Role of rheology in tunning thermal conductivity of polyamide 12/polyamide 6 composites with a segregated multiwalled carbon nanotube network

Abstract

Effect of multiwalled carbon nanotubes in thermal conductivity of an immiscible blend of polyamides, 50/50 (wt%/wt%) polyamide 12/polyamide 6, was analyzed as function of nanofiller amount and temperature. Effect of the molding temperature in the structure of conductive network was investigated by rheology.

Data show that 5 vol% multiwalled carbon nanotubes caused an increase of 41% in thermal diffusivity and 78% in thermal conductivity respect to polyamide blend values. Thermal conductivity improvement could be described by percolation theory, with a low threshold composition (φ_c = 0.09 vol% carbon nanotube). Fitting parameters obtained from Agari’s adjustment model show that polyamides structure is not affected by carbon nanotubes and the nanofillers can easily form conductive paths in the polyamide 12/polyamide 6 matrix.

The temperature increase facilitates nanofiller dispersion causing the formation of a denser carbon nanotube network and rising the thermal diffusivity of carbon nanotube composites with low percolation level, as was proved on annealed samples at 255℃.

Keywords

Polyamide carbon nanotube composites rheology percolation thermal conductivity

Introduction

In the manufacturing of electrical and electronic devices, the use of polymers is widespread because these materials offer unique properties as good processability, light weight, low water absorption, high electrical resistivity, high voltage breakdown strength, corrosion resistance and most importantly, low cost, in comparison with other materials. By contrast, most polymers have a low thermal conductivity (TC), not enough to dissipate heat quickly which is critical to the performance, lifetime, and reliability of electronic devices. The TC of polymers depends on many factors, such as their physico-chemical properties, crystallinity, morphology, processing conditions, etc. In general, the phonon scattering through numerous defects or at the interface between the crystalline and amorphous phases (in semicrystalline polymers) causes low values in TC for traditional polymers. For this reason, the development of polymers with improved TC is a topic of great interest.^1–4

The incorporation of conductive fillers, into a polymer matrix is a commonly used method to obtain materials with tailored and controlled TC without compromising the processing ease of the polymer matrix.^5–8 Traditionally, graphite, carbon black, carbon fibers, ceramic, or metallic particles were used as thermal conductive fillers. With the development of nanotechnology, numerous studies were focused on the use of conductive nanofillers, as carbon nanotubes (CNTs), to improve the TC of polymers.⁹

CNTs exhibit a longitudinal TC between 2000 and 6000 W/mK.^9–11 The great part of these values is based on theoretical simulations or indirect measurements due to the experimental difficulties associated with the measurements in nanoscale. Nevertheless, most researchers agree that aspects such as nanotube morphology, structural defects, functionalization, or the presence of impurities affect the TC of nanotubes. Furthermore, the TC of CNT polymer composites depends on structure formed during the processing step, the dispersion state of filler, and on the interfacial thermal resistance (polymer–nanotube).^12,13 Due to all these reasons, thermal properties of CNT/polymer composites are lower than would be expected.¹⁴

Localization of fillers into well-defined co-continuous region can be an option to enhance the thermal contact area between conductive particles of filler.^15,16

In our previous work, different quantities of multiwalled carbon nanotubes (MWCNTs) and an immiscible blend of polyamides, 50 vol%/50 vol%. Polyamide 12/polyamide 6 (PA12/PA6) were melt blending by extrusion to obtain conducting polymer composites. The mixing strategy followed, by using a PA12 masterbatch and an immiscible blend of polyamides, was suitable to form a segregated conductive network in the matrix with low CNT quantities. From electrical and rheological measurements, a low percolation threshold was determined, probably due to the high aspect ratio of the nanotubes which is kept after the composite processing, and to the preferential localization of CNTs in the polyamides interfaces (the latter was confirmed by transmission electron microscopy [TEM]).¹⁷ Other authors found an improvement in electrical behavior using conductive polymer composites with segregated networks.¹⁸ The water uptake at saturation of nanocomposites decreases with respect to the pristine PA6 because of the diffusion of water molecules into the polymer matrix was slower. These results are associated with the increase in crystallinity of polyamides and the migration of nanotubes to PA6 matrix in nanocomposites with high CNT amounts.¹⁹

In view of this outcome, it seems interesting to investigate the TC of these CNT composites where nanofiller forms a segregated conductive network in the polyamide matrix. On the other hand, it is worthwhile to assess the effect of molding temperature in the CNT network structure, since if its structure is modified this could affect the nanocomposites properties. The rheology tests can be a useful tool for this aim.

So, in this manuscript, the TC of the PA12/PA6/MWCNTs composites is studied and related with their rheological properties and their morphology. With the purpose to predict the TC of these nanocomposites, several different models were evaluated and were compared with the experimental data. Besides, from a deeper rheological study, the effect of temperature in the percolation level and the conductive network structure is analyzed. The final target is to assess the impact of this variable in the network structure of nanocomposites and consequently, in their macroscopic properties as TC.

Experimental section

Materials and composite processing

A blend of PA12 (Grilamid supplied by EMS Grivory) and PA6 (Zytel supplied by DuPont) was used in this study. PA6 has a density of 1.14 g.cm⁻³, a melting temperature of 220℃ and a zero shear viscosity of 723.8 Pa.s measured at 235℃. On the other hand, PA12 has a density of 1.01 g.cm⁻³, a melting temperature of 180℃ and a zero shear viscosity 391.7 Pa.s measured at 235℃. To prepare CNT composites, a masterbatch of MWCNT (NC7000, Nanocyl S.A, Sambrevile, Belgium) pre-dispersed at 15 wt% in PA12 was used (Plasticyl PA1502, Nanocyl S.A, Sambrevile, Belgium). MWCNTs have an average diameter of 9.5 nm, a length of 1.5 µm, a carbon purity of 90%, and a surface area of 250–300 m².g⁻¹, according to the supplier.

Composites of a 50/50 wt%/wt% PA12/PA6 blend and different MWCNT contents were prepared by diluting the masterbatch with the same PA12 (Table 1). Before extrusion, masterbatch and pristine polyamides were dried in an oven at 110℃ for 6 h. Then, the different composites were extruded using a co-rotating twin-screw extruder (Brabender DSE 20) with an L/D ratio of 40 (L = 0.8 m) operating at 30 r/min, with a temperature profile between 220℃ and 235℃ and an output rate of 0.5 kg/h. For easy of comparison, as far as possible, the extrusion parameters were maintained constant in all composites. All the components were premixed by tumbling and then were fed simultaneously into the extruder. The extruded composites with the appropriate geometries for thermal and rheological tests were compression molded at 245℃ applying a pressure of 30 bar for 5 min.

Table 1.

Formulations of PA12/PA6/MWCNT nanocomposites.

Sample nomenclature	PA12 (wt%)	PA6 (wt%)	MWCNT (wt%)	MWCNT (vol%)
PA12	100	0	0	0
PA6	0	100	0	0
0	50	50	0	0
0.15	49.875	49.875	0.25	0.15
0.31	49.750	49.750	0.50	0.31
0.46	49.625	49.625	0.75	0.46
0.61	49.500	49.500	1.00	0.61
0.92	49.250	49.250	1.50	0.92
1.23	49.000	49.000	2.00	1.23
1.34	48.750	48.750	2.50	1.34
1.86	48.500	48.500	3.00	1.86
3.12	47.500	47.500	5.00	3.12
5	46.000	46.000	8.00	5.00

MWCNT: multiwalled carbon nanotube; PA12: polyamide 12; PA6: polyamide 6.

Characterization

The composites morphology was analyzed by TEM, an analytical TEM (JEOL JEM 1010) was used to investigate the CNT network formation in the different composites at nanoscale. Ultrathin sections of 70 nm were cut, at room temperature, from compression-molded samples.

Viscoelastic characterization was performed by using a controlled strain rheometer (ARES, TA Instruments) with parallel-plate geometry (25-mm diameter, 1-mm gap) in the linear viscoelastic region (LVE) at various temperatures ranging from 235℃ to 255℃. The rheological tests were performed in the LVE where the modulus is independent of strain. LVE region was determined by a strain sweep test. Furthermore, frequency sweep measurements were set up in the frequency range from 10⁻¹ to 10²rad/s.

Thermal diffusivity of different CNT composites was measured by using the flash diffusivity technique with thermal analyzer (LFA 447 Nanoflash, Germany). For the measurements, round samples were compression molded with 12.5 mm in diameter and 1 mm in thickness. The samples were sprayed with a coating of graphite on both sides before testing (for uniform thermal adsorption). Measurements were done at different temperatures ranging from 25℃ to 100℃. The LFA 447 illumination is a Xenon flash lamp with a wavelength in broadband visible and near infrared (IR). Pulse corrected by Cowan model was used to analyze the data in analysis software. Finally, the thermal conductivities were derived from the following equation

k = α ρ c_{p}

(1)

where k is the TC, α is the thermal diffusivity, ρ is the density of sample, and c_p is the specific heat capacity. The nanocomposites density was calculated using the rule of mixtures, and their specific heat capacity c_p, by differential scanning calorimetry (DSC) using sapphire as standard.

Results and discussion

Morphological analysis

Figure 1 shows the TEM micrograph of PA12/PA6 with 0.46 vol% CNTs. As already seen in a previous work, the two polyamides are distributed in two different phases and CNTs are mainly placed in the interphase between polyamides. This morphology is caused by PA12/PA6 viscosity ratio (lower than 1) and the interfacial energy of CNT–polymers. PA12/PA6 blend displays a sea-island morphology where PA12 (with lower viscosity and lower melting point) is the continuous phase. This structure is seen in Figure 1. The preferential localization of CNTs (in the polyamides interphase), observed in this micrograph, is the desired morphology to form a segregated network and to obtain low percolation thresholds, and it was theoretically predicted by the wettability parameter calculated in an authors’ previous work.¹⁷ Hence, the TC is defined by composite morphology as well as, by the structure and properties of polymer and filler, the effect of this morphology in thermal properties of CNT composites will be evaluated hereinafter.

Thermal conductivity

Figures 2 and 3 show thermal diffusivity and TC of nanocomposites respectively for several temperatures. It is clearly shown that, after adding CNTs, both properties enhanced in comparison with the polyamide blend, at any temperature. The thermal diffusivity of unfilled polymer blend is comparable to values already published for different types of polyamides.⁴ Increases of 41% in thermal diffusivity and 78% in TC (Figures 2 and 3), in comparison with the unfilled material, were observed for nanocomposites reinforced with 5 vol% CNTs at 25℃. The comparison of these values with the data previously published in other papers is difficult because of the different experimental techniques and matrices used for the TC measurements. Han and Fina conducted a summary of thermal conductivities performances for CNT-based nanocomposites reported in the literature. They concluded that the greater part of k/k_P (TC composite/TC matrix) values are lower than 2 in nanocomposites with CNT volume fractions lower than 10 vol%.⁹ Our data are comparable and, in many cases, higher than ones previously published. Figures 2 and 3 show the temperature-dependent changes in thermal properties of PA12/PA6 nanocomposites too. The reduction observed in thermal diffusivity with increasing temperature can be related with the softening of the polymer.^20,21 Whereas, the TC rises lightly with temperature increase (Figure 3).

To analyze if some mathematical model could predict the thermal behavior of nanocomposites, several of them were used to adjust TC data measured at 25℃. Table 2 displays the mathematical equations of used models and Figures 4 and 6, the fit of the experimental data. In the adjustments, a value of 2000 W/mK was used for the TC of MWCNTs according to the literature data.^9–11

Table 2.

Mathematical equations of used models.

Analytical models	Mathematical expression
Parallel	$k = (1 - φ) k_{p} + φ k_{f}$
Series	$k = [\frac{(1 - φ)}{k_{p}} + \frac{φ}{k_{f}}]^{- 1}$
Maxwell–Garnet	$k = k_{p} (1 + \frac{3 φ (δ - 1)}{2 + δ - φ (δ - 1)})$ where δ = k_f/k_P
Bruggeman	$(1 - φ) = \frac{k_{f} - k}{k_{f} - k_{p}} (\frac{k_{p}}{k})^{\frac{1}{3}}$
Agari	log $k = φ C_{2} {logk}_{f} + (1 - φ) log (C_{1} k_{p})$

k: thermal conductivity of the composite, k_P: thermal conductivity of the polymer matrix, k_f : thermal conductivity of the filler, and φ: volume fraction of fillers.

One of the simpler models is the series model. It is based on the assumption that the heat flux is uniform and the temperature gradient is the weighted sum of the temperature gradients through the matrix and filler domains. Our experimental data (see Figure 4) are closer to the prediction of the series model only at low CNT contents. The reason is that this model is most suitable for composites where the fillers are well dispersed in a matrix and there is no percolation even at high volume fractions.⁴

A new approach to the TC behavior of nanocomposites was proposed by Maxwell–Garnett model.^4,22 Nevertheless, the model fitting showed similar results than the simple series model. Maxwell–Garnett model accepts that temperature experiences no discontinuity at the filler surface. This assumption works well on a macroscopic scale, but breaks down on much smaller characteristic length scales where the thermal energy carriers (electron or phonons) scatter at the interface.

Bruggeman model provides an extension of Maxwell model, where the interactions among the randomly distributed fillers are considered.²³ However, in view of Figure 3, none of the models fit perfectly the TC behavior. This may be because none of these micromechanical models takes into account the percolation phenomenon and the subsequent formation of a conductive network in the system from a critical amount of CNT (threshold).

Unfortunately, the graphical representation of TC data versus filler amount (Figure 3) not show clearly, the threshold composition. The main reasons reported in literature in order to explain this lack of percolation threshold are the poor heat transfer between polymer and CNTs and the high thermal resistance between adjacent nanotubes. Nevertheless, there is still a debate whether, for these polymer composites, the TC improvement should be described by means of percolation or by using effective medium approaches.^24–26 In the first case, as suggested Bonnet et al.,²⁷ TC could be proper modeled by the data adjustment to the following equation

Δ k = k_{0} [\frac{φ - φ_{C}}{1 - φ_{c}}]^{t}

(2)

where φ_c is the threshold composition. Since polyamides blend is not a thermal insulator, the contribution of the polyamides to the composite TC is

k_{p} = (1 - φ)

, whereas the difference

Δ k = k - k_{p} x (1 - φ)

reflects the contribution arising from the connected CNTs network. The evolution of Δk with CNTs reduced volume fraction

(φ - φ_{c}) / (1 - φ_{c})

is shown in Figure 5. The solid line is the fit for

φ \geq 0.15 vol . %

with

φ_{c} = 0.09 vol . %

. The best fit for composites gives a prefactor

k_{0} = 6.78 \pm 0.18 W / mK

and

t = 1.14

(

R^{2} = 0.98

). It must be pointed out a reduction of the exponent below 2, as discussed by Foygel et al.²⁵ The TC prefactor k₀ should represent the TC of the CNT network which is nearly three times lower than the 20–30 W/mK value measured on unaligned single-walled carbon nanotubes (SWCNTs) buckypaper²⁸ and nearly 25 times greater than the TC of PA12/PA6 blend. The goodness of lineal fit and the obtained results explain the reasonable use of percolation theory for describing the enhancement of TC with CNTs increase in polyamide blend. This fact clearly suggests that above a certain critical content of CNTs φ_c, TC is mainly controlled by CNTs network in this kind of systems. Besides, this critical composition is in line with the values of electrical threshold (φ_c = 0.258 ± 0.001 vol%) and rheological threshold (φ_c = 0.09 ± 0.01 vol%) previously calculated for these composites.¹⁷ The critical composition is closer to the rheological value; this could be because for these two parameters only contact between CNT clusters is needed, whereas in another case (electrical threshold) a CNT conductive path is desirable.

Since the critical composition or threshold is very low, the previous mathematical models, which do not consider the effects of percolation phenomenon, only are valid for the lowest CNT compositions (see Figure 4).

A different approach to the TC behavior is the one proposed by Agari’s model.²⁹ This empirical model, whose mathematical expression is displayed in Table 2, considers the dispersion state of filler and the matrix structure (or crystallinity) including two coefficients, C₁ and C₂. The first parameter, C_1, is related with the crystallinity and crystalline size of polymer and, the second one, C₂, with the ease in forming conductive paths through the polymeric matrix. Although Agari corroborated the validity of his model in highly filled polymer composites with microparticles, others researchers have proved that Agari’s model can fit reasonably well, the TC data of nanocomposites.¹⁶ Figure 6 shows the adjustment of our experimental data to the Agari’s model. The values of parameters obtained were C₁ = 0.96 ± 0.02 and C₂ = −1.3 ± 0.1 (R = 0.99).

The value of C₁, closer to 1, suggests that the polyamides structure is not affected by the presence of nanotubes. Nevertheless, DSC and X-ray diffraction (XRD) data showed that polymer crystallinity increases when the nanotubes are added.¹⁹ Probably, this change (a maximum increase around a 10% in crystallinity) was not enough to enhance the TC of CNT composites. On the other hand, the value obtained for C₂ parameter (absolute value greater than 1) probes the ease of nanotubes in forming conductive paths in the matrix. This could be linked to the fact that the CNTs are preferably placed in the interface between polyamides, as was already proven.¹⁷

Rheological properties

Since the TC behavior of PA12/PA6/CNT composites can be explained using percolation theory, the percolation level reached by the CNT network should be considered to optimize the TC values with the lowest filler amount. The percolation level and the conductive network structure are influenced by processing or molding temperature of materials, as was previously observed in other composites.^29,30 This aspect was carefully analyzed in PA12/PA6/CNT composites conducting rheological tests at different temperatures in the range between 235℃ and 255℃. These temperatures were selected into the processing window of the nanocomposites. It is known that the changes observed in rheological properties near the percolation threshold of a filler network embedded in a viscoelastic liquid are equivalent to the so-called “liquid-solid transition.” This transition can be observed plotting different rheological parameters. One of these graphs, van Gurp–Palmen plots, are displayed in Figure 7. In these graph, the phase angle, δ, is plotted against the absolute value of the complex modulus, G*, for the temperature of 235℃. In these plot, it is possible to appreciate that the polymer chains corresponding to pristine PA12/PA6 blend are completely relaxed for a value or approximately 90° for δ in the low G* region. This indicates the dominant response of viscous flow in polyamides blend. On the other hand, the deviation of δ from 90° shows the elastic response of the nanocomposites, forming a percolated structure in the melt sample. As it is shown in Figure 7 the value of δ begins to decrease with CNTs increasing. Similar trend was obtained in the tests performed at 245℃ and 255℃ (Figure 8) (although in these pictures only some of the CNT percentages are showed).

The appearance of a maximum in δ at some intermediate value of G*, suggesting a liquid–solid transition, was observed in the rheological tests performed at the three temperatures. At 235℃, the value agrees with a previous study which concluded that from 0.15 vol% CNT the nanocomposites are rheologically percolated (see Figure 7).¹⁷ Moreover, when the test temperature increases, a displacement of this maximum to high values of G* is observed. This means that for the same CNT composite, as test temperature increases, the solid-like behavior is more pronounced. The crossover points (Table 3) calculated from graphical representation of moduli against frequency (some of these graphs were previously published in Arboleda-Clemente et al.¹⁷), proves this fact. From these data, the liquid-like behavior for pristine polyamide blend was confirmed for the three test temperatures. Besides, the crossover points were clearly shifted to higher frequencies as MWCNTs amount increased until a solid-like behavior, in all frequency range, is obtained (G′ > G″). The improvement of the elastic response in CNT composites with high filler contents, indicates that the number of interfaces between CNTs has increased, that is, a denser percolated network was formed and it causes a high melt strength.

Table 3.

Crossover points of different PA12/PA6/MWCNT composites.

	ω_C/G_C (rad.s⁻¹/Pa)
Sample	235℃	245℃	255℃
0	G″ > G′	G″ > G′	G″ > G′
0.31	0.2/131	0.6/245	0.8/318
0.61	1.1/950	1.6/669	1.7/932
1.86	47/35880	G′ > G″	G′ > G″
5	G′ > G″	G′ > G″	G′ > G″

MWCNT: multiwalled carbon nanotube; PA12: polyamide 12; PA6: polyamide 6.

If the rheological data obtained at different temperatures are compared, it can be observed that the transition to solid-like behavior occurs with low CNT amount at the highest temperatures (with 1.86 vol% CNT at 245℃ and 255℃ against 5 vol% CNT at 235℃), according to the trend observed in Figure 8.

With the rheology results in mind, it seems that an increase in molding temperature leads lower viscosity values of polymer matrix, which could facilitate nanofiller dispersion resulting in a better formation of CNT network.³¹ Pötschke and coworkers^32,33 proposed that the density of the networks changes with temperature due to the reduced particle-particle distance and enhanced interactions among CNTs in a lower viscosity matrix.

A denser CNT network could improve the conductive paths into the nanocomposite and consequently, enhance their TC. To ensure this fact, the thermal diffusivity of nanocomposites was measured at 25℃ after annealing at 255℃ during 6 min. This thermal treatment, similar to that suffered the samples during the rheological tests, was carried in order to simulate, in part, the effect of molding temperature. The data obtained are displayed in the graph of Figure 2 for nanocomposites with low CNT amount. From 1.86 vol% CNT, the nanocomposites are percolated (or highly percolated) and the effect of the annealing in the morphology of CNT network does not expect to be significant.

The thermal diffusivity of nanocomposites increased after annealing. In addition to the enhance in thermal diffusivity of PA6/PA12 matrix (probably associated to changes in its crystallinity structure), an increase of 10% was observed for nanocomposite with 1.86 vol% CNT. The strengthening of CNT network, previously observed in rheological tests, favors this behavior.

Conclusion

The TC of PA12/PA6/CNT composites was measured and was related with CNT amount, the composite morphology and the structure of conductive network. The main conclusions are summarized as follows:

CNT incorporation produces significant increment in thermal diffusivity and TC of PA12/PA6 blend (increases of 41% in thermal diffusivity and 78% in TC at 25℃ with 5 vol% CNT).

The thermal diffusivity is temperature-dependent and it decreases as temperature increases due to the softening of polymeric matrix. On the contrary, the TC of nanocomposites remained practically constant or increases slightly in the temperature range of the experiments.

The comparison of the thermal data with theoretical and empirical models reveals that the classic approaches to the TC behavior are not valid to predict the thermal properties of PA12/PA6/CNT composites since they do not take into account the contribution of the conductive network formed into the matrix. This contribution to thermal transport was proved by the data adjustment to the equation proposed by Bonnet. The threshold composition calculated (φ_c = 0.09 ± 0.01 vol%) is in line with the values of electrical threshold and rheological threshold previously calculated for these composites.

The empirical model proposed by Agari is able to predict accurately the TC behavior of nanocomposites at 25℃. The parameters obtained from the data adjustment suggest that the polyamides structure is not affected by the CNTs and the nanofillers can easily form conductive paths in the PA12/PA6 matrix.

Finally, the rheological properties of nanocomposites measured at different temperatures show that the transition to solid-like behavior occurs with lower CNT amount as molding temperature increases. It likely to be due to the lower viscosity of polymer matrix, which facilitates nanofiller dispersion causing the formation of denser CNT network and consequently, rising the number of conductive paths. The enhancement of thermal diffusivity in CNT composites with low CNT amount, after annealing at 255℃, proved this fact.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Authors acknowledge the financial support to Xunta de Galicia-FEDER [Program of Consolidation and structuring competitive research units (GRC2014/036)].

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