923), 2002.

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