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Electrical resistivity as a tool for the characterisation of carbonaceous phases in vapour-grown carbon fibres
Composites Science and Technology 59 (1999) 1613±1623
Electrical resistivity as a tool for the characterisation of carbonaceous phases in vapour-grown carbon ®bres A. MadronÄero a,*, A. Hendry b, L. Froyen c a
Centro Nacional de Investigaciones MetaluÂrgicas, Avda. Gregorio del Amo 8, 28040 Madrid, Spain b Metallurgy and Engineering Materials Group, University of Strathclyde, UK c Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Leuven, Belgium Received 2 March 1998; received in revised form 6 October 1998; accepted 16 December 1998
Abstract By making electrical resistivity measurements as a function of diameter, it has been possible to prove that the kind of carbon ®bres grown from a gaseous stage (VGCF), possess a duplex structure. We have found that these ®bres present a catalytic phase or core, which shows a higher level of crystalline perfection than the pyrolytic or cortical phase. This is clearly revealed by the high electrical conductivity observed for thin ®bres, when compared to thick VGCF. Estimations of electrical resistivity have allowed us to establish that this physical property, for dierent sorts of VGCF, can be accurately expressed by the rule of mixtures. In the same way, we have noticed that ®bres fabricated from acetylene-containing precursor atmospheres show better electrical properties than VGCF grown from standard reactant gases. We have also observed that over-hydrogenation of VGCF, which gives rise to an improvement in mechanical properties, involves a decrease in electrical conductivity. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Electrical resistivity of VGCF; Duplex structure of VGCF; Microstructrure of carbon ®bres; Rule of mixtures; Over-hydrogenation
1. Introduction Vapour-grown carbon ®bres (VGCF), are noncontinuous ®bres, produced by an easy manufacturing process, from which are eliminated the expensive indispensable processing steps involved in the fabrication of PAN-based or pitch-based continuous carbon ®bres. In this process, metallic, iron-based catalyst particles are exposed to a carbon monoxide atmosphere or to mixtures of hydrocarbon gases, such as methane or benzene, and hydrogen at temperatures between 1050 and 1110 C. As a result, lengthening primary ®laments are produced by catalytic decomposition of carbon. At the conclusion of this lengthening process, the ®laments can be thickened by chemical vapour deposition of carbon from vapour phase in order to produce ®bres several microns in diameter. The advantages of VGCF, the technology of which is still in the developmental stage, when compared to present commercial carbon ®bres, are economic (10 U$ kg estimated cost for industrial production [1]), excellent thermal and electrical conductivity (110ÿ5 m and * Corresponding author. Fax: +34-91-534-7425. E-mail address: [email protected] (A. MadronÄero)
0.2 W/cm/K, respectively [2]) and good cost/performance ratio. Development of high strength and very high modulus (0.4±340 and 183±400 GPa, respectively, [3]) are due to the formation of a material with a highly graphitic structure. Studies related to VGCF structure [4±7] and growth [8±10], reveal that this kind of ®bre possesses a duplex grain. In fact, VGCFs are composed of two dierent structures, formed by two dierent mechanisms: a catalytic growth process causes the formation of a central ®lament or nucleus, which is subsequently covered by a cortical layer or pyrolytic phase, deposited from the thermal decomposition of carbonaceous gases present in the precursor atmosphere. Transmission electron microscopy studies [7±11], reveal the dierent structures of the two VGCF constituent phases. It is found that the catalytic phase, compared to the pyrolytic, exhibits a higher degree of crystalline perfection, re¯ected in better mechanical properties. Indeed, the physical properties of the ®bres are fully in¯uenced by the catalytic-phase/cortical-phase volume ratio, and this is the reason for the dependence of VGCF mechanical properties on diameter [12]. Another signi®cant aspect of this type of ®bre is their hydrogen content. Secondary ion mass spectroscopy
0266-3538/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0266 -3 538(99)00005 -6
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studies [13], reveal that the hydrogen content of thin VGCF (5%) is higher than that of thick ®bres (2%). These dierences in hydrogen content are another reason for the dependence of VGCF properties on thickness. One of the methods conventionally used in carbon®bre characterisation is the determination of electrical resistivity. In the case of VGCF, this technique has mainly been employed for studying the dependence of resistivity on temperature of heat-treated ®bres recrystallised at various temperatures [14]. However, the dependence of resistivity on ®bre diameter has not been taken into account. In the present work, from electrical resistivity measurements we have noticed dierent behaviour of the inner and cortical phases of various types of VGCF. We have also found a mathematical expression that accurately describes the dependence of electrical resistivity on VGCF diameter. We have therefore corroborated the in¯uence of diameter and structure on VGCF mechanical properties. 2. Experimental details Electrical resistivity measurements were performed on six dierent kinds of vapour-grown carbon ®bres, denoted as follows: (a) VGCF CH4±H2 as grown, (b) VGCF CH4-H2±10% C2H2 as grown, (c) VGCF CH4± H2 over-hydrogenated at 350 C, (d) VGCF CH4±H2 over-hydrogenated at 550 C, (e) VGCF CH4±H2 overhydrogenated at 760 C and (f) VGCF CH4±H2 previously oxidised and then over-hydrogenated at 550 C. In all cases, ®bres were fabricated in the usual way [12], i.e. by a VLS mechanism [10] from the decomposition of hydrogen±hydrocarbon mixtures, catalysed by iron particles, and at a process temperature of 1060 C. The precursor atmosphere composition in the case of VGCF CH4±H2, was 70% hydrogen±30% methane. VGCF CH4±H2±10% C2H2 were produced from mixtures of 63% hydrogen±27% methane±10% acetylene, this kind of ®bre was included in this study, since as described by MadronÄero et al. [15], they exhibit better mechanical properties and a higher level of crystalline perfection than VGCF fabricated from mixtures of hydrogen and methane as the only present hydrocarbon. Over-hydrogenated VGCF CH4±H2 were similarly produced from mixtures of 70% hydrogen±30% methane, and subsequently annealed in pure hydrogen for a period of 30 min at dierent temperatures (350, 550 and 760 C). In the evaluation of these ®bres, we tried to assess the way in which microstructural changes introduced by the over-hydrogenation aect their electrical parameters.
Choice of annealing temperatures was based in the certainty that absorption±desorption processes occur at that temperatures. Studies of hydrogen adsorption in carbon ®bres [16], show that 350 C is the lowest temperature at which loss of mass starts to be noticed. At 550 C the registered loss of mass is more pronounced, and we consider that this is due to signi®cant hydrogen desorption. In addition, related studies on ®lms of amorphous carbon a-C:H [17], show that marked absorption±desorption of hydrogen takes place, similarly to VGCF at 550 C. Finally, the last selected annealing temperature was 760 C. Nyaiesh et al. [17] detected a large energy release at that temperature which they related to structural transformation of graphitisation. Previously oxidised and then over-hydrogenated VGCF CH4±H2 were produced in the same way as VGCF CH4±H2. After being fabricated, the ®bres were oxidised by means of an air ¯ow of 20 l/min in a mue furnace with a cavity of 1 dm3, at 600 C for a period of 10 min. In this way, we intended to check whether a light activation of the ®bre surface (Fig. 1) induces higher hydrogen absorption capability, since activated surfaces are more porous. The oxidation temperature was chosen according to previous studies conducted by Smith [18], who showed that VGCF burn-o by oxidation in air starts to be noticed at about 600 C. Our intention was to produce little burn-o, thus we did not use higher oxidation temperatures. Subsequently, ®bres were annealed in hydrogen in the same way as VGCF CH4±H2 over-hydrogenated at 550 C. Electrical resistivity measurements were performed by the standard four-points technique [19]. Single ®bres were connected to four minute copper contacts, external ones were employed to apply several currents, and inner ones to read the correspondent potential. Determination of ®bre diameter, prior to the resistivity measurements, was carried out by the laser diraction technique, described by Koedam [20]. A He±Ne laser with l=632.8 nm, 0.6 mm beam diameter and only 0.5 mW power was used. 3. Experimental results Results are shown in Fig. 2 to Fig. 7. In all ®gures, electrical resistivity is represented as a function of ®bre diameter, using a group from a single batch as samples so that all specimens had identical manufacturing and thermal treatments. As can be seen, all types of VGCF shows similar resistivity dependences on diameter. The curves suggest that VGCFs are characterised by a duplex structure (core/cortical), as follows. In all cases, ®bres with very thin diameters, and therefore an insigni®cant cortical phase, present a constant resistivity value. Similarly, resistivities of thick ®bres, when the core proportion in
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the ®bre is very small, are stable, though this value is 60±90% higher than that for the core. In between both nearly constant values, there is an intermediate range of ®bre thicknesses for which the resistivity increases linearly with diameter. Comparing Figs. 2 and 3 to Figs. 4 and 7, it can be seen that for both thin and thick ®bres, the constant resistivity values are higher for over-hydrogenated ®bres than for as-grown ®bres. In the same way, comparing Figs. 4 and 5 to Fig. 7, it can be seen that prior oxidation in air encourages hydrogen absorption by the VGCF during annealing at 350 and 550 C. However, an increase in over-hydrogenation temperature up to 760 C (Fig. 6) also induces an
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improvement in hydrogen absorption, revealed by an increase in resistivity, without the necessity of previous oxidation. Finally, comparing ®bres obtained from CH4±H2 mixtures with those produced from CH4±H2±10% C2H2 atmospheres (Figs. 2 and 3) it can be seen that the only appreciable dierence is an increase in core thickness for the last case. This means that is possible to fabricate ®bres with cores of even 8 mm diameter, when ®bres are grown from precursor atmospheres containing acetylene and methane in appropriate proportion as carbon carrying gases. As VGCF possess two dissimilar phases, and as both are homogeneous, it would be expected that the electrical
Fig. 1. Surface changes induced in VGCF by oxidation in air.
Fig. 2. Electrical resistivity of VGCF CH4±H2 as grown as a function of diameter.
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Fig. 3. Electrical resistivity of VGCF CH4±H2±10% C2H2 as a function of diameter.
Fig. 4. Electrical resistivity of VGCF CH4±H2 over-hydrogenated at 350 C as a function of diameter.
resistivity of this kind of ®bre would agree with a mathematical treatment of a composite constituted by a cylinder or core (®bre) and a coating or hollow cylinder (matrix). In such an equation, the ®bre diameter must be emphasised. In the present paper, the results of experimental measurements could be draw up with a mathematical formula equivalent to a rule of mixtures in which we
consider that the current in the core and in the cortical phase are in series, not in parallel (see Appendix). Then: ÿ R 2 ÿ r2 r2 r 2 1 2 1 ÿ 2 2 1 2 2 R R R where is the electrical resistivity, 1 is the resistivity of the core, 2 is the resistivity of the cortical phase, r is the
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Fig. 5. Electrical resistivity of VGCF CH4±H2 over-hydrogenated at 550 C as a function of diameter.
Fig. 6. Electrical resistivity of VGCF CH4±H2 over-hydrogenated at 760 C as a function of diameter.
radius of the core and R is the external radius of the ®bre. In this equation the independent variable is R, whereas r is an adjustable parameter. When trying to adjust the results obtained to a mathematical expression, more than one analytical function correctly adjusting the resistivities for all range of diameters was found. As we have already established (Figs. 2 to 7) there is a nearly constant resistivity for
small and large diameters, and before adjusting the experimental results to the rule of mixtures, both stable resistivity values were determined by linear regression. The results are shown in Table 1. It is reasonable to consider that they correspond to the electrical resistivities of the core and the cortical phases, and they are thus denoted core and cortical , respectively, and are the values included in the rule of mixtures (1).
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Table 1 Stabilised resistivities, thin and thick ®bres, of dierent sorts of VGCF Sort of VGCF
core cortical (10ÿ5 .m) (10ÿ5 .m)
CH4±H2 as grown CH4±H2±10%C2H2 as grown CH4±H2 over-hydrogenated at 350 C CH4±H2 over-hydrogenated at 550 C CH4±H2 over-hydrogenated at 760 C CH4±H2 oxidised and over-hydrogenated
1.00 1.00 1.10 1.10 1.15 1.10
1.60 1.60 1.65 2.00 2.30 2.20
Once 1 and 2 were obtained for each type of VGCF, they were introduced in the rule of mixtures (1), so that the only parameter still undetermined was the radius of the core for which a better adjustment of experimental results to the rule of mixtures could be obtained. In order to determine this parameter, we performed an iterative calculation, obtaining a dierent correlation coecient for each r value. In this way, we chose the r corresponding to the best correlation coecient. Introducing it together with rcore and cortical in Eq. (1), we completed the rule of mixtures, with correlation coecients shown in Figs. 2 to 7, for each sort of VGCF.It is worth mentioning that small variations in the value of r, for all types of VGCF, lead to low regression coecients. In this way, and denoting as r the diameter of the core, we found that in the case of VGCF CH4±H2 as grown, r =5 mm; for VGCF CH4±H2±10% C2H2 as grown, r =8 mm. On the other hand, for VGCF CH4± H2 over-hydrogenated at the three dierent temperatures, and for VGCF CH4±H2 previously oxidised
and then over-hydrogenated, the core diameter was r =6 mm. It is necessary to point out that the core radius of VGCF can be increased both by adding acetylene to the precursor atmosphere or by annealing in hydrogen. It is also worth mentioning that r is the determining value in the optimisation of a productive process, since from an engineering point of view, produced ®bres should have a ext slightly higher than r . The rule of mixtures, for each type of ®bre, is ®nally expressed as follows: Electrical resistivity of CH4±H2 as grown: 2 2:5 10ÿ6 1 ÿ 2 2 R R ÿ 1:0 10ÿ5 ÿ 1:6 10ÿ5 1:6 10ÿ5 r 2
2
Resistivity of VGCF CH4±H2±10% C2H2 as grown: 2 r 2 4:0 10ÿ6 1 ÿ 2 2 R R ÿ ÿ5 ÿ5 1:0 10 ÿ 1:6 10 1:6 10ÿ5
3
Resistivity of VGCF CH4±H2 over-hydrogenated at 350 C 2 r 2 3:0 10ÿ6 1 ÿ 2 2 R R ÿ ÿ5 ÿ5 1:10 10 ÿ 1:65 10 1:65 10ÿ5
Fig. 7. Electrical resistivity of VGCF CH4±H2 previously oxidised and then over-hydrogenated as a function of diameter.
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Resistivity of VGCF CH4±H2 over-hydrogenated at 550 C 2 3:0 10ÿ6 1 ÿ 2 2 R R ÿ 1:1 10ÿ5 ÿ 2:0 10ÿ5 2:0 10ÿ5 r 2
5
Resistivity of VGCF CH4±H2 over-hydrogenated at 760 C 2 r 2 3:0 10ÿ6 1 ÿ 2 2 6 R R ÿ ÿ5 ÿ5 ÿ5 1:15 10 ÿ 2:30 10 2:30 10 Resistivity of VGCF CH4±H2 previously oxidised and then over-hydrogenated 2 r 2 3:0 10ÿ6 1 ÿ 2 2 7 R R ÿ ÿ5 ÿ5 ÿ5 1:10 10 ÿ 2:20 10 2:20 10 4. Discussion 4.1. Electrical resistivity evaluation for dierent kinds of VGCF Results obtained for all types of VGCF are summarised in Fig. 8 from Figs. 2 to 7.
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It is clear that, for each kind of ®bre, there is an optimum diameter for which the resistivity is stabilised to a minimum value. This resistivity corresponds to the core or catalytic phase, which possesses a better crystalline arrangement than the cortical or pyrolytic phase. Analysing Fig. 8, it is reasonable to think that the deposition of pyrolytic carbon takes place in an epitaxial way, so that as the thickness of the pyrolytic phase increases, the level of crystalline perfection of later layers diminishes. The electrical behaviour of VGCF, as can be seen in Fig. 8, agrees perfectly with the rule of mixtures (1), this is further evidence of the duplex nature of this kind of carbon ®bre. As shown in Fig. 8, we have determined the diameter of the core for each type of VGCF, this is the part of the ®bre with better electrical properties. The core diameter of as-grown VGCF CH4±H2 (5 mm) is lower than that of ®bres produced from precursor atmospheres with 10% acetylene (8 mm). However, since both cores possess the same level of resistivity (Table 1), similar levels of crystalline perfection are expected. Values obtained for cortical , shown in Table 1, suggest that hydrogen is entering the ®bre network structure in an interstitial way, causing an increase in electrical resistivity. In accordance with this, from Fig. 8 it can be appreciated how over-hydrogenation is responsible for resistivity increase. As can be seen, for all over-hydrogenated ®bres, the higher the annealing temperature the
Fig. 8. Electrical resistivity of dierent sorts of VGCF as a function of diameter.
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more marked the increase, corresponding to a thermally activated diusion process. Indeed, at a temperature of 350 C hydrogen absorption is rather modest, so that it slightly aects the electrical resistivity. At 550 C absorption is more signi®cant, as indicated by the marked increase in resistivity, especially for thick ®bres. Finally, at 760 C the highest hydrogen absorption is observed, since there is a marked increase in resistivity not only for thick ®bres, but also for thin ones. The resistivity of the core increases from 1.1010ÿ5 m (®bres annealed in hydrogen at 350 and 550 C), to 1.1510ÿ5 m (®bres annealed at 760 C). This important resistivity increase, a consequence of over-hydrogenation at 760 C, shows that what Nyaiesh et al. [17] identi®ed as graphitisation, even though graphitisation temperatures of pure carbon are between 1300 and 1500 C [21], can be interpreted as a high level of hydrogenation. Bearing in mind that the hydrogen content of thin VGCFs is higher than that of thick ones, it is clear that the lower resistivity exhibited by thin ®bres, when compared with thick VGCF, is fully in¯uenced by crystallinity. Therefore, the high conductivities shown by thin ®bres are due principally to their high level of crystalline perfection. Curves of resistivity against ®bre diameter have also shown that when VGCFs are annealed, their cores are enriched in hydrogen and a small increase in core diameter occurs, from 5 mm (®bres as-grown) to 6 mm (overhydrogenated). These results clarify the concept of core and cortical phases. From the point of view of crystallinity, the core is the catalytic phase, and the cortical layer is the pyrolytic phase. From the point of view of mechanical properties, the core is the phase with higher hydrogen content, and the cortical layer is the phase with lower content.
Thus, over-hydrogenation alters the ®bre properties not by a change in crystalline perfection but by hydrogen redistribution. This hydrogen enrichment and redistribution, in addition to causing a decrease in electrical conductivity, leads to an improvement in mechanical properties, as we have already demonstrated [16], owing to the fact that hydrogen occupies interstitial positions in the carbon network, acting as a hardener or stress concentrator. The same mechanism occurs in ®lms of amorphous carbon, as described by Zou et al. [22]. Regarding the case of ®bres previously oxidised and then over-hydrogenated, an increase in resistivity is observed principally for thick ®bres. This indicates that eectively surface activation (Fig. 1) gives rise to a surface stage more permeable to hydrogen. This hydrogen enrichment, is more pronounced for the pyrolytic layer than for the core, since it possesses a lower level of crystalline perfection and lower hydrogen content. The resistivities found for ®bres produced from a standard methane-hydrogen containing precursor atmosphere, from 1.010ÿ5 to 1.610ÿ5 m, are in accordance with values reported for VGCF by other groups [23]. Resistivities of over-hydrogenated ®bres, with and without previous oxidation, are higher than that of VGCF in the as-grown state. We can arm that annealing in hydrogen is an intercalation process dierent from standard ones [24], since whereas over-hydrogenation causes a decrease in conductivity, with habitual intercalations an increase in conductivity is sought. 4.2. Classi®cation of VGCFs as a function of their diameter On the basis of the behaviour shown by the electrical resistivity of these ®bres (Fig. 8) a classi®cation of
Fig. 9. Classi®cation of VGCF as a function of their diameter.
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VGCFs as a function of their diameter can be performed. We trace the curve shown in Fig. 9, where we make clear that there are three well-de®ned diameters ( ): n , f and g . For diameters higher than g resistivity is stabilised to a maximum value, the stabilisation trend starting at about f . For diameters lower than n , the stable resistivity corresponds to that of the core. In accordance with these diameters, we group the VGCFs in the four classes: very thin, thin, thick and extremely thick. As very thin VGCF, we denote ®bres with no pyrolytic phase: the electrical resistivity is constant and their diameter 4 n . It is worth remembering that n was obtained from resistivity measurements on several ®bres from the same batch. Thin VGCFs are those for which a linear resistivity increase with diameter is observed, the corresponding range of diameters being n < < f . Structurally, they present a cortical phase, not thicker than the core. Thick VGCFs are those for which the cortical phase is starting to predominate over the core. For this range of diameters, f < < g , the highest statistical dispersion in electrical measurements is observed. Finally, in the case of extremely thick VGCFs, the cortical phase predominates absolutely over the core. The corresponding range of diameters is: > g , for which resistivity is diameter independent and maximum, since we are only measuring the resistivity of pyrolytically deposited carbon, higher than that of the catalytic phase. 5. Conclusions By means of electrical resistivity measurements made as a function of diameter, it has been possible to establish that VGCF possess a duplex structure, composed of a catalytic phase, correspondent to the core of the ®bre, and a pyrolytic phase or cortical layer. The cores possess better crystalline arrangements than the pyrolytic layers, as indicated by the high electrical conductivity observed for the core by comparison with that of the cortical phase. Resistivity determinations on a batch of VGCFs, allow us to estimate the core diameter and the resistivities of each constituent phase, that is, catalytic (1 ) and pyrolytic (2 ). Where obtained 2 is always higher than 1 , since the cores possess a higher level of crystalline perfection than the cortical layers. VGCF resistivity can be interpreted with great accuracy, when manufacturing process and thermal treatment are known. With a simple measurement, by means of the curve corresponding to the particular case (Figs. 2 to 7), the values of r and R can be established, avoiding the imprecision involved in scanning electron microscopy observations. By acetylene additions to the conventional methanehydrogen containing precursor atmosphere, VGCFs
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with thicker cores can be fabricated, allowing the production of ®bres with better properties from mechanical and electrical points of view. Over-hydrogenation processes cause hydrogen enrichment in VGCFs, which becomes more marked with increasing annealing temperature, as indicated by the decrease in electrical conductivity, since hydrogen occupies interstitial positions in the carbon network. However, in accordance with technical literature, improvement in mechanical properties is achieved, since hydrogen acts as hardener. Activation of ®bres surface, performed by light oxidation in air, encourages the diusion of hydrogen, since super®cial defects permeate the external vitreous surface characteristic of VGCF. Acknowledgements The present work was carried out as an action of the Human Capital and Mobility Network ``Production and Applications of Vapour Grown and other Ceramic Fibres and Filaments'' (Contract CHRX-CT-94-0457). We thank the Commission of the European Communities for the ®nancial help to perform this study. Appendix Mathematical expressions for the resistivity or conductivity of ®brous composites have been extensively described in the literature [24]. Their conductivity is commonly described by the equation: ÿ c Vf f 1 ÿ Vf m A1 where denotes the conductivity, V the volume, and the subscripts c, f and m indicate composite, ®bre and matrix, respectively. Consequently, their resistivity must be described as: 1 1 1 ÿ Vf 1 ÿ Vf pc pf pm
A2
As we can observe, this mathematical expression is clearly dierent from the one previously used in Eq. (1). It is outlined in the technical literature how Eqs. (A1) and (A2) are veri®ed for composites of polymeric and ceramic matrices [25]. However, when conductive composites are considered this model does not agree with experimental results, for several reasons. For instance, Liebmann and Miller [26] observed that when ®bres and matrix are two dierent conductors, experimental measurements do not agree with Eq. (1). This is due to thermoelectric eects, and it is much more marked when the ®bres are very thin. Karasek and Bevk [27] demonstrated that it is necessary to substitute in Eqs. (A1) and (A2) Vf for a function of ®bre volume and of the thickness
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of the reinforcing ®bres. In other words, the resistivities of ®laments increase when their thickness decreases independently of their microstructure, as a result only of geometric factors. This increment in resistivity with decreasing ®bre diameter is very well known for carbon ®bres [28]. On the other hand, electron microscopy studies on VGCF have shown that on both sides of the catalytic±pyrolytic interphase ®bres are very dissimilar materials [29]. The aspect of the in¯uence of the thickness on the conductivity of a ®lament was established by Dingle [30], who deduced the expression: 1 1 A3 k ÿ k2 ln ÿ C 2 ln 2 1 0 4 k The parameter C is a integration constant, k is equal to 2a=l, where a is the radius of the ®bre and l the mean free path of the electron, and 0 is the conductivity of the bulk material. The validity of Eq. (A3) was proved by Dingle with measurements of capillary columns of mercury. Moreover, the incorporation of ®bres into the matrix also aects the mean free path of electrons in the matrix. This eect is dependent on the ®bre matrix interface. Thus, Roig and Schoutens [31], for instance, established the following equation: 6a2 Ck3 1 ÿ 1 ÿ p A 0
A4
where p is the re¯ectivity coecient of the interface and A is the area of an unit cell of composite. In our particular case, A would be the transverse section of a VGCF. In the case of these ®bres, the re¯ectivity can have signi®cant values on account of the presence of hollow cavities in the interface with a size of about 200 nm, as shown by TEM studies in a previous work [11]. Finally, McLachlan et al. [32] established as a general equation for the conductivity of composites the expression: ÿ A5 cn Vf fn 1 ÿ Vf mn where for each case a proper value of the exponent n brings together all particular circumstances of the composite, orientation of the ®bres, percolation level, etc. The index n has values between 1 and ÿ1, both inclusive. For the case of n=1 the conductivities of ®bres and matrix are additives, whereas for n=ÿ1, the resistivities are additives, explaining the meaning of Eq. (1). References [1] Beck S. How to apply advanced composites technology. Proceedings of the Fourth Annual Conference on Advanced Composites. ASM International Congress, Dearborn, MI, USA, 1988. p. 463±78. [2] Tibbetts GG, Endo M, Beetz Jr CP. Carbon ®bres grown from the vapor phase: a novel material. SAMPLE Journal 1986;September/October:30±5. [3] Koyama T. Formation of carbon ®bres from benzene. Carbon 1972;10:757±8.
[4] Jaeger H, Behrsing T. The dual nature of vapour-grown carbon ®bres. Composites Science and Technology 1994;51:231±42. [5] Koyama T, Endo M, Onuma Y. Carbon ®bers obtained by thermal decomposition of vaporized hydrocarbon. Japanese Journal of Applied Physics 1972;11(4):445±9. [6] Bradley JR, Chen YL, Sturner HW. The structure of carbon ®laments and associated catalytic particles formed during pyrolysis of natural gas in steel tubes. Carbon 1985;23:715±22. [7] Oberlin A, Endo M, Koyama T. Filamentous growth of carbon through benzene decomposition. Journal of Crystal Growth 1976;32:335±49. [8] Baker RTK. Catalytic growth of carbon ®laments. Carbon 1989;27:315±23. [9] Tibbetts GG. Why are carbon ®laments tubular? Journal of Crystal Growth 1984;66:632±8. [10] MadronÄero A. Possibilities for the vapour±liquid±solid model in the vapour-grown carbon ®bre growth process. Journal of Materials Science 1995;30:2061±6. [11] MadronÄero A, Ariza E, Verdu M, Brandl W, Barba C. Some geometrical microstructural aspects of vapour-grown carbon ®bres to disclose their failure mechanisms. Journal of Materials Science 1996;31:6189±93. [12] MadronÄero A, Ariza E, Verdu M. A model of duplex structure for short vapour-grown carbon ®bres. J Mater Chem 1996;6:1059±65. [13] MadronÄero A, Verdu M. Hydrogen content evaluation in vapour-grown carbon ®bres by SIMS. Carbon 1995;33:247±51. [14] Heremans J. Electrical conductivity of vapour-grown carbon ®bres. Carbon 1989;23:431±6. [15] MadronÄero A, Ariza E, Martins M, Mesa G, Froyen L. Improving vapour grown carbon ®bres strength by addition of acetylene to the precursor atmosphere. Eur J Solid State Inorg Chem 1997;34:445±56. [16] MadronÄero A, Ariza E, Verdu M. Adsorption of hydrogen in carbon ®bres made from polyacrylonitrile precursor, and vapour grown. Eur J Solid State Inorg Chem 1995;32:1115±27. [17] Nyaiesh AR, Nowak WB. Chemisorbed hydrogen on a-carbon ®lms. J Vac Sci Technol A 1983;1(2):308±12. [18] Smith GW. Oxidation resistance of pyrolytically grown carbon ®bres. Carbon 1984;22:477±9. [19] Coleman LB. Technique for conductivity measurements on single crystals of organic materials. Rev Sci Instrum 1975;46:1125±6. [20] Koedam M. Determination of small dimensions by diraction of a laser beam. Philips Technical Review 1966;7:208±10. [21] Jede R, Ganschow O, Kaiser U. In: Ion and neutral spectroscopy. New York: John Wiley & Sons, 1992. p. 156. [22] Zou JW, Reichelt K, Schmidtt K, Dischler B. The deposition and study of hard carbons ®lms. J Appl Phys 1989;65:3914±8. [23] Linconln FV. The electrical conductivity of graphite intercalated with superacid ¯uorides: experiments with antimony penta¯uoride. Journal of Materials Science 1977;12:982±6. [24] Newnham RE. Composite electroceramics. Journal of Materials Education 1985;7:601±51. [25] Bhattacharya SK, Chaklader ACD. Review of electrical conductivity in reinforced plastics. Polymer and Plastics Technology and Engineering 1982;19:21±36. [26] Liebmann WK, Miller EA. Preparation phase-boundary, and thermoelectric properties of inSb Sb eutectic alloys with ordered microstructures. J Appl Phys 1963;34(9):2653±9. [27] Karasek KR, Bevk J. Normal-state resistivity of in situ-formed ultra®ne ®lamentary Cu±Nb composites. J Appl Phys 1981;52(3):1370±5. [28] Lee SM. International encyclopedia of composites, vol. 1. New York: VCH, 1990. p. 164. [29] MadroaÄero A, Verdu M, Issi J-P, Martin J, Barba C. Study by a modi®ed scanning electron microscopie fractography of hydrogenation process in vapour grown carbon ®bres. Journal of Materials Science 1998;33:2079±85.
A. MadronÄero et al. / Composites Science and Technology 59 (1999) 1613±1623 [30] Dingle RB. The electrical conductivity of thin wires. Proceedings Royal Society of London 1949;A201:545±60. [31] Roig FS, Schoutens JE. Remarks on the use of Boltzmann's equation for electrical conductions in metal matrix and in
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situ composites. Journal of Materials Science 1986;21:2767± 70. [32] McLachlan DS, Blaszkiewicz M, Newnham RE. Electrical resistivity of composites. J Am Ceram Soc 1990;73(8):2187±203.
Electrical resistivity as a tool for the characterisation of carbonaceous phases in vapour-grown carbon ®bres A. MadronÄero a,*, A. Hendry b, L. Froyen c a
Centro Nacional de Investigaciones MetaluÂrgicas, Avda. Gregorio del Amo 8, 28040 Madrid, Spain b Metallurgy and Engineering Materials Group, University of Strathclyde, UK c Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Leuven, Belgium Received 2 March 1998; received in revised form 6 October 1998; accepted 16 December 1998
Abstract By making electrical resistivity measurements as a function of diameter, it has been possible to prove that the kind of carbon ®bres grown from a gaseous stage (VGCF), possess a duplex structure. We have found that these ®bres present a catalytic phase or core, which shows a higher level of crystalline perfection than the pyrolytic or cortical phase. This is clearly revealed by the high electrical conductivity observed for thin ®bres, when compared to thick VGCF. Estimations of electrical resistivity have allowed us to establish that this physical property, for dierent sorts of VGCF, can be accurately expressed by the rule of mixtures. In the same way, we have noticed that ®bres fabricated from acetylene-containing precursor atmospheres show better electrical properties than VGCF grown from standard reactant gases. We have also observed that over-hydrogenation of VGCF, which gives rise to an improvement in mechanical properties, involves a decrease in electrical conductivity. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Electrical resistivity of VGCF; Duplex structure of VGCF; Microstructrure of carbon ®bres; Rule of mixtures; Over-hydrogenation
1. Introduction Vapour-grown carbon ®bres (VGCF), are noncontinuous ®bres, produced by an easy manufacturing process, from which are eliminated the expensive indispensable processing steps involved in the fabrication of PAN-based or pitch-based continuous carbon ®bres. In this process, metallic, iron-based catalyst particles are exposed to a carbon monoxide atmosphere or to mixtures of hydrocarbon gases, such as methane or benzene, and hydrogen at temperatures between 1050 and 1110 C. As a result, lengthening primary ®laments are produced by catalytic decomposition of carbon. At the conclusion of this lengthening process, the ®laments can be thickened by chemical vapour deposition of carbon from vapour phase in order to produce ®bres several microns in diameter. The advantages of VGCF, the technology of which is still in the developmental stage, when compared to present commercial carbon ®bres, are economic (10 U$ kg estimated cost for industrial production [1]), excellent thermal and electrical conductivity (110ÿ5 m and * Corresponding author. Fax: +34-91-534-7425. E-mail address: [email protected] (A. MadronÄero)
0.2 W/cm/K, respectively [2]) and good cost/performance ratio. Development of high strength and very high modulus (0.4±340 and 183±400 GPa, respectively, [3]) are due to the formation of a material with a highly graphitic structure. Studies related to VGCF structure [4±7] and growth [8±10], reveal that this kind of ®bre possesses a duplex grain. In fact, VGCFs are composed of two dierent structures, formed by two dierent mechanisms: a catalytic growth process causes the formation of a central ®lament or nucleus, which is subsequently covered by a cortical layer or pyrolytic phase, deposited from the thermal decomposition of carbonaceous gases present in the precursor atmosphere. Transmission electron microscopy studies [7±11], reveal the dierent structures of the two VGCF constituent phases. It is found that the catalytic phase, compared to the pyrolytic, exhibits a higher degree of crystalline perfection, re¯ected in better mechanical properties. Indeed, the physical properties of the ®bres are fully in¯uenced by the catalytic-phase/cortical-phase volume ratio, and this is the reason for the dependence of VGCF mechanical properties on diameter [12]. Another signi®cant aspect of this type of ®bre is their hydrogen content. Secondary ion mass spectroscopy
0266-3538/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0266 -3 538(99)00005 -6
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studies [13], reveal that the hydrogen content of thin VGCF (5%) is higher than that of thick ®bres (2%). These dierences in hydrogen content are another reason for the dependence of VGCF properties on thickness. One of the methods conventionally used in carbon®bre characterisation is the determination of electrical resistivity. In the case of VGCF, this technique has mainly been employed for studying the dependence of resistivity on temperature of heat-treated ®bres recrystallised at various temperatures [14]. However, the dependence of resistivity on ®bre diameter has not been taken into account. In the present work, from electrical resistivity measurements we have noticed dierent behaviour of the inner and cortical phases of various types of VGCF. We have also found a mathematical expression that accurately describes the dependence of electrical resistivity on VGCF diameter. We have therefore corroborated the in¯uence of diameter and structure on VGCF mechanical properties. 2. Experimental details Electrical resistivity measurements were performed on six dierent kinds of vapour-grown carbon ®bres, denoted as follows: (a) VGCF CH4±H2 as grown, (b) VGCF CH4-H2±10% C2H2 as grown, (c) VGCF CH4± H2 over-hydrogenated at 350 C, (d) VGCF CH4±H2 over-hydrogenated at 550 C, (e) VGCF CH4±H2 overhydrogenated at 760 C and (f) VGCF CH4±H2 previously oxidised and then over-hydrogenated at 550 C. In all cases, ®bres were fabricated in the usual way [12], i.e. by a VLS mechanism [10] from the decomposition of hydrogen±hydrocarbon mixtures, catalysed by iron particles, and at a process temperature of 1060 C. The precursor atmosphere composition in the case of VGCF CH4±H2, was 70% hydrogen±30% methane. VGCF CH4±H2±10% C2H2 were produced from mixtures of 63% hydrogen±27% methane±10% acetylene, this kind of ®bre was included in this study, since as described by MadronÄero et al. [15], they exhibit better mechanical properties and a higher level of crystalline perfection than VGCF fabricated from mixtures of hydrogen and methane as the only present hydrocarbon. Over-hydrogenated VGCF CH4±H2 were similarly produced from mixtures of 70% hydrogen±30% methane, and subsequently annealed in pure hydrogen for a period of 30 min at dierent temperatures (350, 550 and 760 C). In the evaluation of these ®bres, we tried to assess the way in which microstructural changes introduced by the over-hydrogenation aect their electrical parameters.
Choice of annealing temperatures was based in the certainty that absorption±desorption processes occur at that temperatures. Studies of hydrogen adsorption in carbon ®bres [16], show that 350 C is the lowest temperature at which loss of mass starts to be noticed. At 550 C the registered loss of mass is more pronounced, and we consider that this is due to signi®cant hydrogen desorption. In addition, related studies on ®lms of amorphous carbon a-C:H [17], show that marked absorption±desorption of hydrogen takes place, similarly to VGCF at 550 C. Finally, the last selected annealing temperature was 760 C. Nyaiesh et al. [17] detected a large energy release at that temperature which they related to structural transformation of graphitisation. Previously oxidised and then over-hydrogenated VGCF CH4±H2 were produced in the same way as VGCF CH4±H2. After being fabricated, the ®bres were oxidised by means of an air ¯ow of 20 l/min in a mue furnace with a cavity of 1 dm3, at 600 C for a period of 10 min. In this way, we intended to check whether a light activation of the ®bre surface (Fig. 1) induces higher hydrogen absorption capability, since activated surfaces are more porous. The oxidation temperature was chosen according to previous studies conducted by Smith [18], who showed that VGCF burn-o by oxidation in air starts to be noticed at about 600 C. Our intention was to produce little burn-o, thus we did not use higher oxidation temperatures. Subsequently, ®bres were annealed in hydrogen in the same way as VGCF CH4±H2 over-hydrogenated at 550 C. Electrical resistivity measurements were performed by the standard four-points technique [19]. Single ®bres were connected to four minute copper contacts, external ones were employed to apply several currents, and inner ones to read the correspondent potential. Determination of ®bre diameter, prior to the resistivity measurements, was carried out by the laser diraction technique, described by Koedam [20]. A He±Ne laser with l=632.8 nm, 0.6 mm beam diameter and only 0.5 mW power was used. 3. Experimental results Results are shown in Fig. 2 to Fig. 7. In all ®gures, electrical resistivity is represented as a function of ®bre diameter, using a group from a single batch as samples so that all specimens had identical manufacturing and thermal treatments. As can be seen, all types of VGCF shows similar resistivity dependences on diameter. The curves suggest that VGCFs are characterised by a duplex structure (core/cortical), as follows. In all cases, ®bres with very thin diameters, and therefore an insigni®cant cortical phase, present a constant resistivity value. Similarly, resistivities of thick ®bres, when the core proportion in
A. MadronÄero et al. / Composites Science and Technology 59 (1999) 1613±1623
the ®bre is very small, are stable, though this value is 60±90% higher than that for the core. In between both nearly constant values, there is an intermediate range of ®bre thicknesses for which the resistivity increases linearly with diameter. Comparing Figs. 2 and 3 to Figs. 4 and 7, it can be seen that for both thin and thick ®bres, the constant resistivity values are higher for over-hydrogenated ®bres than for as-grown ®bres. In the same way, comparing Figs. 4 and 5 to Fig. 7, it can be seen that prior oxidation in air encourages hydrogen absorption by the VGCF during annealing at 350 and 550 C. However, an increase in over-hydrogenation temperature up to 760 C (Fig. 6) also induces an
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improvement in hydrogen absorption, revealed by an increase in resistivity, without the necessity of previous oxidation. Finally, comparing ®bres obtained from CH4±H2 mixtures with those produced from CH4±H2±10% C2H2 atmospheres (Figs. 2 and 3) it can be seen that the only appreciable dierence is an increase in core thickness for the last case. This means that is possible to fabricate ®bres with cores of even 8 mm diameter, when ®bres are grown from precursor atmospheres containing acetylene and methane in appropriate proportion as carbon carrying gases. As VGCF possess two dissimilar phases, and as both are homogeneous, it would be expected that the electrical
Fig. 1. Surface changes induced in VGCF by oxidation in air.
Fig. 2. Electrical resistivity of VGCF CH4±H2 as grown as a function of diameter.
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Fig. 3. Electrical resistivity of VGCF CH4±H2±10% C2H2 as a function of diameter.
Fig. 4. Electrical resistivity of VGCF CH4±H2 over-hydrogenated at 350 C as a function of diameter.
resistivity of this kind of ®bre would agree with a mathematical treatment of a composite constituted by a cylinder or core (®bre) and a coating or hollow cylinder (matrix). In such an equation, the ®bre diameter must be emphasised. In the present paper, the results of experimental measurements could be draw up with a mathematical formula equivalent to a rule of mixtures in which we
consider that the current in the core and in the cortical phase are in series, not in parallel (see Appendix). Then: ÿ R 2 ÿ r2 r2 r 2 1 2 1 ÿ 2 2 1 2 2 R R R where is the electrical resistivity, 1 is the resistivity of the core, 2 is the resistivity of the cortical phase, r is the
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Fig. 5. Electrical resistivity of VGCF CH4±H2 over-hydrogenated at 550 C as a function of diameter.
Fig. 6. Electrical resistivity of VGCF CH4±H2 over-hydrogenated at 760 C as a function of diameter.
radius of the core and R is the external radius of the ®bre. In this equation the independent variable is R, whereas r is an adjustable parameter. When trying to adjust the results obtained to a mathematical expression, more than one analytical function correctly adjusting the resistivities for all range of diameters was found. As we have already established (Figs. 2 to 7) there is a nearly constant resistivity for
small and large diameters, and before adjusting the experimental results to the rule of mixtures, both stable resistivity values were determined by linear regression. The results are shown in Table 1. It is reasonable to consider that they correspond to the electrical resistivities of the core and the cortical phases, and they are thus denoted core and cortical , respectively, and are the values included in the rule of mixtures (1).
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Table 1 Stabilised resistivities, thin and thick ®bres, of dierent sorts of VGCF Sort of VGCF
core cortical (10ÿ5 .m) (10ÿ5 .m)
CH4±H2 as grown CH4±H2±10%C2H2 as grown CH4±H2 over-hydrogenated at 350 C CH4±H2 over-hydrogenated at 550 C CH4±H2 over-hydrogenated at 760 C CH4±H2 oxidised and over-hydrogenated
1.00 1.00 1.10 1.10 1.15 1.10
1.60 1.60 1.65 2.00 2.30 2.20
Once 1 and 2 were obtained for each type of VGCF, they were introduced in the rule of mixtures (1), so that the only parameter still undetermined was the radius of the core for which a better adjustment of experimental results to the rule of mixtures could be obtained. In order to determine this parameter, we performed an iterative calculation, obtaining a dierent correlation coecient for each r value. In this way, we chose the r corresponding to the best correlation coecient. Introducing it together with rcore and cortical in Eq. (1), we completed the rule of mixtures, with correlation coecients shown in Figs. 2 to 7, for each sort of VGCF.It is worth mentioning that small variations in the value of r, for all types of VGCF, lead to low regression coecients. In this way, and denoting as r the diameter of the core, we found that in the case of VGCF CH4±H2 as grown, r =5 mm; for VGCF CH4±H2±10% C2H2 as grown, r =8 mm. On the other hand, for VGCF CH4± H2 over-hydrogenated at the three dierent temperatures, and for VGCF CH4±H2 previously oxidised
and then over-hydrogenated, the core diameter was r =6 mm. It is necessary to point out that the core radius of VGCF can be increased both by adding acetylene to the precursor atmosphere or by annealing in hydrogen. It is also worth mentioning that r is the determining value in the optimisation of a productive process, since from an engineering point of view, produced ®bres should have a ext slightly higher than r . The rule of mixtures, for each type of ®bre, is ®nally expressed as follows: Electrical resistivity of CH4±H2 as grown: 2 2:5 10ÿ6 1 ÿ 2 2 R R ÿ 1:0 10ÿ5 ÿ 1:6 10ÿ5 1:6 10ÿ5 r 2
2
Resistivity of VGCF CH4±H2±10% C2H2 as grown: 2 r 2 4:0 10ÿ6 1 ÿ 2 2 R R ÿ ÿ5 ÿ5 1:0 10 ÿ 1:6 10 1:6 10ÿ5
3
Resistivity of VGCF CH4±H2 over-hydrogenated at 350 C 2 r 2 3:0 10ÿ6 1 ÿ 2 2 R R ÿ ÿ5 ÿ5 1:10 10 ÿ 1:65 10 1:65 10ÿ5
Fig. 7. Electrical resistivity of VGCF CH4±H2 previously oxidised and then over-hydrogenated as a function of diameter.
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Resistivity of VGCF CH4±H2 over-hydrogenated at 550 C 2 3:0 10ÿ6 1 ÿ 2 2 R R ÿ 1:1 10ÿ5 ÿ 2:0 10ÿ5 2:0 10ÿ5 r 2
5
Resistivity of VGCF CH4±H2 over-hydrogenated at 760 C 2 r 2 3:0 10ÿ6 1 ÿ 2 2 6 R R ÿ ÿ5 ÿ5 ÿ5 1:15 10 ÿ 2:30 10 2:30 10 Resistivity of VGCF CH4±H2 previously oxidised and then over-hydrogenated 2 r 2 3:0 10ÿ6 1 ÿ 2 2 7 R R ÿ ÿ5 ÿ5 ÿ5 1:10 10 ÿ 2:20 10 2:20 10 4. Discussion 4.1. Electrical resistivity evaluation for dierent kinds of VGCF Results obtained for all types of VGCF are summarised in Fig. 8 from Figs. 2 to 7.
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It is clear that, for each kind of ®bre, there is an optimum diameter for which the resistivity is stabilised to a minimum value. This resistivity corresponds to the core or catalytic phase, which possesses a better crystalline arrangement than the cortical or pyrolytic phase. Analysing Fig. 8, it is reasonable to think that the deposition of pyrolytic carbon takes place in an epitaxial way, so that as the thickness of the pyrolytic phase increases, the level of crystalline perfection of later layers diminishes. The electrical behaviour of VGCF, as can be seen in Fig. 8, agrees perfectly with the rule of mixtures (1), this is further evidence of the duplex nature of this kind of carbon ®bre. As shown in Fig. 8, we have determined the diameter of the core for each type of VGCF, this is the part of the ®bre with better electrical properties. The core diameter of as-grown VGCF CH4±H2 (5 mm) is lower than that of ®bres produced from precursor atmospheres with 10% acetylene (8 mm). However, since both cores possess the same level of resistivity (Table 1), similar levels of crystalline perfection are expected. Values obtained for cortical , shown in Table 1, suggest that hydrogen is entering the ®bre network structure in an interstitial way, causing an increase in electrical resistivity. In accordance with this, from Fig. 8 it can be appreciated how over-hydrogenation is responsible for resistivity increase. As can be seen, for all over-hydrogenated ®bres, the higher the annealing temperature the
Fig. 8. Electrical resistivity of dierent sorts of VGCF as a function of diameter.
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more marked the increase, corresponding to a thermally activated diusion process. Indeed, at a temperature of 350 C hydrogen absorption is rather modest, so that it slightly aects the electrical resistivity. At 550 C absorption is more signi®cant, as indicated by the marked increase in resistivity, especially for thick ®bres. Finally, at 760 C the highest hydrogen absorption is observed, since there is a marked increase in resistivity not only for thick ®bres, but also for thin ones. The resistivity of the core increases from 1.1010ÿ5 m (®bres annealed in hydrogen at 350 and 550 C), to 1.1510ÿ5 m (®bres annealed at 760 C). This important resistivity increase, a consequence of over-hydrogenation at 760 C, shows that what Nyaiesh et al. [17] identi®ed as graphitisation, even though graphitisation temperatures of pure carbon are between 1300 and 1500 C [21], can be interpreted as a high level of hydrogenation. Bearing in mind that the hydrogen content of thin VGCFs is higher than that of thick ones, it is clear that the lower resistivity exhibited by thin ®bres, when compared with thick VGCF, is fully in¯uenced by crystallinity. Therefore, the high conductivities shown by thin ®bres are due principally to their high level of crystalline perfection. Curves of resistivity against ®bre diameter have also shown that when VGCFs are annealed, their cores are enriched in hydrogen and a small increase in core diameter occurs, from 5 mm (®bres as-grown) to 6 mm (overhydrogenated). These results clarify the concept of core and cortical phases. From the point of view of crystallinity, the core is the catalytic phase, and the cortical layer is the pyrolytic phase. From the point of view of mechanical properties, the core is the phase with higher hydrogen content, and the cortical layer is the phase with lower content.
Thus, over-hydrogenation alters the ®bre properties not by a change in crystalline perfection but by hydrogen redistribution. This hydrogen enrichment and redistribution, in addition to causing a decrease in electrical conductivity, leads to an improvement in mechanical properties, as we have already demonstrated [16], owing to the fact that hydrogen occupies interstitial positions in the carbon network, acting as a hardener or stress concentrator. The same mechanism occurs in ®lms of amorphous carbon, as described by Zou et al. [22]. Regarding the case of ®bres previously oxidised and then over-hydrogenated, an increase in resistivity is observed principally for thick ®bres. This indicates that eectively surface activation (Fig. 1) gives rise to a surface stage more permeable to hydrogen. This hydrogen enrichment, is more pronounced for the pyrolytic layer than for the core, since it possesses a lower level of crystalline perfection and lower hydrogen content. The resistivities found for ®bres produced from a standard methane-hydrogen containing precursor atmosphere, from 1.010ÿ5 to 1.610ÿ5 m, are in accordance with values reported for VGCF by other groups [23]. Resistivities of over-hydrogenated ®bres, with and without previous oxidation, are higher than that of VGCF in the as-grown state. We can arm that annealing in hydrogen is an intercalation process dierent from standard ones [24], since whereas over-hydrogenation causes a decrease in conductivity, with habitual intercalations an increase in conductivity is sought. 4.2. Classi®cation of VGCFs as a function of their diameter On the basis of the behaviour shown by the electrical resistivity of these ®bres (Fig. 8) a classi®cation of
Fig. 9. Classi®cation of VGCF as a function of their diameter.
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VGCFs as a function of their diameter can be performed. We trace the curve shown in Fig. 9, where we make clear that there are three well-de®ned diameters ( ): n , f and g . For diameters higher than g resistivity is stabilised to a maximum value, the stabilisation trend starting at about f . For diameters lower than n , the stable resistivity corresponds to that of the core. In accordance with these diameters, we group the VGCFs in the four classes: very thin, thin, thick and extremely thick. As very thin VGCF, we denote ®bres with no pyrolytic phase: the electrical resistivity is constant and their diameter 4 n . It is worth remembering that n was obtained from resistivity measurements on several ®bres from the same batch. Thin VGCFs are those for which a linear resistivity increase with diameter is observed, the corresponding range of diameters being n < < f . Structurally, they present a cortical phase, not thicker than the core. Thick VGCFs are those for which the cortical phase is starting to predominate over the core. For this range of diameters, f < < g , the highest statistical dispersion in electrical measurements is observed. Finally, in the case of extremely thick VGCFs, the cortical phase predominates absolutely over the core. The corresponding range of diameters is: > g , for which resistivity is diameter independent and maximum, since we are only measuring the resistivity of pyrolytically deposited carbon, higher than that of the catalytic phase. 5. Conclusions By means of electrical resistivity measurements made as a function of diameter, it has been possible to establish that VGCF possess a duplex structure, composed of a catalytic phase, correspondent to the core of the ®bre, and a pyrolytic phase or cortical layer. The cores possess better crystalline arrangements than the pyrolytic layers, as indicated by the high electrical conductivity observed for the core by comparison with that of the cortical phase. Resistivity determinations on a batch of VGCFs, allow us to estimate the core diameter and the resistivities of each constituent phase, that is, catalytic (1 ) and pyrolytic (2 ). Where obtained 2 is always higher than 1 , since the cores possess a higher level of crystalline perfection than the cortical layers. VGCF resistivity can be interpreted with great accuracy, when manufacturing process and thermal treatment are known. With a simple measurement, by means of the curve corresponding to the particular case (Figs. 2 to 7), the values of r and R can be established, avoiding the imprecision involved in scanning electron microscopy observations. By acetylene additions to the conventional methanehydrogen containing precursor atmosphere, VGCFs
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with thicker cores can be fabricated, allowing the production of ®bres with better properties from mechanical and electrical points of view. Over-hydrogenation processes cause hydrogen enrichment in VGCFs, which becomes more marked with increasing annealing temperature, as indicated by the decrease in electrical conductivity, since hydrogen occupies interstitial positions in the carbon network. However, in accordance with technical literature, improvement in mechanical properties is achieved, since hydrogen acts as hardener. Activation of ®bres surface, performed by light oxidation in air, encourages the diusion of hydrogen, since super®cial defects permeate the external vitreous surface characteristic of VGCF. Acknowledgements The present work was carried out as an action of the Human Capital and Mobility Network ``Production and Applications of Vapour Grown and other Ceramic Fibres and Filaments'' (Contract CHRX-CT-94-0457). We thank the Commission of the European Communities for the ®nancial help to perform this study. Appendix Mathematical expressions for the resistivity or conductivity of ®brous composites have been extensively described in the literature [24]. Their conductivity is commonly described by the equation: ÿ c Vf f 1 ÿ Vf m A1 where denotes the conductivity, V the volume, and the subscripts c, f and m indicate composite, ®bre and matrix, respectively. Consequently, their resistivity must be described as: 1 1 1 ÿ Vf 1 ÿ Vf pc pf pm
A2
As we can observe, this mathematical expression is clearly dierent from the one previously used in Eq. (1). It is outlined in the technical literature how Eqs. (A1) and (A2) are veri®ed for composites of polymeric and ceramic matrices [25]. However, when conductive composites are considered this model does not agree with experimental results, for several reasons. For instance, Liebmann and Miller [26] observed that when ®bres and matrix are two dierent conductors, experimental measurements do not agree with Eq. (1). This is due to thermoelectric eects, and it is much more marked when the ®bres are very thin. Karasek and Bevk [27] demonstrated that it is necessary to substitute in Eqs. (A1) and (A2) Vf for a function of ®bre volume and of the thickness
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of the reinforcing ®bres. In other words, the resistivities of ®laments increase when their thickness decreases independently of their microstructure, as a result only of geometric factors. This increment in resistivity with decreasing ®bre diameter is very well known for carbon ®bres [28]. On the other hand, electron microscopy studies on VGCF have shown that on both sides of the catalytic±pyrolytic interphase ®bres are very dissimilar materials [29]. The aspect of the in¯uence of the thickness on the conductivity of a ®lament was established by Dingle [30], who deduced the expression: 1 1 A3 k ÿ k2 ln ÿ C 2 ln 2 1 0 4 k The parameter C is a integration constant, k is equal to 2a=l, where a is the radius of the ®bre and l the mean free path of the electron, and 0 is the conductivity of the bulk material. The validity of Eq. (A3) was proved by Dingle with measurements of capillary columns of mercury. Moreover, the incorporation of ®bres into the matrix also aects the mean free path of electrons in the matrix. This eect is dependent on the ®bre matrix interface. Thus, Roig and Schoutens [31], for instance, established the following equation: 6a2 Ck3 1 ÿ 1 ÿ p A 0
A4
where p is the re¯ectivity coecient of the interface and A is the area of an unit cell of composite. In our particular case, A would be the transverse section of a VGCF. In the case of these ®bres, the re¯ectivity can have signi®cant values on account of the presence of hollow cavities in the interface with a size of about 200 nm, as shown by TEM studies in a previous work [11]. Finally, McLachlan et al. [32] established as a general equation for the conductivity of composites the expression: ÿ A5 cn Vf fn 1 ÿ Vf mn where for each case a proper value of the exponent n brings together all particular circumstances of the composite, orientation of the ®bres, percolation level, etc. The index n has values between 1 and ÿ1, both inclusive. For the case of n=1 the conductivities of ®bres and matrix are additives, whereas for n=ÿ1, the resistivities are additives, explaining the meaning of Eq. (1). References [1] Beck S. How to apply advanced composites technology. Proceedings of the Fourth Annual Conference on Advanced Composites. ASM International Congress, Dearborn, MI, USA, 1988. p. 463±78. [2] Tibbetts GG, Endo M, Beetz Jr CP. Carbon ®bres grown from the vapor phase: a novel material. SAMPLE Journal 1986;September/October:30±5. [3] Koyama T. Formation of carbon ®bres from benzene. Carbon 1972;10:757±8.
[4] Jaeger H, Behrsing T. The dual nature of vapour-grown carbon ®bres. Composites Science and Technology 1994;51:231±42. [5] Koyama T, Endo M, Onuma Y. Carbon ®bers obtained by thermal decomposition of vaporized hydrocarbon. Japanese Journal of Applied Physics 1972;11(4):445±9. [6] Bradley JR, Chen YL, Sturner HW. The structure of carbon ®laments and associated catalytic particles formed during pyrolysis of natural gas in steel tubes. Carbon 1985;23:715±22. [7] Oberlin A, Endo M, Koyama T. Filamentous growth of carbon through benzene decomposition. Journal of Crystal Growth 1976;32:335±49. [8] Baker RTK. Catalytic growth of carbon ®laments. Carbon 1989;27:315±23. [9] Tibbetts GG. Why are carbon ®laments tubular? Journal of Crystal Growth 1984;66:632±8. [10] MadronÄero A. Possibilities for the vapour±liquid±solid model in the vapour-grown carbon ®bre growth process. Journal of Materials Science 1995;30:2061±6. [11] MadronÄero A, Ariza E, Verdu M, Brandl W, Barba C. Some geometrical microstructural aspects of vapour-grown carbon ®bres to disclose their failure mechanisms. Journal of Materials Science 1996;31:6189±93. [12] MadronÄero A, Ariza E, Verdu M. A model of duplex structure for short vapour-grown carbon ®bres. J Mater Chem 1996;6:1059±65. [13] MadronÄero A, Verdu M. Hydrogen content evaluation in vapour-grown carbon ®bres by SIMS. Carbon 1995;33:247±51. [14] Heremans J. Electrical conductivity of vapour-grown carbon ®bres. Carbon 1989;23:431±6. [15] MadronÄero A, Ariza E, Martins M, Mesa G, Froyen L. Improving vapour grown carbon ®bres strength by addition of acetylene to the precursor atmosphere. Eur J Solid State Inorg Chem 1997;34:445±56. [16] MadronÄero A, Ariza E, Verdu M. Adsorption of hydrogen in carbon ®bres made from polyacrylonitrile precursor, and vapour grown. Eur J Solid State Inorg Chem 1995;32:1115±27. [17] Nyaiesh AR, Nowak WB. Chemisorbed hydrogen on a-carbon ®lms. J Vac Sci Technol A 1983;1(2):308±12. [18] Smith GW. Oxidation resistance of pyrolytically grown carbon ®bres. Carbon 1984;22:477±9. [19] Coleman LB. Technique for conductivity measurements on single crystals of organic materials. Rev Sci Instrum 1975;46:1125±6. [20] Koedam M. Determination of small dimensions by diraction of a laser beam. Philips Technical Review 1966;7:208±10. [21] Jede R, Ganschow O, Kaiser U. In: Ion and neutral spectroscopy. New York: John Wiley & Sons, 1992. p. 156. [22] Zou JW, Reichelt K, Schmidtt K, Dischler B. The deposition and study of hard carbons ®lms. J Appl Phys 1989;65:3914±8. [23] Linconln FV. The electrical conductivity of graphite intercalated with superacid ¯uorides: experiments with antimony penta¯uoride. Journal of Materials Science 1977;12:982±6. [24] Newnham RE. Composite electroceramics. Journal of Materials Education 1985;7:601±51. [25] Bhattacharya SK, Chaklader ACD. Review of electrical conductivity in reinforced plastics. Polymer and Plastics Technology and Engineering 1982;19:21±36. [26] Liebmann WK, Miller EA. Preparation phase-boundary, and thermoelectric properties of inSb Sb eutectic alloys with ordered microstructures. J Appl Phys 1963;34(9):2653±9. [27] Karasek KR, Bevk J. Normal-state resistivity of in situ-formed ultra®ne ®lamentary Cu±Nb composites. J Appl Phys 1981;52(3):1370±5. [28] Lee SM. International encyclopedia of composites, vol. 1. New York: VCH, 1990. p. 164. [29] MadroaÄero A, Verdu M, Issi J-P, Martin J, Barba C. Study by a modi®ed scanning electron microscopie fractography of hydrogenation process in vapour grown carbon ®bres. Journal of Materials Science 1998;33:2079±85.
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