Abstract : As the disposal of fly ash (FA) poses a serious problem in terms of land use and potential environmental pollution, there exists a global interest for its utilization. Utilization of fly ash as filler material in polymer composites is considered important from both economic and commercial point of view. In this communication, the effective thermal conductivity and coefficient of thermal expansion (CTE) of composites synthesized with fly ash filler embedded in high-density polyethylene (HDPE) matrix is investigated. Incorporation of fly ash in HDPE enhances both the thermal stability and the effective thermal conductivity of the composites. CTE, however, significantly decreases as the FA content increases in HDPE. Effective thermal conductivity for HDPE containing 70-volume fraction (%) fly ash becomes almost twice than that for unfilled HDPE. Results on both the effective thermal conductivity and CTE of HDPE/FA composites have been discussed in light of various theoretical models. Our analysis indicates formation of conductive channels of FA particulates in HDPE, which causes rapid enhancement in the effective thermal conductivity of the HDPE/FA composites. We also confirm the importance of the role of the interphase volume and the strength of the polymer – filler interactions to successfully predict the CTE of HDPE/FA composites.
Keywords : High-density polyethylene/Fly ash composites, Thermal stability, Effective thermal conductivity, Co-efficient of linear thermal expansion (CTE).
PACS Nos. : 81.05.Qk; 81.20.Hy; 81.70.Pg
1. Introduction
Fly ash (FA), a waste by-product is generated abundantly by combustion of coal in thermal power stations. It is a mixture of oxides rich in silicon (SiO2), iron (Fe2O3), and aluminum (Al2O3). Global production of fly ash estimated in 2006, exceeds 500 million tons and
*Corresponding Author
560 Sanjib Baglari, Madhusree Kole and T K Dey
only a small portion (~25%) of this is utilized for application. Fly ash poses severe environmental threat by contaminating the surrounding atmosphere and occupies huge land area for its dumping [1, 2]. Increasing production of fly ash year by year, from the coal based thermal power plant, is posing a serious problem in terms of its safe disposal and utilization. It is therefore, important to explore the possibility of this environmental polluting industrial waste for effective utilization and / disposal. Fly ash based cements [3] and bricks [4] are popular because of their advantages like energy efficient, cost effective and better thermal insulation property. Recently, fly ash is also being utilized in refractory, mining [5], agriculture [6] etc. In addition, commercial products viz, floor tiles, sinks, automotive parts, textile bobbins, flame-resistant electronic products etc., contain fly ash [7]. The granulometry of fly ash filler and filler blends are reported to be attractive as filler material in polymer composites [8-11]. Such fly ash filled polymer composites posses’ attractive mechanical, thermal, electrical properties, better dimensional stability and are cost effective.
High-density polyethylene (HDPE) plays an important role in various industries like in packaging and is widely used for various commercial products, because of its relatively low cost, low permeability to moisture and other oxidizing agents, sufficient ability to elongate and to withstand occasional surface impacts. HDPE is also considered to be an effective erosion resistant polymer. In general, various kinds of fillers are introduced into polymer matrices to modulate their mechanical, thermal and rheological properties [10, 12-15]. Thermal and mechanical properties of HDPE incorporating inorganic metallic fillers have been widely studied [16-18]. It is known that properties of particulate filled polymer composites are sensitive to the size, shape and distribution of filler particles in the polymeric matrix and also on their adhesion at the interface surface. Investigations on fly ash as filler in polymer matrix mostly concentrated on their mechanical [19,20], morphological and dielectric properties [15, 21-22]. Incorporation of fly ash in PET enhances its compression properties, which makes fly ash thermoplastics composites a viable choice for structural applications [23]. Addition of fly ash to both virgin and recycled thermoplastic matrices viz, PP, HDPE and LDPE also shows promising results in terms of their tensile properties [24-25]. In applications involving electronic packaging, in addition to high thermal conductivity, a low coefficient of thermal expansion (CTE) is needed to reduce the thermal mismatch in thermal expansion amongst different materials in the substrate [26]. Therefore, polymer matrix composites containing low CTE fillers are necessary [27, 28]. Usually, higher loading of fillers is required to decrease the CTE of the polymer to avoid thermal stresses. Reinforcing HDPE with fillers (viz, aluminum and copper particles, short carbon fibers, carbon and boron nitride particles) has been found to improve its thermophysical properties [14, 29]. Kumlutas et al [30] reported a significant improvement of thermal conductivity of HDPE containing 33% by volume of aluminum particles. Sofian et al [31] and Kuriber et al [32] also observed a moderate enhancement in the effective thermal conductivity of metal powder and aligned carbon nanoscale fibers filled in HDPE and polypropylene respectively. However, no systematic studies have so far been reported on the thermal conductivity and the coefficient of thermal expansion of
Effective thermal conductivity and coefficient of linear thermal expansion etc 561
(HDPE/FA) composites. In the present communication, we present the results of our investigations on the effective thermal conductivity and coefficient of thermal expansion of HDPE composites containing fly ash between 0 and 70-volume %. The results obtained are discussed in terms of various theoretical models.
2. Experimental details
The composite for the present studies are prepared using commercial grade high-density polyethylene (HDPE) powder (density of 0.94 g/cc) and fine fly ash powder (density 1.6 g/cc) obtained from Thermal power plant at Kolaghat, West Bengal (India). As received fly ash powder is dried in a furnace at ~2000C for 24 hrs to remove moisture. Various volume concentration of dry fly ash powder is mechanically mixed with appropriate amount of HDPE powder for 0.5 hrs. Calculated amount of xylene is then added and the mixture is slowly heated to about 700C for about 2 hrs. The heating is accompanied with vigorous stirring of the viscous fluid mixture to ensure a homogeneous distribution of fly ash. Heating and stirring are continued till xylene is completely evaporated. The resultant homogeneous mixture of HDPE and fly ash is then slowly cooled to room temperature. Pieces cut from the solidified HDPE/FA mixture are transferred to a stainless steel die and subjected to hot compression molding at 1200C. After cooling and complete solidification under pressure, the HDPE /FA composite sample is carefully taken out of the dye. A typical size of the HDPE/FA composite prepared for the thermal conductivity studies was 35mm long and 25mm diameter.
The chemical composition of fly ash was determined by EDX microanalysis (Figure 1). The EDX analysis shows that silica (54.58%) and alumina (34.92%) are the main constituents in fly ash used for the present investigation. Table 1 gives the detail chemical composition of FA. Fly ash particles as observed under SEM are shown in Figure 2(a). It is seen that the density of finer particles is much higher compared to the larger particle.
Figure 1. EDX spectrum of fly ash.
Counts
400
300
200
100
0 0 2 4 6
Energy (keV)
O Al
Si
C
Ti Fe
562 Sanjib Baglari, Madhusree Kole and T K Dey
It consists of a mixture of both nearly spherical and irregular porous particles. Average the particle size of the FA is <10�m. Figures 2(b) shows a typical scanning electron micrograph of the prepared HDPE/FA composite. The fly ash fillers are mostly spherical in shape and are distributed fairly uniformly in the composites.
Figure 2. (a) SEM photograph for pure fly ash powder (b) HDPE + 50 volume (%) FA composite.
Thermo-gravimetric analysis of the prepared composites is performed in nitrogen atmosphere using Perkin Elmer Pyris Diamond DTA/TGA Analyzer between 45 and 6500C, with a heating rate of ~100C/min. Figures 3(a) and (b) show the TGA curves and the residual weight (char yield) for HDPE/FA composites with increasing fly ash loadings respectively. It is seen that increasing FA loading in HDPE gradually enhances the thermal stability of the composites (Table 2). The temperature at which sample looses 35 % of its weight of given composites (T35) is taken as measure of thermal stability. Observed increase in thermal stability may be attributed to the restriction of mobility of segmental movement of HDPE, due to the enhanced interaction between FA and the polymeric
Table 1. Various compositions for EDX microanalysis
Element Element % At. % Compound Compound %
Al 18.48 14.30 Al2O3 34.92
Si 25.51 18.97 SiO2 54.58
Ti 2.23 0.97 TiO2 3.71
Fe 4.75 1.78 Fe2O3 6.79
O 49.03 63.99
Total 100 100 100
Table 2. Mix code for thermal stability indication
Mix code HDPE 3 vol% 10 vol% 20 vol% 30 vol% 50 vol% FA FA FA FA FA
Thermal stability (T35
0C) 445 458.04 460.90 462.07 469.32 498.08
Effective thermal conductivity and coefficient of linear thermal expansion etc 563
matrix (HDPE). Further, restriction of mobility of polymer chains by oxide particles present in FA also contributes to the improvement observed [33]. The char yield of the composites also increases from 5% to ~65% with increasing content of FA. Similar trend in increase of char yield was reported for Al2O3 – poly (-ether ether ketone) (PEEK) composites [34].
Figure 3. (a). TGA curves of fly ash filled HDPE composites. (b) % residue left vs. volume % of FA.
Effective thermal conductivity of HDPE/FA composites is measured by a 30mm long duel needle sensor (SH-1), which is coupled to the thermal properties analyzer (model KD2 Pro, Decagon Device, Inc). KD2 Pro thermal analyzer is based on transient hot wire method, which has the advantages of convenience, ease of construction, accuracy and short measurement time. The duel needle probe (SH-1) consists of two parallel needles spaced 6mm apart. One needle contains a line heat source and the other a thermocouple. The probe (SH-1) is buried in the homogeneous material (sample) and the heater is excited to produce a constant heat output per unit length. Temperature distribution in the material depends on the thermal properties of the material. Rise in temperature with time is recorded by the temperature sensor located 6mm away from the heat source. When a quantity of constant heat flux per unit wire length q (w/m) is applied to the line heat source over a period of time, the temperature rise at distance, r from the heat source is given by [35]:
���
�� � � �
2
1( , ) 04 4
q rT r t Ei t t
at (1)
where, k and a is the thermal conductivity and diffusivity of the medium respectively, t1 is the heating time and Ei is the exponential integral. The decrease in temperature after the heat is turned off is given by:
���
� �� � � �
2 2
11
.4 4 4 ( )
q r rT Ei Ei t t
at a t t (2)
TG
% ��
0 100 200 300 400 500 600 700
TEMP CELL ��
100
80
60
40
20
0
% R
esid
ue
0 10 20 30 40 50
FA volume %
70
60
50
40
30
20
10
0
564 Sanjib Baglari, Madhusree Kole and T K Dey
Thermal conductivity (K) of the composite is determined by fitting the time-temperature data during heating to eq. (1), and to eq. (2) during cooling. Thermal conductivity at 300C for each sample is measured five times and the mean value is recorded. Overall uncertainty in the measurement of thermal conductivity is 5%.
CTE measurements are performed between 20 and 1000C at 50C/min using Thermo Mechanical Analyzer (M/S, Perkin Elmer). Data for the initial 100C are not considered to take care of the instruments response time. The coefficient of linear thermal expansion was determined from the derivative of the plot between thermal expansion and temperature by using appropriate software. The average dimension of the sample used for TMA was 5mm × 5mm × 5mm. The overall uncertainty in CTE measurements is ~5%.
3. Results and discussions
3.1. Thermal conductivity :
Figure 4 shows the effective thermal conductivity of (HDPE/FA) composites at room temperature, as a function of FA concentration between 0 and 70 volume %. It may be seen that thermal conductivity of the composite increases with the increase of FA content. Incorporation of fly ash in HDPE almost doubles the effective thermal conductivity, viz, from 0.362 W/mK (HDPE) to 0.737 W/mK for HDPE containing 70 volume% fly ash. Heat conduction mechanism of polymeric composite containing non-metallic fillers are usually dominated by lattice vibrations (phonons). In addition, with increasing fly ash content in HDPE composites, fly ash particles come in direct contact with each other and form conductive chains, resulting in the increase of the effective thermal conductivity of the composites. Fly ash, which is formed by combustion of coal, is normally porous.
Figure 4. Effective thermal conductivity of HDPE - Fly ash composites measured as a function of fly ash volume % at T = 30C.
0 10 20 30 40 50 60 70 80
FA volume %
The
rmal
con
duct
ivity
(W/m
K)
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
T = 300C
Effective thermal conductivity and coefficient of linear thermal expansion etc 565
566 Sanjib Baglari, Madhusree Kole and T K Dey
The present set of data on HDPE/FA composites have been examined in light of various models and the results are summarized in Table 4. Figure 5(a) shows the measured effective thermal conductivity of HDPE/FA composites and those predicted by various models. It may be pointed out that the models proposed by Russell [40] and Cheng et al [42] highly over estimate the experimental data and hence those are not included in Figure 5(a). Maxwell model [38] fairly agrees with the experimental data only for composites with lower FA content (<10%). However, it predicts large deviation at high filler concentration, because Maxwell model does not consider the inter-particle interaction and which is expected for composites with high filler content. As the FA particles are spherical in shape and are randomly distributed in the matrix, Lewis and Nielsen eq. (7)
is evaluated taking A = 1.5 (for spherical fillers) and �m =0.637. Again, agreement of the
Table 4. Measured effective thermal conductivity of HDPE/FA composites at T=300C and that estimated on the basis of various models.
FA volume% K (measured) Maxwell Meridth Geomean Russel Lewis Agari
0 0.363 0.362 0.362 0.362 0.362 0.362 0.362
3 0.375 0.376 0.367 0.377 0.377 0.379 0.3731
5 0.393 0.386 0.377 0.390 0.392 0.392 0.381
10 0.402 0.414 0.394 0.425 0.415 0.425 0.400
15 0.422 0.441 0.415 0.443 0.441 0.461 0.4211
20 0.434 0.471 0.432 0.476 0.483 0.500 0.4428
30 0.467 0.535 0.475 0.546 0.570 0.591 0.4897
40 0.559 0.605 0.522 0.626 0.690 0.702 0.5416
50 0.592 0.684 0.574 0.718 0.865 0.842 0.5989
70 0.737 0.874 0.701 0.945 1.669 1.270 0.7326
Figure 5. Comparison between (a) measured and predicted values of effective thermal conductivity in terms of various models (b) Effective thermal conductivity of HDPE - fly ash plotted with the predicted values using Agari - Uno eq. (8).
–10 0 10 20 30 40 50 60 70 80 FA Volume %
The
rmal
con
duct
ivity
(W/m
K)
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
(b)
Expt. Agari
Effective thermal conductivity and coefficient of linear thermal expansion etc 567
values predicted by eq. (7) with the experimental data is seen for composites with low filler content (<15%) only. Meredith & Tobias model [39], which is based on the generalization of models for parallel and series conduction in composites usually, predicts the thermal conductivity of composites with high conductivity fillers and for high filler content. In the present case, it however, underestimates by ~10%, the measured values, probably due to the inherently low thermal conductivity of fly ash.
Based on the generalization of series and parallel conduction in composites, Agari et al [43] correlated thermal conductivity with the ability of fillers to create particle conductive chains and proposed as:
� ��
�
2
11
Cf
c mm
kk C k
C k
which can be rearranged as :
� � � �� �� � �2 1log . .log 1 .log .c f mk C k C k (8)
where kc, km and kf are respectively the thermal conductivity of the composite, polymer matrix and the fillers. � is the filler volume fraction. The parameter C1 and C2 are constants determined by experimental data. According to Agari et al [43], the parameters C1 and C2 should be in between 0 and 1. From Figure 5(b) one may observe that Agari
and Uno model predicts very well � �� �� 2 58 10 , the effective thermal conductivity of
the HDPE /FA composite in the whole range of fly ash concentration (0 to 70 volume %). The values of the parameters C1 and C2 obtained from the best fit of eq. (8) to the measured data are respectively 1.00032 and 0.99982. According to Wong et al [27] C1 indicates the filler effects on the secondary structure of the polymer matrix. For C1<1, the filler may change the thermal conductivity of the polymer matrix by affecting its structure. But when C1 � 1, the filler does not affect the secondary structure of polymer. The parameter C1 in the present case is close to 1, which accordingly implies that the introduction of the FA into HDPE does not have any effect on the secondary structure viz, crystallinity of HDPE. Similar observations were also reported for various HDPE and epoxy based polymer composites, viz, HDPE-BN [14], HDPE-Al2O3 [44], HDPE-Graphite [45] and epoxy resin-AlN composites [46]. However, in various other polymer composites (viz, Polyurethene-Al2O3) [47], the addition of finer filler particles was found to disturb the crystallization of the host (polymer) matrix and in such cases C1 is found to be <1. Thus, it appears that the effect on the crystalinity of the polymer matrix due to addition of filler particles depends on polymer- filler combination, rather than a general feature of particle reinforced polymer composites. The constant C2, on the other hand, indicates how easily the particles contact each other in the polymer matrix. In other words, the C2 values are closure to 1; more easily the conductive chains / channels are formed in composites. It may be noted that, depending on the dispersion state of the particulates, the thermal conductivity of the composites may be different, even if the composition of the composites
568 Sanjib Baglari, Madhusree Kole and T K Dey
is same. Zhou et al [14] reported that composites with smaller particle size of the filler give larger C2 value. High value of C2 (viz. 0.99982) obtained from the fit, together with SEM indicates that FA particles are well dispersed in HDPE and that conductive channels of FA filler are easily formed in HDPE/ FA composites. Formation of conductive channels of fly ash particulates in HDPE also supports the observed rapid enhancement in thermal conductivity for HDPE with high fly ash concentration.
3.2. Coefficient of linear thermal expansion :
Coefficient of linear thermal expansion of the composites is shown in Figure 6(a) as a function of FA content between 0 and 50-volume % and also as a function of temperature (Figure 6(b)). It is apparent that CTE of HDPE/FA composites decreases steadily with increasing FA content in HDPE. However, with increase in temperature, CTE of the composites increases linearly. The slope of the dimensional change with increasing temperature becomes shallower as the filler (FA) volume increases from 0% to 50%. As is expected, the composite with higher filler loading shows consistently lower CTE values than the composites with lower filler concentration. Compared to the CTE of pure HDPE, CTE of HDPE +50 volume% FA is nearly an order of magnitude lower at room temperature. The decrease observed in the CTE of the composite is due to the difference between the CTE’s of the polymeric matrix and the filler particles. In the present case, the filler (FA) particle has a very low CTE value (3.3 x 10–6 per 0C) as compared to HDPE (~100 x 10–6 per 0C). The reduction of CTE is, however, also influenced by the strength of the interfacial adhesion between the matrix and the filler.
Figure 6. (a) CTE of (HDPE – FA) composites as a function of FA volume% at different temperatures. (b) Temperature dependence of CTE of HDPE - FA composites.
Under some assumptions on the performances of matrix and filler, several models were proposed to predict the CTE of composites. Amongst them, most widely used ones are, the rule of mixtures (ROM) [48], Kerner model [49], Turner model [50], and Schapery’s Model [51] etc. The rule of mixtures (ROM) considered the matrix as a liquid and its validity depends on each phase expanding unhampered. Kerner’s model assumes
CT
E (p
er 0 C
)
4.5×10–4
4.3×10–4
3.5×10–4
3.0×10–4
2.5×10–4
2.0×10–4
1.5×10–4
1.0×10–4
5.0×10–3
0×0 0 10 20 30 40 50 60
FA volume (%)
1000C 900C 800C 70oC 60oC 50oC 40oC 30oC
(a)
CT
E (p
er 0 C
)
4.8×10–4
4.0×10–4
3.2×10–4
2.4×10–4
1.6×10–4
8.0×10–4
0×0
20 30 40 50 60 70 80 90 100 110
T (0C)
(b)
5% FA
50% FA
30% FA
20% FA
Effective thermal conductivity and coefficient of linear thermal expansion etc 569
(9)
Turner model [46] � �
� �1
1m m f f
cm f
K KK K
� �
� �� �
�� � (10)
Kerner model [47] � � � � � �1 (1 )(1 ) 3 4
f mc m f f m
m f f m m
K KK K K K G
� � � � � � �
� � � � � � � � � � (11)
Schapery's model [48] � � 1 11 1
c fc f m f
m f
K KK K
�� � �
�
( )
1 143
c m
f mm m
K K
K K K G
��
� � � ��� �
(lower bounds) (13)
( ) 11
43
c f
m ff f
K K
K K K G
��
� �� ��
� �
(Upper bounds) (14)
,c m and f are respectively the CTE of the composite, polymer and the filler. � : the filler volume
fraction. K and G are the bulk and shear moduli, respectively and the subscripts m and f stands for matrix
and filler respectively. The shear modulus is calculated using the standard relationship, � �� �3 3K E E G� � .
CTE of HDPE/FA composites have been estimated in terms of various models and the calculated CTE at T = 300C are given in Table 6 along with the measured CTE. Figure 7(a) shows the comparison of the experimental CTE with the values predicted by various models. It is apparent that most of the models display significant deviations from the measured values. The main reason for the observed deviation lies on the fact that thermal expansion of the composite is influenced by several factors that could not be fulfilled by any single model. The rule of mixtures (ROM) which is widely used for the
570 Sanjib Baglari, Madhusree Kole and T K Dey
calculation of the effective CTE of the composite, fails to predict the measured CTE in the present case. The ROM ignores the role of interphase interaction in the composites, leading to CTE value predictions always higher than the measured data. It may be noted that estimation of CTE based on Turner model significantly under-predicts the measured CTE values of the HDPE/FA composites. Turner model [50] usually predicts well the CTE of composites, only when bulk modulus of both filler and the matrix are of comparable magnitude, which in the present case are widely different (viz., bulk modulus of HDPE and FA are 1.46 G Pa and 107.8 G Pa respectively). Further, Turner model assumes homogeneous strain throughout the composite and each constituent is assumed to change dimensions with the temperature at the same rate as the composite; which may be not be the real situation for the present composite. Similarly, the expression derived by Kerner [49] largely overestimates the measured CTE for HDPE/FA composites. CTE values predicted by the lower and upper bounds of Schapery model [51] lay much above and below the measured values. It may be noted that the upper and lower bound curves tend towards each other and they coincide only if, the bulk modulus, shear modulus and CTE of filler and matrix material are of comparable magnitudes. In the present case, both the bulk and shear modulus of FA are very large compared to those of HDPE,
Table 6. Measured CTE (per0C) of HDPE/FA composites at T=300C and that estimated on the basis of various models.
FA volume CTE ROM Kerner Turner Schapery Schapery Vo et al % (measured) (Upper bounds) (lower bounds)
Figure 7. Comparison between (a) measured and predicted values of CTE of HDPE - FA composites in terms of various models (b) CTE HDPE – fly ash composites plotted with the predicted values using eq. (16).
CT
E (p
er 0 C
)
1.0×10–4
8.0×10–5
6.0×10–5
4.0×10–5
2.0×10–5
0×0 0 10 20 30 40 50
Fly ash volume (%)
(a) exp Upper Lower Komer Turner ROM)
CT
E (p
er 0 C
)
0 10 20 30 40 50 Fly ash volume (%)
(b)
8.0×10–5
7.0×10–5
6.0×10–5
5.0×10–5
4.0×10–5
3.0×10–5
2.0×10–5
1.0×10–5
Effective thermal conductivity and coefficient of linear thermal expansion etc 571
consequently, the bounds are far apart from each other and the experimental values lie in between the upper and lower bounds.
Complex interaction between polymeric matrix and the filler is usually influenced by several factors, including size, shape and type of the filler, the chemical structure of resin and the cross-link conditions, as well as, the interface volume. Recently, Vo et al [53] proposed a model for CTE of polymeric composites, taking into account of the effect of interphase volume surrounding the filler particles embedded in a polymer matrix. The interphase volume (Vint) is derived as:
� �� � � �� � � � � �� � � � � �3 3 2int
4 243
3 3V N r r r f N r r r r (15)
where, N and r are the number of fillers and filler radius respectively. � �� �0 1f frepresents the filler-filler overlapping factor. The effective linear CTE of composite is expressed as:
(16)
where, 0(1 ) (1 )m K� � �� � � is the volume fraction of the matrix. Figure 7(b) shows the
measured CTE of HDPE/ FA composite along with that calculated using the expression
derived by Vo et al [53]. It is clear that the above model is in excellent agreement ( � 2=
5.871x10–12) with the experimental data. The effective CTE of a composite, predicted by Vo et al [53] considering the effect of an interphase zone surrounding the filler particles in a polymer matrix composite. This model claims to resolve several conflicts with respect to the effect of filler concentration, filler shape and size and filler – polymer interactions on the effective CTE of polymeric composite materials. The parameter K0 in eq. (16) reflects strength of the filler-matrix interaction and K1 is the measure of the temperature dependence of K0. For negligible interaction between matrix and filler K0 tends to zero and a large positive value of K0 indicates a strong polymer – filler interaction. The parameter K0 is also sensitive to both the filler size, shape and the preparation conditions. It may be noted that for a given volume fraction of filler, a smaller filler particle size will have a larger fraction of interphase volume. The fitted parameters K0 and K1 obtained in the present case are 3.28082 and -0.00034 respectively. Positive and large K0 obtained for the present composite indicates strong filler - matrix interactions, as well as, better interfacial adhesion between the filler and matrix. Negative value for K1 indicates that the predicted effective CTE will be smaller than that predicted by the ROM model. Thus, compared to all other models, the model proposed by Vo et al [53], achieves an excellent fit to the experimental data and thereby confirms the importance of the role of the interphase volume and the strength of the matrix – filler interactions for successful prediction of CTE of polymer composites.
572 Sanjib Baglari, Madhusree Kole and T K Dey
4. Conclusions
Effective thermal conductivity and coefficient of linear thermal expansion (CTE) of HDPE / FA composites are reported as a function of FA loading between 0 and 70 volume %. Composite samples, prepared by mixing, molding and hot pressing, show fairly uniform distribution of the nearly spherical particles of fly ash in the polymer matrix. TGA analysis confirms that incorporation of FA in HDPE increases the thermal stability of the composite. Effective thermal conductivity of HDPE/ FA composite increases with increasing FA content and becomes nearly double for HDPE with 70% FA, compared to that for pure HDPE. The model proposed by Agari et al predicts very well, the measured effective thermal conductivity of HDPE/FA composites over a wide range of filler (FA) concentration in HDPE. Enhancement in the effective thermal conductivity of HDPE/ FA composites for high volume concentration of FA, originates from the formation of conductive channels in the composites. CTE of the composites display strong dependence on both filler loading and temperature. With FA addition, the CTE of HDPE decreases nearly by an order of magnitude. Analysis of CTE data confirms that the role of interphase volume within the polymeric composite and the strength of matrix-filler interactions is important for correct prediction of the CTE of polymer composites. Summing up, improved effective thermal conductivity and nearly an order of magnitude decrease in CTE due to compositional variation of HDPE/FA composites, should be attractive for various applications, mainly, in electronic packaging where CTE mismatch and heat dissipation is a problem.
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