D. CHAUHAN ET AL.

Copyright © 2012 SciRes. IJMNTA

45

Table 1. Thermal conductivity of various samples used in our computations.

Polymer Matrix Thermal Conductivity (W/m-K) Filler Thermal Conductivity (W/m-K)

Phenol Aldehyde 0.111 Graphite 120

Phenol Aldehyde 0.111 Aluminium Oxide 204

Polypropylene 0.25 Aluminium 237

Polypropylene 0.25 Copper 387

and Russell equations under estimate the experimental

data over the entire range of filler concentrations, while

the Hamilton and Crosser model (with n = 3, spherical

shape of fillers) over estimates the effective thermal con-

ductivity of the materials for phenol-aldehyde/graphite

and phenol aldehyde/aluminum oxide composites. It can

also be seen that, the calculations done by our model for

different shapes are closer to the experimental data then

done by any other theoretical model predicted earlier

Equations (1)-(3). It is seen from the Figures 2-5 that

with the increase in the filler concentration, the effective

thermal conductivity of the composite increases. The

effective thermal conductivity values of the samples used

for our computations are mentioned in Table 1. Table 1

show that the thermal conductivity of the fillers is sig-

nificantly higher than that of the matrix. There is a sig-

nificant change in the eff

of the composite systems as

we change the shape of the filler particles. It is seen from

the figures that the eff

increases nonlinearly with an

increase in the volume fraction of filler particles.

Sphericity is a measure of the roundness of the particle,

denoted by

. The value of

is one for spherical

particles and less than one for other shapes of the parti-

cles. The change in the geometrical configuration of the

particles changes the value of sphericity. An increase in

the value of

means that there is decrease in the an-

gularity, which brings the particles closer and there is an

increase in the eff

of the system. This change in the

sphericity can be seen in the form of small deviations

among the theoretical curves drawn for different shapes

as spherical, elliptical and hexagonal Figures 2-3.

Hence, it is observed that the theoretical values for

eff

calculated by our model proposed for different

shapes, with other existing mathematical models Equa-

tions (1)-(3) are in good agreement with each other for

low volume fractions i.e.

< 0.3. This is because of

the low dispersion of particles in the matrix, due to which

the particles are not able to interact with each other.

However, when the volume fraction increases more than

0.3, there is a rapid increase in the eff

of the system as

the particles come closer as such the interaction between

filler particles become stronger.

4. Conclusions

Theoretical expressions for effective thermal conductiv-

ity for the polymer composites which were established,

was based on the law of minimal thermal resistance and

the equal law of the specific equivalent thermal conduc-

tivity. The different shapes of filler particles as spherical,

elliptical and hexagonal were considered for the calcula-

tions. Equations (17)-(19) gives the relationship between

the effective thermal conductivity (eff

) of filled poly-

mer composites in terms of inclusion volume fraction as

well as other physical parameters of polymer matrix and

fillers when filler volume fraction is less than 60%.

The values of the effective thermal conductivity (eff

)

of phenol-aldehyde/graphite, phenol aldehyde/aluminum

oxide, polypropylene/aluminum and polypropylene/cop-

per composites were then calculated. Good agreement

was found between the theoretical estimations and ex-

perimental data available in the literature. We further

plan to verify these formulae for some more samples.

REFERENCES

[1] C. P. Wong and R. S. Bollampally, “Thermal Conductiv-

ity, Elastic Modulus, and Coefficient of Thermal Expan-

sion of Polymer Composites Filled with Ceramic Particles

for Electronic Packaging,” Journal of Applied Polymer

Science, Vol. 74, No. 14, pp. 3396-3403.

doi:10.1002/(SICI)1097-4628(19991227)74:14<3396::AI

D-APP13>3.0.CO;2-3

[2] X. Lu and G. Xu, “Thermally Conductive Polymer Com-

posites for Electronic Packaging,” Journal of Applied

Polymer Science, Vol. 65, No. 13, 1997, pp. 2733-2738.

doi:10.1002/(SICI)1097-4628(19970926)65:13<2733::AI

D-APP15>3.0.CO;2-Y

[3] H. Tavman, “Thermal and Mechanical Properties of Cop-

per Powder Filled Poly (Ethylene) Composites,” Powder

Technology, Vol. 91, No. 1, 1997, pp. 63-67.

doi:10.1016/S0032-5910(96)03247-0

[4] A. Boudenne, L. Ibos, E. Gehin, M. Fois and J. C. Ma-

jeste, “Anomalous Behavior of Thermal Conductivity and

Diffusivity in Polymeric Materials Filled with Metallic

Particles,” Journal of Material Science, Vol. 40, No. 16,

2005, pp. 4163-4167. doi:10.1007/s10853-005-3818-2

[5] N. M. Sofian, M. Rusu, R. Neagu and E. Neagu, “Metal

Powder-Filled Polyethylene Composites. V. Thermal Pro-

perties,” Journal of Thermoplastic Composite Materials,

Vol. 14, No. 1, 2001, pp. 20-33.

doi:10.1106/9N6K-VKH1-MHYX-FBC4

[6] B. Weidenfeller, M. Hofer and F. R. Schilling, “Thermal

Conductivity, Thermal Diffusivity, and Specific Heat Ca-

pacity of Particle Filled Polypropylene,” Composites Part