Nonlinear Electrical Conductivity of Tin-Filled Urea-Formaldehyde-Cellulose Composites

Gabriel PintoDepartamento de Ingenierıa Quımica Industrial y del Medio Ambiente, E.T.S.I. Industriales, UniversidadPolitecnica de Madrid, 28006 Madrid, Spain

Abdel-Karim MaaroufiLaboratory of Applied Chemistry of Solid, Department of Chemistry, Faculty of Sciences, P.B. 1014, RabatAgdal, Morocco

This work reports on the elaboration and characterizationof composite materials prepared by compression moldingof mixtures of tin powder and a commercial grade thermo-setting resin of urea-formaldehyde filled with alpha-cellu-lose in powder form. The morphology of constituents andcomposites has been characterized by optical micros-copy. The porosity rate of the composites has been deter-mined from density measurements. These results showthat the composites are homogeneous. Furthermore, it hasbeen shown that the hardness of samples remains almostconstant with the increase of metal concentration. Theelectrical conductivity of the composites is <10–11 S/cmunless the metal content reaches the percolation thresholdat a volume fraction of 18.6%, beyond which the conduc-tivity increases markedly by as much as 11 orders of mag-nitude. The results have been well interpreted in the sta-tistical percolation theory frame. POLYM. COMPOS., 26:401–406, 2005. © 2005 Society of Plastics Engineers

INTRODUCTION

Information about numerous existing possibilities ofpolymers containing dispersed conductive fillers and vari-ous methods of manufacture of such materials have beenreported widely in the literature for the last years [1–4], dueto their numerous technological applications in a variety ofareas such as electromagnetic/radio frequency interference(EMI/RFI) shielding for electronic devices (computer andcellular housings for example), self regulating heaters, over-current protection devices, photothermal optical recording,direction finding antennas, chemical detecting sensors usedin electronic noses, and more [5–10].

It is known that, in general, the percolation theory is usedto describe the nonlinear electrical conductivity of extrinsic

conductive polymer composites. Hence, the electrical con-ductivity of polymer composites does not increase contin-uously with increasing electroconductive filler content, butthere is a critical composition (percolation threshold) atwhich the conductivity increases by some orders of magni-tude from the insulating range to values in the semiconduc-tive or metallic range [11]. For efficiency and in order todecrease the difficulty of the process and economic costs,the amount of the conductive phase for achieving materialswith high conductivity should be usually as small as possi-ble. A huge number of different models have been proposedfor the estimation of the conductivity (or inverse resistivity)vs. filler concentration curves [12–17].

This article deals with the study of the electrical conduc-tivity of a polymer filled by two types: on the one handcellulose particles, and on the other hand, tin particles. Theinterest of such a study is due to the fact that at the industriallevel, most polymer-based materials contain a more or lesslarge amount of fillers, for various reasons, such as theimprovement of mechanical properties, dimension stability,and to decrease their price.

This article also presents further developments in previ-ously reported investigations of preparation and character-ization of electroconductive polymer composites [18–23].We report an experimental study about the influence of fillerconcentration on the electrical conductivity of compositesproduced by hot compaction by means of the compressionmolding of mixtures of tin powder and urea-formaldehyderesin molding compound filled with alpha-cellulose in pow-der form. Short fiber of alpha-cellulose is usually used asreinforcing fibers in urea-formaldehyde molding com-pounds. These data, along with those reported previouslymay be helpful in developing theoretical models to betterunderstand the variation of electrical properties of suchpolymer composites. Furthermore, to check the void levelwithin the samples, which influences the electroconductiv-ity remarkably, the porosity rate has been determined from

Correspondence to: G. Pinto; e-mail: gpinto@iqi.etsii.upm.esDOI 10.1002/pc.20106Published online in Wiley InterScience (www.interscience.wiley.com).© 2005 Society of Plastics Engineers

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densities of the composites. Finally, in order to complete thecharacterization of these materials, the study of influence offiller concentration on the hardness of composites has beenpresented.

EXPERIMENTAL

Materials

The matrix polymer used in our experiments was acommercial grade urea-formaldehyde resin filled withalpha-cellulose in the form of powder supplied by AicarS.A., with a density of 1.36 g/cm3, and electrical conduc-tivity of around 10–12 S/cm. The content of alpha-cellulosein the resin is 30 wt%. A micrograph of this powder isshown in Fig. 1, where the longitudinal shape of particles

can be observed.The electrical conducting filler used was tin, delivered by

Panreac, with average particle size of 15 � 10 �m, densityof �7.29 g/cm3, and electrical conductivity, taken as thetabulated value [24] of the order of 104 S/cm. The shape ofthe filler particles is illustrated in Fig. 2.

Both the polymer and the metal powders were thor-oughly dried before use (48 h at 60°C).

Composite Preparation

All the composites were prepared according to the sameprocedure described in detail elsewhere [25]. The compos-ites were obtained by mixing the urea-formaldehyde em-bedded in cellulose and the tin powders, followed by com-pression molding under heat at 150°C during 30 min.

FIG. 1. Photograph of the urea-formaldehyde resin molding compound filled with alpha-cellulose in powderform.

FIG. 2. Photograph of the tin powder used as filler.

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Samples with filler contents on the range 0 to 75 wt%(corresponding to the range 0–0.36 in volume fraction)were elaborated. In order to improve the finish of the sampleand ensure a better electrical contact for resistance measure-ments, the surfaces were polished with sandpaper. Samplethickness (necessary for the calculation of conductivity) wasdetermined using a micrometer, Schmidt model J50 with anaccuracy of 0.01 mm. Thickness measurements were takenat five locations and averaged. Samples were cooled asmuch as room temperature during approximately 30 min.

Composite Characterization Techniques

The microstructures of the samples were observed byreflection by means of a Nikon model 115 optical micro-scope. Then, the density of the composites were measuredin accordance with ASTM D 792-91 norm, by difference ofweight in the air or with the sample immersed in water asthe liquid of known density at 23°C, using a Mettler AJ 100balance equipped with a density determination kit. More-over, the hardness of the samples was determined at 23°Cusing a Durotronic model 1000 Shore D hardness tester, inaccord with ASTM D 2240-68 norm. Five data points weretaken on each samples and no difference was found betweenhardness measurements on both faces of each specimen.

The electrical conductivity was determined from theresistance values that were measured using a two-pointarrangement. Three specimens of each composition weretested taking four data points on each sample. In order todecrease the contact resistance, the sample surfaces werecoated with silver paint.

Measurements of volume electrical resistance higherthan 103 ohm were made using the same equipment andprocedure already used [21, 25].

RESULTS AND DISCUSSION

Figure 3 represents micrographs with the structure of acomposite sample before (Fig. 3a) and after (Fig. 3b) thepercolation threshold (18.6 vol%), which corresponds to theinsulating-conductive phase transition. These photos show adistinction in the contrast, relating to the difference ofdensity. On the basis of optical micrographs (Fig. 3) it canbe appreciated that large aggregates were formed during theprocess. However, the morphology concerning these aggre-gates remains similar and uniformly dispersed indicatinghomogeneous composites.

These phenomena could be verified by density measure-ments. Indeed, the morphology is in partly influenced by theporosity rate in such materials. The porosity rate should bedetermined from comparison between the calculated andmeasured densities.

The theoretical density of the composite is given by therelation [23]:

dt � �1 � Vf� � dm � Vf � df (1)

where dt is the theoretical density of composite and V is thevolume fraction; indexes m and f stand for the matrix andfiller, respectively.

Then, the composites’ porosity � has been deduced fromthe formula [23]:

� � �dt � de

dt� � 100 (2)

where de represents the experimental density.Figure 4 shows the porosity rate of the prepared com-

posites as a function of the filler volume fraction. It is to benoted that in almost all cases, the porosity is low (2–4%)and is almost constant as function of the Sn volume fraction,with small change around the percolation threshold. There-fore, the quality of the obtained composites is good. More-over, the hardness remains approximately constant, as 82� 4 shore D values, independently of the filler composition.The fact that the shore D hardness has no appreciabledifferences among the five data points on each sample onboth faces for each composition is a proof of the materialhomogeneity. These results seem to confirm the opticalmicroscopic observations.

The electrical conductivity of the composites as functionof filler content for the samples shows the typical S-shapeddependency with three regions (dielectric, transition andconductive) (Fig. 5). As expected, samples with low fillercontent were almost nonconductive. However, the electricalconductivity of the composites increases dramatically as theSn content reaches the percolation threshold with 18.6%(v/v) of filler. According to Flandin et al. [4], values closeof 20–40% (vol/vol) are typical of spherical filler particles.The conductivity of composites increases by much as 11orders of magnitude.

As indicated, this behavior could be interpreted with thestatistical percolation theory. Such theory is usually used torelate the electrical conductivity of composite to the exis-tence of clusters of connected particles; which give rise tothe so-called conducting infinite cluster above the threshold.In this theory, the relationship between the electrical con-ductivity of the mixture and the volume fraction of theconductive filler is given by [12]:

� � �o�Vf � V*f �t (3)

where � is the electrical conductivity of the mixture, �0 isthe electrical conductivity of the filler’s particles, Vf is thevolume fraction of the filler, V*f is the critical volume con-centration at the threshold of percolation, and t is an expo-nent determining the increase of the conductivity above V*f.This theory gives a good description of experimental resultsnear the transition point. Nevertheless, discrepancies wereobserved between critical parameters (V*f , t) resulting fromEq. 3 and experimental values [16]: as inasmuch as thebasically classical statistical theory does not take a consid-eration of several parameters. While, the experimental re-

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sults show that the electrical conductivity depends stronglyon the viscosity and the surface tension of the filled poly-mers. It depends also on the filler particles geometricalparameters as well as on the filler/matrix interactions.Mamunya et al. [15, 16] have developed a model in whichspecific parameters for each composite have been intro-duced in the basic theory:

� � �o � ��m � �o� � �Vf � V*fF � V*f

� teff

(4)

where �m is the maximal conductivity reached by compos-ite. F is the filler packing density coefficient (equivalent tothe maximal value of the filler volume fraction), and teff isgiven by the relation:

FIG. 3. Optical microscopy micrographs of the tin-filled urea-formaldehyde and cellulose composites con-taining 15.2 vol% of tin (a) and 30.3 vol% of tin (b).

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teff � t1 � t2 (5)

where t1 is equivalent to the t parameter in the basic Eq. 3,which usually takes a value around 1.7 and t2 depends onthe specific composite. Thus, teff could have higher valuestaking into account of the filler/polymer interactions.

The classical percolation theory (Eq. 3) was tested in ourcase without success. While the Eq. 4, which was used withsuccess in earlier similar studies to interpret the experimen-tal results [21, 23, 25], provides a good result. Therefore, thefit, above the percolation threshold of the electrical conduc-tivity as function of volume fraction of Sn filled in urea-formaldehyde embedded in cellulose powder, is given inFig. 6. It should be noted that the agreement between theexperiment and the theory is good. The obtained parametersare V*f � 18.6%, teff � 2.45, and F � 0.41.

The determined packing density coefficient F value is in

good agreement with the prediction of Eq. 4 [26]. The teff

obtained value is slightly close to which represents theaccepted theoretical value for three-dimensional lattices, inmean-field theory [27, 28]. This theoretical value is inde-pendent of the exact composition of the random composites[27]. On the other hand, the critical threshold percolationvalue obtained is in excellent agreement with that deter-mined by experience, V*f � 18.6%. Elsewhere, this result isalso close to 18.9% found in Zn filled in urea-formaldehydeembedded in cellulose [25]. Indeed, the random compositeselectrical conductivity has already been shown to depend onseveral parameters [18–23, 29, 30]; such as: the viscosityand the polymers surface tension, especially in the case ofthe mixes in which the conductive powder is dispersed; thesize, the shape and the surface energy of the filling particlesand the powder dispersion procedure, i.e., type, duration andstrength of shear. In this study, the particle sizes and shapeof Sn and Zn filled in urea-formaldehyde are similar. Thedispersion procedure has been maintained uniform. Theelectrical characteristics of Sn and Zn are analogous. Con-sequently, the filler/polymer interactions should be taken aclose amount, involving quasiidentical percolation thresh-old values.

CONCLUSIONS

In this experimental work, we have described the effectsof the filler content of Sn-filled urea-formaldehyde embed-ded in cellulose on the electrical conductivity. The opticalmicroscopy shows that the composites morphology is ho-mogeneous. The density measurements indicate that thevoid fraction in almost all samples is low. Moreover, theshore D hardness remains approximately constant with theincrease of filler concentration. The electrical conductivityof composites increases as much as 11 orders of magnitudefor a given range of filler concentration, showing the typical

FIG. 4. Porosity rate versus tin volume fraction.

FIG. 5. Variation of the electrical conductivity of urea-formaldehydeembedded in cellulose powder/Sn composites with filler content.

FIG. 6. Electrical conductivity of Sn/urea-formaldehyde and cellulosecomposites as function of Sn volume fraction above percolation threshold(■). Solid line is the fit with Eq. 4.

POLYMER COMPOSITES—2005 405

percolation transition from dielectric to conductive regionof such polymer composite materials. The percolationthreshold concentration corresponds to a volume fraction oftin is V*f � 18.6%, in good agreement with previous exper-iments. Besides, the electrical conductivity behavior as afunction of filler content is reasonably fitted, above thepercolation threshold, with the extended basic statisticalpercolation theory. The obtained critical parameters arerealistic and coherent with experimental values and earlierstudies.

ACKNOWLEDGMENTS

We would like to thank to Cristobal Morilla fromAICAR S.A. for furnishing us the urea-formaldehyde em-bedded in cellulose powder used as matrix in the samplesand for technical support. We also thank the anonymousreviewers of this journal for their critical review, whichhelped to improve the manuscript.

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