Percolation Network Formation in Poly(4-vinylpyridine)/Aluminum Nitride Nanocomposites: Rheological,Dielectric, and Thermal Investigations

Razvan Florin Barzic,1 Andreea Irina Barzic,2 Gheorghe Dumitrascu1

1“Gheorghe Asachi” Technical University, Faculty of Mechanics, 43 Dimitrie Mangeron,700050 Iasi, Romania

2“Petru Poni” Institute of Macromolecular Chemistry, 41A Grigore Ghica Voda Alley, 700487 Iasi, Romania

This work is concerned with several issues related tothe rheological behavior of poly(4-vinylpyridine)/alumi-num nitride (AlN) nanocomposites. The composites areprepared by solution processing combined with ultra-sonication and magnetic stirring. To understand thepercolated structure, the nanocomposites are charac-terized via a set of rheological, dielectric, and thermalconductivity analyses. The nanoparticle networks aresensitive to the steady shear deformation particularlyat low shear rates, where a shear-thinning domain isobserved. The rheological measurements revealed alsothat the activation energy is significantly lower at highnanofiller loadings suggesting stronger AlN interac-tions. The changes in the terminal behavior of shearmoduli are the result of variations in composite elastic-ity determined by the percolation network. The floccu-lation and percolation thresholds estimated from therheological moduli dependence on AlN loading are cor-related with the dielectric constant values. Thermalconductivity is determined from a new theoreticalmodel involving, besides the contribution of eachphase, both percolation processes and the shape ofthe nanofiller. POLYM. COMPOS., 00:000–000, 2013. VC 2013Society of Plastics Engineers

INTRODUCTION

Blending polymers with inorganic fillers opens new

perspectives in various industries ranging from aeronau-

tics to microelectronics since it leads to hybrid materials

with improved thermal, separation, mechanical and elec-

trical properties [1, 2]. The performance of the composite

is dependent on nanofiller characteristics and its the state

of dispersion. For some properties, a perfectly homogene-

ous dispersion is required, while, in other cases, a perco-

lating network is required, which can be achieved by

controlled aggregation of the particles. Many investigation

techniques have been employed to evaluate the dispersion

degree of nanoparticles in various solvents, including

UV–vis spectroscopy [3], transmission electron micros-

copy (TEM) [4], electron tomography [5], X-ray diffrac-

tion [6], and scanning electron microscopy [7].

Another method that is sensitive to the filler dispersion

in the matrix is rheology [8]. This type of testing of the

nanocomposite viscoelastic properties has both practical

importance related to composite processing and scientific

importance as a probe of the composite dynamics and

microstructure. The formation of a pseudo-solid-like net-

work with strong interactions between polymer and par-

ticles leads to a significant increase of the viscosity [9].

The sudden modification of the rheological properties

denotes the “rheological percolation” transition, which

has been studied for various types of nanoparticle suspen-

sions based on low viscous solvents [10]. Comparatively

to the electrical percolation threshold, the values of the

rheological one are found at subsequently higher filler

contents (0.1–2 wt%), depending on the chemical proper-

ties of the solvent and the method used for nanoparticles

dispersion. The differences between the percolation

thresholds for conductivity and rheology are found in dif-

ferent morphological requirements for a mechanical rigid

or an electrically conductive network [11].

To incorporate nanofillers in polymer matrices, several

methods have been reported, namely solution processing

[12], melt mixing compounding [13], mechanical stretch-

ing [14], curing/in situ polymerization [15], the use of

latex technology [16] or magnetic fields [17], and coagu-

lation method [18]. Most reported studies are focused on

carbon-based nanofillers [19, 20], metal oxides [21], and

less on aluminum nitride (AlN). This is a semiconducting

Correspondence to: Andreea Irina Barzic, e-mail: irina_cosutchi@

yahoo.com

Contract grant sponsor: European Social Fund and Romanian Govern-

ment; contract grant number: ID79407 (POSDRU CUANTUMDOC

“Doctoral Studies for European Performances in Research and

Innovation”).

DOI 10.1002/pc.22807

Published online in Wiley Online Library (wileyonlinelibrary.com).

VC 2013 Society of Plastics Engineers

POLYMER COMPOSITES—2013

compound with relative high thermal conductivity and oxi-

dative resistance; thus, its introduction in a polymer matrix

is expected to enhance both thermal conductivity and

dielectric properties. On the other hand, poly(4-vinylpyri-

dine) (P4VP) is a high-performance polymer with good

physical properties, being used in many industrial sectors.

In this work, new P4VP/AlN nanocomposites are pre-

pared by solution processing followed by ultrasonication.

The rheological behavior of obtained nanocomposites in

light of interactions between AlN and polymer chains or

between AlN nanoparticles is examined. This is a quite

complex and difficult system to investigate because the

typical behavior of polymeric solution is strongly modi-

fied the presence of a nanofiller network. Therefore, typi-

cal analysis methods used for conventional polymeric

systems are not useful in this context, and a more innova-

tive investigation is required to establish the relationship

between the rheological behavior and microstructure of

such a system. This investigation tries to elucidate on the

effect of the AlN content on rheological properties in

order to determine the onset of percolation in these nano-

composites and its impact on the microstructure in light

of thermal conductivity and dielectric characteristics.

The novelty of the manuscript consists in the studied

nanocomposites system, which to the best of our knowl-

edge is not reported in literature from the point of view of

the preparation and characterization. Also, most articles

determine the rheological threshold without considering

the flocculation one. This is one of the few studies linking

the rheological, dielectric, and thermal conductivity proper-

ties with microstructure changes. In addition, for a more

accurate description of the heat transfer in polymer nano-

composites we have developed a new theoretical model

considering the besides the contribution of each compo-

nent, the percolation processes, and shape of the filler.

EXPERIMENTAL

Materials

P4VP with Mw 5 60,000 g mol21 has been used as

polymer matrix as received from Sigma-Aldrich. The sol-

vent N,N-dimethylacetamide (DMAc, 99.5% purity) and

the AlN nanopowder (<100-nm particle size) are pur-

chased from Sigma-Aldrich. The AlN morphology

obtained by TEM is presented in Fig. 1.

Preparation of the P4VP/DMAc Solutions

A standard procedure for preparing the sample solu-

tions is used. The P4VP powder is weighed and put into

a jar (also weighed). The polymer is then mixed with an

appropriate amount of DMAc, to obtain 2, 5, 10, 25, and

50 wt% concentrations. The P4VP solutions are homoge-

nized by vigorously stirring during 30 min. These solu-

tions are rheologically analyzed in order to determine the

flow behavior of the matrix.

Preparation of the AlN/DMAc Dispersions andNanocomposites

The dispersion is prepared by mixing different

amounts of AlN with 2 mL of DMAc solvent in a flask

and then sonicating the resulting mixture for 1 h. The

nanoparticle loading range from 0.05 to 0.34 g in order to

achieve 1, 5, 10, 20, 30, and 40% by weight in regards

with P4VP matrix. All ultrasonication processes are car-

ried out with a sonicator UTR200 Hielscher type (200

watts, 24 kHz) for 1 h. The flask is placed in a bath of

ice water during sonication in order to prevent rising of

the temperature of the mixture. After achieving a maxi-

mum dispersion of AlN in DMAc, different amounts of

polymer powder are added in the nanosuspension. Subse-

quently, the system is homogenized by stirring for 6 h at

room temperature. P4VP and P4VP/AlN films are pre-

pared by casting the corresponding solutions onto Teflon

substrates. Subsequently, they are placed in a preheated

oven at 65�C to remove most of the solvent for 3 h, and

then the resulting samples are dried at 90�C in a vacuum

oven for 24 h. Figure 1 shows the routes used for the

preparation of the P4VP/AlN nanocomposites.

Characterization

The rheological analysis of the P4VP/AlN nanocompo-

site solutions is performed on a stress-controlled Bohlin

FIG. 1. The preparation steps of the studied P4VP/AlN nanocomposites. [Color figure can be viewed in the

online issue, which is available at wileyonlinelibrary.com.]

2 POLYMER COMPOSITES—2013 DOI 10.1002/pc

CS50 rheometer, manufactured by Malvern Instruments.

The measuring system presents cone-plate configuration,

having the following characteristics: the cone diameter of

40 mm, the angle of 4� between the cone and the plate

and the gap is 150 lm. Shear viscosities are recorded

over the 0.01–1000 s21 shear rates domain for surprising

all possible flow regimes, at several temperatures (25–

50�C). Oscillatory shear tests were carried out within the

linear viscoelastic regime of the samples under frequen-

cies and strains for which the storage (G0) and loss (G00)moduli are independent of the strain amplitude. For the

present study, a shear stress of 2 Pa was selected. The

test program included frequency sweep tests from 0.1 to

60 Hz at room temperature.

The morphology of the nanofiller is obtained on a

Hitachi HT7700 120 kV Compact-Digital Biological

TEM. Dielectric constant is determined using a LCR

METER instrument for capacitance measurements. The

films with thickness of 60 mm are placed in contact with

a capacitor. The measurements are carried out at room

temperature and following frequencies are applied: 1 Hz,

1 kHz, and 1 MHz.

RESULTS AND DISCUSSION

The final characteristics of the nanocomposites are

influenced by the nature, properties, and content of com-

ponents, microstructure of composite, and interfacial

interactions between matrix and dispersed phase [22].

When processing the matrix, a careful examination and

control of polymer solution properties, under the influ-

ence of some external factors, is of great importance [23].

The structural composites industry and the electronics

business rely heavily upon rheological testing for product

improvement. During compounding, several factors influ-

ence the final morphology, including shear, solution con-

centration, solvent nature, and specific interactions.

Viscosity is one of the most important rheological

parameters in polymer solution processing, reflecting the

effects generated by molecular structure and chain inter-

actions. In regard with the latter factor, the present study

first aims to determine the molecular entanglements for-

mation and subsequently to prepare the P4VP solution in

this regime since they enhance the matrix strength and

might preserve the AlN network. The P4VP solutions of

various concentrations are subjected to rheological analy-

sis in order to identify the different concentration ranges

in which polymer chain entanglements dominate the flow

behavior. The dilute concentration regime, where the

polymer chains are distributed randomly as separate

spheres, is not studied since in this domain no interchain

entanglements occur and the polymer molecules primarily

interact with the solvent molecules [24]. Therefore, the

working polymer solution concentrations used in the rheo-

logical measurements are in the range of 2–50 wt%. The

modification of the solution properties generated by chain

entanglements are reflected in the specific viscosity, gsp ,

dependence on concentration. Literature [25] shows that,

for neutral linear polymers in a good solvent, in the semi-

dilute range, there are two different power law dependen-

ces: (1) gsp� c1.25 in semidilute unentangled regime and

(2) gsp� c4.2524.5 in semidilute entangled domain [26].

Figure 2 presents the gsp as a function of concentration

for P4VP solutions in DMAc. At low concentrations gsp�c1.06 revealing the onset of the semidilute unentangled,

where the concentration is large to have some chain over-

lap, but not enough to cause any significant degree of

entanglement. As the concentration is further increased,

the topological constraints induced by the larger occupied

fraction of the available hydrodynamic volume in solution

generate chain entanglements. The slope sudden modifica-

tion gsp�c4.03 marks the semidilute entangled regime.

The crossover of concentration from the semidilute unen-

tangled to semidilute entangled regime, defines the criti-

cal entanglement concentration, ce, which is found to be

17.76 wt%. Below ce the solution viscosity is controlled

by the intramolecular excluded-volume effects while

above ce the intermolecular entanglements have a domi-

nant effect on the rheology of the solution [25]. The

P4VP concentration used for the preparation of the com-

posites is chosen from entangled domain, namely 50

wt%.

The rheological properties of the P4VP/AlN nanocom-

posites are investigated with a stress rheometer under

steady state flow procedure. Figure 3 shows the shear vis-

cosity as a function of shear rate for neat P4VP and its

AlN reinforced solutions. The matrix exhibits a Newto-

nian behavior in the entire domain of applied shearing,

whereas the corresponding P4VP/AlN nanocomposites

present an increase in shear viscosity and significant shear

rate dependence. Thus, the Newtonian regime is reduced

as the nanofiller amount is higher, while the thinning

behavior becomes more pronounced. The viscosity of

nanocomposites containing 20, 30, and 40 wt% AlN is

dramatically reduced, probably because the nanoparticle

network formed in P4VP is broken down as the shear rate

increases.

FIG. 2. Dependence of specific viscosity on concentration for P4VP

solutions in DMAc.

DOI 10.1002/pc POLYMER COMPOSITES—2013 3

The experimental data for viscosity and shear stress, r,

are fitted to the power-law relationship described by Eq.

1:

r5K � _cn (1)

where n and K are the shear thinning exponent (flow

index) and consistency index, respectively.

The shear thinning exponent of nanocomposites is

determined at a given volume fraction, as follows: a dou-

ble logarithmic plot of the flow curves is made and a

straight line is fitted to the data at the lowest shear rates,

wherein the rheological response is most representative

for the nanofiller structure in the composite. At high shear

rates, the flow is mostly controlled by the polymer

matrix. Thus, as seen in Fig. 4, the shear-thinning expo-

nent is determined by the slope of the straight line at the

lowest shear rates (under 10 s21). Thus, the flow index pf

P4VP/AlN takes values lower than unity (0.4820.91), as

expected for a pseudoplastic fluid. The obtained values of

n can be used to compare the degree of nanofiller disper-

sion in different nanocomposite samples at fixed filler

concentration. In general, n 5 1 is indicative of a Newto-

nian flow system. If the reinforced samples behave as the

polymer matrix, essentially Newtonian, they are usually

not nanocomposites, and such behavior reveals the pres-

ence of micrometer size aggregates. In contrast, nanocom-

posites demonstrate a considerable shear thinning (n< 1)

at a relatively small filler volume fraction, and thus usu-

ally comprise the morphology of smooth, finely dispersed

nanoscale filler. Additionally, samples with moderate val-

ues of n (around 0.5 or lower) are very good dispersed in

the polymer [8]. The studied materials exhibit low flow

indices, indicating that the AlN nanoinclusions are well

dispersed in P4VP.

The complex viscosity, g�, of the P4VP/AlN nanocom-

posites is comparatively studied at 25�C and different

angular frequencies, as shown in Fig. 5. In the case of the

matrix, g� is independent of frequency, indicating that the

P4VP chains are relaxed. It can be observed that with

addition of AlN the complex viscosity in the low-

frequency range increases, and then after 1 rad s21 it

becomes constant for 1–10 wt% loading. This aspect

related to the fact the long P4VP chain relaxation is

effectively restrained by the presence of the nanofiller. At

high loading (20–40 wt% AlN) the Newtonian plateau

disappears progressively, and a remarkable shear-thinning

domain is noticed. The g� values are varying with several

orders of magnitude comparatively with P4VP. A similar

reduced viscosity with better nanoparticle dispersion has

been observed for polymer containing clays, carbon nano-

tubes, fullerene, or magnetite [27–29].

In order to understand the effect of temperature on the

rheological properties the Arrhenius equation, defined for

the complex viscosity, is used:

g �5BexpðEa=RTÞ (2)

where Ea is the flow activation energy, T is the absolute

temperature, and R is the universal gas constant.

In the case of nanocomposites Ea can be related to the

interactions occurring among polymer chains and nanofil-

ler. The value of Ea is determined by the ease with which

FIG. 3. Shear viscosity as a function of shear rate for studied P4VP/

AlN nanocomposite solutions in DMAc at room temperature.

FIG. 4. Shear stress as a function of shear rate for studied P4VP/AlN

nanocomposite solutions in DMAc at room temperature.

FIG. 5. Complex viscosity dependence on the angular frequency for

the studied P4VP/AlN nanocomposite solutions.

4 POLYMER COMPOSITES—2013 DOI 10.1002/pc

the AlN nanoparticles move through the P4VP chains.

The activation energy is estimated from the slope of the

graphical representation of ln g� (at 0.7 rad s21) versus

1000/RT. Figure 6 reports the values of Ea for different

AlN amounts. For the neat P4VP, the flow activation

energy is found to be 81.48 kJ mol21. The rapid decrease

of the energetic flow barrier with increasing AlN percent

suggests that at higher nanoparticle concentrations, the

AlN is less restricted and are less interacting with the

P4VP chains. Therefore, less wettability with the polymer

matrix and more particle–particle interactions take place.

Literature [30] shows that the increasing energetic inter-

action between the polymer matrix and the nanofiller

with temperature increased the rate of the attachment

(wetting) of the filler to the polymer according to the

Arrhenius law, in which the activation energy is propor-

tional to the polymer–nanoparticle interaction parameter.

Figure 6b shows the dependence of the complex viscosity

on temperature for the sample containing 10 wt% AlN. It

can be noticed from Figure 6c that the activation energy

decreases in the range of 0.7–10 rad s21, while at high-

shear frequency (e.g., 100 rad s21), it increases since the

contribution of the matrix becomes dominant. This result

is consistent with literature data [31, 32], which reports

that at low shear frequencies the viscoelastic behavior

reflects the contribution of the nanoparticles, whereas at

high shearing the response of the polymer prevails.

On the other hand, the increase of g� causes similar

increase in the storage modulus, G0 and storage modu-

lus, G00. Figure 7 presents the dependence of G0 on the

AlN content. In solution state, the pure P4VP exhibits

terminal behavior similar to linear polymers with scaling

properties of approximately G0 / x2 and G00 / x1 [33].

The power law dependence of both rheological moduli

on angular frequency weakens monotonically with

increasing AlN loading. The effect of nanofiller on the

rheological properties of the nanocomposites is strong

especially at low x values. The observed nonterminal

behavior suggests that the nanoparticles not only cause

the restriction of P4VP chain relaxation, but also influ-

ences the short-range dynamics or local motion of poly-

mer chains in the nanocomposites. In other words, the

significant jumps distinguished in the low-frequency

storage modulus, starting with 1 wt% AlN, reveal a

transition from viscoelastic liquid- to solid-like behavior

given by the enhancement of the AlN-AlN interactions,

FIG. 6. (a) Activation energy as a function of AlN loading for the studied P4VP/AlN nanocomposite solu-

tions. The inset graph shows the dependence of ln h� on 1000/T; (b) the temperature dependence of the com-

plex viscosity for 10 wt% AlN at 0.78 rad s21 and (c) complex viscosity dependence on 1000/RT at

different shear frequencies for the sample containing 10 % wt AlN.

DOI 10.1002/pc POLYMER COMPOSITES—2013 5

leading eventually to a percolation network. Compara-

tively with the viscous G00 modulus, the elastic G00 one

is found to be more sensitive to the dispersion quality

of nanofiller, which is dependent on the interfacial

energy [34]. This is the reason for which only G0 values

are presented in Fig. 7.

When characterizing the rheological percolation Kotsil-

kova [8] introduced two critical concentrations. The first

one is called the percolation threshold (flocculation, c*)

and depicts the critical concentration of local percolation

and formation of fractal flocs. The second rheological

threshold delimits the formation of a continuous structural

network of fractal flocs, c**. The two thresholds can be

rheologically determined using the data from the low

amplitude oscillatory shear flow. Most of the studies

reported on the percolation threshold of nanocomposites

are determining this characteristic from a relationship

between sharp change of rheological properties and the

percolation transitions [35, 36]. Figure 8a depicts the low-

frequency curves of G’ and G00 at x 5 0.7 rad s21 against

the AlN amount. The concentration c* is determined by

the crossing point of two distinctive slopes of elastic

modulus. The point at which the two shear moduli are

crossed defines c**. The obtained values are illustrated in

Fig. 8a.

These results can be related with changes in the nano-

composite microstructure, reflected also in other proper-

ties, for instance the dielectric ones. The dielectric

constant, e, of P4VP/AlN is determined from the electri-

cal capacitance data, according to Eq. 3:

e5C � de0 � S

(3)

where d and S represent thickness and area of the sample,

C is the capacitance, and e0 5 8.854 3 10212 F m21 rep-

resents the absolute permittivity.

The dependence of dielectric constant on AlN amount

is shown in Fig. 8b. It can be noticed that there are two

inflexions in e values as the introduced percent nanofiller

in the system increases. These two points can be corre-

lated with the microstructure modifications, denoted by

c* and c**. Thus, in the low concentration domain of

nanoparticles (1–5 wt%) a slightly linear increase of the

dielectric constant is observed. At 5.86 wt%, the slope is

changed owing to the increase of the particle–particle

interactions in the samples resulting in flocculation (frac-

tal flocs). Similar to viscoelastic properties, at this point

takes place the formation of a structure dominated by uni-

form AlN agglomerates, which penetrate the polymer

continuous phase. Further addition of nanofiller in P4VP

determines another increase of the slope at 18.42 wt%

indicating that within the polymer the fractal flocs are

long-range connected, constituting a three-dimensional

(network) supramolecular structure. The introduction of

AlN nanoparticles with higher dielectric constant then

that of the P4VP leads to the enhancement of this prop-

erty for resulting nanocomnposites. Moreover, the micro-

structural modifications in the studied nanocomposites

generate nonlinear augmentation of the dielectric constant

(in regard with the matrix) due to the formation of a high

polarizable network of AlN.

On the other hand, it is observed that the dielectric

constant decreases gradually with increasing frequency.

This fact may be caused by the different polarization

mechanisms, contributing to the sample’s e, which are

FIG. 7. Storage modulus dependence on angular frequency for the

studied P4VP/AlN nanocomposite solutions.

FIG. 8. Variation with AlN loading of (a) rheological moduli and (b)

dielectric constant. The inset graph represents the dependence of dielec-

tric constant with frequency at different AlN percent.

6 POLYMER COMPOSITES—2013 DOI 10.1002/pc

frequency dependent. In the case of polymer nanocompo-

sites, the magnitude of the dielectric constant is influ-

enced by two aspects. The first one is represented by

the ability of the polarizable units from the backbone

to orient fast enough to keep up with the oscillations

of the applied alternating electric field. The second

aspect is related to the number of introduced dipoles

(nanoparticles) in the system. Therefore, the dielectric

properties of a reinforced polymer are determined by

the polarizability of its components at a certain fre-

quency. Electronic (or atomic) polarization involves the

separation of the center of the electron cloud around an

atom with respect to the center of its nucleus under the

application of electric field. This mechanism occurs

prevalently at high frequencies (optical spectral domain,

�1014 Hz) because only the lowest mass species, the

electrons, are efficiently polarized. Dipolar (or orienta-

tion) polarization refers to the orientation of molecular

dipoles in the direction of applied field which other-

wise would be randomly distributed due to thermal ran-

domization. In solid state, the alignment of permanent

dipoles requires considerably more time than electronic

or atomic polarization, taking place at microwave (109

Hz) or lower frequencies. In addition, for multicompo-

nent systems, like polymers with structural inhomoge-

neities (e.g., nanoparticles), space charges are build up

at the interfaces of the constituents owing to the incon-

sistency of their dielectric constants at interfaces. This

phenomenon is known as interfacial or space charge

polarization and can be identified in the low-frequency

dielectric data. The changes of the dielectric constant

versus frequency are assigned to the dielectric relaxa-

tions especially at low frequency, which are caused by

micro-Brownian motion of chain segments. Neverthe-

less, these changes are also influenced by interfacial

polarization process, which is present in heterogeneous

dielectrics and is generated by the traveling of the

charge carriers [37].

In order to evaluate the interdependence between dif-

ferent frequencies, AlN concentrations and the relaxation

processes, the dependence of dielectric constant on fre-

quency (f) is plotted in the inset graph from Fig. 8b. At

low frequencies, there is a variation of e, which becomes

more obvious as the frequency increases. This behavior

results from the orientation ability of all the free dipolar

functional groups in the P4VP chain, leading to a higher

e value. As the electric field frequency increases, the big-

ger dipolar groups find it difficult to follow the alternat-

ing field, so the contributions of these dipolar groups to

the dielectric constant lead to a continuously decreasing

of this parameter for P4VP at higher frequencies. Simi-

larly, the inherent e in AlN nanoparticles is also dimin-

ished with augmentation of the applied field frequency.

This combined decreasing effect of the dielectric constant

for both matrix and the filler particles results in a

decrease in the effective e of the P4VP/AlN nanocompo-

sites when the frequency of the electric field increases.

At 1014 Hz the dielectric constant was determined from

Maxwell’s relation:

e51:1n2 (4)

where the multiplying constant before n represents an

additional contribution of appreciatively 10% from the

orientation polarization, n is the refractive index of the

nanocomposite, and it was determined by considering it a

function of composition in which the refractive indices of

P4VP and AlN were introduced, namely 1.643 and 2.2,

respectively.

The variation of the dielectric constant is more pro-

nounced as the reinforcement percent is raised. This could

be the result of the microstructure changes occurring

within the nanocomposite during loading. The formation

of a percolated structure favors the accumulation of elec-

tric charge around the AlN nanoparticles thus enhancing evalues. In other words, the nanocomposite material is

able to store more electrical energy by an applied volt-

age—property required for construction of electronic pas-

sive components. This type of materials with relatively

high dielectric constant can be used in electronic packag-

ing, where high thermal conductivity is required for dissi-

pating the heat generated in devices and matching the

thermal expansion coefficients to that of silicon chips,

thus reducing thermal failure.

In this context, thermal conduction in the P4VP/AlN

samples is evaluated by using different theoretical mod-

els. Most of these approaches start from different assump-

tions, but all involve the knowledge of thermal

conductivity of filler (kAlN 5 280 W m21 K21) [38], and

of the matrix. For P4VP, the thermal conductivity was

determined from the method proposed by Bicerano [39]:

kP4VP 50:135614 10:126611

� 1vBB =N10:108563 � ðNN1NO20:125NHÞ=N (5)

where 1vBB denotes the portion of the first-order connec-

tivity index contributed by the bonds between pairs of

backbone atoms, NN, NO, NH represent the number of

nitrogen, oxygen, and hydrogen atoms and N is the total

number of nonhydrogen atoms.

All these parameters are described in detail in the

work of Bicerano [39]. The thermal conductivity of P4VP

evaluated with this method is 0.153 W m21 K21.

The basic series model [40] assumes no contact

between particles and so the contribution of particles is

confined to the region of matrix embedding the particle.

The thermal conductivity of composites in this case is

given by the following expression:

k5kP4VP � kAlN

/AlN � kP4VP 1/P4VP � kAlN

(6)

where /P4VP and /AlN are the volume fractions of the

matrix and the filler.

DOI 10.1002/pc POLYMER COMPOSITES—2013 7

In the rule of mixture model, also referred to as the

parallel model [41, 42], each phase is assumed to contrib-

ute independently to the overall conductivity, proportion-

ally to its volume fraction:

k5/AlN � kAlN 1/P4VP � kP4VP (7)

The parallel model maximizes the contribution of the

conductive phase and implicitly assumes perfect contact

between particles in a fully percolating network. Knowing

that these two models provide the upper and lower limits

of the thermal conductivity of composites, other models

have been applied. In the case of the Lichtenecker model

[43], the effective thermal conductivity of the composite

is given by:

k5kUP4VP

P4VP 1kUAlN

AlN (8)

Maxwell–Garnett developed a mixing rule, which con-

siders that the polymer is reinforced with spherical par-

ticles, which do not interact with each other and are

randomly distributed in the system.

k5kP4VP

kAlN ð112/AlN Þ2kP4VP ð2/AlN 22ÞkP4VP ð21/AlN Þ1kAlN ð12/AlN Þ

(9)

Another model is proposed by Vysotsky model [44],

which considers the percolation processes in the polymer

nanocomposites. Thus, the critical volume (/percol) is

introduced to create a thermal conductive percolation

model.

k5kAlN ðkpercol =kAlN Þ 12/AlN

=12/percolð Þn (10)

where kpercol is the critical value of thermal conductivity

corresponding to /percol and n is the percolation network

exponent.

The value of /percol is determined by selecting a vol-

ume fraction between 0.1 and 0.5 as critical volume and

the thermal conductivity of the composite is calculated

from Maxwell–Garnett model. Then, a little higher vol-

ume fraction (/percol 1D/) and kpercol are used in Eq. 10to get the value of k. When ðk2kpercol Þ=k � 5% the set

of volume fraction is the correct value for /percol, thus

resulting 0.16 and 0.11 for kpercol and /percol , respectively.

The exponent n is evaluated by introducing kpercol and

/percol in Eq. 10 and for /50 the calculated thermal con-

ductivity should be close to that of the matrix the value.

The network exponent as determined with Vysotsky

model is of 0.44. However, this approach does not

include clearly the influence of the polymer, leading to

the similar results for systems with the same filler and

different matrices. In this context, we propose a new

model (by modifying the Vysotsky approach) which takes

into consideration the thermal properties of the matrix

and the shape of the filler. The developed approach is

described by the Eq 11:

k 5 /AlN 3kAlN

kpercol

kAlN

� �1f

1-/AlN1-/percol

� �n

1/P4VP 3kP4VP

kpercol

kP4VP

� � 1-/P4VP1-/percol

� �n (11)

where f is the factor of the particle shape, defined as f 53=w(the sphericity is w � 1).

Considering the shape of the used AlN, displayed in

Fig. 1, it can be assumed that for this type of nanofiller wis about 0.8. Following the same procedure for determin-

ing kpercol , /percol , and n, we obtain: 0.47, 0.33 (or 6.11

wt%), and 0.69, respectively.

The results concerning thermal conductivity, derived

from the applied approaches, are presented in Fig. 9. It

can be observed that Maxwell–Garnett and Vysotsky

relations give close values for k, which are comprised

between series and parallel models. Considering the

fact that the percolation model does not express

directly the heat transfer capacity of P4VP, it can be

said that these dependencies do not accurately describe

the thermal behavior of the samples. Literature [45]

shows that Lichtenecker mixing rule leads to values in

agreement with the experimental data. The proposed

Eq. 11 conducts to similar values at high loading per-

cents, but the difference from the Lichteneker relation

is that our model describes more accurately the thermal

behavior of the nanocomposite at low reinforcements.

As observed in Fig. 9, for /50 Eq. 11 gives a thermal

conductivity identical with that of the matrix. Compara-

tively with the rheological percolation threshold, the

value corresponding to the thermal conductivity is

slightly higher. The thermal percolation threshold is

reached when a filler network is formed. A conductive

“infinite” path or cluster is sufficient to obtain a con-

ductive composite. However, when this threshold is

achieved the amount of filler is high enough to signifi-

cantly affect the elasticity/rigidity of the polymer

matrix. Fewer nanoparticles are needed to form an AlN

FIG. 9. The dependence of thermal conductivity of P4VP/AlN nano-

composites on AlN loading evaluated using different theoretical models.

8 POLYMER COMPOSITES—2013 DOI 10.1002/pc

network inside the P4VP matrix that solidifies the lat-

ter. The proposed theoretical approach reveals a sudden

enhancement of thermal conductivity at low AlN per-

cent, whereas after the percolation threshold the rate of

k increasing is lower. The thermal transport in studied

samples is increased at high nanofiller amounts, making

these materials good candidates for applications in

printed circuit boards, connectors, thermal interface

materials, and heat sinks.

CONCLUSIONS

This article reports the preparation of some new nano-

composites using P4VP as matrix in which are incorpo-

rated different percent of AlN nanoparticles. The

synthesis procedure is a traditional one, consisting in

solution mixing of the matrix with the nanofiller suspen-

sion, stabilized by ultrasonication; subsequently, the sys-

tem being homogenized by stirring. The sudden changes

recorded in the shear-thinning index reflect a good disper-

sion of the AlN in the polymer. Also, the response of

complex viscosity and shear moduli at low angular fre-

quencies reflect the formation of a percolated structure.

The concentrations corresponding to the flocculation and

the percolation thresholds are obtained from rheological

measurements and they have found a good correspon-

dence in the dielectric properties. The formation of a per-

colated structure favors the accumulation of electric

charge around the AlN nanoparticles thus enhancing evalues and implicitly the ability of the material to store

electrical energy. A new theoretical model is proposed for

describing the thermal conduction of nanocomposites,

which comparatively with Vysotsky approach takes into

account the contribution of the matrix, the shape of the

nanoparticles and the percolation processes. This

approach describes more accurately the thermal transport

at low loadings and at 40 wt% AlN indicates an augmen-

tation of 69.15 times in regard with the pure P4VP. The

obtained results indicate a relatively high dielectric con-

stant and a good thermal transfer recommending the ana-

lyzed P4VP/AlN nanocomposites as suitable materials for

electronic passive components and high-performance ther-

mal management systems.

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