Nanoplatelet Size to Control the Alignment and ... - ACS Publications

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Nanoplatelet Size to Control the Alignment and Thermal Conductivity in Copper−Graphite Composites André Boden, Benji Boerner, Patryk Kusch, Izabela Firkowska,* and Stephanie Reich Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany S Supporting Information *

ABSTRACT: A controlled alignment of graphite nanoplatelets in a composite matrix will allow developing materials with tailored thermal properties. Achieving a high degree of alignment in a reproducible way, however, remains challenging. Here we demonstrate the alignment of graphite nanoplatelets in copper composites produced via high-energy ball milling and spark plasma sintering. The orientation of the nanoplatelets in the copper matrix is verified by polarized Raman scattering and electron microscopy showing an increasing order with increasing platelet size. The thermal conductivity k along the alignment direction is up to five times higher than perpendicular to it. The composite with the highest degree of alignment has a thermal diffusivity (100 mm2s−1) comparable to copper (105 mm2s−1) but is 20% lighter. By modeling the thermal properties of the composites within the effective medium approximation we show that (i) the Kapitza resistance is not a limiting factor for improving the thermal conductivity of a copper-graphite system and (ii) copper-graphite-nanoplatelet composites may be expected to achieve a higher thermal conductivity than copper upon further refinement. KEYWORDS: Metal-matrix composites (MMCs), copper, graphite nanoplatelets, thermal properties, anisotropy, polarized Raman spectroscopy

M

within a copper matrix. Compared to unaligned samples they enhanced the thermal conductivity along the nanotube alignment direction by a factor of 4. Nevertheless, the resulting thermal conductivity remained 80% below the conductivity of pure copper. In this Letter, we propose a simple approach to align graphite nanoplatelets in a copper matrix. The degree of alignment of the filling materials is quantitatively evaluated with polarized Raman spectroscopy. We show that the alignment is inseparably linked to the lateral size of the nanoplatelets. This relationship results in anisotropic thermal properties of the composites (up to a factor of 5). Our experimental results are accounted for by an effective medium approximation (EMA) model that considers the influence of filler geometry, orientation as well as the thermal interface resistance between matrix and filler material. In view of our findings, we discuss possible routes for enhancement of thermal conductivity in metal−matrix composites. Graphite nanoplatelets with the thickness in the range of ∼10−100 nm are excellent heat conductors with k ≈ 1500 Wm−1K−1 at room temperature.19 To test the GnP as the filler for metal matrix, the Cu and GnP powders were homogenized via planetary ball-milling and consolidated with spark plasma sintering (see Methods for details). The chosen approach requires no chemicals and allows one to produce composites on an industrial scale. To explore the influence of nanoplatelets

odern electronics need better and better cooling systems due to their increasing power densities and decreasing size and weight.1 Copper is a commonly used material for heat sinks, heat spreaders, and heat pipes because of its excellent thermal conduction. However, copper is also heavy and its large coefficient of thermal expansion becomes problematic for cooling silicon and other semiconductors. Efforts were invested to reduce the density of copper and improve (or at least preserve) its mechanical and thermal properties. One approach is to use the exceptional mechanical and thermal properties of nanosized carbon structures (carbon nanotubes,2,3 graphene4,5 or graphite nanoplatelets (GnP)) to refine a copper matrix.6−9 Carbon nanomaterials were beneficial in increasing the thermal conductivity of low conducting materials such as polymers.10−14 Several groups, however, showed that carbon nanotubes decrease the thermal conductivity of a copper matrix composite.15−17 The decrease is due to the poor dispersibility of nanotubes in copper, the weak bonding, and the high thermal interface resistance between the composite components. Finally, carbon nanotubes are excellent heat conductors in only one dimension. An alignment of nanotubes within the matrix is needed for enhancing the thermal conductivity. In carbon nanotube−polymer composites, alignment was achieved, for example, by infiltrating aligned multiwalled carbon nanotube forests with epoxy. This increased the thermal conductivity by a factor of 18 compared to epoxy18 but remained an order of magnitude below expectations. For metal−matrix composites, the infiltration method is difficult to apply. Khaleghi et al.17 used strong magnetic fields to align copper-coated carbon nanotubes © 2014 American Chemical Society

Received: April 16, 2014 Revised: May 14, 2014 Published: May 19, 2014 3640

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determined. The orientation order of composite systems can be efficiently measured by polarized Raman spectroscopy, see, for example, ref 20. Considering a single graphite nanoplatelet Raman scattering is allowed for an in-plane polarization of the incoming and scattered light but forbidden in perpendicular polarization direction.21 In our Raman experiment in which the setup is presented in Figure 2a, the in-plane direction of the fractured composite is oriented within the x−y-plane whereas the polarization is varied in the x−z-plane. Figure 2b shows the normalized intensity of the G-mode measured for M5, M25, and T80. The intensity of the G-peak has a maximum when the polarization of the light is along the in-plane axis of the composite (i.e., ε = 0, π, 2π) and a minimum when the polarization is normal to the x−y-plane. This qualitatively verifies the preferred orientation direction of the GnPs within the copper matrix as observed with SEM. Comparing the intensity ratio (Imin/Imax) of M5, M25, and T80 composites the statistical orientation toward the in-plane direction increases with platelet size with T80 platelets having the best alignment. We now quantitatively evaluate the intensities of Figure 2b. The intensity of the Raman active modes can be calculated using the selection rules for light scattering in crystals described elsewhere.22 With that one can predict the intensity of the E2g mode (G-peak) of graphite in dependence of the light polarization as well as the orientation of the graphite basal plane. To calculate the G-mode intensity as a function of internal GnP alignment and external polarization direction we transform the Raman tensor of the E2g phonon from the frame of an individual GnP into the lab frame. For a single graphite nanoplatelet with a certain orientation in the matrix the Gpeak intensity can then be calculated21,22

geometry on thermal properties of copper we prepared composites with graphite nanoplatelets having lateral dimensions ranging from l = 5 to 80 μm, see Supporting Information S1. The morphology of the nanoscale fillers and composites was verified with scanning electron microscopy (SEM). The microscopy data presented in Figure 1 exemplarily show the morphology of the

Figure 1. SEM study of the filler alignment in a copper matrix. Morphology of the graphite nanoplatelets (left) and the cross-section of the corresponding copper-graphite composites (right).

two nanoscale fillers M5 and T80 and the resulting composites. The SEM images on the left verify the different size of the two GnPs whereas the images to the right of Figure 1 present fractured surfaces of the consolidated copper−graphite composites. In the M5 based composites, no alignment is apparent upon inspection; T80, in contrast, already shows an orientation direction of the filling materials within the copper matrix. The preferred orientation is perpendicular to the force applied during spark plasma sintering. To analyze the influence of GnP alignment on the composite thermal properties, the degree of its alignment must be

IGnP(γ1 , γ2) ∝ ⟨e inΓ†x(γ1)Γ†y(γ2)R1Γx(γ1)Γy(γ2)eSC⟩2 + ⟨e inΓ†x(γ1)Γ†y(γ2)R 2Γx(γ1)Γy(γ2)eSC⟩2

(1)

where ein and esc are the polarization vectors of the incoming and scattered light, R1 and R2 are the Raman tensors of the E2g-mode, and Γx,y(γ1,2) are rotation matrices that rotate the Raman tensors about the x- and y-axis by the angle γ1 and γ2. To obtain the overall intensity we now integrate over all possible GnP orientations

Figure 2. (a) Measurement setup for polarized Raman spectroscopy. (b) G-mode intensity for M5, M25, and T80 composites and HOPG as a function of the angle ε between the polarization of the incoming light and the composite in-plane axis. The measured data (symbols) are fitted to eq 3 (solid lines). 3641

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Figure 3. Measurements of anisotropic thermal diffusivity in GnP-based copper composites. (a) Through-plane and in-plane diffusivity as a function of filler fraction for different graphite nanoplatelets (symbol size indicates measurement accuracy). (b) Anisotropy factor of thermal diffusivity. (c) Densities of the sintered Cu-GnP composites.

Itot ∝

∬ g(γ1)g(γ2)IGnP(γ1, γ2)dγ1 dγ2

thermal diffusivity of the M5, M25, and T80 composites as a function of GnP concentration. For all three composites, the inplane diffusivity is higher than the through-plane diffusivity. In both directions α lies below the reference of pure copper (αCu = 105 mm2s−1) and decreases with increasing filler concentration. Only for the T80 composites the in-plane thermal diffusivity is approximately constant over the entire concentration range. It lies just below copper, that is, around 97 mm2s−1, which is surprising for the large GnP volume fractions of 30%. In previous studies, agglomeration of the filling material was one of the main reasons for values much lower than pure copper17 comparable to copper composites with thermally low-conducting filling materials.23 The high-energy ball milling likely distributed the GnPs evenly within the copper powder before consolidation. Figure 3b shows the anisotropy factor (the ratio of in-plane over through-plane thermal diffusivity) of the three composite materials. With increasing lateral platelet size and filler concentration, the anisotropy increases, which is in very good agreement with SEM and Raman scattering. The bulk density of the composite materials was determined by Archimedes’ principle and is compared to the expected density determined by rule of mixture presented in Figure 3c. By using spark plasma sintering a densification between 96 and 99% was achieved. The measured densities were used to calculate the thermal conductivities (see Methods) that consequently follow the same trend as the thermal diffusivities of the composites. We now discuss why the thermal conductivity decreased in the composites despite adding highly conducting nanocarbon fillers. An increasing porosity with filling fraction would explain the decreased conductivity. However, all composites are almost fully densified (see Figure 3b). To understand the mechanism behind the thermal conductivity enhancement we use the model developed by Nan et al.24 within the effective medium approximation. It describes the effect of geometry, concentration, thermal conductivity, and orientation of the filling material as well as the thermal interface resistance between matrix and filler on the TCE of the composite. The thermal conductivity of the composite with respect to its symmetry axes is given by24

(2)

where g(γ1,2) is the angle distribution for the rotation angles γ1 and γ2. For a random distribution of the GnPs, one expects a constant intensity of the G-peak when varying the polarization angle ε. For perfectly aligned GnPs (i.e., γ1 = γ2 = 0) the intensity has a maximum for the in-plane polarization (ε = 0, π, and 2π); it is zero for ε = π/2, 3π/2. If we assume a normal distribution of the angles γ1 and γ2, one can find a standard deviation σ for all possible intensity dependences between random and full alignment. As a reference, we measured highly oriented pyrolytic graphite (HOPG) were the graphite layers are fully aligned. As presented in Figure 2b one can see that the Raman intensity of the G-peak is not zero for polarization perpendicular to the layers. This is a result of the rough surface of the fractured cross-section as well as introduced disorders of the graphite planes at the point of the fracture due to breaking the material. Furthermore, the finite collection angle of the laser using a NA = 0.25 objective leads to nonzero intensity for ε = π/2, 3π/2. To take this into account we modify eq 2 by introducing the additional intensity contribution I0 which leads to the corrected intensity for HOPG Itot ∝

∬ f (γ1, σ )f (γ2 , σ )IGnP(γ1, γ2 , γ3)dγ1 dγ2 + I0

(3)

From HOPG we obtain I0, thus the standard deviation σ remains the only free parameter to match the Raman intensity for the three composite types. Using eq 3 we find σ = 0.70 for M5, 0.60 for M25, and 0.47 for T80 composites. We will later use the quantitative measure of alignment to model the thermal conductivity enhancement (TCE). The preferred orientation direction of the GnPs within the copper matrix observed by SEM and polarized Raman clearly indicates the anisotropic thermal properties of the composites. Subsequently, the measurements of the thermal diffusivity, α, were carried out with the laser flash technique (Netzsch). In addition to the conventional measurement configuration to measure the through-plane diffusivity, we used a special sample holder, which allows determining α in the in-plane direction, see Supporting Information S1. Figure 3a presents the average k11 = k 22 = km

2 + f [β11(1 − L11)(1 + ⟨cos2 θ ⟩) + β33(1 − L33)(1 − ⟨cos2 θ ⟩)] 2 − f [β11L11(1 + ⟨cos2 θ ⟩) + β33L33(1 − ⟨cos2 θ ⟩)]

(4)

and 3642

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Figure 4. Calculated thermal conductivity enhancement for M5, M25, and T80 composites (solid and dashed lines) depending on the filler fraction in comparison with the experimental data (symbols). The orientation parameters as well as the fitting parameter Rk are given in the corresponding graphs. k 33 = km

1 + f [β11(1 − L11)(1 − ⟨cos2 θ⟩) + β33(1 − L33)⟨cos2 θ⟩] 2

ments, we predict that a further increase of the lateral size of GNP will lead to an in-plane thermal conductivity above pure copper. In addition to the geometrical factor, the inclusion of platelike filler with higher intrinsic thermal properties, like graphene sheets (GS) with k ≈ 2000−5000 Wm−1K−1 28 could be another way to increase TCE of copper. However, practical application of graphene fillers in metal composites could be limited due to the following facts: (i) GS are difficult to produce inexpensively on an industrial scale; (ii) in case of chemically derived graphene, the lateral dimensions of graphene sheets are limited to 30 μm regardless the size of the starting graphite particles;29 (iii) due to its “softness” in the out-of-plane direction it is likely that graphene sheets would rather fold and wrap the metal powder than align in the matrix. Consequently, GnPs show a high potential for the production of high-performance metal composite materials. In conclusion, we proposed a simple approach to control the alignment of the graphite nanoplatelets in a copper matrix. Quantifying the relationship between the alignment and nanoplatelets geometry, polarized Raman spectroscopy measurements, we provided a way to control the alignment by tailoring the lateral size of the GnP. The effect of filler size, thus alignment, is strongly reflected in the anisotropic thermal behavior of the composites; k along the flake alignment direction is found to be up to five times higher than perpendicular to it. Our experimental data together with the EMA modulations suggest that a further increase of the GnP lateral size may result in thermal conductivity above pure copper. On the other hand, the low Rk = 1.0 × 10−9 m2KW−1 is found to be not a limiting factor for achieving high TCE. Such metal matrix composites with superior thermal conductivity have great potential in directed heat dissipation applications. Methods. Sample Preparation. Three types of graphite nanoplatelets from different commercial sources with lateral sizes ranging from 5 (M5), 25 (M25), and 80 μm (T80) were used in this study. The copper powder (3 μm dendritic, Sigma-Aldrich) and GnPs were weighted according to precalculated proportions with GnP concentrations of 2, 5, 7, 20, and 30 vol%. The mixing of the two components was realized by planetary ball-milling (Fritsch) at 250 rpm in rotary speed and 3 h in duration. Cu-GnP discs of 25 mm in diameter and 1 mm thickness were obtained from the composite powders by spark plasma sintering in a Dr. Sinter Lab Jr. 211Lx SPS apparatus (Fuji Electronic Industrial Co.). Spark plasma sintering is performed by sending a pulsed high direct current through the punch-dye-sample assembly that creates high local temperatures and allows high heating rates. The sintering temperature was set to 600 °C, obtained with a heating rate of 100 K min−1. The annealing time

2

1 − f [β11L11(1 − ⟨cos θ⟩) + β33L33⟨cos θ⟩]

(5)

Further details can be found in Supporting Information S3. The statistical orientation of the GnP particles is represented by ⟨cos2 θ⟩ that equals one-third for totally randomly oriented GnP particles and becomes one for fully aligned fillers. It is given by24

∫ φ(θ)cos2 θ sin θ dθ ⟨cos θ ⟩ = ∫ φ(θ) sin θ dθ 2

(6)

where θ is the angle between the symmetry axes of the composite and the GnP particles and φ(θ) describes the statistical distribution of θ. This statistical distribution was obtained from the Raman spectra. To calculate k11 and k33 for M5, M25, and T80 composites with eqs 4 and 5, respectively, we use km = 340 Wm−1 K−1 as the thermal conductivity of the matrix, kGnP11 = kGnP22 = 1500 Wm−1K−1, kGnP33 = 15 Wm−1K−1 19 as the in-plane and through-plane conductivity of the GnPs and the GnP dimensions. The thermal interface resistance Rk is the fitting parameter to match the experimental data. The calculations, displayed in Figure 4, show an excellent agreement between eq 3, 4, and 5 and the experimental observations. The Kapitza resistance obtained from the data in Figure 4 is very similar for the three composites with Rk = 1.0 × 10−9 m2KW−1. This value is consistent with the analysis of coppergraphene composites using acoustic and diffuse mismatch models (Rk = 0.7 × 10−9 m2KW−1)25 and a study of the inplane conductivity of copper-graphene composites, Rk = 0.3 × 10−9 m2KW−1.26 However, the found Kapitza resistance is 1 order of magnitude lower than the thermal interface resistance measured directly between Al, Au, Cr, or Ti and graphite.27 Thus, using copper in metal−nanocarbon composites is beneficial with regard to overall thermal performance. The Kapizta resistance obtained from our fits is comparably low, hence the interface conductance is high. Compared to the intrinsic thermal resistance of, for example, T80 GnPs in the in-plane direction of ∼5 × 10−8 m2KW−1 the interface resistance is 1 order of magnitude lower. Thus, the total thermal resistance is not dominated by the Kapitza resistance. This indicates that the Kapitza resistance is not a limiting factor for a high thermal conductivity of a copper−GnP composite. The EMA calculations show that the improvement of the alignment of the fillers is the major factor for achieving high in-plane thermal conductivity of the composite, see Supporting Information S3. On the basis of these findings and the quantitative relationship between the flake size and degree of alignment obtained from Raman measure3643

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was set to 5 min. A pressure of 40 MPa was applied at the beginning of the process and released after the sample cooled down to room temperature. The entire process was carried out at vacuum pressure below 5 Pa. The powder materials after ball milling and fractured structures of the composites after sintering were observed using scanning electron microscope (SEM Hitachi SU-8030). Measurements. The light flash method was used to measure thermal diffusivity (α) with the Netzsch LFA447 NanoFlash. Both the in-plane and through-plane diffusivity were measured on the same sample using a special sample holder.30 The thermal conductivity k was calculated from k = αc p ρ

(7)

ASSOCIATED CONTENT

S Supporting Information *

Details on used materials as well as consolidated composites such as dimensions and morphology; additional information for the measurement of thermal diffusivity; details on Raman intensity calculations as well as EMA modulations for thermal conductivity enhancement. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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with cp being the specific heat obtained by rule of mixture and ρ bulk density of the sample (see text discussing Figure 3c). Polarized Raman spectroscopy was carried out on a fractured cross-section of the consolidated composites with various GnP concentrations using an excitation wavelength of 532 nm with a power of 1 mW to avoid laser heating. The spectra were recorded using a Horiba T64000 triple monochromator. The incoming light as well as the backscattered light is focused by a 10× objective. The polarization of the incoming and scattered light was chosen parallel to each other. The angle between the polarization direction and the sample normal was rotated with a λ/2 wave plate (see Figure 2a).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: izabela.fi[email protected]. Tel.: +49 30 838 54294. Fax: +49 30 838 56081. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. A.B. wrote the manuscript, led the thermal data analysis, EMA modulation and Raman calculations, and contributed to sample preparations; B.B. contributed to sample preparations and thermal measurements; P.K. performed the polarized Raman measurements; I.F. contributed to the manuscript preparation, performed SEM measurements, and contributed to thermal data analysis; and S.R. contributed to the manuscript preparation, contributed to Raman calculations and data analysis Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Federal Ministry of Education and Research, BMBF (Grant VIP 0420482104) for financial support. 3644

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