J Shanghai Univ (Engl Ed) (2008) 12(1): 85–90

Digital Object Identifier(DOI): 10.1007/s 11741-008-0117-1

Electrical properties of nano-silver/polyacrylamide/ethylene vinylacetate composite

XU Man (� �), FENG Jun-qiang (���), CAO Xiao-long (���)State Key Laboratory of Electrical Insulation for Power Equipment, Xi’an Jiaotong University, Xi’an 710049, P. R. China

Abstract Nano-Ag particles/polyacrylamide (PAM) composites were synthesized by γ irradiation method and then blendedwith ethylene vinyl acetate (EVA). Dielectric behaviors of the Ag/PAM/EVA composites are investigated as a function ofboth the concentration and size of Ag particles. When concentration of the Ag fillers is rarely low, dielectric anomalieswere first observed in contrast to the traditional percolation theory. As concentration of Ag increases, volume resistivityand breakdown field strength are enhanced, loss tangent (tan δ) reduced and dielectric constant kept invariable. In addition,the above variation became larger when the diameter of the Ag nano-particles is smaller. Such dielectric anomalies may beunderstood by considering the unique “Coulomb Blockade Effect” of the nano-sized Ag particles.

Keywords nano-silver (Ag), dielectrics, composite, electrical property.

1 Introduction

Metal-polymer composites have attracted much at-tention because they can possess high dielectric constantwhile retaining flexibility of the polymer matrix[1−3].With this feature, the metal-polymer composites havebroad applications such as electrostrictive materials,charge-storage capacitor and gate dielectric of semicon-ductor devices[4−6]. In view of these applications, previ-ous investigations are most concentrated on enhancingdielectric constant and reducing percolation threshold ofthe composites. The composites studied are correspond-ingly those with high filler concentration, e.g., near17 vol% (0.17 volume fraction)[1], 9 vol%[2] and20 vol%[3], etc.

The metal-polymer composite undergoes a metal-insulator transition at a certain concentration of itsmetallic phase (i.e., the percolation threshold), which isoften characterized by an abrupt drop of resistivity anda divergence of the real part of the dielectric constant[2].Such transition is attributed to the formation of thecontinuous conductive network in the composites andis commonly studied with the famous power law of thepercolation theory. In this paper, we report an interest-ing phenomenon that when the content of the conduc-tive filler is at a certain low concentration, the dielectricbehavior of the metal-polymer composite exhibits char-acteristics in contrast to the percolation theory, i.e., asthe concentration of Ag increases, the volume resistiv-ity and breakdown field strength enhanced, loss tangent

(tan δ) reduced and dielectric constant kept invariable.In addition, the above variation became larger when thediameter of the Ag nano-particles is smaller.

2 Experiment

The AgNO3 solutions with different concentra-tion (0.01∼0.13 M) are mixed with 3 M acrylamidemonomer and radical scavenger and then irradiated with3 × 104 Gy in the field of a 2.59 × 1015 Bq 60Co γ-raysource. The diameter of the Ag nano-particles can bewell controlled by either the reaction ratio or the timeof radiation. The obtained gelatinous solid mixtures aredried in oven at 100 ℃ for 72 h and milled into grainswith a diameter smaller than 45 µm.

The polyacrylamide (PAM) is known as a hard andbrittle material thus the above Ag/PAM compositescannot be hot-molded into samples that are appropri-ate for dielectric measurements. Thus, ethylene vinylacetate (EVA) (modified PE, vinyl acetate is 28%) isselected as stick matrix to form the final composite. Atthis time, the Ag concentration of Ag/PAM/EVA com-posite can be controlled by the content of the Ag/ PAMpowder. The mixture of PAM and EVA is selected asthe control sample for the dielectric measurements.

Ag/PAM and EVA are blended together on aHAAKE-90 rheometer at 130 ℃ with a rotor speed of60 r/min for 10 min, and then molded with a hot-pressing procedure at 170 ℃. The final samples aresquare plate with a side length of 100 mm and a thick-

Received Jun.19, 2006; Revised Sept.18, 2006Project supported by the National Natural Science Foundation of China (Grant No.50277029)Corresponding author XU Man, PhD Candidate, E-mail: xumman@mail.xjtu.edu.cn

86 J Shanghai Univ (Engl Ed) (2008) 12(1): 85–90

ness of about 1 mm. Aluminum foils were pasted ontoboth side of the samples using vaseline to form three-electrode system for the electrical measurement accord-ing to the IEEE standard. Resistance of the sampleis measured by high resistance meter ZC36. Strengthof the breakdown field is measured by power frequencyvoltage instrument. The parameters tan δ and εr aremeasured by QS-36 Schering bridge.

3 Results and discussion

Fig.1 shows a transmission electron microscope(TEM) photo of Ag/PAM/EVA composite with Ag con-centration of 0.05wt%. From the photo it is evident thatthe Ag nano-particles with an average diameter of about20 nm dispersed uniformly in solution. Fig.2 shows XRDpattern of the nano-composite. It can be seen that thesample is composed of two phases, i.e., the metallic sil-ver as indicated by diffraction peaks (111), (200), (220),(311) and non-crystalline polyacrylamide.

Fig.1 TEM photo of the nano-composite solution

(311)(220)(200)

(111)

Inte

nsity

(a.u

.)

20 30 40 50 60 70 802θ(°)

Fig.2 XRD pattern of the nano-composite

Nano-sized particles tend to agglomerate because oftheir high surface energy[7]. Thus, it is quite difficultto prepare nano-particles with both tiny size and homo-geneous dispersion. Traditionally, the polymer matrixand metal nano-particles are synthesized separately andthen hybridized physically to form polymer-metal nano-composites, which may lead to the non-uniform disper-sion of the metal particles in the polymer matrix. Inaddition, the nano-particles in the composite preparedby such procedures usually agglomerated and the diam-eter of them often exceeds 100 nm[8].

In the presented synthesizing procedure, the metalsalt and organic monomer are mixed homogeneouslyat the molecule level in the solution, which made theformation of crystalline metal nano-particles and poly-merization of monomers proceeded simultaneously. Themacromolecular chains of the polyacrylamide on the sur-face of Ag nano-particles prevent them from agglomerat-ing. Thus a homogeneous dispersion of nanocrystallinemetal particles in the polymer matrix is realized per-fectly.

Fig.3 shows the volume resistivity (hereinafter, theresistivity) of the Ag/PAM/EVA composites plottedversus the weight concentration of Ag measured at bothroom temperature and cryogenic temperature. The av-erage diameter of the Ag nano-particles in the compos-ites studied is about 10 nm. At room temperature, whenthe content of Ag is below 2.0×10−2 wt%, the resistivityvaries little compared with pure EVA. When the contentof Ag is between 2.0 × 10−2 wt% and 5.0 × 10−2 wt%,the resistivity rises obviously and reaches a peak valuewhen the content of Ag is 5.0× 10−2 wt%. The value ofthe peak is 4.5×108 Ω ·m, which is almost 4 times largerthan that of EVA matrix (0.8×108 Ω ·m). Nevertheless,the resistivity of the composite decreases gradually whenthe content of Ag is more than 0.025%. At cryogenictemperature (77 K), the resistivity curve resembles thatmeasured at the room temperature with a peak valueof 9× 1013 Ω ·m. Compared with the resistivity of pureEVA at cryogenic temperature (1.5 × 1013 Ω · m), it is6 times larger. In order to study the effect of the parti-cle size on the dielectric behavior of the Ag/PAM/EVAcomposites, the resistivity of composites with Ag parti-cles of 20 nm in diameter is also measured as a functionof the weight fraction of Ag at both room temperatureand cryogenic temperature, as shown in Fig.4. It clearlyexhibits the similar characteristics with that of the com-posites with 10 nm Ag nano-particles, while only the en-hancement of the resistivity is a little smaller than thatof the composites with 10 nm Ag nano-particles. The

10

8

6

4

2

0

10

8

6

4

2

00 2 4 6 8 10Ag content (×10–2 wt%)

Res

istiv

ity a

t roo

mte

mpe

ratu

re (×

108

Ω ·

m)

Res

istiv

ity a

t cry

ogen

icte

mpe

ratu

re (×

1013

Ω ·

m)

Fig.3 Resistivity of nano-composite at room and cryogenictemperature (Ag: 10 nm)

J Shanghai Univ (Engl Ed) (2008) 12(1): 85–90 87

Ag content (×10–2 wt%)

Res

istiv

ity a

t roo

mte

mpe

ratu

re (×

108

Ω ·

m)

Res

istiv

ity a

t cry

ogen

icte

mpe

ratu

re (×

1013

Ω ·

m)6

5

4

3

2

1

0

6

5

4

3

2

1

00 2 4 6 8 10

Fig.4 Resistivity of nano-composite at room and cryogenictemperature (Ag: 20 nm)

peak value is 2.5 and 3 times larger than that of the pureEVA at room temperature and cryogenic temperature,respectively.

The polymer includes both crystalline and amor-phous phases[9], when the electrons are transmitting inthe polymer, they cannot move freely in the amorphousphase as that in the crystalline phase. When the elec-trons in the conduction band transit between differentcrystalline zones, they must overcome an amorphouszone barrier through thermal vibration, therefore, theelectron hopping conduction is the main conduction inthe polymers, and the conductivity is given as follows[9]:

γ =nq2a2υ

6KBTe−

u0KBT ,

where γ is conductivity, n is the concentration of car-rier, q is the charge quantity, a is the average distancebetween micro-crystal, υ is the thermal vibration fre-quency of electron and u0 is the energy barrier in micro-crystals.

In electrical conducting polymer-based composites,many of the microsized metal fillers contact with eachother so the current could flow in these metal fillers.The transport of electrons between discontiguous mi-crosized metal particles is by means of tunneling. Tun-neling may happen because the distance between themicrosized metal particles and their agglomerations isas short as several angstroms, and the volume of ag-glomeration is big so that the energy barrier betweenthem is low. When the size of metallic particles in thepolymer reaches a few nanometers, the energy barrierbetween the particles will increase rapidly because thecapacitance between the particles and their surroundingdielectric may be as small as almost 10−16 F resultedfrom the extremely small size of the particles. In thiscase, every time a single electron tunnels into a metallicparticle (so called the “Coulomb Island”), it will chargethe particles with a charging energy of V = e2

2C (wheree is the charge of a single electron, and C is the capaci-tance between the metallic particle and dielectric). Such

charging effect may block the tunneling of the next elec-tron; otherwise, the energy of the system would keep onincreasing, which is in contrast to the mechanism of thetunneling. This is the Coulomb Blockade Effect[10,11].Thus, there will be interlaced barriers in the compos-ites. These barriers will block not only the transport ofthe electrons in the composites but also the tunneling ofthe electrons between different zones. In the composites,the barrier e2

2C raises the amorphous zone barrier signif-icantly. So the rate of tunneling reduces. The enhancedenergy barrier blocks the movement of the electrons aswell as other charge carriers in the certain direction,which results in the enhancement in the resistivity ofthe composite.

In the following part, we estimate the energy barrier,V, established by the Ag nano-particles in the compos-ite.

For a system consisting of three or more charged con-ductors, voltage between two conductors is dominatednot only by their own charge, but also by the charge onother conductors[12]. Thus, the relationship of the volt-age and charge between different conductors cannot berepresented in partition capacitance rather than one sin-gle capacitance, and the partition capacitances betweenmany conductors form a capacitance network. Fig.5(a)shows a four-conductor-system composed of three

100

50

–50

0

C10C13

C30

C20

C23

C12

1

2

(a) Four-conductor-system composed of three metallic conductors and the earth

(b) Capacitance network composed of six partition capacitance

Fig.5 Partition capacitance and capacitance network

88 J Shanghai Univ (Engl Ed) (2008) 12(1): 85–90

metallic conductors and the earth, and Fig.5(b) showsa capacitance network composed of six partition capac-itance.

According to the calculation in the previous work[13],in a pure polymer with dielectric constant of 3, the par-tition capacitance C and energy barrier V are 3.9 ×10−19 F and 205 meV, respectively, when the diam-eter of the nano-particles is 20 nm, and the distancebetween them is 50 nm. However, the values will be1.08 × 10−19 F and 740.74 meV when the diameter ofthe nano-particles is 10 nm, and the distance betweenthem is 50 nm. In the system of present paper, the di-electric constant of the matrix EVA/PAM is 8.5, thus,the partition capacitance and energy barrier are respec-tively 1.105 × 10−18 F and 72.4 meV when the diame-ter of the nano-particles is 20 nm, and the values arerespectively 3.06 × 10−19 F and 261.44 meV when thediameter of the nano-particles is 10 nm. Therefore theenergy barrier between particles is much larger than thethermal energy of the thermal motion at room tempera-ture, namely, V � KBT (T = 300 K, KBT = 26 meV),the electron conduction of the composites is restrainedand the resistivity is enhanced.

In the Ag/PAM/EVA nano-composites, when thecontent of Ag is less than 2.0×10−2 wt%, the amount ofthe nano-sized Ag particles in the composite is too small,so the blocking effect on the free electrons is not obvi-ous. When the content of Ag is between 2.0×10−2 wt%and 5.0×10−2 wt%, the nano-sized Ag particles are dis-persed in the matrix uniformly without contact witheach other, the condition of the establishment of the en-ergy barrier e2

2C is satisfied�so tunneling of electronsis blocked[14,15]. Thus current in the Ag/PAM/EVAnano-composites decreases and the volume resistivity in-creases. In addition, at cryogenic temperature, KBT =6.67 meV (T = 77 K), the blocking condition V � KBT

can be satisfied much more easily and therefore the re-sistivity increases more obviously.

When the content of Ag is larger than 5.0 ×10−2 wt%, the distance between Ag particles reducesgradually. This results in a low potential barrier be-tween particles so that the electrons can easily tunnelfrom one Ag particle to another.

The breakdown field strength of the composites ex-hibits strong dependence on the concentration of nano-Ag as well. Fig. 6 shows the composites breakdownfield strength of the Ag/PAM/EVA composites con-taining Ag fillers of 10 nm and 20 nm in diameter re-spectively, both plotted as a function of the concen-tration of nano-Ag. Note that the breakdown fieldstrength shown in both figures possesses almost thesame characteristic as the resistivity of the composites,

i.e., keep steady when the Ag concentration is less than2.0 × 10−2 wt%, rises abruptly when the content of Agis between 2.0×10−2 wt% and 5.0×10−2 wt% and thengoes down. Such similarity may be attributed to the factthat the breakdown of the composite is a consequenceof the high-speed movement of the electrons, which isalso strongly correlated with the resistivity of the com-posites. The peak values of composites with 10 nm and20 nm fillers are all more than twice of that of the purematrix.

4

3

2

10 2 4 6 8 10

Ag:10 nm Ag:20 nm

Ag content (×10–2 wt%)

Bre

akdo

wn

field

stre

ngth

(×10

4 kV

/m)

Fig.6 Breakdown electrical field of nano-composite,

the diameters of Ag particles are 10 nm and

20 nm separately

According to the collision breakdown principle ofsolid dielectric[9], the electrons in the conduction bandwould be accelerated by the external high electrical fieldand gain more kinetic energy. At the same time, the freeelectrons will transfer the electrical energy to the latticeand so as to excite the lattice vibration. These twoprocedures would reach equilibrium at certain temper-ature and electrical field, namely stable conduction isestablished. However, if the energy the electron gainedfrom the electric field is more than the energy that theelectron transferred to the lattice, the kinetic energy ofelectron would be enlarged more and more. When theenergy is large enough, new electron can be generatedfrom the interaction between the original electron andlattice. Thus, the number of free electrons is increasedrapidly. The electric conduction comes into unstableprocedure and breakdown begins. In high voltage elec-trical field, kinetic energy of electrons with orientatedmovement is much larger; the dielectric is correspond-ingly easier to breakdown. The energy barrier networkin the polymer established by nano-Ag particles forcesthe electrons going through one by one and blocks theorientating motion of the carrier in the certain electricalfield. If the content of Ag is lower, the distance betweentwo nano-metal particles is too far. The electron accel-erated by electrical field would be blocked by the lowerenergy barrier only after longer distance transfers. Soit is not prominent that the kinetic energy of electron is

J Shanghai Univ (Engl Ed) (2008) 12(1): 85–90 89

reduced. If the content of Ag is too high, the distancebetween Ag particles would be so close that the turneleffect becomes dominating. The block effect reduces andeven disappears, so the breakdown electrical field fallsdown. At the content of about 5× 10−2 wt%, the blockenergy barrier is high and thick. The electrons movingin one direction can be restrained effectively, that is tosay, the kinetic energy is reduced to slow down the col-lision effect, which is applied to the lattice by electrons.So it needs higher electrical field to make the compositebreakdown.

Figs.7 and 8 show the loss tangent (tan δ) and dielec-tric constant (εr) of the composites plotted as a func-tion of the concentration of Ag, with tan δ decreasingand εr keeping almost invariable as the concentrationof Ag increases. Such features are very different withthose of the common percolative metal/polymer com-posites, which may be attributed to the absence of thecontinuous conductive network resulted by the rarelylow content of the Ag fillers. More physically, tan δ andεr indicate the loss and polarization of the dielectric.Conductance loss and relaxation polarization loss aretwo main kinds of loss form in polymer. When nano-Agparticles added in EVA, strong electrostatic attractionbetween nano-Ag particles and the functional groups of

0.05

0.04

0.03

0.02

0.010 2 4 6 8 10

Ag:10 nm Ag: 20 nm

Content of Ag (×10–2 wt%)

Die

lect

ric lo

ss

Fig.7 Dielectric loss (tan δ) of nano-composite

at power frequency

Ag: 20 nm

Ag:10 nm

11

10

9

8

7

6

50 2 4 6 8 10

Die

lect

ric c

onst

ant

Content of Ag (×10–2 wt%)

Fig.8 Dielectric constant (εr) of nano-composite

at power frequency

the polymer chain makes the dipoles difficult to rotatewith the electrical field. As a result, the relaxation po-larization loss of the composite is reduced. The block-ade effect of nano-Ag limits charge transmission in thepolymer. So the conductance loss is also reduced. Bothfactors make tan δ of the composites decrease. The di-electric constant of the composite depends on the con-tribution of every component in composite. For the lowcontent of nano-Ag particles, εr value of the compositeswith all nano-Ag contents is very close with εr of pureEVA material.

4 Conclusions

Nano-Ag particles/PAM composites were synthe-sized using γ irradiation and then were physi-cally blended with EVA, forming the thermoplasticAg/PAM/EVA composites. The nano-Ag particles werecharacterized by TEM and XRD. Dielectric propertiesof the composites with a rarely low concentration of Agconcentration are investigated. Room resistivity of thecomposites containing nano-Ag particles with 10 nmand 20 nm in diameter can be 4 and 2.5 times largerthan that of pure EVA while strength of the break-down electrical field of the composites can be 3.5 and2.2 times larger than that of pure EVA, respectively.At cryogenic temperature the resistivity can be raisedeven more. The dielectric loss decreases and dielectricconstant keeps invariable as the content of Ag increases.These novel properties of the Ag/PAM/EVA compositeare explained by the mechanics of Coulomb blockade.

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(Editor CHEN Ai-ping)