- Email: [email protected]
multi-walled carbon nanotube nanocomposite foams for thermal insulation
Accepted Manuscript Advanced bimodal polystyrene/multi-walled carbon nanotube nanocomposite foams for thermal insulation Pengjian Gong, Guilong Wang, Minh-Phuong Tran, Piyapong Buahom, Shuo Zhai, Guangxian Li, Chul B. Park PII:
S0008-6223(17)30475-X
DOI:
10.1016/j.carbon.2017.05.029
Reference:
CARBON 12005
To appear in:
Carbon
Received Date: 4 January 2017 Revised Date:
23 April 2017
Accepted Date: 6 May 2017
Please cite this article as: P. Gong, G. Wang, M.-P. Tran, P. Buahom, S. Zhai, G. Li, C.B. Park, Advanced bimodal polystyrene/multi-walled carbon nanotube nanocomposite foams for thermal insulation, Carbon (2017), doi: 10.1016/j.carbon.2017.05.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Advanced Bimodal Polystyrene/Multi-Walled Carbon Nanotube Nanocomposite Foams for Thermal Insulation
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Pengjian Gong1,2*, Guilong Wang2,3, Minh-Phuong Tran2, Piyapong Buahom2, Shuo Zhai1,2, Guangxian Li1 and Chul B. Park2*
1. College of Polymer Science and Engineering, Sichuan University, 24 Yihuan Road, Nanyiduan, Chengdu, Sichuan, People’s Republic of China, 610065
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2. Microcellular Plastics Manufacturing Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto,
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Ontario, Canada M5S 3G8
3. School of Material Science and Engineering, Shandong University, 17923 Jingshi Road, Jinan, Shandong, People’s Republic of China
* Corresponding authors: Pengjian Gong. Email address: [email protected]. Tel: +86-181-8075-6171;
ABSTRACT
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Chul B. Park. Email address: [email protected]. Tel: +1-416-978-3053
We developed an advanced bimodal polystyrene (PS)/multi-walled carbon nanotube (MWCNT) nanocomposite foam with a very low thermal conductivity of 30
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mW/m-K without using any insulation gas. The MWCNTs significantly decreased the radiative thermal conductivity of the foams with the high infrared (IR) absorption
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capability and increased the optimal expansion ratio of the foams to minimize the total thermal conductivity. The radiative blocking effect of MWCNTs was quantitatively modeled by calculating the IR absorption index of the unfoamed nanocomposites and calculating the IR extinction coefficient of the foamed nanocomposites. In addition, a theoretical model to analyze the optimal expansion ratio in synergistic bimodal nanocomposite foam was developed for the first time. The calculated values were in good
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agreement with the experimental data to verify the superior heat-blocking characteristics of the MWCNTs in the bimodal cellular morphology.
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KEYWORDS: MWCNTs, IR absorption index, IR extinction coefficient, optimal expansion ratio, bimodal nanocomposite foam, thermal insulation
1.
INTRODUCTION
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There is a strong global demand for innovative materials with superthermal insulation properties to help save energy. Numerous countries have invested heavily in
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developing renewable energy to replace conventional energy, but these large investments have not proven as profitable as expected [1]. For example, there was very little contribution, less than 0.2%, of the wind, tidal, and solar energy to the total produced energy in Canada during 2010 - 2014 [2]. Therefore, it would be more prudent to focus on reducing the energy waste through enhanced insulation as well. In fact, industrial and
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residential buildings typically consume more than 60% of the total energy produced [2], and it will be desirable to decrease the waste energy from the heating and cooling system with improved insulation. To this end, the European Commission introduced the Energy Saving 2020 to increase the energy efficiency 20% by 2020 [3]. In this context,
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superthermal insulation materials are urgently required to reduce energy loss and to address the concerns of scarce energy resources.
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Polymeric foam is one type of insulation materials with a low thermal
conductivity [4]. An environmentally hazardous insulation gas is often used in these foams to enhance their thermal insulation performance. Fluorocarbons, for example, are one type of insulation gas. Their thermal conductivity of ~ 12 mW/m-K is much lower than that of air at 26 mW/m-K [5]. But the 1996 Montreal Protocol called for an international ban on the ozone-depletion potential (ODP) posed by chlorofluorocarbon (CFC)-based blowing agents [6]. At that time, the foam industry had been using low ODP 2 / 28
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hydrochlorofluorocarbon (HCFC)-based blowing agents, such as HCFC-22, HCFC-141b and HCFC-142b, during its transition away from CFCs. However, the HCFC-based foams were phased out in January 2002 from Europe and in January 2010 from North
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America. Some companies then started to use hydrofluorocarbons (HFCs), but their high global warming potential (GWP) limited the usage. With these insulation gases, the polymeric foams’ initial thermal conductivity is typically around 28 mW/m-K [7]. Along with the insulation gases’ escape over time, the thermal conductivity of foams may
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become higher than 30 mW/m-K in a few years [7]. It should also be noted that an increased expansion ratio with higher insulation-gas dependency may increase the overall
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conductivity, because of a significant increase in radiation [8, 9]. So there is an optimal expansion ratio to minimize the overall thermal conductivity, and the value of the optimal expansion ratio is relatively low for most polymers with a zero or low IR absorption index. But as demonstrated in the later section of this paper, the optimal expansion ratio can be increased by adding carbon materials to block heat transfer.
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Efforts have been made to avoid the environmentally dangerous insulation gas while maintaining a low thermal conductivity of the insulation material. Vacuum panels are an outstanding choice because they offer better insulation properties (below 10 mW/m-K), but they can be easily damaged during installation or during their usage (e.g.,
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by nails in the walls), or by an inevitable and gradual vacuum loss over time. Glassfiberbased insulation products typically have 40 mW/m-K, and they have a moisture
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absorption potential which can increase both their thermal conductivity and the generation of fungus. Loose-fill cellulose has a thermal conductivity similar to glassfiber, i.e., 40 mW/m-K, but the small particles contained in cellulose can cause house dust. Expanded vermiculite mineral in the form of loose particles, on the other hand, has a relatively large thermal conductivity of 70 mW/m-K due to its low porosity. Researchers have also tried to reduce the cell size to nano-scale to decrease the gas-conduction contribution using the Knudsen Effect. But the overall conductivity of the nanocellular 3 / 28
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foams increased, ranging 80 to 110 mW/m-K [10, 11], because of the increased polymerconduction contribution through a lower expansion ratio from the severe cell rupture. In a nutshell, it has been found extremely difficult to further decrease the thermal conductivity
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to below 31 mW/m-K without using the environmentally problematic insulation gas [1214]. The low expansion ratio of the foams with small cells can be increased by introducing large cells into the foams, i.e., by forming a bimodal cellular structure [15]. But the increased expansion ratio will increase the radiative heat transfer and, therefore,
with a large expansion ratio for insulation.
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an effective radiation blocking mechanism is desperately needed for the use of foams
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Uniquely structured nanocomposite foams that use carbonaceous materials as additives would be of great value in achieving low conductivity without using any insulation gas. Carbonaceous materials are, in fact, often added to these foams to act as a black body and to block heat radiation. The black body effectively absorbs the electromagnetic radiation for all of the frequencies and all of the incident angles [16].
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Multi-walled carbon nanotube (MWCNT) is one kind of carbonaceous material that can be brought to an excited electronic state after absorbing radiation in an electromagnetic field. The absorbed radiative energy is finally converted into thermal energy after the rapid relaxation from an excited electronic state to a ground state [17, 18]. In the near-
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infrared (NIR) radiation region, MWCNTs have been applied in the selective thermal ablation of tissues [19]. In the infrared (IR) radiation region, MWCNTs have been used
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in thermal insulation applications [20]. In addition, MWCNTs with a high aspect ratio [18, 21] have acted as effective heterogeneous cell-nucleating agents in the scCO2 foaming process. This has increased the cell density, reduced the cell size, and altered the cellular morphology [22-24]. When a nanocomposite foam with a complicated cellular morphology has a strong IR absorption index, a largely expanded and small-size cell structure effectively blocks both radiation and conduction, and thus lowers the overall thermal conductivity [20]. Polystyrene (PS) has strong non-bond interactions with 4 / 28
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MWCNTs that ensure a good dispersion of the MWCNTs [25, 26]. The PS/MWCNT’s foam morphology is easily tailored by controlling the foaming pressure and temperature [27-29]. Therefore, PS/MWCNT was selected as a case example in the preparation of
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nanocomposite foams for the insulation purpose. In our study, we prepared novel bimodal PS/MWCNT nanocomposite foams by the scCO2 foaming process. By adding MWCNTs, the IR absorption index of the nanocomposite foams increased from 0.004 to 0.02 at 1 wt% concentration, and their
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expansion ratios could be increased up to 31-fold with this bimodal structure. Consequently, these foams had an extremely low thermal conductivity of 30 mW/m-K,
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without the use of any insulation gas. The model we developed showed that the bimodal MWCNT nanocomposite foams’ superior thermal insulating property had accurately predicted the system’s thermal conductivity. Further, based on this model, the fundamental study of heat transfer in bimodal PS/MWCNT foams showed that the exceedingly low thermal conductivity had been due to this foams’ unique synergy: (1)
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The MWCNTs decreased the thermal conductivity by radiation because of their ability to absorb it and, thereby, to increase the optimal expansion ratio that minimizes the total thermal conductivity; (2) The bimodal cellular structure decreased the thermal
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conductivity via conduction by increasing the expansion ratio.
THEORETICAL
FUNDAMENTALS
OF
HEAT
TRANSFER
IN
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BIMODAL POLYMERIC FOAMS
When the polymeric foams have cells of less than 3 mm in diameter, the
convection in foam is negligible [30], and the total thermal conductivity (ktotal) of polymeric foams can be expressed as follows:
ktotal = krad + kcon
(1)
where krad is the thermal conductivity by radiation. kcon is the thermal conductivity via conduction including the solid conductivity and the gas conductivity. 5 / 28
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2.1
Radiation Radiation can easily pass through the high-porosity polymeric foams. Due to the
very low radiative absorption of low-density polymeric foams, radiation can contribute
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up to 40% of the total thermal conductivity [31]. Therefore, blocking radiation is essential to reduce the total thermal conductivity. When radiation passes through polymeric foams, it can be attenuated either by reflection on the cell wall surfaces or by absorption via the dense polymer thin films (cell walls). Because radiation is multi-
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reflected inside the foam, the surrounding cell walls will ultimately absorb it. Consequently, we can apply the diffusion-approximated Rosseland Equation to the foam
2.2
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structure [8, 32]. The detailed calculation can be found in the supporting information.
Conduction
The thermal conductivity of a material with repeat units can be represented by the thermal conductivity of a single unit. In case of bimodal polymeric foams, although they
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have a non-uniform foam structure, their primary large cells are normally distributed evenly throughout the whole foam due to the uniformly distributed cell-nucleation agent in the polymer matrix. Therefore, a repeat bubble cluster unit, with a primary large cell surrounded by secondary small cells, can be extracted from the bimodal foam
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morphology, as Figure 1a and b show. The heat flow in the single bubble cluster is sufficient to represent the heat transfer in the whole foam structure, as shown in the
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supporting information.
To fully consider the mismatch at the interface between the primary cell and the
surrounding secondary cells, the repeat unit in Figure 1b can be divided into six parts, as shown in Figure 1c. The horizontal heat transfer among the parts is ignored unless they are considered as one piece, and only the vertical heat transfer among the parts is considered. The corresponding heat flow then depends on how these six parts are connected, and two models are proposed as good approximations. 6 / 28
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Figure 1 Schematic diagram (a) for bimodal polymeric foams, (b) for one repeat unit of bubble cluster with secondary cells surrounding one primary cell, and (c) for six parts in
Model 1 for Conduction
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one repeat unit
In this model, parts 1 and 2 are considered as one piece with the same temperature profile and gradient in the vertical direction. Likewise, parts 5 and 6 are also considered as one piece. Therefore, the repeat unit in Figure 1b has four pieces, and their
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corresponding thermal resistances are: (1) Secondary cells with a thermal resistance of Rsec1_M1 at the top of the repeat unit, perpendicular to the temperature gradient; (2) Secondary cells with a thermal resistance of Rsec1_M1 at the bottom of the repeast unit,
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perpendicular to the temperature gradient; (3) Secondary cells with a thermal resistance of Rsec2_M1 in the repeat unit surrounding the primary cell, parallel to the temperature
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gradient; and (4) Primary cell with a thermal resistance of Rpri_M1 at the center of the repeat unit. The value of those thermal resistances and the thermal conductivity (k1con) of the repeat unit based on Model 1 are presented in Equations S15-S18.
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Figure 2 Schematic graph (a), and thermal resistance (b) for Model 1
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Model 2 for Conduction
In this model, parts 1, 3 and 5 are considered as one piece. Unlike in Model 1, parts 1 and 2 are not connected. Likewise, parts 5 and 6 are also not connected. Therefore, the repeat unit in Figure 1b has four pieces, and corresponding thermal resistances are: (1) Secondary cells with a thermal resistance of Rsec1_M2 at the top of the repeat unit,
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perpendicular to the temperature gradient; (2) Secondary cells with a thermal resistance of Rsec1_M2 at the bottom of the repeat unit, perpendicular to the temperature gradient; (3) Secondary cells with a thermal resistance of Rsec2_M2 in the repeat unit surrounding the parts 2, 4 and 6, parallel to the temperature gradient; and (4) Primary cell with a thermal
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resistance of Rpri_M2 at the center of the repeat unit. The value of those thermal resistances and the thermal conductivity (k2con) of the repeat unit based on Model 2 are presented in
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Equations S19-S22. Compared with Model 1, Model 2 has more horizontal disconnections and hence gives lower thermal conductivity.
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Figure 3 Schematic graph (a), and thermal resistance (b) for Model 2
Due to the different assembly of six parts in Model 1 and Model 2 as shown in Figure 2 and Figure 3, the calculated values of these two models may show discrepancy.
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For Model 1, parts 1 and 2 have the same temperature gradient; because these two parts are connected as one piece. However, for Model 2, parts 1 and 2 are disconnected to block the horizontal heat transfer at the interface, and hence the temperature gradient in part 2 are different from that in part 1. Therefore, to what degree the temperature profiles in parts 1 and 2 are different, and to what extent parts 1 and 2 contribute to the heat
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transfer will have great effects on the discrepancy between Model 1 and Model 2. When the secondary cells are small enough to significantly decrease the gas conductivity, parts 1 and 2 in Model 2 will have great temperature difference, and hence the values
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calculated by Model 1 and Model 2 are divergent as shown in Figure S3. On the other hand, when the secondary cells have a large volume fraction in the bimodal foams, heat
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transfer through parts 1 and 2 will contribute much to the thermal conduction and, therefore, the discrepancy between Model 1 and Model 2 will be also significant.
3.
MWCNTs’ advantage to block heat transfer in bimodal foams With an increase in the expansion ratio, the conductivity through conduction
decreases while the radiative thermal conductivity increases. Therefore, an optimal expansion ratio exists to minimize the total thermal conductivity. Figure 4 shows the calculated total thermal conductivity of PS foam with 100 µm primary cells and 0.1 µm 9 / 28
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secondary cells as a function of expansion ratio. Due to the significantly increased radiative thermal conductivity with an increased expansion ratio, the optimal point to minimize the total thermal conductivity of PS foams is relatively low, at 13-fold
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expansion, and the corresponding total thermal conductivity is 37.8 mW/m-K. The addition of carbonaceous nanoparticles with strong IR absorption will increase the radiative absorption efficiency of the foams (calculated by Equation S14), will decrease their radiative thermal conductivity, and therefore will increase their
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optimal expansion ratios to minimize their total thermal conductivity. Apparently, MWCNTs are vitally important to increase the radiative absorption efficiency of the PS
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foam. Figure 4 shows that when the radiative absorption efficiency increases to 70%, the minimal total thermal conductivity decreases to 31.8 mW/m-K, but the optimal expansion ratio to achieve the minimal total thermal conductivity increases to 25-fold. In the case of unimodal foam with 0.1 µm cells, the maximum achievable expansion ratio was still low because of the opening of the thin cell walls [33]. By contrast, in the case of a bimodal
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foam, the expansion ratio could be easily increased by increasing the primary cell volume
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ratio as shown in Figure 4.
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Figure 4 Total thermal conductivity of foams with 100 µm primary cells and 0.1 µm secondary cells. The solid and dash curves represent the values calculated by Model 1 and Model 2, respectively. The dash with dot curve is the primary cell volume ratio of the corresponding foams.
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In our earlier work, we made a qualitative study of the effect of MWCNTs on the gas conductivity, the solid conductivity, the radiative thermal conductivity, and the total thermal conductivity of PS/MWCNT unimodal foams [20]. However, because a
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systematic and quantitative study was lacking, the distinct behavioral effect of increasing the optimal expansion ratio for the total thermal conductivity with increased MWCNT
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concentrations had not been made entirely clear. This important aspect of MWCNTs in relation to foams is critical because it enhances their thermal insulation performance. The fundamental role of MWCNTs is to increase the IR absorption index of the PS/MWCNT cell walls, and then increase the foams’ radiative absorption efficiency. This leads to an increased optimal expansion ratio. Therefore, in our study, we quantitatively calculated the intrinsic IR absorption index of the unfoamed PS/MWCNT nanocomposites. Then we calculated the intrinsic IR extinction coefficient of the PS/MWCNT foams to show how the optimal expansion ratio was fundamentally changed by adding MWCNTs. Further, 11 / 28
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due to the unimodal foams’ limited expansion ratios, bimodal foams, which have larger expansion ratios, were also prepared. This experiment was undertaken to show how the optimal expansion ratio was changed by adding MWCNTs to the foams. This systematic
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study enabled us to take full advantage of MWCNTs in blocking the heat transfer in foams. It also helped us to design a thermal insulation material with a proper MWCNT concentration and foam morphology.
Using the bimodal structure, our experiment allowed us to attain the large
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expansion ratio needed to demonstrate the optimal expansion ratio concept. Therefore, we can now optimize the cell structure and thereby minimize the conductivity by using
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the bimodal foam structure. Previously the powerful characteristic of radiation absorption could not be fully applied because there was no way to increase the expansion ratio. But now it can be put to use with a proper cell structure. The synergistic effect of the MWCNTs’ radiative absorption ability and the bimodal cell structure have made it possible to decrease the total thermal conductivity to a level of 30 mW/m-K, without
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using any insulation gas. All of these optimized and experimental verifications have now become quantitatively possible. This is because we have developed a theoretical model for the thermal conductivity of a bimodal cell structure that uses MWCNTs.
EXPERIMENTAL
4.1
Materials
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4.
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General purpose polystyrene, GPPS 3100, was purchased at Styrolution (melt
flow rate = 10 g/10 min at 200°C/5 kg, density = 1.04 g/cm3) and was used as received. MWCNTs (average outer diameter = 10 nm, average length = 1.5 µm, surface area = 250 ~ 300 m2/g, carbon purity 90%, density = 1.44 g/cm3) were supplied by NanocylTM, Belgium, and were produced by Catalytic Carbon Vapor Deposition (CCVD). Carbon dioxide (Linde Gas, purity over 99%) and pentane (Caledon Laboratories Ltd., water content less than 0.02%) were used as physical blowing agents. 12 / 28
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4.2
Preparation of PS/MWCNT nanocomposites Melt blending is an efficient method to disperse MWCNTs in the PS matrix [34,
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35]. PS/MWCNT 10 wt% masterbatch was supplied by NanocylTM, Belgium. The 1.0 and 2.0 wt% nanocomposites were then prepared by mixing the masterbatch with pristine PS using a DSM twin-screw compounder (Berstorff ZE25, screw length 48D, chamber volume 15 ml) at 200°C and 100 rpm for 10 min. The 0.1 wt%, 0.25 wt%, and 0.5 wt%
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nanocomposites were prepared by mixing the 1.0 wt% nanocomposite with pristine PS at
the PS matrix.
4.3
Supercritical CO2 foaming
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200°C and at 100 rpm for 5 min. to make sure that the MWCNTs were well dispersed in
Pristine PS and PS/MWCNT rod samples measuring ~ 5 mm in diameter and 30 mm in length were placed into a high-pressure autoclave to dissolve both CO2 and
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pentane. Before pressurizing CO2, 0 ml, 10 ml, 30 ml or 60 ml of liquid pentane (boiling point: 36.1°C) was poured into the autoclave (chamber volume: 163 ml). The autoclave was then heated to 50°C, so that the pentane phase became gas and was miscible with the CO2 phase [36]. When the required pressure (13.8 MPa, 20.7 MPa or 27.6 MPa) and
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temperature (50°C) were achieved, the system was held for three days to absorb a sufficient amount of the blend blowing agents. Under these foaming conditions, CO2 and
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pentane were miscible at any concentration [36]. Due to the strong plasticization effect of the blowing agents, the glass transition temperature (Tg) was decreased to below the gassaturation temperature of 50°C, and foaming was induced by rapid depressurization alone in 2 s. The samples foamed by the blend blowing agents with 0 ml, 10 ml, and 30 ml pentane had a unimodal foam morphology. The bimodal foams were prepared by the blend blowing agents with 60 ml pentane. The bimodal foams with relatively small expansion ratios were prepared by two-step depressurization using CO2 alone as the 13 / 28
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blowing agent. In this experiment, the 1st depressurization occurred by 6.9 MPa in 1 s, and then the pressure was maintained for 1 h before the 2nd depressurization to the ambient pressure occurred. All of the foamed samples were then placed in 100°C boiling
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water for 2.5 min. to further expand the cells. Amongst all the 48 foam samples, the 6 foam samples prepared at 13.8 MPa with 30 ml Pentane were from Ref 20. To achieve a large expansion ratio, three factors in this system were important: (1) Saturation under a relatively low temperature to dissolve a large amount of CO2 in the matrix and to enhance
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bubble nucleation; (2) Placed at 100oC after depressurization to soften the matrix and to facilitate bubble growth; (3) Added pentane to plasticize the matrix (when pentane still
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remained in the matrix) and to expand the cells (after pentane diffused into the cells). Before any characterizations were done, all of the foam samples were vacuumed for one week, and then they were left for over one month to ensure that air permeated into the cells and was the only gas in them.
Characterization
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4.4
The transient plane source (TPS) Hot Disk thermal constants analyzer (Therm Test Inc., TPS 2500, Sweden) was used to measure the thermal conductivity of the PS/MWCNT nanocomposites and foams. Two sample pieces around 15 mm in diameter
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were used to conduct the test. According to the testing samples’ thermal characteristics, the power output (0.005 ~ 0.020 W), test duration (5 ~ 20 s) and sensor size (2 or 3 mm
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in radius) were determined. The measurement was performed 3 times for each sample, and the experimental deviation was less than 5%. Details of the TPS method can be found in Refs 37-39.
Fourier transform infrared spectroscopy (FTIR) (PerkinElmer spectrum one) was
used to measure the spectral properties of the films and foams. We collected the spectral data by averaging 8 scans in a spectral range of wavelength from 2.5 to 25 µm (4,000 to 400 cm-1). The airborne H2O and CO2 background noise was registered before recording 14 / 28
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the samples’ IR transmittance. For the complex refractive index of the PS/MWCNT nanocomposites, both the reflectance (Ref) and transmittance (τ) of the film samples with ~ 50 µm thickness (lfilm) were recorded. The imaginary part of the complex refractive
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index (Img), corresponding to the IR absorption index of the PS/MWCNT nanocomposites, is calculated as follows [40]: Img = − ln τ film λ 4π l film
(2)
1 − 1 C − C 2 − 4 Ref ( 2 − Ref ) τ
τ film =
2 Ref ( 2 − Ref
)
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The film internal transmittance (τfilm) can be expressed as follows [40]:
(3)
C = 1 + 2 Ref + τ 2 − Ref 2 .
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where C is used to simplify the equations, and it is calculated as
(4)
For IR radiation through the foams, to eliminate the sample thickness’s effect on the IR transmittance, the foams were cut into plate shapes of 15 mm in diameter, with a
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thickness ranging from 0.2 to 2 mm. At least 6 plate samples of different thicknesses were measured to calculate the radiative thermal conductivity.
RESULTS AND DISCUSSION
5.1
Increased IR absorption index by adding MWCNTs
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5.
MWCNTs as black body has strong IR absorption capability to block the IR
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transmittance in PS/MWNCT nanocomposites. For pristine PS, the aromatic =C-H outof-plane deformation vibrations attributes to the IR absorption peaks at 13.2 µm and 14.3 µm, and the out-of-plane ring deformation vibration attributes to IR absorption peak at
18.5 µm [41]. However, the IR absorption for pristine PS in the whole wavelength ranges of 2.5 ~ 25 µm was still very weak, and the IR transmittance of pristine PS film (~ 50 µm thick) was over 80% as shown in Figure 5a. Due to the MWCNTs’ strong IR absorption [42], the addition of MWCNTs in films decreased the IR transmittance. For instance, 15 / 28
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adding 1wt% MWCNTs effectively reduced the IR transmittance from 84% to 30% at a wavelength of 25 µm. To quantitatively study the effect of MWCNTs on IR absorption, the intrinsic IR
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absorption index of PS/MWCNT nanocomposites was calculated by Equation 2 and the results are summarized in Figure 5b. It is noteworthy that despite the absorption peaks, the IR absorption index of pristine PS in the whole wavelength ranges of 2.5 ~ 25 µm was almost 0. The addition of MWCNTs then enhanced the IR absorption and increased
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the baseline of the index curves significantly. From the wavelength-averaged IR absorption index shown in Table 1, it is noted that increasing MWCNTs almost linearly
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increased the IR absorption index from 0.004 to 0.03 at 2 wt% MWCNT concentration. Furthermore, at the long wavelength of 25 µm, the IR absorption index of PS/MWCNT 2wt% was 0.08, 20 times larger than that of pristine PS, 0.004. MWCNTs’ characteristic of much strong IR absorption at long wavelength range is a great advantage in the
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application of thermal insulation foams.
Figure 5 (a) Spectral transmittance of the pristine PS and PS/MWCNT nanocomposite films (~ 50 µm thick) and (b) the IR absorption index
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5.2
Increased IR extinction coefficient by adding MWCNTs
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Table 1 Wavelength-averaged IR absorption index of pristine PS and PS/MWCNT
Due to the MWCNTs’ strong IR absorption in PS/MWNCT nanocomposites, the
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IR transmission through PS/MWCNT foams was also effectively blocked. In the foam structure with a large expansion ratio, the short wavelength IR was blocked by the
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reflection at the cell walls, while the long wavelength IR easily passed through the foams [20]. Due to the weak IR absorption and the large expansion ratio of the pristine PS foam, its IR transmittance was over 80% in the long wavelength range of 20 ~ 25 µm as shown in Figure 6a. Adding 0.25 wt% MWCNT then decreased the IR transmittance from 80% to 65%. When the MWCNT content was further increased to 2.0 wt% in the PS matrix,
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the IR transmittance was decreased to less than 10%. To reveal the intrinsic IR absorption performance of MWCNTs in the foam structure, the IR extinction coefficient of PS/MWCNT foams was calculated by Equation S9 and the results are summarized in Figure 6b. Similar to PS/MWCNT nanocomposites, the addition of MWCNTs to the
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foams enhanced the IR absorption and increased the baseline of the extinction coefficient curves: despite the absorption peaks, the IR extinction coefficient of pristine PS foam at
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long wavelength range was almost 0, while that of PS/MWCNT 2wt% foam became 4.0. By recording the IR-transmitted energy through the foams, the radiation can be
measured based on FTIR spectrometry. The higher the transmittance, the more radiative thermal conductivity there will be. For the pristine PS foam with a large expansion ratio and a weak IR-absorbing matrix, the long wavelength IR energy still contributed much to the radiative thermal conductivity and correspondingly increased the total thermal conductivity of the foams, although the short wavelength IR energy was blocked by the 17 / 28
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porous structure. The addition of MWCNTs then absorbed the incidental long wavelength
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IR radiation, and effectively helped block IR radiation in this PS foam system.
Figure 6 (a) Spectral transmittance of the pristine PS and PS/MWCNT bimodal foam sheet samples (foaming condition: 13.8 MPa with 60 ml pentane added) of ~ 600 µm thickness (namely, 680 µm thickness for PS foam, 660 µm thickness for PS/MWCNT 0.1
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wt% foam, 590 µm thickness for PS/MWCNT 0.25 wt% foam, 540 µm thickness for PS/MWCNT 0.5 wt% foam, 620 µm thickness for PS/MWCNT 1 wt% foam, and 630 µm thickness for PS/MWCNT 2 wt% foam) and (b) IR extinction coefficient of the pristine PS and PS/MWCNT foams. For each foam, the value was calculated based on at least 6
Increased optimal expansion ratio by adding MWCNTs
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5.3
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samples of different thicknesses.
The total thermal conductivity of foams includes the radiative thermal
conductivity (which increases with an increased expansion ratio) and the gas and solid conductivity (which decreases with an increased expansion ratio). Hence, there is an optimal expansion ratio that minimizes the total thermal conductivity. This optimal expansion ratio is increased with the addition of MWCNTs because of their strong IR absorption capability. 18 / 28
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The effect of MWCNTs on thermal radiation was quantitatively studied using the Rosseland Equation (Equation S13) to calculate the transmitted radiative energy. Figure 7 summarizes the calculated radiative thermal conductivity of both the unimodal and
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bimodal foams. The foam morphology is presented in the supporting information. We note that the radiative thermal conductivity through the PS foam with a large expansion ratio was very high due to the PS matrix’s low IR absorption index of 0.004 (Figure 5b). Figure 7 shows that the foamed samples’ radiative thermal conductivity increased almost
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linearly with the expansion ratio’s increase, which ranged from 8- to 30-fold. Therefore, a linear regression (y = ax+b) was applied to fit the data shown in Figure 7. The slope and
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interception of the fitted curves are summarized in Table S1. Then the radiative absorption efficiency was calculated using Equation S14, and the result is shown in Figure 8a. The average radiative absorption efficiency was obtained by calculating the corresponding values of eight samples (four samples from unimodal foams and the other four samples from bimodal foams) at each MWCNT concentration as shown in Figure 8b.
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It is noted that the increased MWCNT concentration enhanced the IR absorption index of
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the solid matrix, and then increased the radiative absorption efficiency of the foams.
Figure 7 Radiative thermal conductivity in foams (curves obtained by linear fitting the experimental data) 19 / 28
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Figure 8 (a) The radiative absorption efficiency of the PS/MWCNTs matrix (curves
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obtained based on the linear regression for the radiative thermal conductivity) and (b) the average radiative absorption efficiency versus wavelength-averaged IR absorption index
Due to their strong IR absorption capacity, the MWCNTs added to the PS matrix helped to block the thermal radiation in the foams. Their influence on the reduction of IR
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radiation was especially prominent when the nanocomposite foam had a large expansion ratio. For instance, 1 wt% MWCNTs reduced the radiative thermal conductivity by 8.5 mW/m-K in the bimodal foam with a 28-fold expansion ratio. In the unimodal foam with
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an 18-fold expansion ratio, 1 wt% MWCNTs only decreased the radiative thermal conductivity by 6.5 mW/m-K. Consequently, the MWCNTs in a bimodal nanocomposite
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foam with a larger expansion ratio could absorb more radiative energy than they could in unimodal foam.
Furthermore, the unimodal and bimodal cell structures of PS/MWCNT foams also
affected the thermal insulation performance due to their difference in the achievable expansion ratio. Figure 9 shows the total thermal conductivity of the unimodal and bimodal PS/MWCNT foams, together with the calculated values based on Model 1 and Model 2 in Section 2. Because of their limited expansion ratio, the conduction through the unimodal foams was dominant. And the radiative absorption capacities of the 20 / 28
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MWCNTs had only a limited effect in reducing the total thermal conductivity. On the other hand, bimodal foams with a large expansion ratio were easily achieved. Therefore, the contribution of the conductivity via conduction to the total thermal conductivity in
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these bimodal foams was decreased. Meanwhile, the radiative thermal conductivity became significantly large in bimodal PS foam. But this increase in the radiative thermal conductivity (and in the total thermal conductivity) along with the expansion ratio’s increase was arrested when the MWCNTs were introduced. Because the MWCNTs
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dramatically absorbed radiation in the bimodal foams, the total thermal conductivity was decreased at larger expansion ratios. Correspondingly, the MWCNTs helped increase the
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optimal expansion ratio in bimodal foams to minimize their total thermal conductivity. By adjusting the MWCNT concentration and the expansion ratio, the lowest thermal conductivity of the unimodal PS/MWCNT foams obtainable in this study was 32.8 mW/m-K. The application of MWCNTs with a bimodal cellular structure was effective in further decreasing the total thermal conductivity. This was because the
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primary large cells present in the bimodal foams induced a larger expansion ratio than they would do in unimodal foams. This expansion reduced the solid conduction while the secondary small cells in the bimodal foams also experienced the Knudsen effect, which reduced gas conduction. Most importantly, the MWCNTs in the bimodal foam with a
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large expansion ratio then absorbed more radiation and contributed to less solid conduction than they did in the unimodal foams. As a result, by tailoring the MWCNT
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concentration and the bimodal cellular structure, the PS/MWCNT 1.0 wt% bimodal foam achieved a minimum thermal conductivity of 30.2 mW/m-K, as will be discussed below in detail.
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Figure 9 Total thermal conductivity of (a) unimodal foams and (b) bimodal foams. The solid and dash curves represent the values calculated by Model 1 and Model 2,
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respectively. Note that the unimodal foams (a) could not be expanded as high as the bimodal foams (b).
The total thermal conductivity of the foams with different carbonaceous additive concentrations and foam morphologies made from various materials were summarized
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and compared. Figure 10 shows the reported values in the references, and it is clearly observed that the total thermal conductivity of nanocomposite foams decreased with an increased carbonaceous additive concentration and expansion ratio.
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In the case of no carbonaceous additives, when the polymeric foams had a small expansion ratio below 5-fold, their thermal conductivity was over 50 mW/m-K,
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regardless of the micro- or nano-cells, as Figure 10 shows. This was because the heat transfer in polymeric foams with an expansion ratio of less than 5-fold is dominated by solid conduction. The expansion ratio has to be at least 10-fold to make the polymeric foams’ thermal conductivity below 40 mW/m-K. Therefore, in such a high-density foam system, an increase in the expansion ratio will significantly decrease the total thermal conductivity. On the other hand, as discussed from Figure 7 and S8, the total thermal conductivity of the foams with a large expansion ratio became very large as well because of the increased radiative thermal conductivity. For instance, the total thermal 22 / 28
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conductivity of the low-density expandable PS (i.e., EPS) foams seen in Figure 10 becomes higher than 35 mW/m-K for the expansion ratio over 60-fold [43]. In the case of having carbonaceous additives, compared with the unimodal
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nanocomposite foams, the bimodal nanocomposite foams consisting of primary large cells and secondary small cells had a unique synergy to effectively block the heat transfer through radiation (carbonaceous additives), solid conduction (primary large cells), and gas conduction (secondary small cells). Zhang et al. prepared a bimodal PS/active carbon
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0.5wt% foam with a 25-fold expansion ratio and over 50 µm secondary cells. The corresponding thermal conductivity was 31.5 mW/m-K [15]. Based on the heat transfer
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behavior in nanocomposite foams presented in Figure 10, the total thermal conductivity can be further decreased by increasing carbonaceous additive concentration and the expansion ratio. We prepared a novel bimodal PS/MWCNT 1wt% foam with a 28-fold expansion ratio and 5.8 µm secondary cells. The 1 wt% MWCNTs absorbed a large amount of thermal radiation, and this bimodal foam structure has an advantage of
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expansion ratio control while utilizing the Knudsen effect. Therefore, a very low thermal conductivity of 30.2 mW/m-K was achieved by adding 1 wt% MWCNTs to the bimodal
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foam.
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Figure 10 Total thermal conductivity of polymeric foams as a function of the carbonaceous additive content and the expansion ratio [10, 12, 13, 15, 43-47] * The thermal conductivity of EPS foams was measured at 10°C
CONCLUSION
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6.
In this study, we prepared PS/MWCNT nanocomposite foams using the scCO2 foaming system. Due to MWCNTs’ strong IR absorption performance, their addition to PS matrix greatly increased the IR absorption index of the solid matrix. Correspondingly,
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the radiative absorption efficiency of the PS/MWCNT nanocomposite foams increased with increasing MWCNT concentration. For the first time, a model based on the thermal
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resistances in the primary and secondary cell regions was proposed to quantitatively investigate the change of optimal expansion ratio with the addition of MWCNTs. The calculated thermal conductivity in the model was in good agreement with the experimental data. Based on the model, we optimized the cellular structure and the MWCNT’s concentration, and then we achieved a minimum total thermal conductivity in the bimodal PS/MWCNT 1.0 wt% foam system with a 28-fold expansion ratio and 5.8 µm secondary cells. The MWCNTs reduced radiation and increased the optimal
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expansion ratio. The primary large cells in the bimodal foams then increased the expansion ratio. Because of this action, a very low thermal conductivity of 30.2 mW/m-K was successfully obtained without using any insulation gas. In the above advanced
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bimodal foam, the MWCNTs’ ability to decrease radiative heat transfer by 8.5 mW/m-K was of great importance.
Acknowledgements
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The authors would like to thank the Korea Institute of Construction Technology (KICT), the Microcellular Plastics Manufacturing Laboratory (MPML) and the Starting
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funds from Sichuan University for their financial support of this project.
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S0008-6223(17)30475-X
DOI:
10.1016/j.carbon.2017.05.029
Reference:
CARBON 12005
To appear in:
Carbon
Received Date: 4 January 2017 Revised Date:
23 April 2017
Accepted Date: 6 May 2017
Please cite this article as: P. Gong, G. Wang, M.-P. Tran, P. Buahom, S. Zhai, G. Li, C.B. Park, Advanced bimodal polystyrene/multi-walled carbon nanotube nanocomposite foams for thermal insulation, Carbon (2017), doi: 10.1016/j.carbon.2017.05.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Advanced Bimodal Polystyrene/Multi-Walled Carbon Nanotube Nanocomposite Foams for Thermal Insulation
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Pengjian Gong1,2*, Guilong Wang2,3, Minh-Phuong Tran2, Piyapong Buahom2, Shuo Zhai1,2, Guangxian Li1 and Chul B. Park2*
1. College of Polymer Science and Engineering, Sichuan University, 24 Yihuan Road, Nanyiduan, Chengdu, Sichuan, People’s Republic of China, 610065
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2. Microcellular Plastics Manufacturing Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto,
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Ontario, Canada M5S 3G8
3. School of Material Science and Engineering, Shandong University, 17923 Jingshi Road, Jinan, Shandong, People’s Republic of China
* Corresponding authors: Pengjian Gong. Email address: [email protected]. Tel: +86-181-8075-6171;
ABSTRACT
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Chul B. Park. Email address: [email protected]. Tel: +1-416-978-3053
We developed an advanced bimodal polystyrene (PS)/multi-walled carbon nanotube (MWCNT) nanocomposite foam with a very low thermal conductivity of 30
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mW/m-K without using any insulation gas. The MWCNTs significantly decreased the radiative thermal conductivity of the foams with the high infrared (IR) absorption
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capability and increased the optimal expansion ratio of the foams to minimize the total thermal conductivity. The radiative blocking effect of MWCNTs was quantitatively modeled by calculating the IR absorption index of the unfoamed nanocomposites and calculating the IR extinction coefficient of the foamed nanocomposites. In addition, a theoretical model to analyze the optimal expansion ratio in synergistic bimodal nanocomposite foam was developed for the first time. The calculated values were in good
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agreement with the experimental data to verify the superior heat-blocking characteristics of the MWCNTs in the bimodal cellular morphology.
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KEYWORDS: MWCNTs, IR absorption index, IR extinction coefficient, optimal expansion ratio, bimodal nanocomposite foam, thermal insulation
1.
INTRODUCTION
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There is a strong global demand for innovative materials with superthermal insulation properties to help save energy. Numerous countries have invested heavily in
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developing renewable energy to replace conventional energy, but these large investments have not proven as profitable as expected [1]. For example, there was very little contribution, less than 0.2%, of the wind, tidal, and solar energy to the total produced energy in Canada during 2010 - 2014 [2]. Therefore, it would be more prudent to focus on reducing the energy waste through enhanced insulation as well. In fact, industrial and
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residential buildings typically consume more than 60% of the total energy produced [2], and it will be desirable to decrease the waste energy from the heating and cooling system with improved insulation. To this end, the European Commission introduced the Energy Saving 2020 to increase the energy efficiency 20% by 2020 [3]. In this context,
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superthermal insulation materials are urgently required to reduce energy loss and to address the concerns of scarce energy resources.
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Polymeric foam is one type of insulation materials with a low thermal
conductivity [4]. An environmentally hazardous insulation gas is often used in these foams to enhance their thermal insulation performance. Fluorocarbons, for example, are one type of insulation gas. Their thermal conductivity of ~ 12 mW/m-K is much lower than that of air at 26 mW/m-K [5]. But the 1996 Montreal Protocol called for an international ban on the ozone-depletion potential (ODP) posed by chlorofluorocarbon (CFC)-based blowing agents [6]. At that time, the foam industry had been using low ODP 2 / 28
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hydrochlorofluorocarbon (HCFC)-based blowing agents, such as HCFC-22, HCFC-141b and HCFC-142b, during its transition away from CFCs. However, the HCFC-based foams were phased out in January 2002 from Europe and in January 2010 from North
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America. Some companies then started to use hydrofluorocarbons (HFCs), but their high global warming potential (GWP) limited the usage. With these insulation gases, the polymeric foams’ initial thermal conductivity is typically around 28 mW/m-K [7]. Along with the insulation gases’ escape over time, the thermal conductivity of foams may
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become higher than 30 mW/m-K in a few years [7]. It should also be noted that an increased expansion ratio with higher insulation-gas dependency may increase the overall
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conductivity, because of a significant increase in radiation [8, 9]. So there is an optimal expansion ratio to minimize the overall thermal conductivity, and the value of the optimal expansion ratio is relatively low for most polymers with a zero or low IR absorption index. But as demonstrated in the later section of this paper, the optimal expansion ratio can be increased by adding carbon materials to block heat transfer.
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Efforts have been made to avoid the environmentally dangerous insulation gas while maintaining a low thermal conductivity of the insulation material. Vacuum panels are an outstanding choice because they offer better insulation properties (below 10 mW/m-K), but they can be easily damaged during installation or during their usage (e.g.,
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by nails in the walls), or by an inevitable and gradual vacuum loss over time. Glassfiberbased insulation products typically have 40 mW/m-K, and they have a moisture
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absorption potential which can increase both their thermal conductivity and the generation of fungus. Loose-fill cellulose has a thermal conductivity similar to glassfiber, i.e., 40 mW/m-K, but the small particles contained in cellulose can cause house dust. Expanded vermiculite mineral in the form of loose particles, on the other hand, has a relatively large thermal conductivity of 70 mW/m-K due to its low porosity. Researchers have also tried to reduce the cell size to nano-scale to decrease the gas-conduction contribution using the Knudsen Effect. But the overall conductivity of the nanocellular 3 / 28
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foams increased, ranging 80 to 110 mW/m-K [10, 11], because of the increased polymerconduction contribution through a lower expansion ratio from the severe cell rupture. In a nutshell, it has been found extremely difficult to further decrease the thermal conductivity
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to below 31 mW/m-K without using the environmentally problematic insulation gas [1214]. The low expansion ratio of the foams with small cells can be increased by introducing large cells into the foams, i.e., by forming a bimodal cellular structure [15]. But the increased expansion ratio will increase the radiative heat transfer and, therefore,
with a large expansion ratio for insulation.
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an effective radiation blocking mechanism is desperately needed for the use of foams
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Uniquely structured nanocomposite foams that use carbonaceous materials as additives would be of great value in achieving low conductivity without using any insulation gas. Carbonaceous materials are, in fact, often added to these foams to act as a black body and to block heat radiation. The black body effectively absorbs the electromagnetic radiation for all of the frequencies and all of the incident angles [16].
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Multi-walled carbon nanotube (MWCNT) is one kind of carbonaceous material that can be brought to an excited electronic state after absorbing radiation in an electromagnetic field. The absorbed radiative energy is finally converted into thermal energy after the rapid relaxation from an excited electronic state to a ground state [17, 18]. In the near-
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infrared (NIR) radiation region, MWCNTs have been applied in the selective thermal ablation of tissues [19]. In the infrared (IR) radiation region, MWCNTs have been used
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in thermal insulation applications [20]. In addition, MWCNTs with a high aspect ratio [18, 21] have acted as effective heterogeneous cell-nucleating agents in the scCO2 foaming process. This has increased the cell density, reduced the cell size, and altered the cellular morphology [22-24]. When a nanocomposite foam with a complicated cellular morphology has a strong IR absorption index, a largely expanded and small-size cell structure effectively blocks both radiation and conduction, and thus lowers the overall thermal conductivity [20]. Polystyrene (PS) has strong non-bond interactions with 4 / 28
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MWCNTs that ensure a good dispersion of the MWCNTs [25, 26]. The PS/MWCNT’s foam morphology is easily tailored by controlling the foaming pressure and temperature [27-29]. Therefore, PS/MWCNT was selected as a case example in the preparation of
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nanocomposite foams for the insulation purpose. In our study, we prepared novel bimodal PS/MWCNT nanocomposite foams by the scCO2 foaming process. By adding MWCNTs, the IR absorption index of the nanocomposite foams increased from 0.004 to 0.02 at 1 wt% concentration, and their
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expansion ratios could be increased up to 31-fold with this bimodal structure. Consequently, these foams had an extremely low thermal conductivity of 30 mW/m-K,
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without the use of any insulation gas. The model we developed showed that the bimodal MWCNT nanocomposite foams’ superior thermal insulating property had accurately predicted the system’s thermal conductivity. Further, based on this model, the fundamental study of heat transfer in bimodal PS/MWCNT foams showed that the exceedingly low thermal conductivity had been due to this foams’ unique synergy: (1)
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The MWCNTs decreased the thermal conductivity by radiation because of their ability to absorb it and, thereby, to increase the optimal expansion ratio that minimizes the total thermal conductivity; (2) The bimodal cellular structure decreased the thermal
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conductivity via conduction by increasing the expansion ratio.
THEORETICAL
FUNDAMENTALS
OF
HEAT
TRANSFER
IN
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BIMODAL POLYMERIC FOAMS
When the polymeric foams have cells of less than 3 mm in diameter, the
convection in foam is negligible [30], and the total thermal conductivity (ktotal) of polymeric foams can be expressed as follows:
ktotal = krad + kcon
(1)
where krad is the thermal conductivity by radiation. kcon is the thermal conductivity via conduction including the solid conductivity and the gas conductivity. 5 / 28
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2.1
Radiation Radiation can easily pass through the high-porosity polymeric foams. Due to the
very low radiative absorption of low-density polymeric foams, radiation can contribute
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up to 40% of the total thermal conductivity [31]. Therefore, blocking radiation is essential to reduce the total thermal conductivity. When radiation passes through polymeric foams, it can be attenuated either by reflection on the cell wall surfaces or by absorption via the dense polymer thin films (cell walls). Because radiation is multi-
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reflected inside the foam, the surrounding cell walls will ultimately absorb it. Consequently, we can apply the diffusion-approximated Rosseland Equation to the foam
2.2
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structure [8, 32]. The detailed calculation can be found in the supporting information.
Conduction
The thermal conductivity of a material with repeat units can be represented by the thermal conductivity of a single unit. In case of bimodal polymeric foams, although they
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have a non-uniform foam structure, their primary large cells are normally distributed evenly throughout the whole foam due to the uniformly distributed cell-nucleation agent in the polymer matrix. Therefore, a repeat bubble cluster unit, with a primary large cell surrounded by secondary small cells, can be extracted from the bimodal foam
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morphology, as Figure 1a and b show. The heat flow in the single bubble cluster is sufficient to represent the heat transfer in the whole foam structure, as shown in the
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supporting information.
To fully consider the mismatch at the interface between the primary cell and the
surrounding secondary cells, the repeat unit in Figure 1b can be divided into six parts, as shown in Figure 1c. The horizontal heat transfer among the parts is ignored unless they are considered as one piece, and only the vertical heat transfer among the parts is considered. The corresponding heat flow then depends on how these six parts are connected, and two models are proposed as good approximations. 6 / 28
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Figure 1 Schematic diagram (a) for bimodal polymeric foams, (b) for one repeat unit of bubble cluster with secondary cells surrounding one primary cell, and (c) for six parts in
Model 1 for Conduction
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one repeat unit
In this model, parts 1 and 2 are considered as one piece with the same temperature profile and gradient in the vertical direction. Likewise, parts 5 and 6 are also considered as one piece. Therefore, the repeat unit in Figure 1b has four pieces, and their
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corresponding thermal resistances are: (1) Secondary cells with a thermal resistance of Rsec1_M1 at the top of the repeat unit, perpendicular to the temperature gradient; (2) Secondary cells with a thermal resistance of Rsec1_M1 at the bottom of the repeast unit,
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perpendicular to the temperature gradient; (3) Secondary cells with a thermal resistance of Rsec2_M1 in the repeat unit surrounding the primary cell, parallel to the temperature
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gradient; and (4) Primary cell with a thermal resistance of Rpri_M1 at the center of the repeat unit. The value of those thermal resistances and the thermal conductivity (k1con) of the repeat unit based on Model 1 are presented in Equations S15-S18.
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Figure 2 Schematic graph (a), and thermal resistance (b) for Model 1
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Model 2 for Conduction
In this model, parts 1, 3 and 5 are considered as one piece. Unlike in Model 1, parts 1 and 2 are not connected. Likewise, parts 5 and 6 are also not connected. Therefore, the repeat unit in Figure 1b has four pieces, and corresponding thermal resistances are: (1) Secondary cells with a thermal resistance of Rsec1_M2 at the top of the repeat unit,
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perpendicular to the temperature gradient; (2) Secondary cells with a thermal resistance of Rsec1_M2 at the bottom of the repeat unit, perpendicular to the temperature gradient; (3) Secondary cells with a thermal resistance of Rsec2_M2 in the repeat unit surrounding the parts 2, 4 and 6, parallel to the temperature gradient; and (4) Primary cell with a thermal
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resistance of Rpri_M2 at the center of the repeat unit. The value of those thermal resistances and the thermal conductivity (k2con) of the repeat unit based on Model 2 are presented in
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Equations S19-S22. Compared with Model 1, Model 2 has more horizontal disconnections and hence gives lower thermal conductivity.
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Figure 3 Schematic graph (a), and thermal resistance (b) for Model 2
Due to the different assembly of six parts in Model 1 and Model 2 as shown in Figure 2 and Figure 3, the calculated values of these two models may show discrepancy.
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For Model 1, parts 1 and 2 have the same temperature gradient; because these two parts are connected as one piece. However, for Model 2, parts 1 and 2 are disconnected to block the horizontal heat transfer at the interface, and hence the temperature gradient in part 2 are different from that in part 1. Therefore, to what degree the temperature profiles in parts 1 and 2 are different, and to what extent parts 1 and 2 contribute to the heat
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transfer will have great effects on the discrepancy between Model 1 and Model 2. When the secondary cells are small enough to significantly decrease the gas conductivity, parts 1 and 2 in Model 2 will have great temperature difference, and hence the values
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calculated by Model 1 and Model 2 are divergent as shown in Figure S3. On the other hand, when the secondary cells have a large volume fraction in the bimodal foams, heat
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transfer through parts 1 and 2 will contribute much to the thermal conduction and, therefore, the discrepancy between Model 1 and Model 2 will be also significant.
3.
MWCNTs’ advantage to block heat transfer in bimodal foams With an increase in the expansion ratio, the conductivity through conduction
decreases while the radiative thermal conductivity increases. Therefore, an optimal expansion ratio exists to minimize the total thermal conductivity. Figure 4 shows the calculated total thermal conductivity of PS foam with 100 µm primary cells and 0.1 µm 9 / 28
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secondary cells as a function of expansion ratio. Due to the significantly increased radiative thermal conductivity with an increased expansion ratio, the optimal point to minimize the total thermal conductivity of PS foams is relatively low, at 13-fold
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expansion, and the corresponding total thermal conductivity is 37.8 mW/m-K. The addition of carbonaceous nanoparticles with strong IR absorption will increase the radiative absorption efficiency of the foams (calculated by Equation S14), will decrease their radiative thermal conductivity, and therefore will increase their
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optimal expansion ratios to minimize their total thermal conductivity. Apparently, MWCNTs are vitally important to increase the radiative absorption efficiency of the PS
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foam. Figure 4 shows that when the radiative absorption efficiency increases to 70%, the minimal total thermal conductivity decreases to 31.8 mW/m-K, but the optimal expansion ratio to achieve the minimal total thermal conductivity increases to 25-fold. In the case of unimodal foam with 0.1 µm cells, the maximum achievable expansion ratio was still low because of the opening of the thin cell walls [33]. By contrast, in the case of a bimodal
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foam, the expansion ratio could be easily increased by increasing the primary cell volume
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ratio as shown in Figure 4.
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Figure 4 Total thermal conductivity of foams with 100 µm primary cells and 0.1 µm secondary cells. The solid and dash curves represent the values calculated by Model 1 and Model 2, respectively. The dash with dot curve is the primary cell volume ratio of the corresponding foams.
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In our earlier work, we made a qualitative study of the effect of MWCNTs on the gas conductivity, the solid conductivity, the radiative thermal conductivity, and the total thermal conductivity of PS/MWCNT unimodal foams [20]. However, because a
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systematic and quantitative study was lacking, the distinct behavioral effect of increasing the optimal expansion ratio for the total thermal conductivity with increased MWCNT
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concentrations had not been made entirely clear. This important aspect of MWCNTs in relation to foams is critical because it enhances their thermal insulation performance. The fundamental role of MWCNTs is to increase the IR absorption index of the PS/MWCNT cell walls, and then increase the foams’ radiative absorption efficiency. This leads to an increased optimal expansion ratio. Therefore, in our study, we quantitatively calculated the intrinsic IR absorption index of the unfoamed PS/MWCNT nanocomposites. Then we calculated the intrinsic IR extinction coefficient of the PS/MWCNT foams to show how the optimal expansion ratio was fundamentally changed by adding MWCNTs. Further, 11 / 28
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due to the unimodal foams’ limited expansion ratios, bimodal foams, which have larger expansion ratios, were also prepared. This experiment was undertaken to show how the optimal expansion ratio was changed by adding MWCNTs to the foams. This systematic
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study enabled us to take full advantage of MWCNTs in blocking the heat transfer in foams. It also helped us to design a thermal insulation material with a proper MWCNT concentration and foam morphology.
Using the bimodal structure, our experiment allowed us to attain the large
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expansion ratio needed to demonstrate the optimal expansion ratio concept. Therefore, we can now optimize the cell structure and thereby minimize the conductivity by using
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the bimodal foam structure. Previously the powerful characteristic of radiation absorption could not be fully applied because there was no way to increase the expansion ratio. But now it can be put to use with a proper cell structure. The synergistic effect of the MWCNTs’ radiative absorption ability and the bimodal cell structure have made it possible to decrease the total thermal conductivity to a level of 30 mW/m-K, without
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using any insulation gas. All of these optimized and experimental verifications have now become quantitatively possible. This is because we have developed a theoretical model for the thermal conductivity of a bimodal cell structure that uses MWCNTs.
EXPERIMENTAL
4.1
Materials
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4.
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General purpose polystyrene, GPPS 3100, was purchased at Styrolution (melt
flow rate = 10 g/10 min at 200°C/5 kg, density = 1.04 g/cm3) and was used as received. MWCNTs (average outer diameter = 10 nm, average length = 1.5 µm, surface area = 250 ~ 300 m2/g, carbon purity 90%, density = 1.44 g/cm3) were supplied by NanocylTM, Belgium, and were produced by Catalytic Carbon Vapor Deposition (CCVD). Carbon dioxide (Linde Gas, purity over 99%) and pentane (Caledon Laboratories Ltd., water content less than 0.02%) were used as physical blowing agents. 12 / 28
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4.2
Preparation of PS/MWCNT nanocomposites Melt blending is an efficient method to disperse MWCNTs in the PS matrix [34,
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35]. PS/MWCNT 10 wt% masterbatch was supplied by NanocylTM, Belgium. The 1.0 and 2.0 wt% nanocomposites were then prepared by mixing the masterbatch with pristine PS using a DSM twin-screw compounder (Berstorff ZE25, screw length 48D, chamber volume 15 ml) at 200°C and 100 rpm for 10 min. The 0.1 wt%, 0.25 wt%, and 0.5 wt%
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nanocomposites were prepared by mixing the 1.0 wt% nanocomposite with pristine PS at
the PS matrix.
4.3
Supercritical CO2 foaming
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200°C and at 100 rpm for 5 min. to make sure that the MWCNTs were well dispersed in
Pristine PS and PS/MWCNT rod samples measuring ~ 5 mm in diameter and 30 mm in length were placed into a high-pressure autoclave to dissolve both CO2 and
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pentane. Before pressurizing CO2, 0 ml, 10 ml, 30 ml or 60 ml of liquid pentane (boiling point: 36.1°C) was poured into the autoclave (chamber volume: 163 ml). The autoclave was then heated to 50°C, so that the pentane phase became gas and was miscible with the CO2 phase [36]. When the required pressure (13.8 MPa, 20.7 MPa or 27.6 MPa) and
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temperature (50°C) were achieved, the system was held for three days to absorb a sufficient amount of the blend blowing agents. Under these foaming conditions, CO2 and
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pentane were miscible at any concentration [36]. Due to the strong plasticization effect of the blowing agents, the glass transition temperature (Tg) was decreased to below the gassaturation temperature of 50°C, and foaming was induced by rapid depressurization alone in 2 s. The samples foamed by the blend blowing agents with 0 ml, 10 ml, and 30 ml pentane had a unimodal foam morphology. The bimodal foams were prepared by the blend blowing agents with 60 ml pentane. The bimodal foams with relatively small expansion ratios were prepared by two-step depressurization using CO2 alone as the 13 / 28
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blowing agent. In this experiment, the 1st depressurization occurred by 6.9 MPa in 1 s, and then the pressure was maintained for 1 h before the 2nd depressurization to the ambient pressure occurred. All of the foamed samples were then placed in 100°C boiling
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water for 2.5 min. to further expand the cells. Amongst all the 48 foam samples, the 6 foam samples prepared at 13.8 MPa with 30 ml Pentane were from Ref 20. To achieve a large expansion ratio, three factors in this system were important: (1) Saturation under a relatively low temperature to dissolve a large amount of CO2 in the matrix and to enhance
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bubble nucleation; (2) Placed at 100oC after depressurization to soften the matrix and to facilitate bubble growth; (3) Added pentane to plasticize the matrix (when pentane still
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remained in the matrix) and to expand the cells (after pentane diffused into the cells). Before any characterizations were done, all of the foam samples were vacuumed for one week, and then they were left for over one month to ensure that air permeated into the cells and was the only gas in them.
Characterization
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4.4
The transient plane source (TPS) Hot Disk thermal constants analyzer (Therm Test Inc., TPS 2500, Sweden) was used to measure the thermal conductivity of the PS/MWCNT nanocomposites and foams. Two sample pieces around 15 mm in diameter
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were used to conduct the test. According to the testing samples’ thermal characteristics, the power output (0.005 ~ 0.020 W), test duration (5 ~ 20 s) and sensor size (2 or 3 mm
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in radius) were determined. The measurement was performed 3 times for each sample, and the experimental deviation was less than 5%. Details of the TPS method can be found in Refs 37-39.
Fourier transform infrared spectroscopy (FTIR) (PerkinElmer spectrum one) was
used to measure the spectral properties of the films and foams. We collected the spectral data by averaging 8 scans in a spectral range of wavelength from 2.5 to 25 µm (4,000 to 400 cm-1). The airborne H2O and CO2 background noise was registered before recording 14 / 28
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the samples’ IR transmittance. For the complex refractive index of the PS/MWCNT nanocomposites, both the reflectance (Ref) and transmittance (τ) of the film samples with ~ 50 µm thickness (lfilm) were recorded. The imaginary part of the complex refractive
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index (Img), corresponding to the IR absorption index of the PS/MWCNT nanocomposites, is calculated as follows [40]: Img = − ln τ film λ 4π l film
(2)
1 − 1 C − C 2 − 4 Ref ( 2 − Ref ) τ
τ film =
2 Ref ( 2 − Ref
)
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The film internal transmittance (τfilm) can be expressed as follows [40]:
(3)
C = 1 + 2 Ref + τ 2 − Ref 2 .
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where C is used to simplify the equations, and it is calculated as
(4)
For IR radiation through the foams, to eliminate the sample thickness’s effect on the IR transmittance, the foams were cut into plate shapes of 15 mm in diameter, with a
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thickness ranging from 0.2 to 2 mm. At least 6 plate samples of different thicknesses were measured to calculate the radiative thermal conductivity.
RESULTS AND DISCUSSION
5.1
Increased IR absorption index by adding MWCNTs
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5.
MWCNTs as black body has strong IR absorption capability to block the IR
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transmittance in PS/MWNCT nanocomposites. For pristine PS, the aromatic =C-H outof-plane deformation vibrations attributes to the IR absorption peaks at 13.2 µm and 14.3 µm, and the out-of-plane ring deformation vibration attributes to IR absorption peak at
18.5 µm [41]. However, the IR absorption for pristine PS in the whole wavelength ranges of 2.5 ~ 25 µm was still very weak, and the IR transmittance of pristine PS film (~ 50 µm thick) was over 80% as shown in Figure 5a. Due to the MWCNTs’ strong IR absorption [42], the addition of MWCNTs in films decreased the IR transmittance. For instance, 15 / 28
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adding 1wt% MWCNTs effectively reduced the IR transmittance from 84% to 30% at a wavelength of 25 µm. To quantitatively study the effect of MWCNTs on IR absorption, the intrinsic IR
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absorption index of PS/MWCNT nanocomposites was calculated by Equation 2 and the results are summarized in Figure 5b. It is noteworthy that despite the absorption peaks, the IR absorption index of pristine PS in the whole wavelength ranges of 2.5 ~ 25 µm was almost 0. The addition of MWCNTs then enhanced the IR absorption and increased
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the baseline of the index curves significantly. From the wavelength-averaged IR absorption index shown in Table 1, it is noted that increasing MWCNTs almost linearly
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increased the IR absorption index from 0.004 to 0.03 at 2 wt% MWCNT concentration. Furthermore, at the long wavelength of 25 µm, the IR absorption index of PS/MWCNT 2wt% was 0.08, 20 times larger than that of pristine PS, 0.004. MWCNTs’ characteristic of much strong IR absorption at long wavelength range is a great advantage in the
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application of thermal insulation foams.
Figure 5 (a) Spectral transmittance of the pristine PS and PS/MWCNT nanocomposite films (~ 50 µm thick) and (b) the IR absorption index
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5.2
Increased IR extinction coefficient by adding MWCNTs
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Table 1 Wavelength-averaged IR absorption index of pristine PS and PS/MWCNT
Due to the MWCNTs’ strong IR absorption in PS/MWNCT nanocomposites, the
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IR transmission through PS/MWCNT foams was also effectively blocked. In the foam structure with a large expansion ratio, the short wavelength IR was blocked by the
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reflection at the cell walls, while the long wavelength IR easily passed through the foams [20]. Due to the weak IR absorption and the large expansion ratio of the pristine PS foam, its IR transmittance was over 80% in the long wavelength range of 20 ~ 25 µm as shown in Figure 6a. Adding 0.25 wt% MWCNT then decreased the IR transmittance from 80% to 65%. When the MWCNT content was further increased to 2.0 wt% in the PS matrix,
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the IR transmittance was decreased to less than 10%. To reveal the intrinsic IR absorption performance of MWCNTs in the foam structure, the IR extinction coefficient of PS/MWCNT foams was calculated by Equation S9 and the results are summarized in Figure 6b. Similar to PS/MWCNT nanocomposites, the addition of MWCNTs to the
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foams enhanced the IR absorption and increased the baseline of the extinction coefficient curves: despite the absorption peaks, the IR extinction coefficient of pristine PS foam at
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long wavelength range was almost 0, while that of PS/MWCNT 2wt% foam became 4.0. By recording the IR-transmitted energy through the foams, the radiation can be
measured based on FTIR spectrometry. The higher the transmittance, the more radiative thermal conductivity there will be. For the pristine PS foam with a large expansion ratio and a weak IR-absorbing matrix, the long wavelength IR energy still contributed much to the radiative thermal conductivity and correspondingly increased the total thermal conductivity of the foams, although the short wavelength IR energy was blocked by the 17 / 28
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porous structure. The addition of MWCNTs then absorbed the incidental long wavelength
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IR radiation, and effectively helped block IR radiation in this PS foam system.
Figure 6 (a) Spectral transmittance of the pristine PS and PS/MWCNT bimodal foam sheet samples (foaming condition: 13.8 MPa with 60 ml pentane added) of ~ 600 µm thickness (namely, 680 µm thickness for PS foam, 660 µm thickness for PS/MWCNT 0.1
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wt% foam, 590 µm thickness for PS/MWCNT 0.25 wt% foam, 540 µm thickness for PS/MWCNT 0.5 wt% foam, 620 µm thickness for PS/MWCNT 1 wt% foam, and 630 µm thickness for PS/MWCNT 2 wt% foam) and (b) IR extinction coefficient of the pristine PS and PS/MWCNT foams. For each foam, the value was calculated based on at least 6
Increased optimal expansion ratio by adding MWCNTs
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5.3
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samples of different thicknesses.
The total thermal conductivity of foams includes the radiative thermal
conductivity (which increases with an increased expansion ratio) and the gas and solid conductivity (which decreases with an increased expansion ratio). Hence, there is an optimal expansion ratio that minimizes the total thermal conductivity. This optimal expansion ratio is increased with the addition of MWCNTs because of their strong IR absorption capability. 18 / 28
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The effect of MWCNTs on thermal radiation was quantitatively studied using the Rosseland Equation (Equation S13) to calculate the transmitted radiative energy. Figure 7 summarizes the calculated radiative thermal conductivity of both the unimodal and
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bimodal foams. The foam morphology is presented in the supporting information. We note that the radiative thermal conductivity through the PS foam with a large expansion ratio was very high due to the PS matrix’s low IR absorption index of 0.004 (Figure 5b). Figure 7 shows that the foamed samples’ radiative thermal conductivity increased almost
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linearly with the expansion ratio’s increase, which ranged from 8- to 30-fold. Therefore, a linear regression (y = ax+b) was applied to fit the data shown in Figure 7. The slope and
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interception of the fitted curves are summarized in Table S1. Then the radiative absorption efficiency was calculated using Equation S14, and the result is shown in Figure 8a. The average radiative absorption efficiency was obtained by calculating the corresponding values of eight samples (four samples from unimodal foams and the other four samples from bimodal foams) at each MWCNT concentration as shown in Figure 8b.
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It is noted that the increased MWCNT concentration enhanced the IR absorption index of
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the solid matrix, and then increased the radiative absorption efficiency of the foams.
Figure 7 Radiative thermal conductivity in foams (curves obtained by linear fitting the experimental data) 19 / 28
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Figure 8 (a) The radiative absorption efficiency of the PS/MWCNTs matrix (curves
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obtained based on the linear regression for the radiative thermal conductivity) and (b) the average radiative absorption efficiency versus wavelength-averaged IR absorption index
Due to their strong IR absorption capacity, the MWCNTs added to the PS matrix helped to block the thermal radiation in the foams. Their influence on the reduction of IR
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radiation was especially prominent when the nanocomposite foam had a large expansion ratio. For instance, 1 wt% MWCNTs reduced the radiative thermal conductivity by 8.5 mW/m-K in the bimodal foam with a 28-fold expansion ratio. In the unimodal foam with
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an 18-fold expansion ratio, 1 wt% MWCNTs only decreased the radiative thermal conductivity by 6.5 mW/m-K. Consequently, the MWCNTs in a bimodal nanocomposite
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foam with a larger expansion ratio could absorb more radiative energy than they could in unimodal foam.
Furthermore, the unimodal and bimodal cell structures of PS/MWCNT foams also
affected the thermal insulation performance due to their difference in the achievable expansion ratio. Figure 9 shows the total thermal conductivity of the unimodal and bimodal PS/MWCNT foams, together with the calculated values based on Model 1 and Model 2 in Section 2. Because of their limited expansion ratio, the conduction through the unimodal foams was dominant. And the radiative absorption capacities of the 20 / 28
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MWCNTs had only a limited effect in reducing the total thermal conductivity. On the other hand, bimodal foams with a large expansion ratio were easily achieved. Therefore, the contribution of the conductivity via conduction to the total thermal conductivity in
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these bimodal foams was decreased. Meanwhile, the radiative thermal conductivity became significantly large in bimodal PS foam. But this increase in the radiative thermal conductivity (and in the total thermal conductivity) along with the expansion ratio’s increase was arrested when the MWCNTs were introduced. Because the MWCNTs
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dramatically absorbed radiation in the bimodal foams, the total thermal conductivity was decreased at larger expansion ratios. Correspondingly, the MWCNTs helped increase the
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optimal expansion ratio in bimodal foams to minimize their total thermal conductivity. By adjusting the MWCNT concentration and the expansion ratio, the lowest thermal conductivity of the unimodal PS/MWCNT foams obtainable in this study was 32.8 mW/m-K. The application of MWCNTs with a bimodal cellular structure was effective in further decreasing the total thermal conductivity. This was because the
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primary large cells present in the bimodal foams induced a larger expansion ratio than they would do in unimodal foams. This expansion reduced the solid conduction while the secondary small cells in the bimodal foams also experienced the Knudsen effect, which reduced gas conduction. Most importantly, the MWCNTs in the bimodal foam with a
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large expansion ratio then absorbed more radiation and contributed to less solid conduction than they did in the unimodal foams. As a result, by tailoring the MWCNT
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concentration and the bimodal cellular structure, the PS/MWCNT 1.0 wt% bimodal foam achieved a minimum thermal conductivity of 30.2 mW/m-K, as will be discussed below in detail.
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Figure 9 Total thermal conductivity of (a) unimodal foams and (b) bimodal foams. The solid and dash curves represent the values calculated by Model 1 and Model 2,
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respectively. Note that the unimodal foams (a) could not be expanded as high as the bimodal foams (b).
The total thermal conductivity of the foams with different carbonaceous additive concentrations and foam morphologies made from various materials were summarized
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and compared. Figure 10 shows the reported values in the references, and it is clearly observed that the total thermal conductivity of nanocomposite foams decreased with an increased carbonaceous additive concentration and expansion ratio.
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In the case of no carbonaceous additives, when the polymeric foams had a small expansion ratio below 5-fold, their thermal conductivity was over 50 mW/m-K,
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regardless of the micro- or nano-cells, as Figure 10 shows. This was because the heat transfer in polymeric foams with an expansion ratio of less than 5-fold is dominated by solid conduction. The expansion ratio has to be at least 10-fold to make the polymeric foams’ thermal conductivity below 40 mW/m-K. Therefore, in such a high-density foam system, an increase in the expansion ratio will significantly decrease the total thermal conductivity. On the other hand, as discussed from Figure 7 and S8, the total thermal conductivity of the foams with a large expansion ratio became very large as well because of the increased radiative thermal conductivity. For instance, the total thermal 22 / 28
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conductivity of the low-density expandable PS (i.e., EPS) foams seen in Figure 10 becomes higher than 35 mW/m-K for the expansion ratio over 60-fold [43]. In the case of having carbonaceous additives, compared with the unimodal
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nanocomposite foams, the bimodal nanocomposite foams consisting of primary large cells and secondary small cells had a unique synergy to effectively block the heat transfer through radiation (carbonaceous additives), solid conduction (primary large cells), and gas conduction (secondary small cells). Zhang et al. prepared a bimodal PS/active carbon
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0.5wt% foam with a 25-fold expansion ratio and over 50 µm secondary cells. The corresponding thermal conductivity was 31.5 mW/m-K [15]. Based on the heat transfer
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behavior in nanocomposite foams presented in Figure 10, the total thermal conductivity can be further decreased by increasing carbonaceous additive concentration and the expansion ratio. We prepared a novel bimodal PS/MWCNT 1wt% foam with a 28-fold expansion ratio and 5.8 µm secondary cells. The 1 wt% MWCNTs absorbed a large amount of thermal radiation, and this bimodal foam structure has an advantage of
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expansion ratio control while utilizing the Knudsen effect. Therefore, a very low thermal conductivity of 30.2 mW/m-K was achieved by adding 1 wt% MWCNTs to the bimodal
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foam.
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Figure 10 Total thermal conductivity of polymeric foams as a function of the carbonaceous additive content and the expansion ratio [10, 12, 13, 15, 43-47] * The thermal conductivity of EPS foams was measured at 10°C
CONCLUSION
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6.
In this study, we prepared PS/MWCNT nanocomposite foams using the scCO2 foaming system. Due to MWCNTs’ strong IR absorption performance, their addition to PS matrix greatly increased the IR absorption index of the solid matrix. Correspondingly,
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the radiative absorption efficiency of the PS/MWCNT nanocomposite foams increased with increasing MWCNT concentration. For the first time, a model based on the thermal
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resistances in the primary and secondary cell regions was proposed to quantitatively investigate the change of optimal expansion ratio with the addition of MWCNTs. The calculated thermal conductivity in the model was in good agreement with the experimental data. Based on the model, we optimized the cellular structure and the MWCNT’s concentration, and then we achieved a minimum total thermal conductivity in the bimodal PS/MWCNT 1.0 wt% foam system with a 28-fold expansion ratio and 5.8 µm secondary cells. The MWCNTs reduced radiation and increased the optimal
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expansion ratio. The primary large cells in the bimodal foams then increased the expansion ratio. Because of this action, a very low thermal conductivity of 30.2 mW/m-K was successfully obtained without using any insulation gas. In the above advanced
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bimodal foam, the MWCNTs’ ability to decrease radiative heat transfer by 8.5 mW/m-K was of great importance.
Acknowledgements
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The authors would like to thank the Korea Institute of Construction Technology (KICT), the Microcellular Plastics Manufacturing Laboratory (MPML) and the Starting
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funds from Sichuan University for their financial support of this project.
REFERENCES
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[1] Key world energy statistics. International Energy Agency; 2015. [2] Canadian Energy Overview 2014: National Energy Board; 2014. [3] Energy savings 2020: European Commission; 2010. [4] Suh KW, Park CP, Maurer MJ, Tusim MH, Genova RD, Broos R, et al. Lightweight Cellular Plastics. Adv Mater. 2000;12(23):1779-89. [5] Gallant RW. Physical Properties of Hydrocarbons. XXII. Fluorinated Hydrocarbons. Hydrocarb Process. 1968;47(3):89-95. [6] Montzka SA, Butler JH, Elkins JW, Thompson TM, Clarke AD, Lock LT. Present and Future Trends in the Atmospheric Burden of Ozone-Depleting Halogens. Nature. 1999;398(6729):690-4. [7] Vo CV, Bunge F, Duffy J. Advances in Thermal Insulation of Extruded Polystyrene Foams. Blowing Agents and Foaming Processes. Dusseldorf, Germany: Smithers Rapra; 2011; p. 1-14. [8] Ferkl P, Pokorný R, Bobák M, Kosek J. Heat Transfer in One-Dimensional Micro- and Nano-Cellular Foams. Chem Eng Sci. 2013;97:50-8. [9] Ferkl P, Pokorný R, Kosek J. Multiphase approach to coupled conduction– radiation heat transfer in reconstructed polymeric foams. Int J Therm Sci. 2014;83(0):6879. [10] Notario B, Pinto J, Solorzano E, de Saja JA, Dumon M, Rodríguez-Pérez MA. Experimental Validation of the Knudsen Effect in Nanocellular Polymeric Foams. Polymer. 2015;56:57-67.
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