Conductivity variation induced by solvent swelling of an elastomer–carbon black–graphite...

Conductivity Variation Induced by Solvent Swellingof an Elastomer–Carbon Black–Graphite Composite

ALFREDO MARQUEZ, JORGE URIBE, RICARDO CRUZ

Centro de Investigacion CientıB fica de Yucatan, Km. 7 ant. carr. a Progreso, A.P. 87, Cordemex, C.P. 97310,Merida, Yucatan, Mexico

Received 17 November 1995; accepted 2 June 1997

ABSTRACT: The behavior of a polybutadiene–carbon black composite entering into con-tact with organic solvents and gasoline was investigated. The composite used has aconductivity of 3.0 { 0.1 V01 cm01 . However, if it comes into contact with organicsolvents (gasoline, for instance) the matrix absorbs them and consequently swells. Thisswelling causes the separation of the carbon particles and the concomitant diminutionof the composite conductivity. During the tests performed, the resistivity of the compos-ite grows exponentially with the exposure time to solvents. Typically, the materialsamples show a reduction of approximately 30% of its initial conductivity after only1.5 min of exposure to solvents. Also, it was observed that the rate at which theconductivity decreases is related to the chemical nature of the solvent used in the test.To model the drop on composite conductivity induced by solvent swelling we use aneffective media percolation approach. This approach was adapted to the needs of ourexperiments by modifying the definition of one of its main parameters (the criticalvolume of the low-conductivity fraction). The experimental data were successfully de-scribed by this model. Finally, the test performed shows that this composite is a verypromising material that can be employed, for example, in various security and controldevices to warning of accidental organic solvent or hydrocarbon leaks in pipelines orcontainers of chemical industries and refineries. q 1997 John Wiley & Sons, Inc. J ApplPolym Sci 66: 2221–2232, 1997

Key words: electric; polymeric; composite; swelling; solvents

INTRODUCTION ones, it is possible to design and produce sensorscapable of detecting leakages of organic solventsor gasolines. These sensors can be employed inLittle attention has been paid in the literaturevarious security and control devices for pipelinesto the effect of organic solvents on the electricalor containers in industrial plants, refineries, orproperties of polymeric conductive composites.gas stations.3–6 Indeed, it is possible to design anFor example, after an extensive bibliographicelectric conductive composite that would be sensi-search,1–101 we found just two scientific papers,1,2

tive to organic solvents.some patents,3–6 and one thesis85 on the topic.Polymers and organic solvents are usually ex-Nevertheless, it is important to stress that using

cellent electrical insulators; however, it is possiblepolymer composites, especially the elastomericto make up polymer composites with a relativelygood electrical conductivity by adding conductive

Correspondence to: A. Marquez. particles to the polymer at concentrations aboveContract grant sponsor: CONACyT; contract grant num- a threshold called ‘‘the electrical percolation con-

ber: G500–55/95.centration.’’ On the other hand, for each organic

Journal of Applied Polymer Science, Vol. 66, 2221–2232 (1997)q 1997 John Wiley & Sons, Inc. CCC 0021-8995/97/122221-12 solvent used in the industry there is at least one

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8ED3 4993/ 8ED3$$4993 10-20-97 15:39:23 polaa W: Poly Applied

2222 MARQUEZ, URIBE, AND CRUZ

Table I Matrix Characteristicspolymer capable of absorbing it by a dissolutionor swelling process. Hence, by choosing a polymer

Industrial Grade S200with high affinity for a determinate solvent, itis possible, by filling it with electrical conductive

Structure Branchedparticles, to make up a composite that changes itsMicrostructure (w/w %):electrical properties when it comes into contact Cis 1,4 44.0

with this solvent. This is possible because the Trans 1,4 47.0swelling of the matrix by the solvent causes the Vynil 1,2 9.0separation of the conductive particles into the Stabilizers (w/w %) 0.400composite, producing a decrease of its electrical Mn 344.600

Mw 494.900conductivity. This effect is produced, in a revers-Density at 257C (g/cm3) 1.01 { 0.01ible way in several composites, especially in thoseDegrading temperature (7C) 220.0 { 5.0filled with carbon black.1Melt Index (g/10 min) 0.961 { 0.01 (1907C)In our laboratory we have developed an electri-

cal conductive composite that is sensible to thepresence of organic solvents and gasolines. Thiscomposite is constituted of an elastomeric matrix effective, or large volume average, of the electricalhighly filled with two types of carbon particles: and thermal conductivities, dielectric constant,carbon-black and graphite. The carbon black im- gaseous diffusion, and magnetic permeability ofparts the main electrical characteristics of the composites. In the present work we use this lastcomposite, but also causes an important increase model to describe the variations on the compositeof its viscosity. This fact avoids the processing of conductivity induced by solvent swelling.composite by fast molding methods such as extru-sion or injection. Therefore, to diminish the com-posite viscosity, graphite was added as a lubricant EXPERIMENTALduring the shaping processes. The resulting com-posite has an acceptable conductivity (s Ç 3 V01- Materials and Processing of the Compositecm01) , and a viscosity of 3.98 1 104 Pa s (mea-sured at 1907C and a strain rate of 10 s01) . The matrix used in this work was a polybuta-

diene, industrial grade S-200, from Negromex,On the other hand, it is important to indicatethat several theories have been developed to de- Inc. Two types of conductive particles were used;

carbon-black, type Vulcan XC72, from Cabot Inc.,scribe the properties of the conductive polymericcomposites with an aleatory distribution of the and graphite, type ‘‘o’’ grade 325, from Grafito de

Mexico, Inc. The main characteristics of these ma-conducting particles. Among such theories themore important ones are: the percolation theory, terials are reported in Tables I–III.

For the present work, a composite was pre-which describes macroscopically the electricalflow through a medium haphazardly distributed7–78; pared with the following composition; 40% w/w

polybutadiene, 25% w/w carbon black, and 35%and the tunnel effect theory, which describes mi-croscopically the passage of electrons through a w/w graphite. The elaboration procedure was as

follows: first of all, the materials were dried for 1thin potential barrier, for example, the polymerlayers that cover the conducting particles in a h at 1057C. Subsequently, the polybutadiene was

dissolved in a nafta from Petroleos Mexicanos,polymer composite.7,79–83

The percolation theory describes the formation Inc., using a ratio polymer/solvent of 1 : 8 w/w.The graphite and carbon black were added to thisof a continuous path of conductive particles where

the electrons can flow. To form this path it is nec- solution using a RATIO mixer, model LPM #4,with double vertical blades. The mixing was car-essary to reach a certain concentration of conduc-

tive particles, such concentration is called ‘‘electri- ried out for 45 min at room temperature and at aspeed of 44 rpm. The slurry formed was spreadcal percolation concentration.’’ At this concentra-

tion the particles come into electrical contact and on four trays of 1.2 m2 and dried for 24 h at 807Cin a chamber with an integrated facility for thegenerate a continuous mesh. There are several

percolation models such as statistical, geometri- extraction and condensation of solvents. Once thesolvent was eliminated, the composite was takencal, thermodynamical, etc.87 However, the effec-

tive media theory8 may be the more general one. from the trays and immediately ground in a Bra-bender mill, model LS 100L1, and sieved throughThis theory was successfully used to predict the


POLYBUTADIENE–CARBON BLACK COMPOSITE AND ORGANIC SOLVENTS 2223

Table III Graphite Characteristicsa 2-mm mesh. Afterward, it was processed in alaboratory Brabender extruder, model PLE-330,

Percentwith an L/D ratio of 20. A screw with a compres-Components (w/w)sion ratio of 2/1 and a die for filaments of 2 mm

in diameter were used to extrude the composite.Carbon 96.500The process was performed at a temperature of SiO2 1.610

1807C in the barrel, and 1907C in the die. The Fe2O3 0.830screw speed was 20 rpm. A filament of 2.7{ 0.005 H2O 0.500mm in diameter was obtained. This filament was Al2O3 0.300quenched in water, at 257C, immediately after ex- Other Impurities 0.260trusion. Finally, the filament was wound up. Al-most 2000 meters of filament were produced fol-

thermocouple fixed to its surface. This thermocou-lowing the previous procedure. To perform theple was connected to a Cole-Palmer temperatureelectrical and mechanical tests, samples of 30 cmregister, model 8373–72. All the experimentsof this filament were used.were carried out at room temperature.To assess the effect of organic solvents on the

The variation of the electrical conductivity ofelectrical properties of the composite, the follow-the samples, when they come into contact withing solvents were utilised; benzene, diethyl ether,organic solvents, was evaluated in the followinghexane, tetrahydrofurane (THF), and xylene. Allway: a filament specimen was placed at the bot-these solvents were supplied by Aldrich Inc. Also,tom of a Petri dish of 15 cm in diameter. Its ex-two types of gasoline: a leaded one (Nova) andtremities were connected in a similar way as pre-an unleaded one (Magna), supplied by Petroleos viously described. The electrodes were placed outMexicanos, S.A., were used. of the dish. A voltage of 1 V was applied to thefilament and the intensity of the current flowingthrough it was registered continually. Once theElectrical Characterizationsteady state was reached, 100 mL of one of the

The conductivity of the samples was measured organic solvents was poured into the Petri dish.at different voltages (0.1–30 V) according to the The voltage was maintained at constant value andASTM B-193 method. These measurements were the reduction of the current intensity was continu-carried out with a Cole-Palmer multimeter, model ously registered. To evaluate the increase in both2030–0000, which has a facility to record the cur- length and transverse area of the sample due torent intensity continuously. The samples and the swelling, the whole sample and its central partmultimeter were connected in series to a BK Dy- were photographed every 90 s with two Nikkonnascan source of direct current, model 1650. Cy- cameras, model F-601M. One of them, providedlindrical copper electrodes of 10 mm length were with a zoom lens that was focused directly to theused to connect the samples to the circuit. Also, central part of the specimen. To calibrate the mea-to diminish the contact resistance between the sures a stainless steel scale was placed at a side ofelectrodes and the specimens they were stuck the sample during the tests. Finally, the specimenwith silver ink to the extremities of the samples. temperature was monitored in a similar way asDuring the tests, the specimen temperature was previously described.continuously monitored using a cromel-alumel The preceding procedure was repeated for each

solvent, using Petri dishes carefully cleaned andthree different filament samples. The variation ofTable II Carbon Black Characteristicsmaterial resistivity (r ) was determined from the

Vulcan XC72 current intensity ( i ) values. This determinationIndustrial Grade (Pellets) was performed taking into account the increase

in the transverse section area (a ) and length ( l )Nitrogen surface area (m2/g) 254 of the filament due to swelling, according to theParticle size (nm) 30 equation: r Å av / li , where v is the constant volt-Pore volume (dibutyl phthalate age applied.

absortion, cc/100 g) 178Pore area (m2/g) 94 Mechanical CharacterizationVolatile content (%) 1.500 Five filament samples were submitted to tensionDensity (g/dm3) 273 at a stretching rate of 10 mm/min in an Instron



Figure 2 Evolution of the resistivity with the currentFigure 1 Relation between current intensity andintensity.voltage applied.

mechanical testing machine, model 1125. Pneu- higher resistivities. The evolution of the resisti-matic clamps were used to hold the specimens. vity with both current intensity and voltage in theThe Young’s modulus was measured using a specimens is illustrated in Figures 2 and 3. Thestrain gage extensiometer, model 2630–002 ac- composite resistivity stays practically constant upcording to the ASTM-D638 method. The large to a voltage of approximately 5 V, correspondingstrains were evaluated by measuring the distance to a current intensity of roughly 50 mA; increas-between two point marks drawn on the samples ing, however, with higher voltages. This resisti-with an initial separation of 10 mm. The instanta- vity increase is due to the self-heating of the mate-neous distance between the marks was measuredby photographic means, according to the methoddescribed by G’sell84 and Uribe.85

RESULTS

The measured resistivity of the composite was of0.33 { 0.01 V cm, at 25 { 1.07C (using a voltageof 1.0 V during the measure). This value is ingood agreement with the carbon-black supplierstandards.86 It must be mentioned, however, thatthe resistivity of the polymer composites couldvary with the value of the voltage used.9,87–89 In-deed, Figure 1 shows the relation between thecurrent intensity and the voltage applied. We canobserve that at low voltages, less than 5 volts, alinear relationship between the current intensityand voltage is established. The slope in this rangecorresponds to a resistivity of approximately 0.33{ 0.01 V cm, or to a conductivity of roughly 3.0V01 cm01 . However, at higher voltages another Figure 3 Evolution of the resistivity with the voltage

applied.relationship is established corresponding to



Figure 5 Normalized values of the current intensityFigure 4 Increase of the resistivity due to self-heat-through the samples versus the exposure time to sol-ing of the material by Joule’s effect.vents.

rial produced by Joule’s effect. Indeed, as shown ations on the composite electrical properties. As ain Figure 4, the self-heating produced by current result, at room conditions, a temperature increaseintensities higher than 50 mA causes a consider- causes a net augmentation of the composite re-able temperature rise, which produces the resisti- sistivity.83,92,93 Concerning our experiments, wevity increase. Concerning this phenomenon, it avoid the previous resistivity variation by fixingmust be mentioned that a temperature increase a voltage of 1 V to perform all the subsequenthas a dual effect on the resistivity of the carbon– tests.polymer composites. On one hand, a temperature Figures 5 and 6 show the normalized values ofrise favors the electron transport through thepolymer layers by tunneling,79,82,83 because itmagnifies the thermal fluctuations. These fluctu-ations lower the potential barrier established bythe polymer between carbon aggregates. This phe-nomenon promotes the decrease of the compositeresistivity79,83 because the electrons also can betransported through some zones of the matrix andnot only through the percolative mats. It must bementioned, however, that the previous effect isvery significant at temperatures close to 0 K, butat higher temperatures it becomes much less im-portant. On the other hand, as the thermal expan-sion coefficient of the polybutadiene is almost 10times greater than that of carbon particles,90,91 atemperature rise produces an increase of the gapwidth between these particles that hinders thetunnel effect, and even could disconnect some ofthe particles in the percolative chains, increasingthe composite resistivity. It is apparent that thesemechanisms have opposing effects; however, atroom temperature the effect of the matrix dilation Figure 6 Normalized values of the resistivity of the

samples versus the exposure time to solvents.largely surpasses the influence of thermal fluctu-



Figure 8 Relation between the current intensity dataFigure 7 Sample swelling versus the exposure timeand sample swelling.to solvents.

the previous figures, an important influence of thethe current intensity ( i / i0) through the samplessolvent nature on the relationship between theand their resistivity (r /r0) plotted vs. the expo-current intensity, or the resistivity, and swellingsure time of samples to each solvent. It is observedmust be noted. Also, it is interesting to observethat the current intensity falls while the corre-that the intensity falls and the resistivity growssponding resistivity increases with the exposurein a monotonical way until an approximately nor-time. In these figures, each datum represents themalized intensity i / i0 of 0.35, or a normalized re-average of three different samples (the error barssistivity r /r0 of 5, when a very defined inflectionwere not drawn in the figures because they over-

lap, leading to confusion; however, the experimen-tal error was lower than 5% in all the cases). Inthese figures it is observed that the diethyl etherproduces a faster decrease in current intensitythan the other solvents. In contrast, the hexaneproduces the slowest one. Also, the results showthat in contact with solvents the resistivity of thecomposite increases by roughly 30% after just 1.5min. More important, the composite conductivityis practically annulled after only 20 min.

Figure 7 shows the rate at which the samplesswell when entering in contact with each solvent.In this figure the normalized values of the samplevolume (V /V0) is plotted as a function of the expo-sure time. It is observed that THF and benzeneproduce the highest composite swelling, while theleaded gasoline and the diethyl ether caused thelowest one.

Furthermore, Figures 8 and 9 display the rela-tion between the current intensity and the resisti-vity data in function of the swelling. As expected,the current intensity falls and the resistivity Figure 9 Relation between the resistivity values and

sample swelling.grows when the swelling proceeds. However, in



point appears. This point indicates a change in tion of effective demagnetisation coefficients andthe critical volume fraction fC .the electron transport mechanisms inside the

composite. This change is mainly due to the dras- The previous equation could be solved for rM ,giving the next expression:tic diminution of the particle volume fraction into

the composite (due to the introduction of the sol-vent) that becomes closer to the percolation

rM Å H0 12 fC

( (a 0 b ) fthreshold.87 Or, in other words, it is due to theseparation of the particle clusters by the solvent,thus disconnecting the percolation networks. It is

/ b 0√gf 2 / df / 1 )J0 t

(3)important, however, to mention that the previouschange could be enhanced by the appearance offlaws in the material, produced by the matrix

whereswelling, that could block the electrical flow. Forexample, it was observed that the diethyl ether

a Å r01/ tL 0 r01/ t

H fR (4)promotes the formation of fissures in the compos-ite when the matrix swells. This phenomenon pre-

b Å r01/ tH 0 r01/ t

L fR (5)vents the current flow in the filament, producing

g Å r01/ tL (r01/ t

L 0 2r01/ tH ) ( fR / 1)2 (6)a faster diminution of the current intensity and

the subsequent decrease of the overall composited Å 2r01/ t

L ( fR / 1)(r01/ tH fR / b ) (7)

conductivity.1 Å r01/ t

L fR (r01/ tL fR / 2r01/ t

H ) . (8)Finally, the results of the mechanical charac-terisation show that the samples had an averageYoung’s modulus of 124 { 3.5 MPa, an average This equation is valid for a system of only two

components. However, we can utilize it if the fol-maximum strength of 15.5 { 0.05 MPa, and anaverage strain at break of 0.265 { 0.015 (see Ta- lowing approximations are accepted: (1) As the

resistivities of polymer matrix and solvents are ofble IV). These results indicate that the materialresistance and flexibility are definitely enough to the same order of magnitude, and they are sub-

stantially different from the resistivity of the car-permit the handling of the filament and the useof it as a sensor in any standard chemical installa- bon particles, we may treat both phases (polymer

and solvent) as a unique phase. Then, using thetion.swelling data, it is possible to evaluate the instan-taneous value of the high resistivity volume frac-tion f . (2) Also, we may impose to this phase anANALYSIS AND DISCUSSIONarbitrary high resistivity value (rH Å 1 1 1016 Vcm), which is in the order of magnitude of theAs previously mentioned, in the present work wereal values. This last assumption can be made,use the generalized effective media (GEM) equa-because if we use, in the interval studied, thetion proposed by McLachlang8 to model the influ-value of the polymer resistivity or that of the sol-ence of swelling on the composite resistivity. Thisvent to evaluate the result of expression (1), theequation relates the medium resistivity to the re-resulting composite conductivity differs in lesssistivities and volume fractions of its componentsthan a 10015%. (3) Similarly, we have utilized asby the following expression:the low resistivity value rL , the value that pre-dicts correctly the experimental resistivity of thef (r01/ t

H 0 r01/ tM )

r01/ tH / fRr

01/ tH

/ (1 0 f ) (r01/ tL 0 r01/ t

M )r01/ t

L / fRr01/ tM

Å 0 (1) composite evaluated. This value was of rL Å 81 1002 V cm. It is important to observe that thelast value is almost equal to the graphite resisti-fR Å

fC

1 0 f(2)

vity (rL Å 8.7r1002 V cm).Using the previous approximations, the GEM

equation was fitted to the experimental data. Fig-where rL , rH , and rM are the resistivities of lowand high resistivity components and the compos- ure 10 shows the theoretical prediction of the pre-

vious equation (continuous lines). We can observeite itself, respectively. As well as, f and fC are thevolume fraction and the critical volume fraction that this model predicts very satisfactorily the ex-

perimental results (points).of the high resistivity component. fR is defined byeq. (2), and t is an exponent related to a combina- In Table V the values of fC and t , for each sol-



j interfase. This coefficient is a measure of theaffinity of a substance to each phase of a compos-ite.34,100 By using this last parameter and similararguments other than Miyasaka,34,100 the nextphenomenon could be predicted:

when

vpolymer-carbon ú 1 the solvent distributeswithin the polymerphase

01 õ vpolymer-carbon ú 1 the solvent distributesat the interface

vpolymer-carbon õ 01 the solvent distributesin the carbon clusters.

The values obtained for the diffusion coeffi-cient, the molecular weight, and the wetting coef-ficient are listed in Table VI.

Furthermore, in Figures 11–13 the influenceFigure 10 Comparison between the experimental re- of the previous parameters on the critical volumesistivity values and the theoretical ones. fraction fc and the exponent t is shown. The two

first parameters (diffusion coefficient and molecu-lar weight) do not have apparent influence on thevent are reported. The first parameter, fC , variesvalues of fc and t . In contrast, the wetting coeffi-between 0.65 and 0.75, while the second one, t ,cient seems to have a definitive influence on thesevaries between 0.68 and 0.98. These values arevalues. It is apparent that when this coefficientsimilar to the equivalent parameters previouslyapproaches 01, the corresponding values of fc andcalculated in the literature.8 However, it is im-t increase.portant to observe the influence of the solvent na-

It is interesting also to note that, even thoughture on the value of these parameters. This ques-all the vpolymer-carbon values are inferior to01, whention could have several answers. First of all, theit approaches 01, there is a possibility that a sol-solvents utilized have different molecular sizesvent fraction would be placed at the interface be-and diffusion coefficients. Therefore, its concen-tween carbon clusters and matrix instead of justtration profiles through the transverse section ofin the matrix. It is important to note that, in ourthe filament must be unequal, producing a dis-experiments, a high value of fc means that an ad-tinct swelling behavior in the bulk rather than onditional volume of absorbed solvent is necessarythe skin of the filaments. It is also possible thatto reach the percolation threshold (see Fig. 10).solvents would be heterogeneously distributed inThen, it seems reasonable to consider that thethe composite. Indeed, some solvents could be ex-solvent fraction placed at the interface exerts aclusively concentrated in the matrix, while otherssmaller influence on the resistivity increase thancould be located in the matrix and in the interfacethe solvent fraction concentrated in the matrix.between the particle clusters and matrix, or evenThis could be explained by considering that theat the interior of the clusters. To have an idea ofsolvent in the interface exerts a pressure on thethe importance of the previous factors, the diffu-percolation chains but do not separate them. Insion coefficient of solvents in the composite hascontrast, the solvent concentrated exclusively inbeen evaluated following the method described bythe matrix separates these chains in a more effec-Crank.77 The solvent molecular weight was ob-

tained from tables,101 and a wetting coefficientdefined by eq. (9) has been evaluated. Table IV Mechanical Properties of the

Compositevpolymer-carbon Å (gsolvent-carbon 0 gsolvent-polymer) /

Young modulus (MPa) 123.98 { 3.50gpolymer-carbon (9)

Maximum strength (MPa) 15.5 { 0.05Strain at break (%) 30.0 { 2.0where gi– j is the interfacial free energy of the i–



Table V fc , fc , and t Values Obtained from the Fit of the McLachlangEquation to the r Versus f Curves

Solvent fc fc t

THF 0.748 0.252 0.938Hexane 0.686 0.314 0.762Benzene 0.723 0.277 0.851Xylene 0.728 0.272 0.982Diethyl ether 0.654 0.346 0.687Leaded gasoline 0.681 0.319 0.919Unleaded gasoline 0.711 0.673 0.807

tive way. On the other hand, as previously men- graphite particles, in a specific proportion,tioned, some solvents (as, e.g., the diethyl ether) through a mixing process in solution followed bypromotes the formation of fissures in the matrix the extrusion of the material. The conductivity ofleading to a disconnection of several sections of the composite obtained, in the form of filaments,the filament. Then this phenomenon could dimin- was 3.0 { 0.1 (V01 cm01) . It has been observed,ish the volume fraction of solvent needed to reach however, that this conductivity depends on thethe percolation threshold. However, it is evidently voltage applied. This variation is not significantnecessary to perform a more detailed study to elu- for voltages that produce current intensities lowercidate the previous behavior. than 50 mA; nevertheless, when higher intensi-

Finally, it is important to stress that the com- ties are produced the conductivity falls as muchposite obtained is a very promising material that as 30%. This fall is due to the increase in tempera-can be utilized in several applications. For exam- ture produced by Joule’s effect. Indeed, this tem-ple, the composite filaments can be integrated in perature increase is small at current intensitiesa convenient casing into a leak detection system, lower than 50 mA.which can monitor the periphery of reservoirs and Moreover, the swelling test performed with sev-containers that stocks gasolines and organic sol- eral organic solvents shows that the electrical re-vents,4 considering that a fall of 10% in the cur- sistivity of the composite increases very fast withrent intensity is a convenient threshold to set off the exposure time, observing a reduction of 30%an alarm system when a leak is produced.1–4 We of the initial conductivity after 1.5 min, and ofcan see that these filaments, conveniently dis- 60% after 5 min, of exposure to these solvents. Toposed on the pipes and containers, need only model the previous behavior, an effective mediaabout 36 s to detect the leak. Therefore, a system percolation approach was used. This approachbased on the use of this material can be very sensi- was adapted to the needs of our experiments bytive and efficient. modifying the definition of one of its main parame-

ters (the critical volume value of the nonconduc-tive fraction). The experimental data were suc-CONCLUSIONScessfully described by this model. Also, we foundthat the effect of swelling on the composite con-A conductive composite was obtained by mixing a

polybutadiene rubber with carbon black and ducting capacity depends notably on the solvent

Table VI Values of the Diffusion Coefficient, Molecular Weight,and Wetting Coefficient Used

Diffution Coefficient Molecular WeightSolvent 1106 (cm2 s01) (mol/g) vPolymer-carbon

THF 3.799 72.000 01.520Hexane 2.841 86.000 02.460Benzene 2.671 78.000 01.260Xylene 2.673 93.000 01.320Diethyl ether 3.571 74.000 02.650



Figure 11 Influence on the solvent diffusion coeffi- Figure 13 Influence on the wetting coefficient on thecient into the samples on the critical volume fraction critical volume fraction and the exponent t values.and the exponent t values.

The authors are grateful to CONACyT for the awardnature. This behavior could be attributed mainlyof the Research Grant No. G500–551/95, to Jafet Qui-to the distinct distribution of solvents into the jano for his assistance in performing several of the

composite phases and interfaces, another possible mathematic calculations, and to Ingrid Olmsted for herorigin of this dependence is the tendency of some useful advice.solvents to promote the formation of fissures inthe matrix leading to disconnection of some sec-tions of the filament.

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