Compacted exfoliated natural graphite as heat conduction medium

Carbon 39 (2001) 2151–2161 Compacted exfoliated natural graphite as heat conduction medium M. Bonnissel a , *, L. Luo b , D. Tondeur b a b IMP, UP CNRS 8521, Universite´ de Perpignan, 52, Avenue de Villeneuve, 66860 Perpignan, France ´ Laboratoire des Sciences du Genie Chimique, LSGC, CNRS 1, rue Grandville BP 451, 54001 Nancy Cedex, France Received 20 September 2000; accepted 29 January 2001 Abstract Graphite has been used in mixtures with adsorptive or reactive material in order to manufacture compressed blocks with ` These ` de doctorat, Universite´ de Perpignan, 1999]. In the present work, the intrinsic heat conductive properties [Olives, transfer properties of recompressed exfoliated graphite have been studied. Porous graphite matrices with a bulk density of 50 to 1800 kg m 23 were fabricated by one-directional pressing of exfoliated graphite powders, in order to use them as heat conductive media. They were characterized using optical microscopy and helium pycnometry. Gas permeabilities and thermal diffusivities were measured for graphite matrices with different bulk densities. The gas permeability was in the range of 10 211 to 10 216 m 2 . Thermal conductivity values in the axial and the radial directions were in the range 3 to 9 and 3 to 350 W m 21 K 21 , respectively. A semi-empirical model was developed to correlate the heat and mass transfer properties of the material with the solid conductivities, bulk density and porosity.  2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Exfoliated graphite; D. Thermal conductivity; Thermal diffusivity; Transport properties 1. Introduction Graphite is, like diamond, an allotropic state of carbon. Covalent bonds result in carbon atoms being arranged in ˚ plane sheets according to regular hexagons with 1.42 A side length [1]. The spacing between elemental planes is ˚ because it is determined by van der larger (3.35 A), Waals-type forces. The difference between bond strength in the two directions is responsible for the anisotropic properties of the graphite, including phenomena like thermal conduction. Due to the weakness of the van der Waals-type forces, it is possible to insert various atoms or molecules between the planes [2]. Intercalation of various chemical species leads to so-called graphite intercalation compound (GIC). GIC particles are about 1 mm diameter and 0.1 mm thick and are used for their interesting electrical properties [3]. Another use of GIC is natural exfoliated graphite (NEG) *Corresponding author. Tel.: 133-4-6855-6855; fax: 133-46855-6869. E-mail address: [email protected] (M. Bonnissel). manufacturing. GIC particles are submitted to a short thermal shock, and expand to a small garland looking like an accordion as shown in Fig. 1a. The volume occupied by the garland, and thus the powder apparent density, is linked to the temperature level of the thermal shock (Table 1). The NEG type has very little influence on the thermal properties according to Han [4]. Nevertheless Coudevylle [5] notices inferior thermal transfer properties of the G38 compared to G12 and G3. On the other hand, mass transfer is better with G12 than with G3 [4,6]. Some manufacturers use compacted NEG as high temperature resistant gaskets (PapyexE or GrafoilE). The gasket density is about 1100 kg m 23 . The NEG is also used in polymeric resins in order to obtain electrical and mechanical properties (shocks and vibrations absorption) [7,8]. Because of its high porosity (around 84% at 350 kg m 23 ) as shown in Fig. 1, and its thermal properties, the NEG is used in thermochemical processes to improve thermal transfer in porous media. There are two different ways to use NEG to improve the overall thermal properties of materials: the blend method and the fin method. The blend method, developed since 1983 at IMP in Perpignan [9,10] is based on intimate mixing [5] of the 0008-6223 / 01 / $ – see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S0008-6223( 01 )00032-X 2152 M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 Nomenclature a, b, c, d, e, f cp d h ko K L, l m n P T u V x y Z Greek letters a d ´ l L m r ro r1 r2 rM rm u Subscripts c f gr m M o p s t i ' empirical constants used in Eqs. (22), (26), (30) specific heat capacity, J kg 21 K 21 diameter, m sample dimension in the compacting direction, m shape coefficient, – permeability, m 2 sample dimensions, m mass of the sample, kg empirical constant in Eq. (30), – pressure, Pa tortuosity, – gas velocity, m s 21 volume, m 3 reduced length, – abscissa, m length of the sample in the flow direction, m thermal diffusivity, m 2 s 21 deformation ratio, – porosity, – thermal conductivity, W m 21 K 21 overall anisotropy, – viscosity, Pa s density, kg m 23 uncompacted initial NEG density, kg m 23 upper density of the isotropic zone, kg m 23 upper density of the non-oriented graphite planes zone, kg m 23 maximal density of compact graphite, kg m 23 overall bulk density, kg m 23 average rotation angle, rad relative to capillary tube relative to fluid relative to graphite average, bulk maximal, at rM 5 2200 kg m 23 initial porous relative to solid overall parallel to compression direction perpendicular to compression direction NEG powder with the active product (activated carbon [11], zeolite, metallic salt [12] . . . ). The fin method is based on the use of highly conductive fins regularly spaced in the porous medium. The fins could be made of metal (copper [13,14]) or compacted NEG [15]. The main drawback of the metallic fins is their chemical sensitivity (copper) and their relatively low thermal diffusivity as compared to the thermal diffusivity of graphite. The NEG densities used in the blend method are in the range of 50 to 400 kg m 23 and in the range of 200 to 2200 kg m 23 for the fin method. The mass and heat transfer properties have been widely studied for low densities (below 400 kg m 23 ) [16–18] but the properties at higher densities are not well known. The present article presents a model of the variations of the transfer properties (thermal conductivity and permeability) with the apparent density and experimental measurements, compared to the numerical solution of the model. 2. Samples manufacturing The graphite samples are manufactured by unidirectionally compacting natural exfoliated graphite (NEG). Initial- M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 2153 pressed into consolidated porous graphite matrices. The interlocking of the particles produces a cohesive solid without a binder. For the present study, small blocks (2532535 mm) and sheets (150355 mm with various thicknesses) were manufactured. 3. Modeling The essential points in the present approach are that a density gradient exists in the sample in the direction parallel to the compression force and that the properties in the perpendicular direction are different. In the following, several densities are used: • rm is the overall bulk density of the block determined by dividing the mass of the block by its overall volume Vt m rm 5 ]. Vt (1) • rM is the maximal density of the compacted graphite. It is determined by helium pycnometry measurements of the total porous volume Vp of the block. rM is given by: m rM 5 ]]. Vt 2Vp (2) • r1 is defined as the upper limit of rm below which the material remains isotropic for heat and mass transfer. Fig. 1. NEG particle. Electronic microscopy 3150 magnification. Compacted NEG sample with density of 352 kg m 23 . Electronic microscopy 32000 magnification. ly, NEG particles are 0.25 mm in diameter and a few millimetre long cylinders as shown in Fig. 1a. The apparent density of this non-consolidated material is very low (about 1.7 kg m 23 ). Expanded graphite powder can be We can separate the compression phenomenon into two stages. For low average densities ( rm , r1 ) the compression is essentially isotropic. The local bulk density r is homogeneous and is equal to the overall bulk density rm . For higher overall bulk densities ( rm . r1 ) the local bulk density near the piston head and the bottom die is higher than in the middle of the sample as shown in Fig. 2. The Table 1 Exfoliation temperature and NEG powder densities a Temperature (8C) Apparent density (kg m 23 ) Name 300 500 600 700 800 1000 1000 1000 38 8.2 5.4 4.9 4.5 12 4 3 G38 b EG5 c EG6 c EG7 c EG8 c G12 d G4 b G3 d Non-porous graphite density: 2250 kg m 23 . IMP-CNRS. c Ref. [4]. d Le Carbone Lorraine. a b Fig. 2. Schematic representation of the compacting process with non-uniform distribution of the local density along the compacting axis. 2154 M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 reduced length x for different values of the apparent bulk density rm . Another transition value of r, designated by r2 is reached when the graphite layers begin to rearrange perpendicular to the direction of compression [12]. Below this value the orientation of the graphite layers is random and leads to isotropic properties (thermal diffusivity, thermal conductivity and permeability). Table 2 shows the qualitative variations of the sample properties with the apparent bulk density. The aim of this modeling is to describe the overall heat and mass transfer properties as a function of the overall bulk density rm , taking into account the distribution of local properties. The next section is therefore concerned with describing local values of thermal conductivity and permeability. Fig. 3. Variations of the local density (kg m 23 ) with reduced length x for different values of the overall bulk density rm , calculated from Eq. (4). vertical position is measured from the die bottom (x 5 0) to the middle of the sample (x 5 1). The reduced position x is given by: y x 5 ]. L (3) The local bulk density r in the middle of the sample (reduced position x 5 1) is assumed to remain equal to r1 . On the other hand the local bulk density near the piston head tends toward the maximal bulk density rM . The distribution of local bulk density is assumed to be described by: r 5 rms1 2 xd ( r M / r m 2 r M )21 1 r1 . (4) This expression takes into account the above constraints, but is otherwise arbitrary. Over other possibilities of representing this distribution, it has the advantage of being smooth and having only physical parameters. The choice of this expression is justified a posteriori by the final results. 23 In our experiments rM 5 2200 kg m and r1 5 50 kg 23 m . Fig. 3 shows the variations of the local density with the 3.1. Local properties 3.1.1. Local thermal conductivity The thermal conductivity of the sample depends on the porosity and the structure of the material. Many models exist for describing the apparent properties of porous media considered as binary mixtures (solid1fluid) and are reviewed for example by Kaviany [19]. We will use the Hashin and Shrinkman model (Maxwell upper bound [20,21]) because it leads to high values of the effective thermal conductivity of the porous medium. In this model the local apparent thermal conductivity of the matrix is given by: l 5 ls 3 S D ls 3´ 1 2 ] lf 1 1 ]]]]] ls 1 2 ´ 1 ]s2 1 ´d lf 4 (5) where ls is the thermal conductivity of the solid phase, lf the thermal conductivity of the fluid and ´ the matrix porosity. The thermal conductivity of graphite is much higher, above 5 W m 21 K 21 , than the thermal conductivity of the gas (0.026 W m 21 K 21 for air). Therefore Eq. (5) may be simplified to: S D ´ l 5 ls 1 2 3 ]] . 21´ (6) Table 2 Variations of the sample properties with the overall bulk density Property Density Local bulk density Compression Particle deformation Graphite layers Local thermal conductivity Global thermal conductivity , r1 Isotropic No Not oriented Isotropic Isotropic , r2 Anisotropic Yes Not oriented Isotropic Anisotropic , rM Anisotropic Yes Oriented Anisotropic Anisotropic M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 In our case the solid thermal conductivity depends on the graphite layers orientation. During compaction, the orientation of the graphite layers induces a local anisotropy. One may define a parallel and a perpendicular local thermal conductivity (relative to the direction of compression) which may be described by: r lsi 5 f lMi f(u ) 1 lM's1 2 f(u )d g ] rM (7) r ls' 5 f lMis1 2 f(u )d 1 lM' f(u ) g ] rM (8) where lMi is the limit parallel thermal conductivity and lM' the limit perpendicular thermal conductivity as r tends toward rM . These two values are unknown and are considered as parameters and must be adjusted. f(u ) is some weighting function with the following properties: • for r # r2 , f(u ) is constant and equal to 0.5 • for r $ r2 , f(u ) increases with r from 0.5 to 1. The following expressions satisfy these criteria f(u ) 5 0.5 1 f(u ) 5 ] f 1 2 cos2u g 2 for r # r2 for r $ r2 (9) where u is related to r by: p u 5] 4 r 2r . F2 2 ]] r 2r G M M 2 (10) 2155 The physical interpretation of u is the average angle of the graphite planes with the direction of compression. It can be verified that for r 5 r2 the value of u is p / 4, that is the average random value of this angle, and for r 5 rM , at maximal compression, u 5 p / 2, that is, all the graphite layers are oriented perpendicular to the direction of compression. Eqs. (7)–(10) are the basic elements of the present original model. The thermal diffusivity is defined by: l a 5] rcp (11) where c p is the specific heat capacity of the graphite. Eq. (6) allows to evaluate the parallel and perpendicular thermal conductivity of the material using lsi and ls' for ls . 3.1.2. Local permeability As in the Carman–Kozeny model [22], the graphite matrix porosity is supposed to be composed of a bundle of capillary tubes of effective length Lc . Z where Z is the thickness of the medium in the direction of flow. The Hagen–Poiseuille relationship gives a relation between the local fluid velocity u c (velocity in pore) and the pressure drop across the pore (see Fig. 4 for definition of geometric quantities): DP 32k o mf u c ]f 5 ]]] Lc d 2c Fig. 4. Elementary model of porosity. Circular pore of length Lc and diameter d c in the parallel direction. (12) M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 2156 where k o is a shape coefficient for non circular tubes (k o 5 1 for a circular tube). The Darcy law links the filtration velocity u (evaluated without porous medium) to the pressure drop relative to the medium thickness Z: K DPf u5] ] mf Z (13) where K is the permeability. The average pore velocity u c and the filtration velocity u are related by: u Lc u c 5 ] ]. ´ Z (14) Defining the tortuosity as T 5 Lc /Z and eliminating the velocity in Eq. (12) with Eqs. (13) and (14), we obtain the following expression of the matrix permeability K: ´d 2c K 5 ]]2 . 32k o T (15) Using the porosity definition: r ´512] rM (16) we have, with k o 5 1 (circular tubes): S r 1 K5] 12] 32 rM D S]dT D . 2 c (17) This establishes a general relation between permeability and pore morphology. We shall next establish relations between this morphology and the local density. 3.1.3. Permeability in parallel direction Let us consider a small volume of non-porous graphite around a circular pore of length Lc as shown in Fig. 4. During the compression the volume of the graphite crystals, Vgr , remains constant, and the diameter and the length of the pore change. Here, the tortuosity T is equal to Lc /L. The solid volume is given by: S D 2 p d c2 T dc Vgr 5 Ll 2 2 p ] Lc 5 Ll 2 1 2 ]] . 4 4l 2 l 1 ]. D] 8p T 2 2 (21) 3 The permeability is proportional to the square of the porosity and inversely proportional to the cube of the tortuosity. Assuming a linear variation of the tortuosity with the bulk density we obtain: S S D D r 2 12] rM l2 Ki 5 ] ]]]] 3 r 8p c ]1d rM (22) where c and d are empirical constants. 3.1.4. Permeability in the perpendicular direction Let us consider a small volume of non porous graphite around a circular pore of length Lc as shown in Fig. 5. During the compression, the graphite volume remains constant, and the pore diameter decreases. The real crosssection varies with the compression but we use an equivalent circular pore. The tortuosity is defined in this case by T 5 Lc /l. The solid volume is given by: S D d 2c p d 2c T Vgr 5 Ll 2 2 p ] Lc 5 Ll 2 1 2 ]] . 4 4Ll (23) Combining Eqs. (19) and (23), and assuming that the total graphite mass and the length l remain constant we get instead of Eq. (20): 2 pd c T r ] 5 1 2 ]] . rM 4Ll (24) Combining with Eq. (17) we obtain: Ll 1 ] S D] 8p T r L l 1 r 5S1 2 ]D ] ] ]. r r 8p T r K' 5 1 2 ] rM 2 3 2 M M 3 (25) M Assuming a linear variation of the tortuosity with the bulk density we get: r 1 2 ]D L l r S r 5 ] ] ]]]] r 2p r 1 fD Se] r 2 (19) K' where LM is the minimal thickness of the block when r 5 rM . Combining Eqs. (18) and (19), and assuming that the total graphite mass and the length l remain constant we have: p d 2c T r ] 5 1 2 ]] . rM 4l 2 S r Ki 5 1 2 ] rM (18) This volume can also be calculated using the non-porous graphite density m ] 5Vgr 5 LM l 2 rM This relation allows to express the pore diameter d c as a function of the ratio r /rM . Substituting into Eq. (17) we get: M M M 3 (26) M where e and f are empirical constants. 3.2. Overall bulk properties (20) The overall bulk properties are obtained by averaging M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 2157 Fig. 5. Elementary model of porosity. Circular pore of length Lc and diameter d c in the perpendicular direction. the local property over the whole sample, that is by integrating over the sample thickness, in the direction of compression. For example, it is possible to obtain the perpendicular overall bulk permeability using: E 1 K̄' 5 K' dx (27) 0 which expresses the addition of parallel conductances. Similarly, the parallel overall bulk permeability is written: E where ro is the initial bulk density for non-compacted graphite powder, and rm the measured overall bulk density. The a zone corresponds to the particle packing phenomenon, where the graphite matrix is isotropic. In the b zone, particle deformation occurs, and the graphite matrix becomes anisotropic. d follows the empiric expression: F S ro d 5 sa ln P 1 bd n 1 1 1 ] rM DG n 1/n (30) 1 1 1 ] 5 ] dx Ki K¯ i (28) 0 which expresses the addition of conductances in series. In these integrations, K is a function of r through Eqs. (22) and (26), respectively, and r is a function of x through Eq. (4). 4. Experiments 4.1. Density variation with the applied pressure The density measurements have been made by direct geometrical measurements of the sample. The variation of the deformation ratio d with the applied pressure is shown in Fig. 6. d is given by: ro d 512] rm (29) Fig. 6. Variations of the deformation ratio with the applied pressure. The a zone corresponds to particle packing and the b zone to particle deformation. 2158 M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 with a 5 0.097; b 5 0.9; n 5 2 17; ro 5 1.7 kg m 23 and rM 5 2200 kg m 23 . Thus combining Eqs. (29) and (30) we obtain a relationship between the overall bulk density rm and the applied pressure to form the matrix. Fig. 7 shows this relationship for various values of the initial bulk density ro . 4.2. Permeability The permeability measurements have been made with a comparison of the sample permeability with tubes of known diameter and length. Permeability measurements have been performed with air flow in the parallel direction (the direction of compression). For apparent bulk densities higher than 400 kg m 23 , the graphite matrix is practically impermeable. Fig. 8 shows the variation of the permeability with the overall bulk density. The Hagen–Poiseuille relation allows to estimate an equivalent mean pore radius between 10 mm for low density and 0.05 mm for the higher density. Parameters c and d in Eq. (22) have been estimated, by least square fitting, to 485.3 and 22.61310 4 , respectively. 4.3. Thermal diffusivity Thermal diffusivity measurements have been made in the two directions with the flash method [23]. The method consists in measuring the temperature response on a face of the material to a light flash on the other face. This was done in the parallel and in the perpendicular direction. The main uncertainties are due to the manufacturing of the samples especially for the thickness. The uncertainty of 0.1 mm on the sample thickness induces an uncertainty of about 1 W m 21 K 21 . The perpendicular thermal diffusivity (3.31310 24 m 2 Fig. 7. Variations of overall bulk density (kg m 23 ) with the applied pressure (bar). Arrow indicates increasing initial bulk density (2.7, 4.7, 6.7 and 10.7 kg m 23 ). Fig. 8. Experimental variations of the parallel permeability (m 2 ) with the overall bulk density (kg m 23 ). Eq. (22) integrated by (28) for parallel permeability. s 21 at 1300 kg m 23 ) may be higher than the thermal diffusivity of metals like copper (1.14310 24 m 2 s 21 ) or even silver (1.74310 24 m 2 s 21 ) as shown in Table 3. Fig. 9 shows the comparison with values evaluated with Eqs. (7) and (8) integrated using the analog of Eq. (27), with the following values of parameters: lM' 5 750 W m 21 K 21 , lMi 5 4.7 W m 21 K 21 and r2 5 400 kg m 23 . Fig. 9 shows the comparison for the diffusivity. The latter is in the range of common values of metals as shown in Table 4. 4.4. Thermal conductivity The thermal conductivity is deduced from the thermal diffusivity by taking a constant value of the specific heat. We have measured, with a differential calorimeter, c p 5 850 J kg 21 K 21 . Fig. 10 shows the variation of the perpendicular thermal conductivity with the overall bulk density. This conductivity increases with the bulk density to an impressive value of 350 W m 21 K 21 at 1350 kg m 23 , very close to that of copper (401 W m 21 K 21 ). We have not been able to obtain measurements of the perpendicular thermal conductivity for bulk densities above 1400 kg m 23 . Table 5 shows the variations of the thermal conductivities (parallel and perpendicular) for various bulk densities and the thermal conductivities of some common metals. Fig. 10 also shows the variation of the parallel thermal conductivity with the overall bulk density. In the first part of the curve, it increases with the bulk density, corresponding to particle packing. In the second part, it decreases slowly as the bulk density increases. In this latter domain, two opposite factors compete: firstly, the packing of particles which tends to increase the thermal conductivity; secondly, the orientation of elemental graphite M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 2159 Table 3 Perpendicular thermal diffusivity of the compacted NEG and corresponding metals diffusivity Bulk density kg m 23 Porosity – a' 10 6 m 2 s 21 Metal 10 6 m 2 s 21 200 400 800 1200 1400 1800 0.91 0.82 0.64 0.45 0.36 0.18 147 176 250 274 286 327 a Aluminum (97) Copper (117) Gold (127) Silver (174) Silicon carbide (230) Diamond IIa (1291) a Extrapolated value from model. ls' L 5 ]. lsi (31) Fig. 12 shows the variations of the anisotropy L 5 l' /li , computed using the model values, with the overall bulk density. The dotted line corresponds to the extrapolated zone above 1400 kg m 23 . 5. Conclusion 23 Fig. 9. Variation with overall bulk density (kg m ) of the perpendicular thermal diffusivity (empty circles) and parallel thermal diffusivity (full circles) (m 2 s 21 ). Experimental data and model, using Eq. (8) integrated by Eq. (28) and Eq. (7) integrated by Eq. (27). planes which tends to decrease the thermal conductivity down to the limit value lMi . Fig. 11 shows the variations of the two thermal conductivities at low values of the overall bulk density. For a bulk density lower than ro 550 kg m 23 the parallel and the perpendicular conductivity are equal: the graphite matrix is isotropic. For a density higher than ro , the two thermal conductivities diverge: the matrix becomes more and more anisotropic. The overall anisotropy is defined by the ratio of the apparent thermal conductivities: With respect to the objective of the work, namely the characterization of mass and heat transfer properties of NEG, a number of partial conclusions can be drawn, although further experimental work is needed. 1. The compacted NEG presents a high anisotropy due on the one hand to the anisotropic particle deformation and elemental graphite planes rearrangement, and on the other hand, to the uniaxial compaction inducing a nonuniform density distribution along the compaction axis. 2. The permeability of the compacted NEG is very low even though the material is very porous. The parallel permeability is in the range of 10 212 to 10 216 m 2 for a material with a porosity between 0.98 and 0.82. Even in the perpendicular direction, the permeability is relatively low. 3. Compacted NEG is a porous material with perpendicular thermal conductivity in the range of the best metallic thermal conductors (copper and aluminum). On Table 4 Parallel thermal diffusivity of the compacted NEG and corresponding metals diffusivity Bulk density kg m 23 Porosity – ai 10 6 m 2 s 21 Metal 10 6 m 2 s 21 200 400 800 1200 1400 1800 0.91 0.82 0.64 0.45 0.36 0.18 47 26 12 7.4 5.9 4.2 Zinc (41.8) Lead (24.1) Carbon steel (17.7) Stainless steel 316 (3.5) M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 2160 Fig. 10. Variation with overall bulk density (kg m 23 ) of the perpendicular thermal conductivity (empty circles) and parallel thermal conductivity (full circles) (W m 21 K 21 ). Experimental data and model, both calculated from data of Fig. 9. Table 5 Thermal conductivities of the compacted NEG and corresponding metals conductivity Bulk density kg m 23 Porosity – li W m 21 K 21 l' W m 21 K 21 Metal W m 21 K 21 200 400 800 1200 1400 1800 0.91 0.82 0.64 0.45 0.36 0.18 8 9 8 7.5 7 6.5 25 60 170 280 340 500 a Stainless steel 316 (13.4) Carbon steel (60) Magnesium (156) Aluminum (237) Copper (401) Silicon carbide (490) a Extrapolated value from model. Fig. 12. Variation of the anisotropy L with the overall bulk density (kg m 23 ). Dotted line corresponds to extrapolated values. Fig. 11. Variation with the overall bulk density (kg m 23 ) of the thermal conductivities (W m 21 K 21 ) at low bulk density. Experimental data. Isotropic and anisotropic zones. the other hand, the parallel conductivity is much lower than that of pure metals, but comparable to that of metallic alloys. Besides, the perpendicular thermal M. Bonnissel et al. / Carbon 39 (2001) 2151 – 2161 conductivity is from one to two decades higher than the parallel conductivity. 4. Due to its low density, the perpendicular thermal diffusivity of the compacted NEG is higher than that of metals. In the parallel direction, the thermal diffusivity is similar to that of common metals. These properties may lead to interesting practical applications. For example, in what we have called the fin method, it can be seen that fins made of highly compressed NEG have properties comparable to the best conductive metals in terms of conductivity. But perhaps the most interesting aspect concerns the high thermal diffusivity related to a low r c p ; this property is of interest in all transient operations where low inertia is desirable, such as chemical heat-pumps [12], and temperature-swing-adsorption [15]. In the blend method, where lower NEG are considered, the thermal diffusivities larger than that of aluminum or copper (see Table 3) illustrate the interest of using NEG in mixtures with low conducting materials, to enhance their heat conductive properties. In addition, NEG lends itself well to the manufacture of intimate mixtures with other particulate materials. References ´ ´ [1] Legendre A. Le materiau carbone: des ceramiques noires aux fibres de carbone, Eyrolles, 1992. [2] Yoshida A, Hishiyama Y, Inagaki M. Exfoliated graphite from various intercalation compounds. Carbon 1991;29(8):1227. ´ [3] Gerl M, Issi J-P. In: Physique des materiaux, Traite´ des ´ materiaux, vol. 8, Lausanne: Presses Polytechnique et Universitaires Romandes, 1997. [4] Han JH, Cho KW, Lee K-H, Kim H. Porous graphite matrix for chemical heat pumps. Carbon 1998;36(12):1801–10. ´ [5] Coudevylle O. 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