Materials and Design 51 (2013) 620–628

Contents lists available at SciVerse ScienceDirect

Materials and Design

journal homepage: www.elsevier .com/locate /matdes

The mechanical and adhesive properties of electrically and thermallyconductive polymeric composites based on high density polyethylenefilled with nickel powder

0261-3069/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.matdes.2013.03.067

⇑ Corresponding author at: Center for Advanced Materials, QAPCO Polymer Chair,Qatar University, P.O. Box 2713, Doha, Qatar. Tel.: +974 4403 5671.

E-mail address: igor.krupa@qu.edu.qa (I. Krupa).

Igor Krupa a,e,⇑, Volkan Cecen b, Abderrahim Boudenne c, Jan Prokeš d, Igor Novák e

a Center for Advanced Materials, QAPCO Polymer Chair, Qatar University, P.O. Box 2713, Doha, Qatarb Baskent University, Mechanical Engineering Department, 06810 Baglica/Ankara, Turkeyc Université Paris-Est Creteil Val de Marne/CERTES, 61 Av. du Général de Gaulle, 94010 Créteil Cedex, Franced Charles University in Prague, Faculty of Mathematics and Physics, V Holešovickách 2, 182 00 Prague 8, Czech Republice Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 84541 Bratislava, Slovakia

a r t i c l e i n f o

Article history:Received 26 January 2013Accepted 21 March 2013Available online 13 April 2013

Keywords:High density polyethyleneNickel powderComposites, electrical conductivityThermal conductivityMechanical propertiesAdhesion

a b s t r a c t

Electrically and thermally conductive composites made using high density polyethylene (HDPE) matrixblended with a special grade of branch-structured nickel particles were studied. Composites with highfiller content were highly electrically and thermally conductive. The electrical conductivity of compositesreached a value of 8.3 � 103 S m�1 when filled with 30 vol.% of the filler, and the thermal conductivityobtained using this filler content was found to be 1.99 W m�1 K�1. The percolation concentration ofthe filler within the HDPE matrix, which was determined from electrical conductivity measurements,was determined to be 8 vol.%.

Young’s modulus of composites significantly increased from 606 MPa to 1057 MPa when compositeswere filled with 20 vol.% of the filler. Further increasing the filler content caused no further increase inYoung’s modulus, probably due to high aggregation of the filler. The stress at break of the compositesbehaved nonlinearly; the low filler content suppressed necking, resulting in a decrease in stress at break,whereas higher filler content (higher than 10 vol.%) led to reinforcement of the composites and thereforeincreased the stress at break.

The presence of nickel particles throughout the HDPE matrix increased the hydrophilicity of the com-posites. The contact angle of water on the neat HDPE decreased from 93� to 80� as the nickel content ofthe matrix was increased to 13 vol.% of nickel. Further increases in the filler content did not alter the con-tact angle. Similarly, the strength of the adhesive joint formed by the composite and aluminum foilincreased from a value of 16 N m�1 for the neat HDPE to 27 N m�1 when the HDPE matrix was filled with13 vol.% of the filler.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Generally speaking, common industrial polymers are materialswith extremely low thermal and electrical conductivity [1]. How-ever, many industrial applications require polymeric systems thathave high thermal or electrical conductivity and maintain theadvantageous properties of the composites from which these sys-tems are made. The applications of thermally conductive compos-ites include circuit boards, heat exchangers, electronics protectionand phase-change materials [2–5]. Electrically conductive materi-als (antistatic, semi-conductive or conductive) are frequently usedas, for instance, heating elements, temperature-dependent

resistors and sensors, self-limiting electrical heaters and switchingdevices and antistatic materials for electromagnetic interferenceshielding of electronic devices [6].

Thermally and electrically conductive materials are designed byblending polymeric matrices with the convenient fillers. A filler withhigh electrical conductivity often also possesses high thermal con-ductivity and vice versa. Such fillers include graphite [7–9], exfoli-ated graphite and graphene [10–12], metals [13,14], metalizedfillers [15–17] and carbon nanotubes [18–20]. However, the oxida-tion of certain metals (e.g., aluminum, copper, iron) causes them tobecome electrically insulating, although they still maintain highlevels of thermal conductivity [21]. Sometimes, this effect can beadvantageous; for instance, particularly in electronic devices, highthermal conductivities are required to facilitate heat release, butfor safety reasons, it is desirable that electrical conductivities bekept low. Fillers with high thermal but low electrical conductivities

Fig. 1. SEM micrograph of nickel particles.

I. Krupa et al. / Materials and Design 51 (2013) 620–628 621

include diamond [22] and boron nitride [23], which have low elec-trical conductivities due to the absence of free electrons. In this case,the heat transport is caused only by phonons.

Conversely, certain fillers are efficient electrical conductors, buttheir thermal conductivities are low. Special grades of conductivecarbon blacks have significant electrically conductivities but exhi-bit low thermal conductivities due to the low graphitic-phase lev-els deposited on the surface of inherently amorphous particles[24]. Another example of this type of filler is produced by coatinginsulating fillers with electrically conductive polymers, such aspolypyrrole [25].

Despite immense research efforts focused on utilizing new fill-ers, such as carbon nanotubes or graphene, metallic powders con-tinue to be used as fillers for the preparation of composites that areboth highly electrically and thermally conductive. The presentstudy briefly surveys the most common metallic fillers used to im-prove both electrical and thermal conductivities.

Although iron, due to its high tendency to oxidize, is not com-monly used as a filler to increase electrical conductivity, stainlesssteel powder and fibers are useful in electrically conductive com-posites, especially the fibrous form composed of high aspect-ratiofibers [26,27]. Copper and its alloys are frequently used as powders[28]. These materials are prepared by several methods, includingair atomization of molten copper solutions and hydrogen reductionof copper salts in solution. The powders usually are spherical inshape; however, certain grades have special dendritic shapes withhigh aspect ratios. When used in polymeric composites, copperpowders tend to oxidize and become nonconductive. However,certain grades that are available maintain their electrical conduc-tivities through the use of special anti-corrosion surface treatment[6,26,27].

Aluminum particles, fibers and flakes can be also used as elec-trically conductive fillers; however, as for copper, these fillers re-quire special surface treatments to prevent surface oxidation. Thefibers and flakes are often produced by a melt extraction processof solidification using a spinning wheel to throw off particles ofmolten aluminum alloy [6,26,27].

High-purity nickel powders are manufactured through carbonylrefining technology that uses Ni(CO)4. The powder morphology ishighly specific, and different types of nickel, all of which are ferro-magnetic, are available. One type of nickel is composed of individ-ual spherical particles with spiky surfaces and diameters of 5 lm.Another type is characterized by strings of spherical particles withspiky surfaces (a string contains up to 50 beads). The powders areoften stabilized with an oxide coating and contain approximately0.8% oxygen. This type of nickel is black. Nickel spheres and flakescan be coated with silver to improve their resistivity to highhumidity [6,26,27].

Silver is produced in powder and flake forms as a filler fordesigning conductive composites. The flakes are mechanically flat-tened to provide a large surface area and aspect ratio. Fatty acids,such as stearates and oleates, are used to prevent agglomerationof the flakes. This coating can be subsequently washed off to im-prove electrical conductivity. The flat-shaped filler is conduciveto the preparation of highly conductive thin films because highelectrical conductivities result from the overlapping of adjacentparticles [6,26,27]. The powder composed of spherical silver parti-cles also tends to agglomerate in common polymers (LDPE, HDPEand PS) [29,30]. Silver is an excellent conductor, and unlike lesscostly metals, its oxides, sulfates, and carbonates are also goodconductors [27].

Although nobel metals are seldom used as fillers in polymericcomposites, several such systems have been studied and reported.Gold and palladium powders [29–31] have been observed to be-have in considerably different ways when mixed into commonpolymers (LDPE, HDPE and PS). Powders containing spherical gold

particles tend to agglomerate, exhibiting percolation threshold val-ues of approximately 11 vol.%. In contrast, palladium powders ex-hibit threshold values above 30 vol.%, most likely due to lowagglomeration.

This paper presents results pertaining to the preparation andcharacterization of electrically and thermally conductive compos-ites, the production of which is based on an HDPE matrix and nick-el powder. The mechanical adhesive properties of these compositesare also reported and discussed. Comparisons between the exper-imental data and some theoretical models are also discussed.

2. Experimental details

2.1. Sample preparation

High-density polyethylene (HDPE BP 5740 3VA, British Petrol,UK, melting temperature = 129.3 �C, melting enthalpy = 199 J/g)was used as the matrix, while a special grade of fine nickel particleswith the trade name Inco Type 210 (Novamet Ltd. Sins, England)was used as the filler. The shape of the filler is shown in Fig. 1.The size distribution of particles is shown in Fig. 2. Several physicalproperties of nickel and HDPE are summarized in Table 1.

Composites were prepared by mixing both components in the50-ml mixing chamber of a Brabender Plasticorder PLE 331 (Ger-many) at 180 �C for 10 min at a mixing speed of 35 rpm.

2.2. Electrical conductivity measurements

The electrical conductivities of composites were determined atroom temperature using a two-point method (insulating/semi-conductive samples) or a four-point method (conductive samplesabove the percolation threshold) in a van der Pauw [32] arrange-ment using a Keithley 237 High-Voltage Source Measurement Unitand a Keithley 2010 Multimeter equipped with a 2000-SCAN 10Channel Scanner Card. For sample conductivities below 10�4 -S cm�1, a two-point method employing a Keithley 6517 electrom-eter was used. Circular gold electrodes were deposited on bothsides of the measured samples. Each measurement was repeatedat least 2–3 times.

2.3. Thermophysical measurement

For thermal conductivity measurements, specimens with dimen-sions of 4 � 4 � 0.5 cm were compressed and molded at 170 �C for3 min using a laboratory press (Fontijne 200, The Netherlands).

Fig. 2. Differential (dQ3) and integral (Q3) distribution curves of nickel particles.

Table 1Selected properties of HDPE and nickel powder [1,26,27].

Component q (kg m�3) r (S m�1) k (W m�1 K�1) Cp (kJ kg�1 K�1)

HDPE 969 �10�18 0.468 2.24Nickel 8902 1.44 � 107 90.9 0.54

q is the specific density, r is the electrical conductivity, k is the thermal conduc-tivity and Cp is the specific heat capacity.

622 I. Krupa et al. / Materials and Design 51 (2013) 620–628

A periodical method was used to estimate the thermal conduc-tivities of polymer composites at room temperature. This methodemployed a small temperature modulation in a parallelepiped-shaped sample (44 mm on each side and 4 mm in thickness) andenabled all measured thermophysical parameters to be obtained(with their corresponding statistical confidence bounds) via onlyone measurement [33–35]. A parameter estimation techniquewas then used to estimate simultaneously both thermal conductiv-ity (k) and diffusivity (a).

2.4. Mechanical tests

One-millimeter-thick slabs were prepared by compression-molding the mixed composite using a laboratory press (FontijneSRA 100, The Netherlands) at 170 �C for 3 min. Dog-bone speci-mens with a working area of 35 � 3.6 � 1 mm were cut from theslabs. The mechanical properties were measured at room temper-ature using an Instron 4301 (England) universal testing machine ata deformation rate of 10 mm min�1 at room temperature.

2.5. Peel strength of adhesive joint

The peel strength of adhesive joint of melted HDPE/nickel com-posites to aluminum alloys was measured by peel testing the adhe-sive joint at a constant angle of 90�. Aluminum alloys were chosento model the metallic substrate. The peel test was performed usingthe universal testing machine Instron 4301 with an additive alumi-num peeling wheel at a crosshead speed of 10 mm min�1 and ajoint length of 100 mm. The width of the HDPE/nickel hot-meltadhesive layer was 0.1 mm. The adhesive joints were preparedby fixing two aluminum alloy foils (in strips of 25 � 160 mm) withmelted HDPE/nickel composites in a hydraulic press at 200 �C. The90� peeling of the adhesive joints was performed along the lengthof each adhesive joint. The peel strength (Ppeel [N m�1]) of theadhesive joint was calculated to be Ppeel = F/b, where F (N) is theforce of peeling, and b (m) is the width of the adhesive joint.

2.6. SEM

The filler morphology as well as fracture surfaces of the sampleswere investigated by scanning electron microscopy (JSM 6400,JEOL Japan). Brittle fractures of the samples were achieved in liquidnitrogen. Each specimen surface was sputtered with a Pt layer(4 lm) using a Sputter-coater (Baltec-SDC 050).

2.7. Granulometry

Particle-size distribution was determined (using SYMPATEC HE-LOS H067 equipment) by measuring the sedimentation of the par-ticles in water at room temperature.

2.8. The specific density measurements

The specific densities of the composites were evaluated usingthe Archimedes method by weighing (using a Sartorius R160P bal-ance at room temperature) the pellets in air and immersed indecane.

2.9. BET analysis

The total nickel-powder surface area was determined usingstandard BET analyses based on nitrogen adsorption isotherms(Autosorb-1 Quantachrome, USA).

2.10. The contact-angle measurement

The polarities of composites were characterized simply by mea-suring the contact angles of re-distilled water droplets placed onthe surface of the HDPE/nickel composites. The contact angleswere measured using a Surface Energy Evaluation System (SEE)equipped with a CCD camera (Masaryk University, Czech Republic).Six drops of re-distilled water (with a volume of 3 ll) were placedon a cleaned composite surface. At least six contact-angle mea-surements were obtained and averaged.

3. Results and discussion

3.1. Filler characterization

The nickel-powder shape is shown in Fig. 1. It can be seen thatnickel has a special chain-like structure in which the chains areformed of individual particles of submicron size.

The differential and integral volume distributions of particlesize are shown in Fig. 2. The results indicate that the particle sizedistribution is bimodal. Most particle sizes range from 1 to50 lm; with the most frequently occurring fractions having a sizeof about 2 and 20 lm. These results indicate that individual parti-cles are strongly linked into clusters of various sizes.

The total nickel-powder surface area was determined using BETanalysis. The total surface area was found to be 1.620 m2/g. The to-tal surface area (Sa) of homogeneous, smoothly spherical, uniformparticles can be expressed in the following form:

Sa ¼6qD

; ð1Þ

where q is the specific density of the filler, and D is the diameter ofthe filler. The predictions of Sa for various selected diameters are asfollows: for D = 2 lm, Sa = 0.337 m2/g; for D = 10 lm, Sa = 0.067 m2/g; for D = 20 lm, Sa = 0.034 m2/g. These values show that theexperimentally determined total-surface areas are larger than pre-dicted values, indicating that chain-linked individual particles aresmaller than experimentally determined ones (obtained from the

Fig. 4. Thermal conductivities of the HDPE/nickel composites.

I. Krupa et al. / Materials and Design 51 (2013) 620–628 623

distribution curves in Fig. 2). These results also confirm that distri-bution curves pertain more to the size distribution of the clustersthan to the distribution of individual particles.

3.2. Morphology of composites

The morphology of the HDPE/nickel composite (arbitrarily cho-sen with a composition of 50/50 w/w) at various length scales isshown in Fig. 3a–d. The internal structure of the filler within acomposite is visible at the lowest used length scale (1–5 lm),depicting its chain-like morphology (Fig. 3a and b). At 100-lmscale, the filler particles seem to be dispersed evenly within thematrix; only a notably small number of aggregates are observable.

3.3. Thermal conductivity

The dependence of the thermal conductivities of composites (kc)upon volume filler content is shown in Fig. 4.

A non-linear increase of kc with increasing filler content was ob-served in the whole concentration region. This increase is a com-mon behavior of composites filled with thermally conductivefillers.

In describing the thermal conductivity of a heterogeneousmaterial, we must take into account the influence of variousparameters, including the geometry and orientation of filler parti-cles in the matrix, the filler concentration and the ratio betweenthe filler’s thermal conductivity and the thermal conductivity ofthe matrix. Based on these factors, many different models havealready been developed, but none of these has general validity[2,36]. Most previously published models were established forpolymers filled with spherical particles and partly for fibers, flakesand irregularly shaped particles. Usually, these models also con-sider uniform particle-size distribution and even dispergation ofthe filler within the matrix [36]. The nickel particles used in thiswork exhibited far more complicated behavior than that predictedby the simple morphology for which the thermal conductivitymodels were commonly developed. At the submicron level, thefiller is formed by roughly spherical particles; however, theseparticles link to one another and form branched, chain-like mor-phologies, as seen in Fig. 1. For this reason, it is difficult to selectany one model that correctly describes the experimental results.

Fig. 3. (a–d) The SEM micrographs

To demonstrate this fact, we applied the most simplified approach,i.e., the models describing the thermal conductivities of compos-ites filled with spherical particles.

The Hashin–Shtrikman model [37,38] is considered one of thebest for estimating the lower bound when no information aboutparticle distribution in the matrix is available [39]. The lowerbound is expressed by the following equation:

kc ¼ km þUf

1kf�km

þ 1�Uf

3km

; ð2Þ

where kc, km and kf are the thermal conductivities of the composite,matrix and filler, respectively, and Uf and Um are the volume frac-tions of filler and matrix, respectively.

This model usually describes the experimental data notablywell up for cases where up to 10–12 vol.% of fillers are employed[8,40]. Up to 12 vol.% filler, the particles can be considered to beindividual entities without any contacts among them. The modelfails when the filler content increases further, which is a phenom-enon reported by many different authors [39,40].

As can be seen in Fig. 4, the Hashin–Shtrikman model describesthe experimental data only up to 5 vol.%, far below the common

of HDPE/nickel = 50/50 w/w.

Fig. 5. Electrical conductivities of the HDPE/nickel composites.

624 I. Krupa et al. / Materials and Design 51 (2013) 620–628

predictions for cases where up to 10–12 vol.% fillers are employed.For these higher concentrations, the experimental data are signifi-cantly higher than those calculated from the model, indicating thatnickel particles cannot be considered as individual particles dis-persed within a matrix. As a consequence of the specific nickelstructure (Fig. 1), there are numerous inter-particle contacts, evenat the lowest filler content. These contacts increase the value ofthermal conductivity of composites.

Self-consistent calculation of kc of composites was presented byBudiansky [41]. This model is based on the calculation of an anal-ogous electrostatic problem [42]. The model enables us to calculatethe thermal conductivities of N-components system knowing onlythe thermal conductivities of the pure components (ki) and theirvolume portions (Ui) according to Eq. (3):

XN

i¼1Ui

23þ 1

3ki

kc

� �� ��1

¼ 1 ð3Þ

For a two-component system consisting of matrix and filler, Eq. (3)can be rewritten to the form given by Eqs. (4.1)–(4.4):

kc ¼�bþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 � 4ac

p2a

ð4:1Þ

a ¼ 2 ð4:2Þ

b ¼ kf � 2km � 3ðkf � kmÞUf ð4:3Þ

c ¼ �kf km ð4:4Þ

Recently, we demonstrated that if the spherical particles arerandomly dispersed within a polymeric matrix, this model aptlydescribes the experimental data up to 25 vol.% of filler [43]. In con-trast, the thermal conductivity of HDPE/nickel composites behavesaccording to this model only up to 5 vol.% of filler, similar to theHashin–Shtrikman model. The fact that these models are not ableto properly describe the thermal conductivity of composites, evenat low filler contents, as seen in Fig. 4, indicates that numerous in-ter-particle contacts (between particles) result from the specificnickel chain-like morphology, which leads to a more pronouncedincrease in the thermal conductivities of these composites.

The Lewis–Nielsen model is defined by Eq. 5.1, 5.2 for variousshapes of fillers, as shown below [36,44,45]:

k ¼ km1þ ABUf

1� BwUf; ð5:1Þ

where

w ¼ 1þ ð1�UmaxÞUf

U2max

B ¼kfkm�1

kfkmþA

8>><>>: ð5:2Þ

A is a parameter that depends on the shape of the particles, andUmax is the maximum packing fraction. Different values A and Umax

are reported in the literature [2] for various shapes (spheres, fibers,flakes, irregular particles and various packing geometries (e.g., hex-agonal, face and body centered cubic, simple cubic, random close,random loose and broad). In our case, it is difficult to select correctvalues for A and Umax to be able to predict thermal conductivities asa function of the volume filler content. For this reason, we have keptthese parameters adjustable. In this case, the Lewis–Nielsen modelreasonably describes the experimental data. The aforementionedparameters, computed by fitting the experimental data, have thefollowing values: A = 5.5 ± 0.7 and Umax = 0.6 (R2 = 0.982). Con-versely, this model accurately fits our experimental data; however,it does not enable us to predict thermal conductivities merely fromthe properties of the neat components.

3.4. Electrical conductivity

The dependence of the electrical conductivities of HDPE/nickelcomposites on filler volume content is shown in Fig. 5.

Electrically conductive composites composed of an insulatingpolymeric matrix and an electrically conductive filler demonstratetypical sigmoidal behavior, as shown in Fig. 5. The percolation ef-fect is experimentally observed in the dependence of conductivityversus filler content and manifests itself as a dramatic increase inconductivity (by several orders of magnitude) in a rather narrowfiller concentration range within the area of the percolation thresh-old. In general, the percolation effect is a well-known phenomenonobserved in filler-matrix systems as abrupt extreme changes incertain physical properties within rather narrow concentrationranges of heterogeneity [6,46]. The effect is explained as the forma-tion of conductive paths (through the matrix) in such a way thatthe conductive particles are in close contact at a filler concentra-tion corresponding to the percolation threshold. The percolationthreshold is a mathematical term related to percolation theory,which is the formation of long-range connectivity in random sys-tems. In engineering, percolation is the slow flow of fluids throughporous media or current flow though a heterogeneous conductor.However, in mathematics and physics, percolation generally refersto simplified lattice models of random systems and the nature ofthe connectivity within them [47]. An important task is to findthe so-called percolation threshold, that is, the critical value ofthe occupation probability such that infinite connectivity (percola-tion) first occurs.

To describe the electrical behaviors of composites, a large num-ber of different models were developed, taking into account vari-ous parameters [6,46]. The most prominent one, which belongsto the groups of geometrical percolation models, is Kirkpatrick’s[48]. In this model, the correlation between the electrical conduc-tivities of composites and the volume portions of the fillers is givenby the following equation:

rc ¼ rf ðUf �UcÞb; ð6Þ

where rc is the electrical conductivity (of the composite), rf is theconductivity of the filler, Uf is the volume portion of the filler, Uc

is the percolation concentration, b is a parameter determining thepower of the conductivity increase above Uc (the so-called percola-tion exponent).

Kirkpatrick [48] gave the following values for the exponent b:

� b = 1.6 ± 0.1 (for bond percolation model)� b = 1.5 ± 0.1 (for point percolation model)

I. Krupa et al. / Materials and Design 51 (2013) 620–628 625

However, other percolation exponents can be found in the liter-ature. According to Tchmutin et al. [49], for example, the percola-tion exponent for a three dimensional system is b = 1.6–1.9, whilethe percolation concentration is 0.17.

The experimental results were evaluated according to the line-arized form of Eq. (6), where parameter rf was kept constant(Fig. 6).

The value b = 6.6 ± 0.3 for the percolation exponent andUc = 0.08 ± 0.01 was found. The value for the percolation exponentis far from the aforementioned coefficients. This high value indi-cates a sharp increase in electrical conductivity above the percola-tion threshold, and this increase is steeper than that which isexpected based only on the percolation mechanism.

From experimental and engineering points of view, it is some-times useful to fit the dependence of the electrical conductivityon the volume filler content to an arbitrary function to describethe behavior in the whole concentration region and to determinethe percolation concentration easily. Recently, we introduced thefunction expressed by Eq. (7) for fitting experimental data [50,51]:

f ¼ logrc

rm

� �¼ C 1� exp �aUf

� �� �n; ð7Þ

where C, a, n are adjustable parameters, rc is the electrical conduc-tivity of the composite, rm is the electrical conductivity of the poly-meric matrix and Uf is the filler volume fraction. These parameterswere determined by fitting experimental data with Eq. (6), as fol-lows: C = 23 ± 2, a = 18 ± 6 and n = 4 ± 2, with a regression coeffi-cient of R2 = 0.9699.

This equation also enables us to determine the percolationthreshold (Uc); in this equation, the percolation point has beenarbitrarily identified as the inflexion point in an empirical fittingcurve expressed by Eq. (7) [50,51]. The inflexion point (Ui) is calcu-lated according to Eq. (8).

Ui � Uc ¼lnðnÞ

að8Þ

Using the aforementioned parameters n and a, the percolation con-centration is estimated as Uc = 8 vol.% of the filler, which is a similarvalue to that found from classic Kirkpatrick’s model (Eq. (6)).

From an experimental point of view, as shown in Fig. 5, it alsomakes a sense to divide the experimental dependence of electricalconductivity versus volume filler content into three regions. Thefirst region (I) represents insulating materials; the filler is ran-domly distributed within a matrix without any observable connec-tivity. In the second region, the connectivity of the filler particles

Fig. 6. Electrical conductivities of composites evaluated according to the linearizedEq. (6).

becomes critical; the infinity clusters are formed, and the electricalconductivity sharply increases. Obviously, in the real case, this in-crease is connected not only with one point; rather, the network-building process occurs over a concentration region (II). The widthof this region can be on the order of a few percent, depending onthe shape of the filler, matrix, processing, etc. This region can beroughly bordered by two points (these points are marked as ‘‘o’’and ‘‘p’’ in Fig. 5): the point ‘‘o’’ is where the connectivity of theparticles begins to become significant, while infinity clusters beginto accumulate at the point ‘‘p’’, where cluster formation is more orless finished. An important point in this area is the inflection point(‘‘i’’) of the experimental (or phenomenological) dependence. Forthe purpose of the present study, we have arbitrarily identified itwith the percolation concentration (Uc). Finally, in region III, onlya small internal network additionally develops as more particlesare incorporated into the matrix; thus, there is no significant fur-ther increase in the electrical conductivity. A relatively accurateapproach to determining the borders of these regions (I, II andIII) can be based on the use of Eq. (7). The tangents (t1, t2, and t3)can be defined as follows: t1 is the tangent of the curve describedby Eq. (7) at the point [0,0], t2 is the tangent of the curve at thepoint ‘‘i’’[ Ui, f(Ui)], and t3 is the tangent of the curve at the pointrelated to the highest experimentally determined filler concentra-tion. In this equation, we refer to this latter point as ‘‘e’’ [Ue, f(Ue)]where Ue is the highest filler content (0.3) and f(Ue) is its relatedvalue (20.37) calculated from Eq. (7).

Now, in order to identify point ‘‘o’’ and the cross-section of tan-gents t2 and t3 for the determination of point ‘‘p’’, the borders of theregions I, II and III (the coordinates of the points ‘‘o’’ and ‘‘p’’) can becomputed as the cross-section of tangents t1 and t2. Using simplecalculations, one can derive Eqs. (9.1)–(9.4) for tangents 1, 2 and3 as follows:

ft1 ¼ 0 ð9:1Þ

ft2 ¼ f ð/iÞ þdf

d/f

!/i

/f � /i

� �ð9:2Þ

ft3 ¼ f ð/eÞ þdf

d/f

!/e

/e � /f

� �ð9:3Þ

dfd/f

!/f

¼ Anað1� expð�a/f ÞÞn�1 expð�a/f Þ ð9:4Þ

From equation ft1 = ft2 we found /o = 0.035 and from equationft3 = ft2 we found /p = 0.146.

In summary, for the composites investigated in this study, theconductive network begins to develop at a filler content of3.5 vol.%, and the network is developed at 14.6 vol.%. The percola-tion threshold was arbitrarily determined as 8 vol.%.

3.5. Mechanical properties

The mechanical properties, namely Young’s modulus, the stressat break and the elongation at break were obtained by evaluatingthe stress–strain curve.

The dependence of Young’s modulus (of the HDPE/nickel com-posites) is shown in Fig. 7.

Throughout the whole concentration region, the Young’s modu-lus values monotonically increase as the filler content increases,which is common behavior for polymers filled with inorganic fill-ers. Many models have been developed to describe the behaviorof Young’s modulus values for a material filled with various fillers;of these models, the most well-known is the Nielsen and Lewis

Fig. 7. Young’s modulus of the HDPE/nickel composites. Fig. 8. The stress at break of the HDPE/nickel composites.

Fig. 9. The elongation at break of the HDPE/nickel composites.

626 I. Krupa et al. / Materials and Design 51 (2013) 620–628

model [44,45]. This model describes not only Young’s modulus butalso the electrical and thermal conductivities of the composites[45].

Nielsen and Lewis [45] proposed the following model to de-scribe the dependence of Young’s modulus (also called the shearmodulus) on filler content using the set of Eqs. (10.1)–(10.3):

Ec ¼ Em1þ AbUf

1� bwUfð10:1Þ

b ¼ Ef =Em � 1Ef =Em þ A

ð10:2Þ

w ¼ 1þ ð1�UmaxÞUf

U2max

ð10:3Þ

where Ec, Ef and Em are the Young’s modulus values of the compos-ites, filler and matrix, respectively, Uf is the volume portion of thefiller, Um is the maximum packing fraction, and A is a parameterthat depends on the shape of particles

Because Young’s modulus of nickel is 200 GPa, we can keepb � 1. Similarly, as mentioned above with regard to describingthe thermal conductivities of composites, different values of Um

are reported in the literature [2] for different shapes. For this rea-son, similar to the previous case, we kept A and Um as adjustableparameters. In this case, the Lewis–Nielsen model reasonably de-scribes the experimental data, and the following parameters werefound: Umax = 0.5 ± 0.1 and A = 6.5 ± 1.1 (R2 = 0.975). Similarly, as isthe case for describing the thermal conductivities of composites,this model accurately fits experimental data but does not enableYoung’s modulus values to be predicted from the properties ofthe neat components.

The composites’ values of stress at break and the dependence ofthese values on the filler concentration, which varies linearly, aredepicted in Fig. 8.

The behavior depicted in Fig. 8 is caused by two distinguishedeffects of the filler that influence the stress at break. On the onehand, we must consider the reinforcing effect of the filler that leadsto an increase in tensile stress values with increasing filler content;on the other hand, we must consider the strengthening that iscaused by the orientation of semicrystalline polymers at highdeformation. The latter effect is indirectly influenced negativelyby the presence of filler and by the steep decrease of the deforma-tion that prohibits orientation of the matrix. At low filler contents,the deformation is low enough to prevent matrix orientation, butthe reinforcing effect of the filler is marginal. The particles of thefiller represent defects and stress concentrators. Thus, the behavior

of the stress–strain curve is changed; orientation hardening andcold flow is suppressed. The samples break close to the yield point.The initial stress at break of HDPE (34 ± 2 MPa) decreases15 ± 2 MPa when it was filled with 10 vol.% of filler. This reinforc-ing effect is more pronounced as the filler content is increased,while the further decrease in deformation has no additional effecton orientation. The reinforcing effect is significant for filler concen-trations of approximately 30 vol.%, where the stress at breakreaches the value of pure HDPE (33 ± 1 MPa). Obviously, in thiscase, the composite does not present necking, and brittle ruptureoccurs at this point.

The dependence of the elongation at break on the volume fillercontent is shown in Fig. 9.

The data are expressed as the ratio of elongation at break of thecomposites and their matrices (eb,c/eb,m). The dependence clearlydemonstrates a significant drop in drawability after the additionof filler. A decrease in the elongation at break of the polymers,filled with inorganic fillers, is obvious and always observed. Afew models for describing this behavior have been reported inthe literature. These assume a homogeneous distribution of parti-cles, a regular (usually spherical) shape and homogeneous draw-ing. The most known model that describes the decrease inelongation at break with increasing filler content is the Nielsenmodel given by Eq. (11) [45]:

eb;c

eb;m¼ 1�U1=3

f ; ð11Þ

Fig. 11. The peel strength of adhesive joints (Ppeel) between HDPE/nickel andaluminum. The solid line is the linear fit. The dashed line is a guide to the eye.

I. Krupa et al. / Materials and Design 51 (2013) 620–628 627

where eb,c and eb,m are the elongation at break of the composite andmatrix, respectively, and Uf is the volume portion of the filler.

It is important to note that the Nielsen model is valid only forcomposites filled with spherical-shaped particles and assumingperfect adhesion between phases. Obviously, many types of fillersdo not fulfill these conditions. Recently, we have studied the corre-lation between the dependence of elongation at breaks on the fillercontent and the electrical conductivities of those composites[50,51]. We have demonstrated a reasonable correlation betweenthe sharpest increase in electrical conductivity and the sharpestdecrease in elongation at break as a consequence of the internalnetwork of filler formation. In the composites investigated, thesharpest decrease in elongation at break is observed even at thelowest used concentration (2.3 vol.%) [50]. Particles of the fillerrepresent defects and stress concentrators and significantly reducethe drawability of the matrix.

According to an analysis of various sets of experimental data[43,50,51], it seems there is a close correlation between the forma-tion of an internal network of particles within a matrix and a de-crease in the elongation at break. In the case of conductive fillers,the increase in the network of particles can be characterized interms of the percolation concentration. For a description of thedependence of elongation at break versus filler content, we havesuggested a phenomenological equation (Eq. (12)) [50]:

eb;c

eb;m¼ exp �Uf

Uc

� �; ð12Þ

where the exclusive parameter is the percolation concentration ofthe filler (Uc), as determined from the electrical conductivity mea-surement (Uc). As seen in Fig. 9, Eq. (12) describes the experimentaldata more accurately than Eq. (11).

3.6. Surface properties

Polyethylene is generally non-polar in nature, leading to lowsurface free-energy and poor adhesive properties. Various methodshave been used to improve PE adhesive properties. These methodsinclude corona discharge [52] or plasma surface modification [53],chemical surface etching [54], and bulk PE modification by addinglow amounts of polar polymers or low-molecular-weight additives.The present paper reports the results of our investigation into hownickel fillers influence the polarities of HDPE-based composites.Increased polarity is determined by measuring the contact anglesof re-distilled water droplets deposited on the surfaces of HDPE/nickel composites. The surface of the sample was not additionally

Fig. 10. The contact angles of water on the surfaces of the HDPE/nickel composites.The solid line is the linear fit. The dashed line is a guide to the eye.

treated before measurement. The dependence of the contact angleon the volume filler content is shown in Fig. 10. The presence ofnickel in the HDPE matrix leads to a decrease in contact angles,indicating that the hydrophilicity of the surface increases. The con-tact angle of water on the neat HDPE (93�) decreases to 80� as thenickel is increased by filling with 60 wt.% of the filler (13 vol.%).The next incremental increase in filler content causes no furtherchange in the contact angle. This behavior corresponds to thedevelopment of a filler network, as discussed above. When this fil-ler network has developed, further increases in the filler content donot lead to further changes in either the electrical conductivity orthe contact angle.

The strength of the adhesive joints between HDPE/nickel com-posites and aluminum was determined by 90� peel tests. The re-sults are illustrated in Fig. 11. The adhesive-joint strengthincreases from a value of 16 N m�1 for neat HDPE to 27 N m�1

for HDPE filled with 60 wt.% of filler (13 vol.%). Further increasingthe filler content does not cause any further changes in the peelstrength, similar to what was observed for the contact angle.

Figs. 10 and 11 also indicate other, less surprising phenomena;in particular, changes in the contact angle closely correlate withthe peel strength. The slope of the dependence of the contact angleon volume filler content in the linear region is – 99 ± 9�, and theslope of the dependence of peel strength on volume filler contentis 78 ± 9 (N m�1).

4. Conclusions

A new type of electrically and thermally conductive compositesbased on an HDPE matrix and nickel particles was prepared andinvestigated. The percolation concentration of the filler withinthe HDPE matrix, as determined from electrical conductivity mea-surements, was found to be 8 vol.%. Composites with high fillercontent were highly electrically and thermally conductive; theelectrical conductivity of composites reached 8.3 � 103 S m�1

when the composite was filled with 30 vol.% of the filler. In thiscase, the thermal conductivity of the composite was found to befour times higher than the thermal conductivity of neat matrix.

Young’s modulus of composites significantly increased from606 MPa to 1057 MPa when the matrix was filled with 20 vol.%of the filler. Further increases in filter content did not cause furtherincreases in modulus values. Composites filled with 30 vol.% ofnickel had even lower Young’s modulus values than compositesfilled with 20 vol.% of nickel. This result is most likely due to insuf-ficient wetting of the filler and de-bonding of the matrix. The stress

628 I. Krupa et al. / Materials and Design 51 (2013) 620–628

at break of the composites behaved nonlinearly; low filler contentsuppressed necking, resulting in a decrease in stress at break,whereas higher filler content (higher than 10 vol.%) reinforcedthe composites, thereby increasing the stress at break. The elonga-tion at break sharply decreased with increasing filler content. Theexperimental data were correlated with the models.

The presence of nickel in the HDPE matrix leads to a decrease inthe contact angles, indicating that the hydrophilicity of the surfaceincreases. The contact angle of water on neat HDPE (93�) decreasedto 80� as the nickel was increased via filling with 60 wt.% of the filler(13 vol.%). Further increases in the filler content did not lead to fur-ther changes in the contact angle. Similarly, adhesive-joint strengthincreased from a value of 16 N m�1 for neat HDPE to 27 N m�1 whenthe HDPE was filled with 60 wt.% of the filler (13 vol.%).

Acknowledgments

This work was supported by grants NMT-ERANET ‘‘APGRAP-HEL’’ and by project VEGA 2/0119/12.

References

[1] Brandrup J, Immergut E, Grulke E. Polymer handbook. 4th Ed. New York: JohnWiley & Sons Inc.; 1999.

[2] Bigg DM. Thermal and electrical conductivity of polymer materials. Adv PolymSci 1995;119:1–30.

[3] Zhang Z, Fang X. Study on paraffin/expanded graphite composite phase changethermal energy storage material. Energy Convers Manage 2006;47(3):303–10.

[4] Stappers L, Yuan Y, Fransaer J. Novel composite coatings for heat sinkapplications. J Electrochem Soc 2005;152(7):C457–61.

[5] Klason C, McQueen DH, Kubat J. Electrical properties of filled polymers andsome examples of their applications. Macromol Symp 1996;108:247–60.

[6] Gul VE. Structure and properties of conducting polymercomposites. Utrecht: VSB BV; 1996.

[7] Chang-Ming Y, Bao-Qing S, Shi-Xue W. Thermal conductivity of high densitypolyethylene filled with graphite. J Appl Polym Sci 2006;101:3806–10.

[8] Krupa I, Chodák I. Physical properties of thermoplastic/graphite composites.Eur Polym J 2001;37:2159–68.

[9] Pelíšková M, Vilcáková J, Moucka R, Sáha P, Stejskal J, Quadrat O. Effect ofcoating of graphite particles with polyaniline base on charge transport inepoxy–resin composites. J Mater Sci 2007;42(13):4942–6.

[10] Fukushima H, Drzal LT, Rook BP, Rich MJ. Thermal conductivity of exfoliatedgraphite nanocomposites. J Therm Anal Calorim 2006;85(1):235–8.

[11] Kalaitzidou K, Fukushima H, Drzal LT. Multifunctional polypropylenecomposites produced by incorporation of exfoliated graphite nanoplatelets.Carbon 2007;45(7):1446–52.

[12] Xie SH, Liu YY, Li JY. Comparison of the effective conductivity betweencomposites reinforced by graphene and carbon nanotubes. Appl Phys Lett2008;92(24). Article No. 243121.

[13] Mamunya YP, Davydenko VV, Pissis P, Lebedev EV. Electrical and thermalconductivity of polymers filled with metal powders. Eur Polym J2001;38(9):1887–97.

[14] Boudenne A, Ibos L, Fois M, Majeste JC, Gehin E. Electrical and thermalbehavior of polypropylene filled with copper particles. Composites A2005;36:1545–54.

[15] Dai H, Li H, Wang F. An alternative process for the preparation of Cu-coatedmica composite powder. Surf Coat Technol 2006;201(6):2859–66.

[16] Agoudjil B, Ibos L, Majesté JC, Candau Y, Mamunya YP. Correlation betweentransport properties of ethylene vinyl acetate/glass, silver-coated glass spherescomposites. Composites A 2008;39:342–51.

[17] Krupa I, Miková G, Novák I, Janigová I, Nógellová Z, Lednicky F, et al.Electrically conductive composites of polyethylene filled with polyamideparticles coated with silver. Eur Polym J 2007;43:2401–13.

[18] Evseeva LE, Tanaeva SA. Thermal conductivity of micro- and nanostructuralepoxy composites at low temperatures. Mech Compos Mater2008;44(1):87–92.

[19] Wu U, Liu C, Huang H, Fan SSY. The carbon nanotube based nanocompositeswith enhanced thermal conductivity. Diffusion and defect data. Solid StatePhenom 2007;121–123(Part 1):243–6.

[20] Xue QZ. Model for thermal conductivity of carbon nanotube-based composites.Physica B: Condens Matter 2005;368:302–7.

[21] Boudenne A, Ibos L, Gehin E, Fois M, Majeste JC. Anomalous behavior ofthermal conductivity and diffusivity in polymeric materials filled with metallicparticles. J Mater Sci 2005;40(16):4163–7.

[22] Twitchen DJ, Pickles CS, Coe SE, Sussmann RS, Hall CE. De Beers: IndustrialDiamonds (UK) Ltd., Ascot, Berkshire, UK. Diamond Relat Mater 2001;10(3–7):731–5.

[23] Hag HY, Lau SK, Lu X. Thermal conductivity, thermo-mechanical andrheological studies of boron nitride-filled polybutylene terephthalate. MaterSci Forum 2003;437:239–42.

[24] Manson A, Sperling LH. Polymer blends and composites. New York: PlenumPress; 1976.

[25] Micušík M, Omastová M, Prokeš J, Krupa I. Mechanical and electrical propertiesof composites based on thermoplastic matrices and conductive cellulosefibres. J Appl Polym Sci 2006;101(1):133–42.

[26] Katz HS, Milewski JV, editors. Handbook of fillers for plastics. 1st ed. New York:Van Nostrand Reinhold; 1987.

[27] Wypych G, Andrew W, editors. Handbook of fillers for plastics. 2nd ed. PlasticsDesign, Library; 1998.

[28] Luyt AS, Molefi JA, Krump H. Thermal, mechanical and electrical properties ofcopper powder filled low-density and linear low-density polyethylenecomposites. Polym Degrad Stab 2006;91(7):1629–36.

[29] Kuzel R, Krivka I, Kubát J, Prokeš J, Nešpurek S, Klason C. Multi-componentpolymeric composites. Synth Met 1994;67:255–61.

[30] Kubát J, Kuzel R, Krivka I, Bengtsson P, Prokeš J, Stefan O. New conductivepolymeric systems. Synth Met 1993;54(1–3):187–94.

[31] Kuzel R, Kubát J, Krivka I, Prokeš J, Klason C, Stefan O. Heterogeneous systemsbased on precious metal powders and polymers. Mater Sci Eng: B1993;17:190–5.

[32] Van der Pauw LJ. A method of measuring specific resistivity and Hall effect ofdiscs of arbitrary shape. Philips Res Rep 1958;13:1–9.

[33] Boudenne A, Ibos L, Gehin E, Candau Y. A simultaneous characterization ofthermal conductivity and diffusivity of polymer materials by a periodicmethod. J Phys D Appl Phys 2004;37:132–9.

[34] Boudenne A, Ibos L, Candau Y. Analysis of uncertainties in thermophysicalparameters of materials obtained from a periodic method. Meas Sci Technol2006;17:1870–6.

[35] Cecen V, Boudenne A, Ibos L, Novák I, Nógellová Z, Prokeš J, et al. Electrical,mechanical and adhesive properties of ethylene–vinylacetate copolymer (EVA)filled with wollastonite fibers coated by silver. Eur Polym J2008;44(11):3827–34.

[36] Hana Z, Fina A. Thermal conductivity of carbon nanotubes and their polymernanocomposites: a review. Prog Polym Sci 2011;36:914–44.

[37] Hashin Z, Shtrikman S. A variational approach to the theory of the effectivemagnetic permeability of multiphase materials. J Appl Phys 1962;33:3125–31.

[38] Hashin Z. Analysis of composite materials – a survey. J Appl Mech1983;50:481–505.

[39] Bujard P, Munk K, Kuehnlein G. In: Tong TW, editor. Thermal Conductivity, vol.22. Lancaster Technomic Publ. Co. Inc.; 1994.

[40] Tavman IH. Thermal and mechanical properties of copper powder filledpoly(ethylene) composites. Powder Technol 1997;91:63–7.

[41] Budiansky B. Thermal and thermoelastic properties of isotropic composites. JCompos Mater 1970;4:286–95.

[42] Beran MJ. Statistical continuum theories. New York, NY: IntersciencePublishers; 1968.

[43] Krupa I, Boudenne A, Ibos L. Thermophysical properties of polyethylene filledwith metal coated polyamide particles. Eur Polym J 2007;43:2443–52.

[44] Lewis TB, Nielsen LE. Dynamic mechanical properties of particulate filledcomposites. J Appl Polym Sci 1970;14:1449–71.

[45] Nielsen R. Mechanical properties of polymers and composites, vol. 2. NewYork: Marcel Dekker; 1974.

[46] Lux FJ. Models proposed to explain the electrical conductivity of mixturesmade of conductive and insulating materials. J Mater Sci 1993;28:285–301.

[47] Stauffer D. Introduction to percolation theory. London, Philadelphia: Taylorand Francis; 1985.

[48] Kirkpatrick S. Percolation and conduction. Rev Mod Phys 1973;45:574–88.[49] Tchmutin IA, Letyagin SV, Shevchenko VG, Ponomarenko AT. Polym Sci

1994;36:756–82.[50] Chodák I, Krupa I. Percolation effect and mechanical behavior of carbon black

filled polyethylene. J Mater Sci Lett 1999;18:1457–9.[51] Novák I, Krupa I, Chodák I. Investigation of the correlation between electrical

conductivity and elongation at break in polyurethane-based adhesives. SynthMet 2002;131:93–8.

[52] Bhat NV, Upadhyay DJ. Plasma-induced surface modification and adhesionenhancement of polypropylene surface. J Appl Polym Sci 2002;86:925–36.

[53] Wickson BM, Brash JL. Surface hydroxylation of polyethylene by plasmapolymerization of allyl alcohol and subsequent silylation. Colloids Surf, A1999;156:201–13.

[54] Balamurugan S, Mandale AB, Badrinarayanan S, Vernekar SP. Photochemicalbromination of polyolefin surfaces. Polymer 2001;42(2501–1):2.