Boyu Zheng,
HuiLong Dong and
Feifan Chen*
State Key Laboratory of Precision Measurement Technology and Instrument, Department of Precision Instrument, Tsinghua University, China. E-mail: cff@mail.tsinghua.edu.cn; Fax: +86-1062788681; Tel: +86-1062782010
First published on 3rd February 2016
Polymer composites with layered structures are easily prepared and applied for a range of potential applications due to their excellent thermal properties. This introduces significant demands to characterize the thermal properties of these nanocomposites. In this study, we report an effective compound thermal diffusivity characterization method to predict and furthermore to help regulate the thermal diffusivity of polymer nanocomposites. As a case study, an improved nanoporous template wetting technique was employed to fabricate 20 nm and 200 nm high-density polyethylene (HDPE) nanowires within porous anodic alumina (AAO) substrates. A compound thermal diffusivity model for double-layer structural nanocomposite is proposed to predict the effective overall thermal diffusivity of the HDPE/AAO samples. An infrared sequence transformation technique was introduced for measurement verification. The theoretically predicted results are in accordance with the experimental results, where the in-plane thermal diffusivity of the AAO substrate was reduced by 34.7% and 41.7%, respectively, from 20 nm and 200 nm HDPE nanowire arrays fabrication. The characterization results also revealed that the thermal diffusivity of the polymer nanocomposites could be quantitatively regulated via adjusting the polymer content, which could potentially provide a theoretical basis for thermal management and thermal structure design.
Literature reported to date10,11 gives various ideas of evaluating the thermal diffusivity of polymer composites on an experimental basis. Theoretical models from many research efforts have concentrated on the intrinsic thermal properties of polymers accounting for variation in size and morphology.12,13 As for composites, the Maxwell–Eucken14 equation was originally applied to the thermal conductivity of composites requiring the fillers to be well dispersed and not touching each other only at low loadings. Behrens15 developed methods to predict the thermal property of two-phase composites with cubic symmetry. Agrawal16 established a model to predict the thermal diffusivity of spherical shaped particulate filled polymer composites. The theoretical models mentioned above mostly concentrated on particulate dispersed composites and few studies have been reported regarding theoretical characterization methods for the thermal diffusivity of layer-structured polymer composites. Herein, the aim of our study was to develop an effective characterization method to theoretically predict the thermal diffusivity of double-layer structured polymer composites.
In this study, a compound thermal diffusivity characterization model is proposed to predict the composite's effective thermal diffusivity perpendicular to layers. The overall thermal diffusivity could be determined by each component's thermal properties and volume content. To validate the model, double-layer structured polymer composites have been synthesized where polyethylene (HDPE) nanowires with high densities of 20 nm and 200 nm have been fabricated within the porous anodic alumina (AAO) substrates using an improved nanoporous template wetting technique. An infrared sequence transformation technique has been employed for experimental verification. The measured in-plane thermal diffusivities of HDPE/AAO composites have been compared with results from the predictive model.
A top-view image of the sample with wetting time of 10 h is shown in Fig. 1(a). It can be seen that most of the nanowires have exactly filled in the pores, forming a suitable sample for thermal study. In addition, the AAO template was removed in an aqueous solution of NaOH and the HDPE nanowire arrays were rinsed with deionized water and dried at 30 °C in vacuum. Fig. 1(b) is the cross-section view of HDPE nanowires after removing the AAO template, which shows the uniformly distributed nanowires on the over deposited HDPE film. The X-ray diffraction scans of the HDPE nanowires are displayed in Fig. 2, where the two strong peaks correspond to the (110) and (200) orthorhombic phases of HDPE, when compared with the peak positions of standard PDF#40-1995, indicating the synthesis of high-purity nanowire samples with good crystallization. Subsequently, composites with 20 nm HDPE nanowire arrays were prepared with a wetting time of 124 h.
![]() | ||
Fig. 1 Scanning electron micrographs of (a) top view of 200 nm HDPE nanowires embedded in AAO template and (b) cross-section view of 200 nm HDPE nanowires after removing the AAO template. |
![]() | (1) |
Considering that the double-layer structure is arranged similarly in serial connections, the overall thermal conductivity perpendicular to the layers λ0 follows the in-serial model:23
![]() | (2) |
Assuming that the two components are both equivalently homogeneous in thermal physical effects, the resulting thermal diffusivity depends mainly on the porosity of the AAO substrate. Considering λ0 = α0ρ0c0, the overall thermal diffusivity perpendicular to the layers is obtained as follows:
![]() | (3) |
Eqn (3) is a compound thermal diffusivity model for the nanocomposites with double-layer structures. The effective overall thermal diffusivity can be predicted by the thermal properties of the AAO substrate and HDPE nanowires.
![]() | (4) |
![]() | (5) |
Then, the diffusing area s was derived from the integral of rTmax(θ)24 as follows:
![]() | (6) |
The experimental results were extracted and analyzed using the abovementioned measurement system. Fig. 5(a) shows the raw IR images of the 200 nm HDPE/AAO sample in the range of 0.5–0.85 s. It can be seen that the temperature of the whole sample was below 7 °C, which is considered to not introduce extra measurement errors. The binary thermal diffusing sequences were obtained through the proposed method, as shown in Fig. 5(b), where the boundary (red curves) between the black region (T′ < 0) and the grey region (T′ > 0) indicate the thermal diffusing edge. It is clear that the thermal diffusing edge spreads as time increases and the spreading speed is the slope according to eqn (6).
The area s surrounded by the thermal diffusing edge was calculated by a DRLSE formulation.20 The (si, ti) sequences were therefore extracted and the slopes of the s–t curves were calculated with linear regression. The results for 20 nm and 200 nm HDPE/AAO composites are shown in Fig. 6, where the thermal diffusivities of the 20 nm and 200 nm HDPE/AAO composites were calculated to be 5.92 × 10−7 m2 s−1 and 5.29 × 10−7 m2 s−1, respectively, according to eqn (6).
On the other hand, considering that the specific heat and the density of the nanofibers are the same as those of bulk materials for both parameters and are not sensitive to the crystallinity at room temperature,26 the specific heat and the density of HDPE nanowires are ρHDPE = 945 kg m−3 and cHDPE = 1900 J kg−1 K−1. Knowing that the thermal conductivity of bulk HDPE is λHDPE = 0.5 W m−1 K−1, the thermal diffusivity of HDPE nanowires is calculated to be αHDPE = 2.78 × 10−7 m2 s−1. Moreover, the thermal conductivity of AAO is λAAO = 1.02 W m−1 K−1 and the measured thermal diffusivity is αAAO = 9.03 × 10−7 m2 s−1. Given that the porosities of the 20 nm and 200 nm AAO substrates were 31% and 42%, the overall thermal diffusivity values for the 20 nm and 200 nm HDPE/AAO composites were 5.76 × 10−7 m2 s−1 and 5.03 × 10−7 m2 s−1, respectively, which was calculated using eqn (3).
The experimental and the theoretically predicted results are listed and compared in Table 1, where the experimental and theoretical results are consistent. It can be seen that the in-plane thermal diffusivity of the AAO substrate is reduced by 34.7% and 41.7% from the 20 nm and 200 nm HDPE nanowire arrays fabrication, respectively. The results indicate that the overall thermal diffusivity of the composites could be quantitatively modulated via adjusting the polymer content, which demonstrates that polymer nano-filling is a promising effective thermal control method for base materials. Furthermore, it is interesting to note that the theoretical results from the compound thermal diffusivity model were slightly lower than the experimental results for both the 20 nm and 200 nm HDPE/AAO composites.
Sample | Experimental results (m2 s−1) | Theoretical results (m2 s−1) |
---|---|---|
AAO template | 9.03 × 10−7 | — |
HDPE/AAO (20 nm) | 5.92 × 10−7 | 5.76 × 10−7 |
HDPE/AAO (200 nm) | 5.29 × 10−7 | 5.03 × 10−7 |
The difference between the theoretical and experimental results is probably due to several reasons. First, polymers could probably exhibit scale effects in thermal transport. It was investigated by molecular dynamics simulations27 that a single chain or aligned polymer chains may have enhanced thermal conductivity. The thermal diffusivity of HDPE nanowires could be slightly above that of bulk materials, which was applied in the model. The crystallinity of the polymer nanofibers during the fabrication process, such as pore size and cooling rate, could probably affect the resulting difference.28 Other potential unpredictable factors, such as the extent and quality of thermal contact between the nanofibers and pores in alumina caused during fabrication, could also possibly contribute to the experimental results.
This journal is © The Royal Society of Chemistry 2016 |