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Breaking through the Solid/Liquid Processability Barrier: Thermal Conductivity and Rheology in Hybrid Graphene−Graphite Polymer Composites Maxim Varenik,*,† Roey Nadiv,† Idan Levy,† Gleb Vasilyev,§ and Oren Regev*,†,‡ †

Department of Chemical Engineering and ‡Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel § Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel S Supporting Information *

ABSTRACT: Thermal conductivity (TC) enhancement of an insulating polymer matrix at low filler concentration is possible through the loading of a high aspect ratio, thermally conductive single filler. Unfortunately, the dispersion of highaspect-ratio particles greatly influences the rheological behavior of the polymer host at relatively low volume fractions, which makes further polymer processing or mixing difficult. A possible remedy is using two (hybrid) fillers, differing in their aspect ratios: (1) a plate-like filler, which sharply increases both viscosity and TC, and (2) an isotropic filler, which gradually increases these properties. We examine this hypothesis in a thermosetting silicone rubber by loading it with different ratios, (1)/(2), of graphene nanoplatelets (GNPs) (1) and graphite powder (2). We constructed a “phase diagram” delineating two composite processability regions: solid-like (moldable) or fluid-like (pourable). This diagram may be employed to tailor the mixture’s viscosity to a desired TC value by varying the fillers’ volume fraction. The phase diagram highlights the low volume fraction value, above which the composite is solid-like (low processability) for a single high-aspect-ratio nanofiller. By using hybrid filling, one can overcome this limit and prepare a fluid-like composite at a desired TC, not accessible by the single nanofiller. Thus, it provides an indicative tool for polymer processing, especially in applications such as the encapsulation of electronic devices. This approach was demonstrated for a heat source (resistor) potted by silicon rubber graphene−graphite composites, for which a desired TC was obtained in both solid- and liquid-like regions. KEYWORDS: thermal conductivity, rheology, polymer processing, graphene, hybrid composites

1. INTRODUCTION Thermal management is essential in high-power density applications, such as microelectronics1−3 or batteries.4 Heat can be removed by coupling the heat source to thermally conductive polymer composites,5 by way of potting or a heat sink. This approach offers advantages over traditional metal heat sinks in weight, price, and processability (also termed workability). Most polymers have a low thermal conductivity (TC), on the order of 10−1 W m−1 K−1, that may be improved by adding thermally conductive fillers. At a given filler volume fraction, several parameters affect the TC enhancement:6,7 The first is the filler’s TC coefficient, where higher values will usually lead to superior improvements. Typical fillers are metallic, graphitic, or ceramic particles, with TC in the range of 100−400, 1000−3000, and 100−300 W m−1 K−1, respectively.8 Another important factor is the filler morphology.9−11 TC enhancement is higher when the aspect ratio of a particle is ≫1 (for example, lateral dimension/thickness for platelets or length/diameter for fibers). High-aspect-ratio particles form © 2017 American Chemical Society

conductive networks more easily, which minimizes the heat transfer through the thermally insulating polymeric matrix. Usually, platelets (e.g., graphene) are more efficient than fibrous particles12,13 (e.g., carbon nanotubes) due to their superior interfacial contact area and the subsequent lower contact resistance. TC may also be improved by using a combination of fillers (hybrid) having different shapes and sizes that form networks more efficiently.6,14−17 Polymer viscosity is also greatly affected by the shape of the filler.18−20 The viscosity of high-aspect-ratio particle dispersions rises exponentially near a critical filler volume fraction. This fraction decreases with increased particle aspect ratio. At the critical volume fraction, the rheological response of filler− polymer dispersions changes from liquid to solid-like.21,22 This may affect the polymer processing method23 and, consequently, the required mixing process, type of equipment used, and the Received: November 14, 2016 Accepted: February 1, 2017 Published: February 1, 2017 7556

DOI: 10.1021/acsami.6b14568 ACS Appl. Mater. Interfaces 2017, 9, 7556−7564

Research Article

ACS Applied Materials & Interfaces cost.24,25 Addition of fillers smaller than the polymer’s radius of gyration26 or with weak polymer−filler interactions27 may decrease the dispersion viscosity, but at a cost to thermal conductivity.7 Additives such as solvents can be used to reduce the mixture’s viscosity,28,29 although this also may adversely affect the final composite properties.30,31 While plate-like fillers dispersed in polymers increases the polymer’s TC, they also dramatically increase its viscosity, which, in turn, reduces the workability (the filler concentration limit at which viscosity is too high to allow sample processing by a particular method). In order to overcome this challenge, we suggest using hybrid composites (with two or more types of fillers) that enable tuning of the loaded polymer rheology. In this study, we explore the TC and viscosity of a widely used polymer (silicone rubber, TC = 0.287 ± 0.009 W m−1 K−1) loaded with two types of high TC graphitic fillers: graphene nanoplatelets (GNPs, plate-like) and graphite powder (spherelike). The collective trends in TC and viscosity after filler loading are used to construct a phase diagram encompassing the following parameters: GNP and graphite volume fraction, collective TC, and viscosity. This phase diagram helps us to select the desired composite rheology for a given TC application, as demonstrated by a functional experiment on a heat source (resistor) potted by silicon rubber graphene− graphite composites.

Information (section 2, Figures S3−S7). Values for apparent viscosity are taken at 0.1 1/s and at 1 Hz for G′ and G″. Although viscosity measurements were performed without crosslinker addition, they reflect the rubber-cross-linker mixture rheology well. The addition of cross-linker has a negligible effect on the rheological behavior due to its low concentration (rubber:cross-linker = 20:1 w/w) and long pot life (the time it takes for the viscosity to double after cross-linker addition). The pot life in our case is longer than the mixing time (∼15 min). This approach (i.e., rheology of resin/part A) is widely used in other polymer thermoset systems, such as epoxy.17,35,36 2.5. Scanning Electron Microscopy (SEM). High-resolution cold FEG SEM (JEOL JSM-7400F) operated in secondary electron mode (3 kV) was used to determine the fillers’ morphology. Filler particles were imaged by gently spreading a small amount of powder on a sticky conductive carbon tape. The fillers’ dimensions are measured for more than 100 particles (Nparticles). The surface of the composites was imaged after cryo-fracturing; before imaging, the surface of the crack was coated with carbon using flash deposition. 2.6. Atomic Force Microscopy (AFM). GNP thicknesses were determined by AFM using a Dimension 3100 scanning probe microscope operated in tapping mode, using Veeco RTESP silicon tips. An aqueous dispersion of GNPs was spin-coated on SiO2 wafers and allowed to dry by evaporation at ambient temperature for 24 h before performing the measurements. 2.7. Raman Spectroscopy. Raman spectroscopy of the fillers was performed on a Jobin Yvon HR LabRAM micro-Raman device operated at 514 nm (1 μm spot size) on a quartz slide. 2.8. X-ray Photoelectron Spectroscopy (XPS). XPS data were collected using an ESCALAB 250 ultrahigh-vacuum (10−9 bar) apparatus with an Al Kα X-ray source and a monochromator. Powder samples were pressed into indium foil. The spectra were recorded with pass energies of 150 or 20 eV (high-energy resolution). The spectral components of the C atoms signals were found by fitting a sum of single component lines to the experimental data by means of nonlinear least-squares curve fitting. To correct for charging effects, all the spectra were calibrated relative to a carbon 1s peak positioned at 285.0 eV. 2.9. Thermogravimetric Analysis (TGA). TGAs of the fillers were recorded by a Mettler Toledo analyzer by means of a Stare software system (TGA/STDA85). The samples (4−6 mg in 70 μL alumina crucibles) were heated from 40 to 500 °C at a rate of 10 °C/ min and from 500 to 1000 °C at a 5 °C/min rate, under air flow (50 mL/min). A low heating rate (5 °C/min) was essential, since it significantly enhanced the detection of thermal events in the relevant temperature range (500−1000 °C). A couple of thermal parameters were extracted: the mean combustion temperature (T1/2), at which the combustion step reached half of its total weight loss, and the combustion-temperature range (ΔT), which is the full width at halfmaximum of the derivative thermogravimetry curve (Figure S8 and Figure 2c, right ordinate). 2.10. Thermal Management by Encapsulation. A 40 Ω, 10 × 10 × 30 mm3 resistor (Vishay) was suspended in the middle of a cylindrical mold (diameter = 26 mm, length = 50 mm). A type K thermocouple was pressed against the surface of the resistor, and the resistor was encapsulated by various rubber composites, as shown in Figure 8a and Figure S9. Polymer dispersions with liquid-like behavior were poured directly into the mold, while solid-like pastes were hand molded around the resistor. When hardened, a 5 V potential was applied across the resistor using a SCP-800-24 power supply (Mean Well), and the resistor and ambient temperatures were recorded until the resistor temperature reached a steady state (about an hour). The same resistor was used throughout the experiments. The low temperature range experienced in the experiment (25−60 °C) induced a negligible resistance change due to temperature. Thus, the measured power to the resistor (0.625 W) was constant throughout the experiment.

2. EXPERIMENTAL SECTION 2.1. Materials. Graphene nanoplatelets (GNPs) grade H (H15, XG-Sciences), graphite powder (crystalline, −300 mesh, Alfa Aesar), silicone rubber (RTV 3325, Bentley), and silicone cross-linker (Bluesil CATA 24H, Bentley) were used as received. 2.2. Composite Preparation. The silicone rubber and crosslinker were mixed (20 g of rubber:1 g of cross-linker) in a planetary centrifugal mixer (Thinky, ARE-31032). The fillers were added gradually (0.5 g at a time) and mixed (rotation + revolution at 2000 rpm) until incorporation. Zirconia balls measuring 10 mm in diameter were added to the mixing container to enhance the compression and shearing forces during the mixing process and to aid mixing at high viscosities. The planetary motion throws the balls strongly against each other, generating a high impact energy.33 After reaching the required volume fraction, mixing continued for an additional 10 min, and it was then deaerated (revolution, 5 min at 2200 rpm). Dispersions for viscosity measurements were prepared in a similar manner, but without cross-linker addition. Composites for TC measurements were cast into a plastic mold (Delrin, area = 3 cm × 6 cm with various thicknesses, 0.1−1.5 mm) and left to cure for 24 h at room temperature. Cured samples were cut into disks using a 6 mm hollow punch. 2.3. TC Measurement by Differential Scanning Calorimetry (DSC). TC was measured by a DSC5,6,34 (DSC, Mettler Toledo Star System operated at 80 mL/min N2 and equipped with 70 μL alumina crucibles) procedure that allows the TC measurement of low-volume samples ( ΔTGNP. 3.2. Single Filler Composites. Single filler composites containing either GNPs or graphite were prepared using a planetary mixer to obtain homogeneous filler dispersion in the polymer matrix. The filler morphology does not noticeably change during the mixing process, as confirmed by imaging the fractured composite surface (Figure S10). Increasing the volume fraction (ϕ) of either filler in the matrix increases both the TC and the viscosity (Figure 3).

TCComposite = TCMatrix ϕMatrix +

∑ TCFillerϕFiller Filler

(1)

where the TC of the composite (TCComposite) is calculated by a weighted average of the matrix’s TC (TCMatrix) and the effective TC of the filler (TCFiller ). While a linear model describes the thermal conductivity of graphite composites well, for GNP composites the model holds up to ϕGNP = 0.06, possibly due to percolation.6 The fitting constants are displayed in Figure 3a. The effective TC coefficients of the fillers are much lower than the intrinsic TC of the filler (∼103 W m−1 K−1) due to filler− filler and filler−polymer contact resistance.7,46 The GNP dramatically increases the viscosity, compared to graphite; for instance, at only ϕFiller = 0.02, the composite viscosity is 103 times greater than with graphite at the same volume fraction. The relative viscosity (ηr) dependence on filler’s volume fraction of the polymer composites were fitted by the Krieger−Dougherty model:47,48 ηr =

ηComposite ηMatrix

−[η] φ ⎛ ϕFiller ⎞ Filler M ⎜ ⎟ = ⎜1 − ⎟ φM ⎠ ⎝

(2)

where ηComposite is the measured viscosity of the composite both at a given filler volume fraction and at a given shear rate. ηMatrix is the measured viscosity at the same shear rate without the filler. [η]Filler is the intrinsic viscosity of the filler, defined as the slope of the relative viscosity with ϕFiller at low volume fractions (ηr(ϕFiller → 0) ≈ 1 + [η]Filler·ϕFiller). The use of relative viscosity is also advantageous since it normalizes the temperature effects on the viscosity of the matrix polymer,49 which changes during mixing due to shear heating (Figure S10). φM is the critical volume fraction near which the viscosity increases exponentially (e.g., 0.02 for GNP in Figure 3b), defining the workability limit for the filler dispersion in the matrix. For hard, nonflexible, and noninteracting particles, this volume fraction is determined by the maximum packing fraction.48 At this point, almost no liquid is left to lubricate the motion between the particles, resulting in an exponential rise in the viscosity.18,50 In other systems, such as system with high aspect ratio or soft particles, φM is taken as the volume fraction at which the fillers start interacting and the dispersion starts losing its fluidity.49,51−54 The Krieger−Dougherty model can be applied to high aspect ratio fillers, with both [η]Filler and φM being fitting parameters, which are influenced by the filler’s aspect ratio:18 as the aspect ratio increases, [η]Filler increases and φM decreases. Therefore, GNP has a lower φM and a higher [η]Filler. The viscoelastic moduli (G′ = storage modulus and G″ = loss modulus) are filler volume-fraction dependent (Figure 4), similar to TC and viscosity (Figure 3). A crossover point (the volume fraction at which G′= G″) is observed for both the GNPs and the graphite composites at volume fractions of 0.019 and 0.13, respectively. These volume fractions increase with frequency and reach a plateau above 1 Hz (Figure 6, inset). Below the crossover volume fraction, the suspensions are mostly liquid-like and flow freely, even under small deformation. Above it, the dispersions turn solid-like and require higher strain to initiate flow. Interestingly, these crossover volume fractions are similar to φM, obtained from the Krieger−Dougherty model (eq 2 and Figure 3b), around which the viscosity increases sharply. At the crossover volume fraction, the particles start interacting. They hinder the flow and increase the viscosity as well as the storage modulus.22,55

Figure 3. Single-filler effect on thermal conductivity (a) and on viscosity (b). The markers represent experimental data points, while the solid lines represent the fitting to the additive rule of mixtures (a) and Krieger−Dougherty (b) models (eqs 1 and 2, respectively). The fitting parameters are displayed in each graph. Dashed lines in (b) represent the critical volume fraction found by fitting. In some cases, the error bars are smaller than the marker size.

Loading a sphere-like graphite filler (low aspect ratio) results in a gradual growth of TC up to values of 0.70 ± 0.03 W m−1 K−1 (a TC improvement of 143%) at ϕGraphite = 0.16. However, the loading of GNPs sharply increases the TC to a value of 2.6 ± 0.2 W m−1 K−1 (a much greater improvement of 795%) at the same volume fraction. The higher effectivity of GNPs, as thermal enhancement fillers (compared to graphite), is congruent with its higher aspect ratio and higher T1/2.6 The latter takes into account both the defect density and the lateral size, which also influence TC performance as fillers. Since the TC rises linearly for each filler, the results are fitted by the additive rule of mixtures,44,45 which works well for systems with a high ratio between the filler’s TC and the polymer’s TC and low concentration range ( order of magnitude). In this case, the drag on the larger filler particles exerted by the composite medium (small particles and liquid) is similar to the drag they would encounter if they were passing through a pure liquid with the same properties (density and viscosity).60 Then, the same constants extracted for single-filler systems (eq 2) may be applied. In our system, however, the fillers are of similar size (but have a different aspect ratio). Hence, eq 3 holds, but only for small volume fractions, ϕGraphite ≤ 0.02, for all measured ϕGNP (Figure 5b, dashed lines). The model underestimates the viscosity values at higher graphite loadings and so the viscosity diverges at a lower-than-expected volume fraction (104 Pa s). This system is therefore very difficult to process. However, one may obtain composites with the same TC enhancement by simply using half of the fraction of the GNPs and 0.05 volume fraction of the graphite, in a liquid-like state at a viscosity of ∼103 Pa s (white circle in Figure 7). We plot the graphite crossover volume fraction (Figure 7, dotted) obtained at different GNP loadings (Figure 6, blue circles). This line separates the phase diagram into two regions: below the line the composite mixtures have a more dominant loss modulus (liquid-like) and may be mixed by agitators and impellers,25 termed “liquid mixing”. Mixing composites prepared above this line, termed “solid mixing”, requires equipment with much higher mixing energies, such as extruders or roll milling.23 This makes the diagram in Figure 7 a useful tool for allocating the appropriate equipment required for processing a given composite. 3.5. Thermal Management. To demonstrate the influence of viscosity on the composite preparation, a resistor was potted

(Figure 8a and Figure S9) in three different composites: (1) neat silicone rubber, (2) rubber loaded with GNPs only, and (3) rubber loaded with a GNP−graphite hybrid ((2) and (3) are marked in Figure 7 as red and white circles, respectively). Sample 2 is located above the mixing line on the phase diagram and, thus, termed “solid” rubber, while sample 3 is located below it and termed “liquid” rubber. Using the liquid sample, encapsulation is readily performed by pouring the freshly prepared composite into the mold around the resistor, followed by a degassing process (see Experimental Section). Nonetheless, the “solid” sample is more difficult to process and is prepared by pressing and molding bits of the polymer around the resistor. Degassing is impossible in the “solid” case because the entrapped air cannot flow. However, the compressive forces during the mixing process (see Experimental Section) and hand molding should reduce the amount of entrapped air. Both composites have the same TC (0.5 W m−1 K−1), which is about twice the TC of the neat polymer. The ability to dissipate heat was studied by measuring the temperature difference between the resistor surface (TR) and the air temperature (TS), while applying constant power to the resistor (Figure 8b). Both composites performed better than the neat rubber and lowered the steady-state temperature difference by 10 °C. Because of their similar TC values, these composites behaved almost identically and reached a maximum temperature difference within 1 °C of each other. In summary, the thermal conductivity and rheology of silicone rubber composites loaded by two types of graphitic fillers were examined. These fillers are similar in size (Figure 1) and sp2 content (Figure 2), but differ in their aspect ratios. Loading the matrix with GNP only (aspect ratio >100) is ∼5fold more efficient in enhancing the TC than graphite only (aspect ratio ∼1) with the same volume fraction (Figure 3a). However, exponential increases in the composite’s relative viscosity occur near 0.02 volume fraction GNP compared with 7561

DOI: 10.1021/acsami.6b14568 ACS Appl. Mater. Interfaces 2017, 9, 7556−7564

Research Article

ACS Applied Materials & Interfaces

Figure 8. (a) Schematic illustration of the thermal management experiment: a resistor potted in a rubber composite (see Experimental Section) and thermocouples measuring the temperature of the resistor’s surface (TR) and the ambient surrounding temperature (TS). The difference between these temperatures is recorded (b) for three different potting rubbers: a GNP composite above the mixing line (see Figure 7), a hybrid GNP− graphite composite below the mixing line, and neat rubber (control). Composites prepared above the mixing line are solid-like and do not flow under small stress (upper picture, blue frame, inset in part b), while composites prepared with volume fractions below the mixing line flow even under gravity (lower picture, red frame, inset in part b).

0.15 for the graphite powder (Figure 3b). Around these filler fractions, where the viscosity increases exponentially, the storage modulus surpasses the loss modulus and the material transitions from being liquid, free-flowing and easy to process to being solid-like (Figure 4). In hybrid composites, the TC behavior is completely cooperative and fits a multicomponent mixture rule (eq 1). The viscosity is also cooperative (obeys a multiplicative model) up to relatively low total volume fraction (≤0.04), which may be predicted by the Krieger−Dougherty model (eq 2) from the parameters obtained from a single-filler system. Higher filler volume fractions, however, require adaptation of the critical volume fraction of graphite (eq 3). These models enable the construction of a phase diagram, which maps the TC and the viscosity as functions of GNPs and graphene filler volume fractions. Additionally, the phase diagram is divided by a liquid−solid line, above which the viscosity rises exponentially and the mixture turns solid-like. The diagram shows that high TC values may be reached by loading a plate-like GNP filler even at low volume fractions, but only in the solid (hard to process) region. The isotropic graphite filler has a broader fluid region but requires higher filler volume fractions than the GNP to obtain the same TC values. Utilizing the phase diagram, it is possible to allocate hybrid compositions fulfilling rather strict conditions, e.g., TC > 0.5 W m−1 K−1, a low total filler volume fraction, and a liquid composite may only be obtained hybrid filling. The ability to tune between liquid-like or solid-like was demonstrated by selecting a given TC value and preparing two types of composites: a fluid-like GNP−graphite hybrid and a GNP-only paste. These composites were applied to resistor potting. Since the TC values were the same, identical thermal management performance was demonstrated, however, the solid-like paste was difficult to process and required manual molding around the resistor, while the fluid hybrid was simply poured into a mold.

behavior. We argue that this behavior is associated with the size similarity of the fillers and their very different aspect ratios. The use of hybrid composites enables us to obtain TC values at lower filler volume fraction or lower viscosity, which are not achievable by means of a single-component composite. Including both the composite TC and viscosity in a single phase diagram is useful for polymer processing, for thermal management purposes. To demonstrate this, the diagram was applied to the design of electronic potting composites, differing by their implementation methods: either liquid and pourable or solid and moldable. Using this diagram, one could tailor a required TC value to a desired processing condition for a given polymer composite.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b14568. Thermal conductivity determination by DSC (Figures S1 and S2); flow curves (Figures S3−S7); filler thermograms (Figure S8); image of encapsulated resistor (Figure S9); SEM of cryo-fractured surfaces (Figure S10); mixture temperature during mixing (Figure S11) (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (M.V.). *E-mail [email protected] (O.R.). ORCID

Maxim Varenik: 0000-0001-6034-4970 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Alexander Varenik is thanked for his technical support. Raisa Banshatz is thanked for her help with the rheological measurements. Joergen Jupp is thanked for his help with the AFM measurements.

4. CONCLUSIONS The silicone−rubber hybrid composites, loaded with GNPs and graphite, have a cooperative TC behavior (each filler affects the composite independently) and a partly synergistic viscosity 7562

DOI: 10.1021/acsami.6b14568 ACS Appl. Mater. Interfaces 2017, 9, 7556−7564

Research Article

ACS Applied Materials & Interfaces

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