EFFECT OF SOLVENT INDUCED SWELLING ON THE RESISTIVITY OF POLYBUTADIENE-CARBON BLACK-GRAPHITE COMPOSITES

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1 PM EFFECT OF OLVENT INDUCED WELLING ON THE REITIVITY OF POLYBUTADIENE-CARBON BLACK-GRAPHITE COMPOITE Antonio Carrillo, Ignacio R. Martín-Doínguez, Rigoberto Ibarra and Alredo Máruez * Centro de Investigación en Materiales Avanzados,. C. (CIMAV) Miguel de Cervantes 120, Coplejo Industrial Chihuahua Chihuahua, Chih., México. 1. Introduction Anew analysis that describes the change on electric properties o polyeric coposites, illed with conductive aggregates, during organic solvent absorption processes is introduced in the present work. Figure 1 shows a sipliied typical electric circuit arrangeent. In this coniguration, the solvent diusion process into the coposite gradually changes its electric conductivity, ollowing the solvent concentration proile along the saple radius over a period o tie. In order to odel the previous situation, the ollowing hypotheses were considered: I) olvent diusion process on the saple is one-diensional, taking place only along the radial direction (axial diusion is neglected). II) The polyer atrix and the organic solvents are dielectric aterials. III) olvents are absorbed only by the polyer atrix, and not by the IV) conductive aggregates. olvent diusion into the coposite ollows Fick s Law (this is especially true on elastoer atrix coposites and copolyers). Using those hypotheses it is possible to predict, at constant voltage, the variation o the electric current on the coposite during the solvent diusion process. First o all, Oh s Law can be written as: E I ( = da( l o (1) where I( and ( are the instantaneous electric current on the saple and local coposite resistivity. A(, and l are the transversal section, external radius and length o the saple. Finally E is the applied voltage, which reains constant. E. 1 can be noralized as: I( 2 0 = r( dr 2 I r (2) where r is the radial coordinate and variables indexed with zero represent the state o the coposite beore the solvent gets in touch with it. In order to calculate the electric resistivity, it is necessary to know its relationship with the solvent voluetric raction. This can be done by odiying a odel proposed by McLachlang [11], which describes * Corresponding author; e-ail address: alredo.aruez@ciav.edu.x 1 XIX Congreso Nacional de Políeros. ociedad Poliérica de México altillo, Coahuila. Octubre de 2006

2 PM the conductive coposite electric resistance change as a unction o its conductive and dielectric voluetric ractions. This euation, which is known as the generalized eective edia (GEM) odel, integrates two orphology paraeters: C (the critical percolative value o the conductive raction) and (an experiental exponen. Previous euation can be written as: (1 ) H ( ) ( ) H + R + L L + R where H, L and are the resistivities o the high and low resistive coponents and the coposite resistivity respectively, is the conductive raction and R is given by the ollowing expression: = 0 (3) C R = 1 (4) C It is iportant to ention that the GEM euation was deduced or a coposite o only two coponents. However, we can use it i considering the ollowing approxiation; since the polyer atrix and organic solvents are both dielectrics with a resistivity o the sae order o agnitude and substantially dierent ro that o the conductive raction, we ay treat both phases (polyer and solven as an uniue phase. Thereore, the su o the polyeric atrix raction, P, plus the solvent raction,, will be naed as the non conductive raction. This last approxiation is possible because the resistivity is one o the physical agnitudes that present the broader range o values. Indeed, the resistivity o coon organic substances varies typically between to 10 8 ohs-c, while the conductive aggregates have conductivities between 10 1 to 10 7 ohs-c. To evaluate (r, on each location as unction o tie, the ollowing relation was considered: VT 0) = 1 P = 1 P 0) V (5) = 1 P 0) [1 ] T where V T (r, is the local volue as a unction o tie. The solution o Fick euation, considering previous conditions (7), is: 2 n J 0[ rα n ]...) ax [ ] 2 exp( Dα + = (1 n= 1 α n J1 α n (6) where ax is the insaturation solvent raction, J 0 and J 1 are the irst class Bessel unctions, o zero and irst order respectively, and α n are the positive roots o J 0 [α n ]. The previous solution converges very well or ediu and large ties; however or short ties it is needed a signiicant nuber o additional ters. An alternative is to use the ollowing approxiation or short ties [16]: 2 XIX Congreso Nacional de Políeros. ociedad Poliérica de México altillo, Coahuila. Octubre de 2006

3 PM ( ) ( ) (, ) ( a t r Dt a t r r t = erc + [ r] ierc +...,) r ax (7) 2 Dt 4r r 2 Dt Using the previous euations it is possible to calculate (r,, using the value o (r, in E. 5. Finally, to evaluate the increent o the ilaent external radius the ollowing relation was deduced: 2 2 a ( = a (0) + 2 rdr (8) It is evident that it is not possible to get an explicit expression or using the previous euations, however it is possible to evaluate this paraeter eploying a nuerical ethod Results and discussion. Figure 3 shows the percolation data o both coposites. The continuous lines in this plot represent the best data itted. ubseuently concentration proiles were evaluated or six dierent solvents, as a unction o the radial coordinate at, dierent ties. Figure 3, shows the relationship between the instantaneous radii and the initial one, or a series o dierent solvents. First o all, it is interesting to observe that on the studied case the oving boundary exhibits a very large variation, as the radii increases ore than a 40%. As previously entioned, or large swelling levels the diusion coeicient ay becae concentration dependent, however the results obtained with a constant coeicient correlate satisactorily with the experientally observed data [14-15]. Figure 4 illustrates how the electric current curve alls with the solvent contact tie, or each dierent solvent. It can be noticed that, in general, the current diinishes rapidly with tie, at the exception o the irst solvent, which is in good agreeent with experiental observations [4, 7, 10, 14, 15]. As expected, the current intensity drops aster or solvents that have larger diusion coeicients on the coposite than or those that have saller ones. Moreover, it is evident that the swelling curves o Figure 6 could it in a aster curve, i one changes the contact tie ( as the abscise variable by a diensionless one as Dt/ 2. Finally, it is iportant to ention that this ethodology ay allow a ore precise sensor design, based only on easy obtainable laboratory data. 5. Conclusion A ethodology that describes the change on electric properties o polyeric coposites, during solvent diusion processes, is presented in this work. The euations that result ro this ethodology reuires siple nuerical procedures to be solved, and no nuerical instability was observed during the process. The obtained results correlate very close the available experiental data, and thereore could be very useul or cheical sensor design. 3 XIX Congreso Nacional de Políeros. ociedad Poliérica de México altillo, Coahuila. Octubre de 2006

4 PM Reerences [1] Miyazaka K, Watanabe K, Jojia E, Aida H, uita M, Ishikawa K. Electrical conductivity o carbon-polyer coposites as a unction o carbon content. J. Mat. ci. 1982;17:1610. [2] Biing-lin L. Electrically Conductive Polyer Coposites. Poly. Eng. ci. 1992;32:36. [3] Kortschot M.T, Woodhas R.T. Coputer iulation o the Electrical Conductivity o Polyer Coposites Containing Metallic Fillers, Poly. Cop. 1998;9:60. [4] Lux F. Percolation in Electrical Conductive Polyer According to a New Therodynaic Percolation Model, Poly. Eng. ci., 1993;33:334. [5] Kirkpatrick. Percolation and Conduction, Mod. Phys. Rev., 1973;45:574. [6] Beugtsson P, Kubát J. Electrical Noise Characteristics o Carbon Black-Filled Linear Low Density Polyethylene Near to The Percolation Threshold, Poly. Eng. ci., 1993;33:573. [7] Narkis M, Ra A, tein Z. Electrical Properties o Carbon Black Filled Crosslinked Polyethylene, Poly. Eng. ci. 1981;21:1049. [8] heran R.D, Middlean L.M, Jacobs M. Electron Transport Processes in Conductor-Filled Polyers, Poly. Eng. ci. 1983;23:36. [9] Yacubowicz J, Narkis M. Dielectric Behavior o Carbon Black Filled Polyer Coposites, Poly. Eng. ci. 1986;26:1568. [10] Hsu W.Y, Holtie W.G, Barkley J.R. Percolation Phenoena in Polyer/Carbon Coposites, J. Mater. ci. Lett.,1988;7:459. [11] McLachlan D.., J. Phys. C, 1987;20, 865 [12] Blazkiewcz M, McLachlang D, Newnha R.E. The Volue Fraction and Teperature Dependence o the Resistivity in Carbon Black and Graphite Polyer Coposites: An Eective Media-Percolation Approach., Poly. Eng. ci. 1993;32:421. [13] Lonergan M.C, everin E.J, Dolean B.J, Beaber.A, Grubbs R.H, Lewis N.. Array-Based Vapor ensing Using Cheically ensitive, Carbon Black-Polyer Resistors, Che. Mater., 1996;8:2298. [14] Máruez A, Uribe J, Cruz R.J. Conductivity Variation Induced by olvent welling o an Elastoer-Carbon Black-Graphite Coposite, J. Appl. Poly. ci. 1997; [15] Carrillo A, Caracterización eléctrica de un copuesto conductor sensible a disolventes orgánicos y teperatura, BME thesis, Instituto Tecnológico de Mérida, Mérida, Yucatán, México,1997. [16] Crank J. The Matheatics o Diusion, 2nd Ed., Clarendon Press Oxord, XIX Congreso Nacional de Políeros. ociedad Poliérica de México altillo, Coahuila. Octubre de 2006

5 PM Figure 2.- cheatic o circuit or sensor testing 1,E+06 1,E+05 1,E+04 1,E+03 PB BR 1,E+02 1,E+01 1,E ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Dielectric voluent ric ract ion Figure 3.- Percolation curve or PB and BR coposites. 5 XIX Congreso Nacional de Políeros. ociedad Poliérica de México altillo, Coahuila. Octubre de 2006

6 PM R/R D=3x10-6 c 2 /s D=1x10-6 c 2 /s D=5x10-6 c 2 /s D=7x10-6 c 2 /s D=9x10-6 c 2 /s Tie (in) Figure 3.- Evolution o the instantaneous radii or dierent solvents D=1x10-6 c 2 /s D=3x10-6 c 2 /s D=5x10-6 c 2 /s D=7x10-6 c 2 /s D=9x10-6 c 2 /s I/Io Tie (in) Figure 4.- Falling o the current intensity with the solvent contact tie. 6 XIX Congreso Nacional de Políeros. ociedad Poliérica de México altillo, Coahuila. Octubre de 2006