Reinforcement and shape stabilization of phase-change material via graphene oxide aerogel

Carbon 114 (2017) 334e346

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Reinforcement and shape stabilization of phase-change material via graphene oxide aerogel Yue Xu, Amy S. Fleischer, Gang Feng* Department of Mechanical Engineering, Villanova University, Villanova, PA, 19085, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 August 2016 Received in revised form 22 October 2016 Accepted 25 November 2016 Available online 28 November 2016

Phase change materials (PCMs) are of interest in many applications which may require shapestabilization. In this study, a graphene oxide aerogel (GOxA) reinforced paraffin PCM composite is developed, effectively reinforcing and shape-stabilizing the paraffin. The molecular and diffraction characterizations suggest that the GOxA network potentially affects paraffin's crystallization. The mechanical characterizations using durometer and nanoindentation show that the composite is 3~7
harder than pure paraffin and maintains significant strength even above paraffin's melting temperature. Moreover, the composite is much less strain-rate sensitive than paraffin. The reinforcement via GOxA is much beyond the prediction by the rule-of-mixture, implying a strong GOxA-paraffin interfacial bonding. To our best knowledge, this is the first study on the mechanical behavior of paraffin and GOxA-PCM composite, providing critical insights into their behavior. Additionally, the relationship between the hardness and durometer index first-ever developed here will enable the quantitative durometer testing on materials for many other applications at different ambient conditions due to its versatility and simplicity. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Phase change materials (PCMs) store and/or release thermal energy through the solid-liquid phase transition and exhibit the advantages of low cost and high energy density, making them a popular choice for energy storage materials [1e6]. Paraffin is a high-performance PCM owing to its high latent heat, low super cooling, and chemical stability; however, its intrinsic low thermal conductivity can make it difficult to transfer energy effectively into larger masses, and the possibility of liquid phase leakage can lower the perceived reliability of the systems [1,2,7e9]. Aerogels are porous materials with extremely low bulk density, composed of nanoparticles, nanowires, nanotubes, or nanosheets of oxides [10e12], silicon [12], metals [12e15], and carbon materials [16e19]. Graphene-based three-dimensional (3D) aerogels have drawn attention due to their unique properties, including low density, high porosity, large specific surface area, excellent electrical conductivity and outstanding mechanical properties

* Corresponding author. Mechanical Engineering, Villanova University, 800 Lancaster Ave., Villanova, PA 19085, USA. E-mail address: [email protected] (G. Feng). http://dx.doi.org/10.1016/j.carbon.2016.11.069 0008-6223/© 2016 Elsevier Ltd. All rights reserved.

[9,16,20e29]. This leads to many potential applications including energy storage [1,9,16,30,31], super-capacitors [20,23], air and water purification [32,33], and nanocomposites [34]. Recently, much research has focused on the integration of graphene-based nanomaterials with high thermal conductivities into PCMs to increase their overall thermal conductivity [35e37]. It is also known that graphene aerogel (GA) impregnated with PCM exhibited a rise in thermal conductivity [38]. While the use of nano-inclusions can mitigate the effects of low thermal conductivity, it is also necessary to address the issue of liquid leakage. Some methods are available to mitigate this potential leakage, such as encapsulation and shape stabilization [2,39,40]. Shape stabilization of PCMs occurs through the addition of supporting materials into the PCM which can hold the liquid phase in place with the matrix, usually by capillary action. Possible supporting materials include high density polyethylene (HDPE) [2], opal [8], graphite [41], carbon nanospheres [40], graphene oxide (GOx) [3,4,42], graphene aerogel [30,38], exfoliated graphite nanoplatelets (xGnP) [43], graphite nanoplatelets [5,44], and graphene nanoplatelets [45]. In some cases, large amounts of supporting materials are needed in order to shape stabilize PCMs. For example, a GO-paraffin composite showed no liquid leakage at 51.7 wt% of GO, but the latent heat dropped by 52% [4]. In the case of

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HDPE PCM [2], the shape-stabilization required at least 25e30 wt% of HDPE. In this paper instead, the use of graphene oxide aerogel (GOxA) is explored as both a shape stabilizer and a thermal conductivity enhancer, because its use has been shown to not decrease the latent heat [38]. Most studies of PCMs have focused on their thermal characteristics, but their mechanical properties are also vitally important particularly as related to the shape stabilization behavior. The mechanical properties of graphene-based and GO-based polymer composites have been studied, showing improvements in their strength and modulus [8,46e50] compared to the pure polymer counterparts. However, to our knowledge, the mechanical properties and shape stabilization behavior of GOxA-PCM composite have never been fundamentally studied. A comprehensive fundamental understanding of the mechanical behavior of GOxA-PCM composite is thus vitally important to understand the behavior of GOxA alone, pure paraffin, and the composite. Typically, mechanical properties of porous 3D carbon aerogels/ networks have been studied through either compression or nanoindentation tests. Table A1 in Appendix 1 summarizes some of the recent results, indicating a large discrepancy in the literature values. For example, for pristine graphene aerogel (GA) with density less than ~30 mg/cm3, data on strength is in the wide range of 0.2e40 kPa, while the modulus data shows a range of 2e1200 kPa. In general, by increasing the bonding between carbon nanomaterials, e.g., by noble metal [51] or crosslinking [52], the overall strength and modulus should increase. In this work, by infiltrating GOxA with paraffin, a PCM composite with ~5 wt% of GOxA is formed. The mechanical behavior with respect to both shape stabilization and mechanical properties will be comprehensively characterized at different strain rates as well as at a range of temperatures, including above the melting point of the PCM. While the thermal analysis of this GOxA-PCM composite is also of interest, it will be left for a future paper in order to concentrate here on the mechanical characteristics. To our best knowledge, this is the first study on the fundamental strain-rate-dependent and temperature-dependent mechanical behaviors of paraffin and GOxA-PCM composite, providing critical insights to understand the behavior of graphene-related PCM composites and their application into the design of highperformance energy storage PCM composites with high reliability. 2. Material and methods The graphite powder was purchased from Spectrum Chemical Manufacturing Corp. The sodium nitrate (NaNO3, high purity grade) and potassium permanganate (KMnO4, ACS grade) were obtained from Amresco, Inc. The hydrogen peroxide (H2O2, 29e32% w/w ar. soln.) and Ethylenediamine (EDA, 99%) were purchased from Alfa Aesar. Paraffin wax (IGI 1230A) was purchased from International Group, Inc. All were used in as-purchased conditions. In general, graphene-based aerogels are prepared by assembling 2D graphene sheets into a 3D porous graphene architectures through a sol-gel process and subsequently freeze-drying or supercritical drying to remove the solvents in the wet gels while maintaining the shape of the 3D network [20,28]. Here, by following the method of Hu et al. [20], GOxAs are formed using the ethylenediamine (EDA) - mediated reduction of GOxs followed by supercritical CO2 drying. The GOxA-reinforced paraffin composite is synthesized through infiltrating paraffin into GOxA.

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nitrate were mixed with 120 ml sulfuric acid in an ice bath under vigorous stirring for 2 h. 15 g of potassium permanganate was then slowly added into the system with constant stirring while the temperature was kept below 20  C. After one hour of stirring, the temperature of the mixture was raised to 35  C and then the mixture was stirred overnight for complete oxidation yielding a thick paste. 150 ml of deionized water (DI water) was added to this paste gradually and the mixture was heated to 98  C and stirred for 12 h. 500 ml of DI water and 20 ml of hydrogen peroxide were then added to the mixture. The mixture was then washed with 1 M HCl solution to remove metal ions. The resultant graphite oxide was washed with DI water and centrifuged for 20 min at room temperature repeatedly until the pH reached 5e6. Finally it was fully dried by heating at 65  C for two days. 2.2. Synthesis of graphene oxide aerogel (GOxA) By following the method of Hu et al. [20], the dried graphite oxide powder obtained in last section was first re-dispersed into DI water using a Vibra-cell VC505 ultrasonic processor in order to form a 3 mg/mL graphene oxide (GOx) suspension. It is critical to have the right concentration of GOx in the suspension in order to fabricate GOxA with the lowest possible density [20]. Then, 400 mL of EDA was added into 100 mL of the GOx suspension. This mixture was sealed in a glass bottle and heated for 12 h at 90  C in order to synthesize the graphene oxide hydrogel (GOxH). The obtained GOxH was immersed in DI water for purification for 3 days. The purified GOxH was then immersed in acetone for 24 h in order to fully exchange the water in the GOxH with acetone. The purification and water exchange process was performed 6 times for complete solvent exchange. Finally, the acetone-gel was dried using supercritical drying (Leica EM CPD300) to obtain GOxA. 2.3. Preparation of GOxA-PCM composite Previous studies have shown great success in forming polymernanoparticle composites by infiltrating polymer into a porous nanoparticle structure [54,55]. GOxA and paraffin were heated to 80  C (above the melting point of the paraffin) in a vacuum oven. The GOxA samples were immersed in the melted paraffin which fully infiltrated into the GOxA samples under vacuum. The composites were then formed after cooling. The GOxA and composite samples were weighed using a scale (Citizen Scale CY 204 with 0.0001 g resolution) to calculate the weight percent of paraffin. The GOxA's weight percentage in the composite samples is (5.2±0.51) wt%. 2.4. Structural and mechanical characterization The bulk density was calculated based on the weight and the apparent sample volume. Scanning electron microscope (SEM) images were produced using a Hitachi S-4800 field emission SEM. Fourier transform infrared (FTIR) spectra were recorded on a Nicolet™ iS™10 FT-IR spectrometer. X-Ray diffraction (XRD) spectra were recorded on a Rigaku Miniflex X-ray Diffractometer with Cu Ka radiation. The Brunauer-Emmett-Teller (BET) surface area of GOxA was characterized via a MicroMeritics Gemini VII 2390 Surface Area Analyzer. The macroscale mechanical properties at different temperatures were characterized using a Phase II PHT-960 durometer. The nano/ microscale mechanical properties at different strain rates at room

2.1. Synthesis of graphite oxide The graphite oxide was prepared using a modified Hummers method [53]. First, 5 g of graphite powder and 2.5 g of sodium

1 Throughout this paper, the Dx in the form of “x±Dx” always refers to the standard deviation of quantity x.

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temperature were studied using nanoindentation. The detailed procedures and conditions for durometer and nanoindentation testing will be discussed in the related sections later. 3. Results and discussion 3.1. Morphology and crystal structure characterization of graphene oxide aerogel Images of the GOx suspension, GOxH and GOxA are shown in Fig. 1. The GOxH showed some volume shrinkage after selfassembly (Fig. 1aeb), although this shrinkage is minor compared to other chemical reduction methods [20]. Fig. 1bec show that the GOxH shrank roughly by 1/3 after the supercritical CO2 drying and kept the 3D structure nicely. The GOxAs' density r ranges from 17 to 36 mg/cm3 based on 5 samples. The GOxAs' specific surface area (AS) is determined as high as 476 m2/g. If we assume spherical pores and neglect the graphene's thickness, 3/(rAS) [56] is an estimate for the average pore size r, i.e., 0.17e0.37 mm, which is roughly consistent with the SEM results (Fig. 2a). Fig. 2a shows a SEM image of GOxA, implying interconnected 0.2e1 mm pores formed by thin layers of GOx sheets. Fig. 2bec show the SEM images of the as-synthesized and polished surfaces of GOxA-PCM composite, showing complete infiltration without observable voids. The oxidation of graphite into GOx and the reduction of GOx into GOxA were investigated using FTIR, as shown in Fig. 3. No significant peaks were found for graphite, which is consistent with previous work [57,58]. The FTIR spectrum of GOx indicates absorption bands of eOH at 3000-3500 cm1, COOH at 1721 cm1, CeOH at 1355 cm1, and alkoxy CeOeC at 1047 cm1, which is similar to the GOx spectrum obtained in Han et al.’s work [59]. The spectrum of GOx also shows a peak at 1588 cm1, representing the skeletal vibrations from unoxidized graphitic domains [60,61]. The GOx's carbonyl COOH peak at 1721 cm1 is not shown in GOxA's spectrum, confirming the partial reduction of GOx. The GOx's OeH stretching peak at 3000-3500 cm1 and alkoxy CeOeC peak at 1047 cm1 are not shown in GOxA's spectrum, again confirming the partial reduction of GOx [57,62]. In addition, the GOxA's spectrum shows the epoxy CeOeC peak at 1209 cm1 and the C]C peak at 1568 cm1, indicating an interaction between graphene sheets and carbohydrates as well as the assembly of GOx sheets into 3D structures [20].

microstructure and crystal phases, FTIR spectra and XRD patterns of pure paraffin and GOxA-PCM composite were measured as in Fig. 4. Fig. 4a shows the FTIR spectra of the GOxA-PCM composite and paraffin. The GOxA-PCM FTIR spectrum is almost the superimposition of the spectra of GOxA alone and pure paraffin, with the addition of three new peaks as shown. The spectra of both paraffin and GOxA-PCM show the 2915 cm1 and 2848 cm1 CeH stretching peaks [63], the 1462 cm1 and 1377 cm1 CeH bending peaks [64,65], as well as the 719 cm1 CeH rocking peak that can be seen only in long chain alkanes. The new peaks in the 1800 - 2500 cm1 range appear only for the GOxA-PCM composite, implying new chemical bonding(s) in the GOxA-PCM composite, most likely at the GOxA-PCM interface. For example, the new peak at 2156 cm1 may correspond to C^C stretching [64,65]. Further analysis on the new peaks and possible associated new phase(s) will be left as future work. Fig. 4b shows the XRD patterns of the GOxA-PCM composite and paraffin. Except for the new peak labeled, the GOxA-PCM composite's XRD is almost identical to that of pure paraffin, suggesting that embedding GOxA into paraffin does not significantly change the crystallization of paraffin. Here, the XRD pattern of paraffin corresponds to the orthorhombic structure [66]. Due to GOxA's extremely low density, GOxA alone will not generate significantly sharp peaks; in fact, previous studies indicate a weak and broad peak at around 25 for GOxA [9,26]. Fig. 4b also indicates one new peak at ~37.05 for the composite, corresponding to a plane spacing of 2.43 Å, implying that a potentially new phase may exist in the composite, most likely at the GOxA-PCM interface. A study on the exact structure of this potentially new phase will be left as future work. We also measured the XRD peak broadening to analyze any microstructure changes in the paraffin matrix due to embedding GOxA into paraffin, such as the grain-size change [67,68] and/or the crystal-defect density change [68,69]. As shown in Supplementary Fig. S1b and Table S1, the peak widths (Full-widths-at-halfmaximum) of one typical peak (q ¼ 10.7 ) for both the paraffin and GOxA-PCM are in fact identical (¼0.414 ). The same peak width implies that the microstructure (grain-size and crystal-defect density) has no significant difference between pure paraffin and the paraffin-matrix in the composite. Thus, based on the above analysis of FTIR and XRD, a potentially new phase and/or bonding condition at the graphene-paraffin interface may be generated by embedding graphene into paraffin. 3.3. Shape stabilization and mechanical characterization

3.2. Structure characterization of paraffin and GOxA-PCM composite To investigate the effect of embedding GOxA into paraffin on the

As shown in Supplementary Fig. S2, the GOxA-PCM composite maintains its original shape even above the melting temperature without any leakage of liquid paraffin from the system, proving

Fig. 1. Optical images of (a) GOx dispersion, (b) GOxH, and (c) GOxA. (A colour version of this figure can be viewed online.)

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Fig. 2. SEM images of GOxA and GOxA-PCM. (a) GOxA (a single graphene oxide sheet in the center). GOxA-PCM composite in the (b) as-infiltrated and (c) polished conditions.

Fig. 3. FTIR spectra of graphite, GOx and GOxA. (A colour version of this figure can be viewed online.)

excellent shape stabilization. In order to quantitatively analyze the fundamental mechanism of shape stabilization and investigate the effect of embedding GOxA network into GOxA-PCM composite, we have mechanically tested paraffin, GOxA, and GOxA-PCM at the macroscale (at different temperatures) using a durometer and at the nano/microscale using nanoindentation at different strain rates. 3.3.1. Macroscale mechanical characterization using durometer at different temperatures 3.3.1.1. Durometer testing at different temperatures. Paraffin, GOxA and GOxA-PCM were mechanically characterized using a digital Shore-A durometer at different temperatures. The durometer test is one common technique for simple, quick and semi-quantitative evaluation of materials' resistance to penetration, i.e., hardness. The durometer hardness D is standardized by ASTM D 2240 [70]. One most common durometer scale is Shore A, designated here as

DSA, appropriate for many common materials from rubber band with DSA z25 to shoe heel with DSA z80. For elastomeric materials, durometer hardness D can be correlated to the modulus E roughly by a power-law relationship [71]. However, this correlation cannot be easily established in case of plastic indentation, because the durometer intrinsically tests hardness instead of modulus. Samples of paraffin, GOxA and GOxA-PCM which were 8 mm in diameter and 10 mm high were prepared for durometer testing using a Phase II PHT-960 digital Shore-A durometer. Paraffin and GOxA-PCM samples were tested at different temperatures in the range of 22  Ce67  C. The samples were directly put in a water bath and the sample temperature T was recorded using an E-type thermocouple through a digital OMEGA HH509 thermometer. The dry GOxA samples were tested only at 22  C. The DSA readings for all three materials changed with time after increasing the pressing time, indicating strain rate dependence. For consistency, the DSA values were read ~3 s after applying the load. Fig. 5a shows DSA vs. T for all materials. The GOxA-PCM composite is significantly harder than pure paraffin at all temperatures, implying a significant reinforcement effect from embedding GOxA into the paraffin. It should be mentioned that the standard deviation in measured DSA for all samples over all temperatures is small (0.4e1.0) which ensures sample uniformity and durometer consistency. It is interesting that GOxA-PCM's DSA reaches a plateau at 10.2 ± 0.7 for T > Tm ¼ 55.4  C (paraffin's melting temperature), indicating a significant hardness for T > Tm and hence significant shape stabilization. GOxA-PCM's DSA at T > Tm matches well with the hardness (DSA ¼ 13.5 ± 0.8) of dry GOxA alone at 22  C, implying that the GOxA-PCM composite's hardness at T > Tm is due to the support from GOxA network alone as the paraffin is fully melted. 3.3.1.2. Method for quantitative analysis of Shore-A durometer testing. DSA is a hardness index, which cannot be directly compared to the hardness measured by other techniques, such as nanoindentation. Therefore, in order to have a more quantitative

Fig. 4. (a) FTIR spectra of GOxA, paraffin and GOxA-PCM composite. (b) XRD patterns of paraffin and GOxA-PCM composite. (A colour version of this figure can be viewed online.)

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Fig. 5. (a) Durometer Shore A hardness DSA vs. testing temperature T. (b) Hardness H (calculated from DSA based on Eq. (5)) vs. T. Here, paraffin's Tm (¼55.4  C) and the GOxA's properties at 22  C are also plotted. (c) The correlation of H and DSA based on Eq. (5). (A colour version of this figure can be viewed online.)

comparison, based on the mechanics of the durometer, we derive, for the first time in the literature, a methodology to correlate DSA to hardness, H. Here, H is commonly defined as the mean pressure under an indenter. For an axi-symmetric indenter, we have

H ¼ P=A and A ¼ pa2c ;

(1)

where P is the indentation contact load (e.g., in Newton, or N), A is the projected contact area (e.g., in mm2), and ac is the contact radius (e.g., in mm). As illustrated in Fig. 5c, the durometer test is essentially an indentation test using a truncated axi-symmetric flat punch tip [70,71], and the contact force P and indentation depth h are related to the Shore-A durometer reading DSA by Ref. [70],

P ¼ 0:55 þ 0:075DSA ; in N;

(3)

For an Shore-A durometer, the radius a of the cylindrical truncated flat punch tip at a distance x from the tip end is [70] (see Fig. 5c),




0:395 þ x tan 17:5 0:635

DSA < 70 DSA  70 :

(5)

Fig. 5d shows the plot of H vs. DSA, which demonstrates a transition at DSA ¼ 70 due to the truncated cone part of the tip (see Fig. 5c). For DSA<70, Eq. (5) is simply H ¼ 0.434 þ 0.059DSA (MPa), i.e., a linear correlation (DSA<70). It should be noted that, as advised by ASTM D 2240, the absolute value of DSA is reliable and comparable between durometers only in the range of DSA ¼ 20e90 [70] due to the relatively large manufacturing tolerance requirement of durometers (see Fig. 5c) [70].

(2)

h ¼ 2:5  0:025DSA ; in mm:

a¼

 0:55 þ 0:075DSA MPa; where a pa2 8 > < 0:635 mm     ¼ DSA > tan 17:5 mm : 0:395 þ 2:5 1  100 

H¼

x  1:74mm ; in mm: x > 1:74mm

(4)

When indenting a material with a high ratio of E to H with E/ H > ~40 [72e74], the indentation contact depth hc can be well estimated by the indentation depth h. Consequently, as shown in Fig. 5c, the contact radius ac in Eq. (1) can be estimated by the physical radius a of the indenter tip at the contact boundary. Thus, by replacing x in Eq. (4) by h, the final equation to correlate DSA to H, is given in Eq. (5).

3.3.1.3. Quantitative analysis of durometer testing for GOxA, paraffin, and GOxA-PCM samples. With this correlation in Eq. (5), the DSA values in Fig. 5a can be correlated to H and replotted vs. T as in Fig. 5b. Fig. 5a and b shows same qualitative trends as discussed before. Fig. 5b shows that, at room temperature, the hardnesses of paraffin and GOxA-PCM based on durometer are 6.06 ± 0.4 MPa and 11.3 ± 0.8 MPa, respectively. These results match well with the corresponding values (6.27 ± 0.4 MPa and 15.7 ± 0.3 MPa, respectively) based on nanoindentation as discussed below. Here, based on nanoindentation data, the modulus to hardness ratio E/H are 177 and 71 for paraffin and GOxA-PCM, respectively, i.e., both are larger than 40, so Eq. (5) can be used. This newly developed correlation methodology described by Eq. (5) enables us to quantitatively analyze the durometer measurements, provided the aforementioned key assumptions are satisfied (E/H > 40 and DSA ¼ 20e90). Fig. 5b also indicates that H ¼ 1.23 ± 0.3 MPa for dry GOxA at 22  C and H ¼ 1.04 ± 0.3 MPa at T > Tm, again proving excellent

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shape stabilization capability. It should be noted that the GOxA hardness (H ¼ 1.23 ± 0.3 MPa) based on durometer measurements is much higher than the hardness (H ¼ 238e400Pa) resulting from the nanoindentation measurements discussed later. There may be three major reasons for this difference: (1) for dry GOxA, DSA ¼ 13.5 < 20, so the absolute value of DSA is not reliable; (2) the indentation method is known to overestimate hardness of porous materials due to indentation induced densification effect [75,76], and here, GOxA is highly porous so that the densification effect is very large; and (3) for rapid compression of porous materials in air, the air pressure built-up because of air trapping in the pores dominates the effective compression load [77,78]. Here, we believe the 2nd and 3rd factors may be the dominant ones. In fact, the readings of durometer measurement were ~3 s for ~2.2 mm penetration, while the flat punch nanoindentation tests took about 4e10 min for ~ 7 mm, so the compression/compaction effect under durometer is probably about 300 times larger than that under nanoindenter (the densification (2nd) factor), and the durometer tip moved about five orders of magnitude faster than nanoindenter tip (the built-up air pressure (3rd) factor). In fact, when the durometer was sitting on GOxA, its DSA kept rapidly dropping from ~18 to ~13.5, i.e., ~25%, within ~3s, and then, many GOxA samples would catastrophically break (similar to the case of GOxA nanoindentation as discussed later). Thus, it is difficult to evaluate the further DSA change (after 3s). On the other hand, for paraffin and GOxA-PCM samples, after an initial 5e10% dropping within 1s~2s, their values of DSA quickly stabilized. Nevertheless, at room temperature, even considering the perhaps overestimated value (H ¼ 1.23 ± 0.3 MPa) for GOxA, the H ¼ 11.3 ± 0.8 MPa of GOxA-PCM composite is still significantly larger than the sum of H ¼ 6.06 ± 0.4 MPa of paraffin and H ¼ 1.23 ± 0.3 MPa for GOxA, quantitatively. This reinforcement of embedding GOxA into paraffin is much beyond the prediction by the rule-of-mixture, implying a strong bonding between GOxA and paraffin. Based on the FTIR, XRD, and mechanical characterization, since the microstructure of paraffin-matrix is the same as pure paraffin (as implied by the same XRD peak broadening (see Fig. S1b)), we hypothesize that a potentially new paraffin interphase is created at the surface of graphene oxide (GOx) sheet. This potentially new phase may act as a bonding agent (through probably physical bonding, covalent bonding, hydrogen bonding, and/or van der Waals bonding) to bond the GOx sheet and the rest of the paraffin matrix. A study on the exact nature of the bonding would be left for a future work. More importantly, the GOxA-PCM composite is much harder than pure paraffin at all temperatures and maintains significant strength even at temperatures much higher than paraffin's melting temperature. Therefore, this composite shows strong shape stabilization capability. 3.3.2. Nano/microscale characterization A Keysight™ Nano Indenter™ G200, with two indenter heads: (1) XP and (2) Advance Dynamics Contact Module (DCM II) heads, was used to perform the nanoindentation tests. The XP head has a higher load capacity, while the DCM II head has a higher load resolution. The continuous stiffness measurement (CSM) technique was implemented throughout each test [79e81], with a constant harmonic frequency (50 Hz for XP and 75 Hz for DCM II heads) and harmonic displacement of 1.5 nm for both heads. Due to GOxA's extremely low hardness and modulus, the GOxA was tested using two large flat punch indenters: (1) a 456 mmdiameter diamond circular punch in DCM II, and (2) a 2 mmdiameter steel circular punch in XP head. The tests on GOxA were run with a constant load-rate-to-load-ratio of 0.05s1. Prior to any indentation, the nanoindenter was stabilized to a thermal drift rate

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of <0.05 nm/s. All tests on paraffin and GOxA-PCM were performed using a diamond Berkovich indenter in the XP head. As demonstrated later, paraffin and GOxA-PCM are strain-rate dependent, which to our best knowledge has not been previously studied. Also, as discussed in Appendix 2, the GOxA-PCM composite can be effectively treated well as a homogeneous material for analyzing the indentation results. For a coherent and concise discussion, the general nanoindentation technique is summarized in Appendix 2, and a new technique of multiple-strain-rate nanoindentation characterization is first-ever developed and presented in Appendix 3. 3.3.2.1. Nano/microscale multiple-strain-rate characterization of paraffin and GOxA-PCM. A nanoindenter can control load P and continuously measure the indentation displacement h. The indentation strain rate ε_ is defined as the displacement-rate-to_ _ displacement-ratio (_ε ¼ h=hz P=2P) [82,83]. A multiple-strain-rate indentation method is used in this study: for one indentation, it _ has three sequentially decreasing strain rates (P=P¼2_ ε0 , 0:2_ε0 , and 0:02_ε0 ) during a single loading (see Fig. 6a). The methodology for multiple-strain-rate nanoindentation characterization is developed and discussed in Appendix 3 in detail. Fig. 6a shows the typical load-time (P-t) curves for the two sets of three-strain-rate indentation. One ε_ 0 is equal to 0.05 s1 and the other is equal to 0.0025s1; this corresponds to six preset strain _ rates, i.e., P=P¼ (0.025, 0.25, 0.5, 2.5, 5, 50)
10e3 se1. Fig. 6b shows the indentation load-displacement (P-h) curves of paraffin and GOxA-PCM. Here, for clear comparison, only one typical P-h curve is shown for each loading condition for each 1 _ material. Fig. 6b suggests a transition at P=Pz0.005s : at faster rates, paraffin (black-dash) behaves almost the same as GOxA-PCM (red-dash); at slower rates, paraffin's curve (black-solid) is much lower. In fact, the 20-fold strain-rate drop induces a minimal behavior change for GOxA-PCM (red-dash / red-solid), while inducing a drastic drop for paraffin (black-dash / black-solid). Thus, paraffin's strain rate dependency is qualitatively much 1 _ more pronounced, especially at slower rates (P=P<~0.005s ). As discussed in Appendix 3, the quantitative characterization of strain-rate dependence requires the steady state (SS) condition, _ corresponding to ε_ ¼ P=2P (see Eq. (A9)). Fig. 6ced show the _ _ measured strain rates (_ε ¼ h=h) and P=P vs. h for GOxA-PCM and paraffin, respectively, corresponding to the loading schedules in Fig. 6a. The black curves in Fig. 6ced imply that the instrumental _ _ control of P=P is very accurate at the intended values (P=P¼2_ ε0 , 0:2_ε0 , and 0:02_ε0 ) for both samples; in fact, the complete transition time between any two preset rates is only 0.01e1.0 s (not shown here). On the other hand, the red curves in Fig. 6c show that each responded strain rate needs significant time to reach its steady_ state (SS) value (P=2P), suggesting the viscoelasticity nature of GOxA-PCM. The red curves in Fig. 6d demonstrate that, for pure paraffin, the strain rates reach the SS for the three larger values of _ but not for the three smaller ones. The comparison of Fig. 6ced P=P shows that pure paraffin needs much longer time to achieve SS, indicating that paraffin is much more viscous compared to GOxA1 _ PCM, especially at slower loading rates (P=P<~0.005s ). 3.3.2.2. Analysis of strain-rate-dependent hardness for paraffin and GOxA-PCM. Fig. 7 shows the CSM modulus E and hardness H (see Appendix 2 for general nanoindentation technique) vs. the _ measured strain rate (_ε ¼ h=h) as labeled individually. Here the subscripts show the materials and calculation method: “OP” designates the Oliver-Pharr (OP) method, and “True” designates the true hardness method as described later. It may be surprising that, while

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Fig. 6. (a) Load-time (P-t) curves for the two sets (_ε0 ¼ 0.05 s1 and 0.0025s1) of three-strain-rate testing. (b) Load-displacement (P-h) curves of paraffin and GOxA-PCM cor_ _ and strain rate (_ε ¼ h=h) responding to the loading schedules in (a). (c) P=P vs. h plots for GOxA-PCM and (d) that for paraffin. (A colour version of this figure can be viewed online.)

the CSM hardnesses of paraffin and GOxA-PCM are strain rate dependent, their CSM moduli are apparently independent of strainrate across almost four orders of magnitude (105~101s1). This can be understood by the known fact that the CSM modulus is indeed the dynamic modulus and function of CSM harmonic frequency [84] (constant 50 Hz for all tests). The CSM hardness represents the indentation mean pressure related to the current quasistatic strain rate. It may be also surprising to see that, GOxA-PCM's Oliver-Pharr (OP) modulus (1.111 ± 0.032 GPa) is about 40% lower than that

Fig. 7. CSM modulus E and hardness H vs. strain rate for GOxA-PCM and paraffin. (A colour version of this figure can be viewed online.)

(1.570 ± 0.066 GPa) of pure-paraffin. This appears to contradict the known fact that graphene-reinforced organic materials are normally stiffer than the pure matrix counterparts [85,86]. Since the GOxA-PCM composite sample is very compact without any significant porosity (see Fig. 2c), we believe that this apparent contradiction may be explained by the significant indentation pile-up on paraffin, which is discussed in Appendix 4. It is worth to note that (see Appendix 4), the highly irregular indent shape for pure paraffin is first-ever observed for any homogeneous materials, probably due to the underlying uneven plastic flow and local back-flow after unloading of crystalline paraffin. As discussed in Appendix 5, we could calculate the true hardness HTrue-Paraffin free of pile-up effect for paraffin using a revised Joslin-Oliver method [87]. Here, since the indentations on GOxA-PCM show no pile-up (see Appendix Fig. A1a), the Oliver-Pharr hardness HOP-GOxA-PCM is directly used for the true hardness of GOxA-PCM. In Fig. 7, the HOP-GOxA-PCM curve plot two sets of hardness data for GOxA-PCM: (1) the squares are the results obtained by averaging over the six steady-states (SSs), and (2) the dense small triangles are all individual data. We see a good match between the two sets of data. This match implies that, when the indentation transits from one SS to the sequential SS, the deformation is still in a quasi-steady state (QSS) (instead of in a transient state). Therefore, the hardness results are effectively steady-state results. In Fig. 7, the HTrue-Paraffin curve also plots two data sets for paraffin: (1) the squares of averaging over the three steady-states (SSs) and the tails of the three slower loadings, and (2) the dense individual data. This good matching between the two sets again

Y. Xu et al. / Carbon 114 (2017) 334e346

implies that all indentation data are effectively steady-state results. Moreover, Supplementary Figs. S3aeS3b show that, compared to paraffin, GOxA-PCM has much better indentation data consistency and is a material with better-defined solid behavior (instead of viscous behavior). By comparing paraffin (HTrue-paraffin) and GOxA-PCM (HOP-GOxAPCM) in Fig. 7, GOxA-PCM is always much harder than pure paraffin, and the difference increases by decreasing the strain rate. For example, the composite is 2.7
and 6.7
harder at ε_ ¼ 0.05s1 and 104s1, respectively, suggesting a strong reinforcement effect due to the GOxA. Fig. 7 also indicates that the two materials are strain rate dependent as expected for organic materials. In this log-log plot of HOP-GOxA-PCM vs. ε_ , the slope (i.e., the strain-rate sensitivity m) is nicely a constant (~0.15) for all ε_ , corresponding to a constant power-law exponent n z 6.7 for GOxA-PCM (see Appendix 3). However, for paraffin, by increasing ε_ from ~104 to ~101, m decreases from ~0.45 to ~0.19, i.e., n increases from 2.2 to 5.2. Consequently, the change of n suggests that, the deformation mechanism for pure paraffin might transit from the molecule diffusion (n < 3) at small strain rate to dislocation motion (n > 3) at large strain rates (see Appendix 3). However, due to the space limitation, the investigation of deformation mechanism of paraffin and GOxA-PCM will be left for future work. Thus, compared to paraffin, GOxA-PCM has a smaller m, and hence is much less strain-rate sensitive, especially at smaller strain rates. That is to say, by reinforcing paraffin using GOxA, the hardness (strength) of the composite is not only much higher but also more stable against strain rate change, especially at smaller strain rates, which is critical for practical applications. For example, based on Fig. 7 and Table 1, under a 0.27 MPa compression stress, it takes paraffin only 3 h to deform 10% but would take GOxA-PCM almost two centuries. Thus, the shape stabilization capability of GOxAPCM is drastically increased compared to pure paraffin. Thus, in summary, the paraffin is largely reinforced and shape stabilized by the GOxA-network. In the following, similar to the discussion based on durometer testing, we want to show that this reinforcement cannot be explained by the rule-of-mixture, implying a strong bonding between GOxA and paraffin. 3.3.2.3. Nano/microscale characterization of graphene oxide aerogel (GOxA) alone. In order to test the mechanical properties of GOxA alone using nanoindentation, two large circular flat punch indenters were used: a 2 mm-diameter steel tip and a 456 mmdiameter diamond tip. Here, for any flat punch indenter, the contact area A is a known constant, and the hardness H and modulus E can be determined using Eq. (A1)e(A3) in Appendix 2. Here, the contact radius ac is known. As demonstrated later, since GOxA's modulus E (75e400 kPa) is 6e7 orders of magnitude lower than that (1045 GPa for diamond or 200 GPa for steel) of indenters, Eq. (A3) can be nicely applied. Equations A1 and A3 indicate that, when a cylindrical flat punch indenter (of constant ac) is used, H and E are simply proportional to P and S, respectively. Here, to use Eq. (A3), GOxA's n can be estimated to be ~0.2 [88]. Also, for highly porous materials, the

341

constraint factor, i.e., the ratio of H to strength s, is ~1.0 instead of ~3.0 [89]. Even when using the large flat punch indenters which are much bigger than the pore size (0.2~1 mm as shown in Fig. 2a), it is still very challenging to perform stable nanoindentations on GOxA due to its extremely high porosity and extremely low mechanical properties. Fig. 8 shows the H and E calculated by Eq. (A1) and Eq. (A3) vs. indentation depth h, for two typical indentations (one indentation for each tip). It should be noted that when h reaches around 7 mm, both indentations become unstable, and the GOxA under the indenters were catastrophically collapsed, which generated large circular holes matching with the flat punch shapes (see Supplementary Fig. S6). During the stable stages of indentations as shown in Fig. 8, for both tips, while H (fP) increases continuously and monotonically, E (fS) interestingly steps up on multiple plateaus of ~2 mm steps. Since 2 mm is around the upper bound of pore size (see Fig. 2a), each step-up between E plateaus may be associated with collectively crushing each effective-supporting layer of pores. The increase of H and E with increasing h may be because indentation technique is known to overestimate H and E due to the densification effect for porous materials [75,76]. On the other hand, the increase of E in plateau steps (instead of continuously increasing as for H) may be due to that the CSM stiffness S is much more sensitive to the stiffness of the local supporting densified structure. Also, while the values of H (black symbols) match fairly well using the two tips, the values of E (red symbols) deviate about 4 times between the two tips, probably due to the high heterogeneous local fluctuation in the highly porous GOxA structure as well as the way of how the structure was densified under each indenter. Due to the densification effect, Fig. 8 can be used to estimate the upper bounds of E and H for GOxA alone. Table 2 lists the E and H values at the middle of plateaus based on the number of supporting layers collectively penetrated. Moreover, after penetrating the 3rd collective layer, the GOxA under indentation was catastrophically collapsed, so that the E and H values at the 3rd-layer penetration provides the upper-bound estimates for GOxA's modulus and failure strength sf (noting H/s z 1.0 as aforementioned [89]), i.e., E z 75e389 kPa and sf z H z 238e400 Pa for GOxA alone. These values fall in the ranges for GOxA alone based on previous studies (see Appendix Table A1): 2e1200 kPa for modulus and 200e40000Pa for hardness. However, Fig. 7 demonstrates that the GOxA-PCM is at least 2.7 times harder than pure paraffin whose hardness is in the range of

Table 1 The duration L10 for 10% accumulative strain for paraffin and GOxA-PCM under two values of uniaxial stress su (See Appendix 3 and Eq. (A10) for the discussion). Material

su (MPa)

ε_ u (s1)

L10 Duration to 10% strain

Paraffin GOxA-PCM Paraffin GOxA-PCM

1.67 1.67 0.27 0.27

5.4
103 2.7
106 9.0
106 ~1.8
1011

19 s 8.8 h 3h ~190 year

Fig. 8. H and E calculated by Eq. (A1) and Eq. (A3) vs. h, for two typical indentations on GOxA (one for each tip). Here, because the intrinsic noise of XP head (2 mm tip) is much higher, the associated E data was smoothened and plotted on the background of the original unaltered data. (A colour version of this figure can be viewed online.)

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Y. Xu et al. / Carbon 114 (2017) 334e346

Table 2 The E and H values at the middle of plateaus based on Fig. 8 and the number of layers collectively penetrated. Indenter

Layer# penetrated

h at the middle of plateau (mm)

E (kPa)

H (Pa)

2 mm tip 456 mm tip 2 mm tip 456 mm tip 2 mm tip 456 mm tip

1st 1st 2nd 2nd 3rd 3rd

~1.0 ~1.0 ~4.0 ~4.0 ~6.0 ~6.0

143 30 289 52 389 75

43 30 200 144 400 238

0.85e6 MPa, while GOxA-PCM is almost four orders of magnitude harder than GOxA alone. Thus, the reinforcement due to GOxA in paraffin is drastically higher than the prediction of the rule-ofmixture, indicating a strong bonding between GOxA and paraffin. This is qualitatively consistent with the aforementioned results based on durometer tests. 4. Conclusions A 5 wt% graphene oxide aerogel (GOxA) reinforced paraffin-PCM composite is developed. The composite maintains its original shape above melting temperature of the PCM and to hold the molten paraffin without any leakage, indicating superior shape stabilization. The X-ray diffraction and Fourier transform infrared (FTIR)

Acknowledgements The authors appreciate the support of the National Science Foundation (CBET-1235769). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We thank Nancy Peltier in Biology Department at Villanova for her help with the supercritical CO2 drying. We also appreciate the comprehensive comments and constructive suggestions from the reviewers of this paper. Appendix 1. Literature survey on the mechanical properties of porous 3D carbon aerogels/networks.

Table A1 The mechanical properties of porous 3D carbon aerogels/networks. Materials

Processing/Material condition

Density (mg/cm3)

Strength s (kPa)

Modulus E (kPa)

GA [20] 25  C ammonia treated GA [90] 90  C ammonia treated GA [90] 3D self-assembly of GO [51] CNT-graphene hybrid aerogel [91] CNT-graphene hybrid aerogel [91] GA [26] GA [26] GA [26] Graphene Assembly [52]

Pristine Ammonia treatment, but closer to pristine Ammonia treatment, further reinforced Nobel-metal and glucose assistance Acid-treated CNT Pristine CNT Pristine Pristine Pristine Covalently cross-link GO

3e5 ~16 ~16 ~30 32 41 30.9 47.6 96.1 80e100

0.2e3 (decreasing with more testing cycles) 0.3 0.7 42 30 (at 3% strain) 70 (at 3% strain) 40 150 660 10000

10e16 2 4.8 260 1200 2900 1200 2800 6200 51000

spectra imply a potentially new phase at the GOxA-paraffin interface in the composite. Durometer testing indicates that the composite is much harder than paraffin at both room temperature and elevated temperatures and maintains significant strength above paraffin's melting temperature. Nanoindentation testing shows that the composite is 3e7
times harder and less strain-rate sensitive than paraffin, especially at smaller strain rates. Thus, the composite is not only much harder but also much more stable against strain rate change, which is critical for practical applications. Furthermore, the durometer and nanoindentation tests both quantitatively indicate that the reinforcement of paraffin in GOxA is beyond the prediction by the rule-of-mixture, implying a strong GOxA-PCM interfacial bonding. To our best knowledge, this is the first study on the fundamental mechanical behavior of paraffin and GOxA-PCM composite at different temperatures and different strain rates, providing critical insights into their behaviors. The relationship between the hardness and durometer index first-ever developed here will enable the quantitative durometer testing on materials for many other applications at different ambient conditions (e.g., temperatures and probably chemical environments) due to its versatile and simple nature.

Appendix 2. Nanoindentation characterization Generally, nanoindentation can be used to determine the hardness H and modulus E of the indented material using Eqs. (A1)e(A3) [79,92,93].

H¼

P P ¼ ; A pa2c

(A1)

Er ¼

S 1 1  n2 1  n2i þ ; where ¼ ; 2ac Er E Ei

(A2)

  S E ¼ 1  n2 2ac

if Ei > > E;

(A3)

where P is the indentation load; A and ac are the contact area and radius, respectively. S is the contact stiffness. Er is the reduced modulus as defined in Eq. (A2), where E and n are the modulus and Poisson's ratio of the indented material, while Ei and ni are the quantities of the indenter. A nanoindenter can control P and continuously measure the indentation displacement h. With the continuous stiffness measurement (CSM) technique [79,92,93], a nanoindenter can also

Y. Xu et al. / Carbon 114 (2017) 334e346

continuously measure S. For flat homogenous materials without pile-up, the Oliver-Pharr method can be used to determine the contact radius ac through P, h, S using Eqs. (A4) and (A5) [79,92,93].

(A4)

Ac ¼ pa2c ¼ f ðhc Þ;

(A5)

where hc is the contact depth. Here, Eq. (A5) is called area function, which can be calibrated using standard materials with known moduli or directly determined by visualizing the indenter shape using microscopy [79,92,93]. It should be noted that the measured indentation properties (modulus or hardness) are due to the average responses from the indentation-deformed volume (plastic zone) [72,73,89]. Based on Johnson's expanding cavity model, the plastic zone is normally estimated by a hemisphere with a diameter 1~2
of the contact diameter d [72,73,89]. As shown in Fig. 2a, 1.0 mm would be a good estimate for the upper bound of the pore-size in GOxA and hence used as the characteristic microstructure length scale (lu) in the GOxA-PCM composite. Our indentation results shown in Fig. 7 are always from h > 5 mm, namely, h > 5lu. More importantly, for a Berkovich indenter, the contact diameter d z 7h > 35 mm. Thus, any h > 5 mm indentation corresponds to a plastic zone with diameter >35 mm, i.e., >35lu. Thus, the indented material in the GOxA-PCM composite can be effectively treated well as a homogeneous material for the results in Fig. 7. Appendix 3. Multi-strain-rate characterization using nanoindentation For strain-rate-dependent materials, their strengths depend on not only the strain rate but also the deformation history. For example, after instantaneously applying a constant strain rate (_εu ), the required stress would transiently change and finally reach to a constant steady-state (SS) value. Thus, only at the steady-state, a strain rate can be uniquely correlated to the applied stress, namely flow strength (s). In order to quantitatively study the strain-ratedependence, the mechanical properties should be measured at the steady state (SS). A phenomenological power-law relationship is commonly used to describe the strain-rate dependence of flow strength at the SS,

ε_ u ¼ Asn or alternatively s ¼ B_εm u;

(A6)

where ε_ u and s are the strain rate and stress during a uniaxial testing at the SS; n, m, A and B are fitting parameters, while m is called the strain rate sensitivity, and n (¼1/m) is called the powerlaw exponent. The value of n normally correlates to the deformation mechanism, e.g., for crystals, n < 3 normally indicates diffusive deformation, while n > 3 normally indicates dislocational deformation [94]. The indentation strain rate ε_ is defined as the displacement_ rate-to-displacement-ratio (_ε ¼ h=h) [82,83]. Due to the strong strain gradient and stress concentration under indentation, the equivalent uniaxial strain ε_ u z0:09_ε [95], while s zH/3 [96,97]. Thus, Eq. (A6) can be revised to [94].

ε_ ¼ A

Hn ; alternatively H ¼ 3
0:09m B_εm ; 0:09
3n

Or simply,

ε_ ¼ A0 H n ; alternatively

H ¼ B0 ε_ m

P hc ¼ h  0:75 ; S

343

(A7)

where A' and B' are fitting parameters. Nanoindenter intrinsically controls P (instead of h). Thus, it is much convenient to directly control the loading rate to alter the strain rate. For a self-similar indenter (e.g., a perfect Berkovich or conical indenter) indenting a homogeneous material, by neglecting indentation size effect [98,99], the contact area A is proportional to h2. Thus, A ¼ Ch2, where C is a constant related to indenter geometry. By differentiating H¼P/A ¼ P/(Ch2), we have [100].

h_ P_ H_ dH dP dh ¼  2 ; i:e; 2_ε ¼ 2 ¼  ; h P H H P h . 2_ε ¼ P_ P if H_ ¼ 0:

(A8)

(A9)

Because a constant H (z3s) is expected for a material during a _ steady state deformation, based on Eq. (A9), we have 2_ε ¼ P=P. Therefore, a constant ε_ test can be approximated by running con_ stant load-rate-to-load-ratio P=P (¼2_ε) [100], i.e., exponentially increasing the load. However, in practice, an indentation with one slow strain rate (104~105s1) would take multiple days. Consequently, a constant thermal drift rate - a key assumption for quantitative indentation analysis - may not be valid [101]. Therefore, a multiple-strain-rate indentation technique is developed here, particularly with three _ sequentially decreasing strain rates (P=P¼2_ ε0 , 0:2_ε0 , and 0:02_ε0 ) during a single loading (see Fig. 6a) to minimize its duration (<4 h). The loading portion at each strain rate lasts about 1/3 of the maximum depth. Two sets of three-strain-rate indentations were performed with ε_ 0 equals 0.05 s1 and 2.5
103s1 (see Fig. 6a) in this study, corresponding to six preset strain rates, i.e., (0.025, 0.25, 0.5, 2.5, 5, 50)
103 s1 . An interesting and practical observation should be mentioned: the deformation during each entire three-strain-rate indentation is almost always at either the steady state (SS) or quasi-steady state (QSS). This is because the slow and smooth hardness change during the transition between each pair of preset strain rates. This has been demonstrated for both paraffin and GOxA-PCM composite. The SS (and QSS) deformation during the entire multi-strain-rate testing provides a significant benefit: the SS (and QSS) ε_ (in Eq. (A7)) spans continuously over a wide range (see Fig. 7) instead of only the preset values (e.g., 3 strain rates for each three-strain-rate testing). It may also be important in practical considerations to predict the life L of a stressed structural part made of strain-rate sensitive material. We may define the expected life L10 under a constant uniaxial stress su as the duration for reaching a preset critical cumulative strain εc, say 10% (i.e., εc ¼ 0.1), due to the corresponding steady-state strain rate ε_ u . Noticing that L10 ¼ εc =_εu ¼ 0:1=_εu , based on Eq. (A7), we have

L10 ¼

  10 B0 1=m : 9 3su

(A10)

Here, B' and m can be found experimentally by fitting H vs. ε_ 0 using H ¼ B ε_ m (see Fig. 7). For example, for HOP-GOxA-PCM shown in Fig. 7, the fitting parameters are B’ ¼ 23.35 MPa and m ¼ 0.15, and hence L10 e6.0
109 s z 190 year for su ¼ 0.27 MPa based on Eq. (A10). L10 for paraffin and GOxA-PCM under two values of su are listed in Table 1.

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Y. Xu et al. / Carbon 114 (2017) 334e346

Appendix 4. Irregular localized pile-ups around each indentation on Paraffin Fig. A1a shows the optical image of a typical indent on GOxAPCM, displaying flat indent surfaces and straight edges without pile-up. Thus, we expect that the Oliver-Pharr method can be used to determine the modulus and hardness well for GOxA-PCM composite. On the contrary, Fig. A1b shows a typical indent on paraffin with bumpy indent surfaces and wavy indent edges, which is the case for every indentation on paraffin (also see the SEM image in Supplementary Fig. S4). To our best knowledge, this highly irregular indent shape is first-ever observed for any homogeneous materials. This is probably due to the underlying uneven plastic flow and local back-flow (resulted from the residual stress field in the permanent indent) after unloading of crystalline paraffin. The investigation of this surprising irregular indentation plasticity of paraffin is not the focus of this paper and hence will be left for a future work. Preliminary investigation using ex-situ optical microscopy on post-indentation morphology shows that the indent irregularity happens almost spontaneously (within 2 s); thus, the recrystallization of paraffin crystal in the indented area may be ruled out as the key reason as it requires diffusion.

pile-up [79,92,93]. In order to determine the true hardness free of the pile-up effect, it is essential to determine the true contact area A. Two existing methods to correct for the pile-up effect are (1) estimate A at the maximum indentation depth by directly measuring the residual indent's area using an appropriate microscopy [103,104], and (2) a revised Joslin-Oliver method [87] as discussed below. Unfortunately, it is very difficult to have a precise estimate for the indent area due to the strong indent irregularity and possible plastic back-flow. Therefore, we could use a revised Joslin-Oliver method [87] (see Eq. (A11)) to estimate the true hardness HTrue free of the pile-up effect, provided we know the true modulus ETrue.

HTrue ¼

2 H ETrue OP 2 EOP

;

(A11)

where HOP and EOP are the Oliver-Pharr hardness and modulus, respectively. Here, as aforementioned, the GOxA-PCM is expected to be slightly stiffer than the paraffin, and the GOxA-PCM composite's Oliver-Pharr modulus (EOP-GOxA-PCM ¼ 1.111 ± 0.032 GPa in Fig. 7) would be free of pile-up effect, which could be a good upper bound estimate for paraffin's true modulus, i.e., ETrue-paraffin

Fig. A1. Optical images of (a) a typical 30 mm-deep indent on GOxA-PCM and (b) one on paraffin. (c) and (d) The magnified optical images of the boxed region in (b), where the focal depths are (c) 0 mm and (d) 8 mm, respectively, showing two large ~8 mm-tall localized pile-ups.

Due to the uneven plastic flow, Fig. A1b-A1d interestingly indicate multiple localized pile-ups (instead of the common form of single pile-up [93,102]) on each indent edge. For example, Fig. A1bA1d show that, an edge of a 30 mm indentation has two large ~8 mm-tall localized pile-ups which did not exist prior to the indentation (not shown here). Moreover, in order to further confirm the existence of pile-ups for paraffin, additional indentations were done using a 300 mm sapphire spherical indenter (see Supplementary Fig. S5). Those indents clearly show multiple localized pile-ups. Unfortunately, as shown in Fig. A1b and Supplementary S4, it is very difficult to have a precise estimate for the indent area due to the strong indent irregularity, and more importantly, the indent may be altered significantly from the contact under load due to the possible aforementioned plastic backflow (see Fig. A1b and Supplementary S4). Appendix 5. Calculation of true hardness free of the pile-up effect for paraffin As discussed in Appendix 4, significant pile-ups are observed around each indentation on paraffin. The Oliver-Pharr method based on Eq. (A4) assumes no pile-up, and it underestimates the contact depth hc and hence the contact area A in case of indentation

z1.111 GPa. Thus, Eq. (A11) can be used to calculate HTrue-paraffin (a good upper bound) as plotted in Fig. 7. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.carbon.2016.11.069. References [1] J.F. Li, W. Lu, Y.B. Zeng, Z.P. Luo, Simultaneous enhancement of latent heat and thermal conductivity of docosane-based phase change material in the presence of spongy graphene, Sol. Energy Mater. Sol. Cells 128 (0) (2014) 48e51. [2] R. Ehid, A.S. Fleischer, Development and characterization of paraffin-based shape stabilized energy storage materials, Energy Convers. Manag. 53 (1) (2012) 84e91. [3] G.-Q. Qi, C.-L. Liang, R.-Y. Bao, Z.-Y. Liu, W. Yang, B.-H. Xie, M.-B. Yang, Polyethylene glycol based shape-stabilized phase change material for thermal energy storage with ultra-low content of graphene oxide, Sol. Energy Mater. Sol. Cells 123 (2014) 171e177. [4] M. Mehrali, S.T. Latibari, M. Mehrali, H.S.C. Metselaar, M. Silakhori, Shapestabilized phase change materials with high thermal conductivity based on paraffin/graphene oxide composite, Energy Convers. Manag. 67 (0) (2013) 275e282. [5] J.-L. Zeng, S.-H. Zheng, S.-B. Yu, F.-R. Zhu, J. Gan, L. Zhu, Z.-L. Xiao, X.-Y. Zhu, Z. Zhu, L.-X. Sun, Z. Cao, Preparation and thermal properties of palmitic acid/

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