Engineering interfaces in carbon nanostructured mats for the creation of energy efficient thermal interface materials

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journal homepage: www.elsevier.com/locate/carbon

Engineering interfaces in carbon nanostructured mats for the creation of energy efficient thermal interface materials Ronald J. Warzoha, Di Zhang, Gang Feng, Amy S. Fleischer

*

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:

One of the few remaining opportunities to increase heat dissipation in IC circuitry is to sub-

Received 25 January 2013

stantially decrease the thermal interface resistance between solid–solid contacts from

Accepted 14 May 2013

source to sink. In this study, heterogeneous nanostructured mats (1–100 lm thick, ran-

Available online 23 May 2013

domly oriented networks of nanostructures) are synthesized for use as thermal interface materials (TIMs). Recent studies suggest that mats composed entirely of carbon nanotubes (CNTs) or graphite nanofibers (GNFs) can act as thermal insulators due to significant phonon scattering at interfaces. In this work, graphene nanoplatelets (xGnPs) with high surface areas are included in CNT and GNF mats in order to increase the contact area between nanostructures and mitigate phonon scattering. Results indicate that an increase in contact area between nanostructures increases the thermal conductance across nanostructure networks by nearly an order of magnitude. Additionally, a study of the surface topography of CNT and GNF mats using atomic force microscopy (AFM) indicates that they are able to conform well to the asperities between rough, mating surfaces. Thus, an increase in contact area between CNT junctions not only produces a thermally conductive network, but also increases the reliability of a CNT mat TIM by avoiding common issues associated with the use of wetting agents. Ó 2013 Elsevier Ltd. All rights reserved.

1.

Introduction

Thermal management techniques for electronics applications are fast approaching their performance limits as the pace of technology scaling of integrated circuitry (IC) continues unabated. However, one realm in which significant improvements can still be achieved is at component interfaces. At these interfacial regions, mismatched surface asperities create micron-sized pockets of air between solid components. Due to the very low thermal conductivity of air (kair = 0.026 W/m K at 300 K [1]), these surface asperities result in a sharp temperature difference at the interface. In order to reduce the temperature across the interface, thermal engineers rely on

the insertion of a highly deformable, thermally conductive material (or thermal interface material (TIM)) between the mating surfaces. In an effort to develop novel TIMs, researchers have recently turned their attention to the implantation of highly conductive carbon nanostructures into ‘‘wetting agents’’ [2–8]. ‘‘Wetting agents’’, like PCMs and thermal greases, are typically used to connect mating materials because they are able to conform well to the material’s surface asperities. Carbon nanotubes (CNTs) and nanofibers (CNFs) have been of particular interest for use in TIMs due to their high intrinsic thermal conductivities and low densities [9– 11]. Few layer graphene (FLG) has also been of interest lately as a filler material for thermal interface applications [6]. Bal-

* Corresponding author. E-mail address: [email protected] (A.S. Fleischer). 0008-6223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carbon.2013.05.028

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andin [6] presents an excellent review of the thermal transport mechanisms in low-dimensional carbon allotropes and nanomaterials, specifically citing FLG as a promising candidate for future TIMs due to its low dimensionality and low phonon scattering as the number of atomic carbon layers (n) approaches 1. In an attempt to reveal the promising use of graphene in TIM applications, Shahil and Balandin [12] embedded liquid-phase exfoliated multilayer graphene at volume fractions ranging from 1.5% to 10% in an epoxy and found that its thermal conductivity is enhanced by a factor of 25. The authors found that the graphene-based nanocomposites outperformed nanocomposites with carbon nanotubes or metal nanoparticles due to graphene’s high aspect ratio and good conformability to the surrounding matrix material, confirming the claims made in [6]. The simplest, safest and least expensive way to utilize carbon nanostructures in TIMs is to fabricate a randomly oriented network of nanostructures [13,14]. However, preliminary results suggest that the inclusion of randomly oriented nanostructure networks does not significantly increase the thermal transport across the aforementioned wetting agents [15]. This is primarily due to the high rate of phonon boundary scattering that occurs at nanostructure interfaces in large nanostructure networks, which results in a thermally insulating material [16] (depending on the thickness of the mat, the thermal transmissivity through it may even be lower than through the mating materials in the absence of a TIM). Phonon boundary scattering largely occurs due to the weak van der Waals bonding (or adhesion energy) between nanostructures [17,18]. However, recent theoretical studies also suggest that the low interfacial area between cylindrical nanostructures results in a significant increase in boundary scattering at nanostructure junctions [18,19]. To date, these theoretical studies represent the only substantial investigations into the effect of contact area on thermal transport in nanostructure networks. In this study, highly conductive carbon nanostructures are randomly ‘‘woven’’ into thin mats (1–100 lm thick, randomly oriented nanostructure networks) for use as TIMs and are thermally characterized via experiment. The mats are fabricated with and without exfoliated graphite nanoplatelets (xGnPs) in an effort to augment the thermal conductance across nanostructure interfaces. An assessment of the mats’ ability to conduct heat across a set of copper reference bars, designed to emulate the components used in thermal management systems, is made using a cut-reference bar apparatus in accordance with ASTM D5470. Additionally, the ability of the mats’ surfaces to conform to the asperities of the copper interfaces is made using atomic force microscopy (AFM). Highly conductive microstructures and/or nanostructures have long been used to improve the thermal conductivities of different types of TIMs. Typically, nanostructures are used at low concentrations in order to improve the thermal conductivities of so-called ‘‘wetting agents’’, which conform well to micron-sized asperities at interfacial regions [20–22]. These ‘‘wetting agents’’ include thermal greases, phase change materials (PCMs), elastomers, adhesives and tapes. In the absence of any highly conductive filler material(s), each of the aforementioned ‘‘wetting agents’’ typically performs poorly in application due to their inferior thermal properties (less

than 1 W/m K [23]). Additionally, many of these materials suffer from ‘‘dry out’’, ‘‘pump out’’ and ‘‘hardening’’ after repeated thermal cycling (an excellent review of these issues can be found in [24]). Thus, it is desirable to fabricate a TIM that has a high intrinsic thermal conductivity and avoids the common complications associated with conventional filler materials. Carbon-based nanostructures, like carbon nanotubes (CNTs) and graphite nanofibers (GNFs), are light-weight and known to exhibit excellent thermal properties [9–11]. They are therefore considered to be excellent candidates for the replacement of conventional filler materials in TIMs. The high thermal conductivity of many carbon-based nanostructures is primarily a function of the large phonon mean free path across the strong sp2 bonds in networks of carbon atoms [25]. Therefore, CNTs are used most effectively in interfacial regions when they are vertically oriented and not in contact with one another, so as to limit any scattering mechanism that may inhibit phonon transport through the TIM [26,27]. Xu and Fisher [28] used a chemical vapor deposition (CVD) method to grow vertically aligned nanotube ‘‘forests’’ on a silicon die. The silicon die was used to emulate the surface of a conventional integrated circuit chip. The authors found that the nanotube forests performed well against commercial TIMs, including a highly conductive paraffin PCM and a thermal grease. They also found that when the nanotube forest was saturated with a PCM, a thermal contact resistance of less than 6 mm2 K/W was achievable between substrates with average surface roughness values (Ra) of 0.02 lm (silicon die) and 1.4 lm (oxygen-free high conductivity copper). However, in order to attach the nanotube forest to the silicon die, the assembly was subjected to very high temperatures (upwards of 880 K). Exposure to such high temperatures can potentially result in significant damage to the die. Additionally, the vertical nanostructures are prone to significant mechanical deformation at the pressures typically encountered in application, leading to the formation of randomly oriented, contacting nanotubes [29]. It is therefore anticipated that phonon boundary scattering increases as a function of applied pressure, potentially mitigating the thermal enhancement caused by any reduction in bond layer thickness and eliminating the benefits associated with vertically aligned carbon nanotube arrays in application. At the moment, the growth process is also prohibitively expensive to commercialize. A simpler, cheaper and safer way to utilize highly conductive carbon nanostructures in TIMs is to develop randomly oriented networks of nanostructures [30,31]. Random networks of nanostructures can be synthesized through a vacuum filtration process that is both cheap and simple to operate. This fabrication process prevents the major components (silicon die, copper heat spreader, etc.) from being damaged during production and has the potential to allow for the direct attachment of the nanostructured mat onto any geometry through the use of advanced attachment techniques (electrostatic deposition, atomic layer deposition, etc.). Unlike the fabrication method used by Xu and Fisher [28], care is not taken to ensure that there is minimal contact between nanostructures (in fact, nanostructure contact is required for mat stability). As has been mentioned, this results in additional

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interfaces over which boundary scattering of phonons is likely to occur. Thus, the challenge for thermal engineers is to reduce the thermal boundary resistance between individual nanostructures in larger, randomly oriented networks. Such an accomplishment would allow for the creation of practical CNT mats that exceed the performance and reliability of current state-of-the-art TIMs. Prasher et al. [17] first characterized the thermal properties of multi-walled and single-walled CNT mats in the crossplane direction. In all cases, the authors found that the mats possessed a thermal conductivity of less than 0.2 W/m K. Similar results were reported by Yue et al. [32], who used a steady-state electro-Raman-thermal (SERT) technique to characterize two MWCNT mats. Other research groups have found a two order of magnitude increase in the thermal conductivity of CNT mats in their in-plane direction [33–35]. Despite these encouraging results, the nanostructure networks remain sufficiently poor thermal conductors relative to the intrinsic thermal conductivity of individual carbon nanostructures, of which the mats are composed. These studies confirm that, despite the high intrinsic thermal conductivity of individual nanostructures, the thermal boundary scattering at nanostructure junctions significantly reduces phonon migration in nanostructure networks, which results in a bulk nanostructured mat that behaves as a thermal insulator. One way to reduce the thermal boundary resistance between nanostructures is to increase the adhesion energy at their interface [36–38]. Yang et al. [16] synthesized MWCNTbased nanostructured mats to use as TIMs for the thermal management of IC circuitry. The authors used a sintering technique to ‘‘tune’’ the thermal conductivity of nanostructured mats in the cross-plane direction. To accomplish this, the mats were subjected to temperatures between 500 and 1500 K. The mats were exposed to the aforementioned temperatures in an effort to increase the adhesion energy at interfacial regions. Their results indicate that the thermal conductivity of the nanostructured mats can be increased by as much as an order of magnitude when subjected to such temperatures. However, the authors do not account for the effect of sintering on the mechanical properties of the nanostructured mats. Research investigating the effect of sintering temperature on the hardness and brittle fracture of nanostructured mats indicates that they become increasingly brittle as a function of sintering temperature [39]. Accordingly, mats that are sintered are thought to be unsuitable for use in TIM applications, particularly when moderate to high clamping pressures are used to connect devices. An alternative, less studied method to reduce the thermal boundary resistance between nanostructures is to increase the contact area between them. In 2009, Xu and Buehler [18] conducted a preliminary theoretical investigation to examine the effect of contact area and adhesion energy on interfacial thermal transport between randomly oriented networks of nanotubes. In their study, the authors reveal that the interfacial area between contacting nanotubes is as important as the adhesion energy between CNT interfaces when determining the thermal boundary resistance at the junction. To date, there is limited experimental evidence to support this claim. In one study, Chen et al. [15] found that nanostructured mats performed better as TIMs with the incorporation of larger

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diameter CNTs. The authors found that small diameter (10 nm) MWCNT mats produced a thermal impedance of 1.58 cm2 K/W, while large diameter (50 nm) MWCNT mats produced a thermal impedance of 0.53 cm2 K/W. Although the authors do not acknowledge the primary reason for this discrepancy, it is clear from these results (and the supporting microscopy) that the increased contact area between large diameter nanostructures results in less boundary scattering at CNT–CNT junctions, particularly when one considers the reduction in thermal transport across larger diameter MWCNTs due to the presence of additional graphene layers. In order to significantly increase the contact area between nanostructures while maintaining the high intrinsic thermal conductivity of CNTs and GNFs, exfoliated graphite nanoplatelets (xGnPs) with a high surface area are used to produce ‘‘thermal highways’’ in this study. It should be noted that while a homogenous mat composed entirely of xGnP would contain nanostructures that are in very good contact with one another, an advanced and expensive sintering technique must be used to obtain sufficient mechanical stability in the absence of an interwoven network [40]. Thus, cylindrical nanostructures are required for sufficiently flexible and mechanically stable nanostructured mats. In this study, heterogeneous nanostructured mats that contain both cylindrical inclusions (SWCNTs, MWCNTs and CNFs) and high surface area inclusions (xGnP) are synthesized. The xGnP inclusions are used to create novel carbonnanostructured TIMs that exhibit fewer issues related to thermal boundary resistance between individual nanostructures. Other advantages include low mat surface roughness and no need for a wetting agent, avoiding issues such as ‘‘dry out’’ and ‘‘pump out’’ during operation. The nanostructured mats are thermally characterized using a method defined by ASTM D5470. A quantitative assessment of the mats with and without a wetting agent (phase change material) is presented. A qualitative observation of the nanostructured mats’ ability to conform to the asperities of copper interfaces is made via the generation of three-dimensional topographic images of their surfaces by atomic force microscopy (AFM).

2.

Experimental methods

2.1.

Sample preparation

In this study, nanostructured mats were created using an acetone vapor filter-decomposition fabrication process. Nanostructures were dispersed in an aqueous solution with the aid of a sonic horn and a surfactant (Triton x-100, 1 lL). The resulting solution was vacuum filtrated onto a 47 mm mixed cellulose ester (MCE) filter (Sterlitech) and left to dry for 1 h. The mat was then soaked in deionized water twice for 20 min and subsequently in methanol for an additional 20 min in order to remove any excess surfactant. This process is similar to the method used for the fabrication of homogenous nanostructured mats in [30,31]. Typically, the MCE filter is dissolved in an acetone bath in order to obtain a freestanding, homogenous mat. However, the use of an acetone bath prohibits the incorporation of a secondary set of nanostructures within the mat and thus is unsuitable for this study.

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This is primarily due to the weak adhesion between the dissimilar nanostructures, coupled with the rapid infiltration of acetone into the porous nanostructure network. Additionally, the use of a soaking process prohibits the formation of nanostructured mats under 100 lm thick, which is undesirable for the creation of sufficiently thin thermal interface materials. Instead, a ‘‘delicate’’ processing technique is developed here to dissolve the MCE filter in such a way that the fabrication of freestanding, heterogeneous mats with thicknesses ranging from 1 to 100 lm is achievable. In this case, the mat-filter assembly is deposited onto a stainless steel mesh (34% porosity) and suspended above an acetone-based solution. Above the mat-filter-mesh assembly rests a constant temperature, steel plate condenser (T = 20 °C) regulated by a thermal bath/cold plate assembly. After the apparatus is fully assembled, the acetone is vaporized and allowed to condense on the steel plate. The condensed acetone then drops onto the filter in order to wash away any filter remnants that have not been disintegrated via exposure to the vaporized acetone. In order to minimize the impact force of the acetone droplets on the mat, the mat-filter-mesh assembly is suspended from a height of 0.5 mm below the condenser. The filter requires 30 min of exposure to acetone vapor in order to fully dissolve. After the filter is fully dissolved, the mat is left to dry in air. During the drying process, the nanostructure network naturally peels away from the stainless steel mesh and a freestanding mat remains. An example of a freestanding, homogenous HGNF mat (on its stainless steel mesh) is shown in Fig. 1. The nanostructured mats fabricated in this study feature various combinations of MWCNTs (US-nano), SWCNTs (USnano), herringbone graphite nanofibers (HGNF), and xGnP (XG Sciences). The HGNF were synthesized in-house via the process described in [41–44]. Three of the heterogeneous samples are saturated with a paraffin phase change material (IGI 120A Paraffin Wax) in order to determine whether a wetting agent significantly enhances thermal transport across the mat when xGnP are included. The geometry and thermal properties of each nanostructure are listed in Table 1. In Table 1, the properties for the xGnP, SWCNTs and MWCNTs were provided by the manufacturer (xGnP: XG Sciences, CNTs: US-nano), and the properties for the synthesized HGNF and paraffin wax were obtained through experimental

measurements [46,48]. Where possible, the thermal conductivity for each type of nanostructure was obtained from experimental data available in the literature [9,25,45]. The thermal conductivities of the nanostructures are provided as a reference and are compared to graphene [6] in order to give the reader a sense of their magnitude (Table 2). Clearly, the different nanostructures listed here have drastically different intrinsic thermal conductivities. This is primarily a function of the dimensionality and bonding strength between the carbon atoms and graphene layers within the nanostructures. The different nanostructures listed in Table 2 are thus used in order to determine the effect of other parameters on thermal transport in networks of nanostructures. For instance, the intrinsic thermal conductivities of SWCNTs and xGnP are shown to be the same order of magnitude. Thus, if a the thermal resistance across an SWCNT mat drops significantly when it also contains xGnP, then the thermal augmentation must be caused by a phenomenon unrelated to the nanostructures’ intrinsic thermal conductivity. Similarly, the intrinsic thermal conductivity of the HGNFs is significantly lower than the both the SWCNTs and MWCNTs. Thus, if the HGNF mats perform as well as the SWCNT or MWCNT mats in application, it will also be clear that intrinsic thermal conductivity is not the dominant mechanism governing thermal transport across the mat. The nine samples created for this study are shown in Table 2. In addition to the nine mats tested below, MWCNT mats with varying weight concentrations of xGnP (9–54% in 9% increments) were tested in order to confirm that the contact area between nanostructures is a dominant thermal transport mechanism in networks of nanostructures. In samples 2, 3, 5, 6, 8 and 9, the xGnP are added at a weight fraction of 54%. This was experimentally found to be the maximum concentration of xGnP within nanostructured mats in order to maintain mechanical stability. The mat thickness can be precisely controlled during the fabrication process by altering the weight fraction of nanostructures. In this study, the total weight of the nanostructures in each mat was held constant. Finally, certain films were impregnated with the paraffin PCM using a vacuum oven according to [49].

2.2.

Morphology of interwoven mats

A Hitachi S-4800 Field Emission Scanning Electron Microscope (SEM) is used to characterize the morphologies of the interwoven nanostructured mats. A qualitative observation of the mechanical contact between nanostructures can be made to better identify the dominant thermal transport mechanisms within the nanocomposite mats. SEM micrographs are also used to determine the saturation state of the nanostructured mats when a PCM is infiltrated into their porous network.

2.3. Measurement topography

Fig. 1 – Homogenous, HGNF nanostructured mat.

of

nanostructured

mat

surface

The surface topography of the nanostructured mats is measured using an Agilent 5500 Atomic Force Microscope (AFM). The measurements made by the AFM include qualitative

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Table 1 – Geometry and physical properties of materials.

*

Material

Diameter/ thickness (nm)

Length/ radius (lm)

Specific surface area (m2/g)

Thermal conductivity (W/m K)

Melt temperature (°C)

SWCNT MWCNT xGnP HGNF Graphene IGI 120A Wax

1–2 50–80 6–8 2–1000 <20 nm –

5–30 10–20 25 10–50 0.5–5 –

380 40 120–150 37 [46] 650–750 –

3000 [9] 650–830 [25] 3000 [45]* 10–25 [47] 2000–5000 [6] 0.2 [48]

– – – – – 56

Radially.

Table 2 – Composition of mats created for this study. Sample number

Material

Concentration of xGnP (% by weight)

1 2 3 4 5 6 7 8 9

SWCNT SWCNT/xGnP SWCNT/xGnP/PCM MWCNT MWCNT/xGnP MWCNT/xGnP/PCM HGNF HGNF/xGnP HGNF/xGnP/PCM

0 54 ± 1.2 54 ± 3.6 0 54 ± 3.7 54 ± 4.2 0 54 ± 3.7 54 ± 4.2

and quantitative measures of surface roughness. A silicon, pyramidal tip with a 6 nm radius of curvature is used to measure the mats’ surface textures in tapping mode. Tapping mode atomic force microscopy is widely used as a non-destructive, high-resolution imaging technique for soft or fragile materials, and has previously been used to produce extremely high-resolution images of SWCNT mats, which have constituent particles with diameters on the order of 1–2 nm [50–52]. For this study, a tip with low stiffness (<1 N/m) is used to maintain a low tip-sample force (i.e. the force exerted on each individual nanostructure during testing). The set-point amplitude was chosen to be as close to the amplitude of the probe when freely oscillating (2 V) and the scanning rate was programmed at less than 1 Hz for all sample measurements. Gwyddion, an open-source AFM platform, is used to produce three-dimensional topographic images of the mats’ surfaces in order to qualitatively and quantitatively determine how well the mats conform to the asperities of the copper reference bars. For each mat, five different regions are mapped and their topographical statistics are averaged.

2.4.

Measurement of thermal interface resistance

The primary focus of this work is to assess the impact of increased contact area between nanostructures on the performance of heterogeneous, nanostructured mats as thermal interface materials. The mats are evaluated as TIMS between mating copper bars per the testing standard identified in ASTM D5470. Copper is the preferred interface due to its widespread use in electronics cooling applications [22]. The thermal resistance across the interface of the copper substrates is experimentally determined as a function of applied pressure using a cut-reference bar apparatus (Fig. 2).

Fig. 2 – Schematic of cut-reference bar apparatus for the measurement of thermal interface resistance across nanostructured mats.

The thermal interface resistance measured by the equipment shown in Fig. 2 is defined by RTIM according to Eq. (1) [53]. RTIM ¼

thickness þ Rc1 þ Rc2 kTIM

ð1Þ

In Eq. (1), it can be seen that the total thermal interface resistance, RTIM, is a function of the thermal conductivity of the TIM, its in situ thickness under pressure, and the contact resistance of the two bounding surfaces (Rc1 and Rc2). While each individual parameter defined in Eq. (1) contributes substantially to the performance of a TIM, its overall performance is typically evaluated using RTIM only [23,28,53]. In this work, RTIM is measured in order to determine the pertinent thermal transport mechanisms across networks of

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nanostructures. RTIM has typically been used as the major parameter for comparing the performance of nanomaterial TIMs to current state-of-the-art TIMs in application [23] and is of great interest to many fields of study. As such, the cutreference bar apparatus, which has been standardized by ASTM, is utilized for the measurement of RTIM here. The equipment shown in Fig. 2 is designed to transfer heat along the reference bars in one dimension. In this system, a ‘‘hot plate’’ is heated by a constant flow-rate, constant temperature ethylene–glycol loop. A constant heat flow-rate, q, is maintained through the set of reference bars via a ‘‘cold plate’’ opposite the ‘‘hot plate’’, whose temperature is also controlled using a constant flow-rate, constant temperature ethylene–glycol loop. The hot plate is located on top of the upper reference bar and the cold plate below the bottom reference bar in order to ensure that unstable buoyancy forces are not able to occur and thus natural convection is completely avoided during testing, creating 1-D heat flow by conduction only through the mat. Each of the constant temperature plates is made of oxygen-free, high conductivity copper (OFHC) and contains a three-pass fluid loop (6.35 mm diameter) from a constant temperature bath. The oxygen-free high conductivity copper reference bars are cylindrical and have a cross-sectional area of 5.07 cm2. A 10.16 cm thick Wrap-Onâ fiberglass insulation material (kinsulation = 0.14 W/m K) is used to cover the equipment during testing in order to minimize convective and radiative heat losses. The interface pressure on the mats is controlled using a pneumatic piston. The thermal resistance across the interface is calculated from data obtained by a series of thermocouples embedded within the reference bars. The thermocouples are calibrated using a constant temperature bath and a NIST calibrated thermometer over a temperature range of 0–110 °C. Three thermocouples are inserted into the center of each reference bar at a spacing of 12.7 mm in order to obtain a linear temperature gradient from source to sink. The thermal interface resistance across the TIM is obtained via Eqs. (2)–(6), in accordance with ASTM D5470. RTIM ¼

DT  Asample Q

ð2Þ

Q ¼ ðQ top þ Q bottom Þ=2

ð3Þ

Q top ¼ kOFHC  Asample  ðslopetop Þ=DL

ð4Þ

Q bottom ¼ kOFHC  Asample  ðslopebottom Þ=DL

ð5Þ

 DT ¼

T3 

   DL DL ðT1  T3 Þ  T4  ðT6  T4 Þ d3 d4

ð6Þ

In Eq. (3), Qtop and Qbottom represent the heat flow through the top and bottom reference bars, respectively. In Eqs. (4) and (5), kOFHC is the thermal conductivity of oxygen-free, high conductivity copper, Asample is the cross-sectional area of the nanostructured mat, slopetop and slopebottom are the slopes of the linear temperature gradients along each reference bar and DL is the distance between thermocouples 1 and 2, which is the same as the distance between thermocouples 2 and 3, 4 and 5 and 5 and 6 (6.35 mm). In Eq. (6),

d3 and d4 represent the distances from the edge of the copper reference bar to thermocouples 3 and 4, respectively (12.7 mm). Thermocouples 1 through 6 are denoted as T1, T2, T3, etc. The thermal interface resistance across each mat is normalized (Rn) against the average root mean square (RMS) surface roughness, rRMS, of the copper reference bars in addition to the thickness of each mat. This is done to compare mats with different thicknesses. The mat thickness is precisely controlled during the fabrication process by altering the weight fraction of nanostructures. The total weight of the mat is held constant, yielding mats with slightly different thicknesses. Thus, a normalizing factor must be used in order to make accurate comparisons between results. The normalizing factor is given in Eq. (7). Rn ¼

DT  Asample rRMS  Q tmat

ð7Þ

In Eq. (7), Rn represents the normalized thermal interface resistance, rRMS represents the average RMS surface roughness of the copper reference bars and tmat represents the in situ thickness of the nanostructured mat. A strict comparison of thermal transport across each TIM using Eq. (2) is meaningless if the TIM thicknesses are different according to Eq. (1). Thus, Eq. (7) is used in this analysis for comparing the thermal transport across each of the TIMs fabricated for this work due to the different thicknesses of each CNT- or CNF-based mat. It is important to note that Rn is strictly used as a comparative parameter and does not represent RTIM, which is commonly used to evaluate TIMs in application. However, in order to evaluate the practical performance of each of the CNT- or CNF-based mats in application, RTIM as a function of TIM thickness is evaluated and presented as a final result in this work. The initial thickness of each mat was determined using a scanning electron microscope (SEM). To do this, each mat was inserted into a clamping stage at a constant pressure and its thickness was measured using SEM. For confirmation of the measurement of the mat thicknesses in situ, thicker mats (>1 mm) were fabricated and their deformation rates measured with a micrometer while sandwiched between two rectangular copper blocks at the pressures used in this study. The applied pressure was controlled with a pneumatic piston in the same way it is controlled in the reference bar apparatus. The deformation rates were used to approximate the thickness of each thin mat (<0.1 mm) under pressure in the reference bar apparatus and had a maximum deviation of 13% from the results obtained by SEM. The deviations were used to approximate standard error in Table 3 and are included in the uncertainty associated with the measurement of the thermal interface resistance across each mat in Figs. 11–14. A profilometer was used in order to determine the RMS roughness values of the upper and lower reference bars and averaged to yield rRMS. The surface roughness was measured over a total of four line segments on the face of each reference bar and averaged to produce the RMS roughness values for both the upper and lower reference bars. Results from this study indicate that the upper and lower reference bars have an RMS surface roughness of 0.877 and 1.653 lm, respectively.

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Table 3 – In situ film thicknesses. Sample number

Material

Free-standing mat thickness (lm)

Initial mat thickness at 0.14 MPa (lm)

Final mat thickness at 0.56 MPa (lm)

1 2 3 4 5 6 7 8 9

HGNF HGNF/xGnP HGNF/xGnP/PCM MWCNT MWCNT/xGnP MWCNT/xGnP/PCM SWCNT SWCNT/xGnP SWCNT/xGnP/PCM

69.4 ± 0.6 39.4 ± 0.2 68.2 ± 0.3 10.3 ± 0.1 42.0 ± 0.2 56.8 ± 0.8 34.9 ± 1.9 85.3 ± 1.0 63.3 ± 1.7

69.3 ± 0.3 34.8 ± 0.2 66.4 ± 0.3 10.1 ± 0.1 39.6 ± 0.2 55.6 ± 0.3 34.2 ± 0.7 83.3 ± 1.0 61.3 ± 0.7

68.1 ± 0.3 33.7 ± 0.2 62.9 ± 0.3 9.7 ± 0.1 37.2 ± 0.2 53.9 ± 0.3 29.6 ± 0.7 75.3 ± 1.0 58.4 ± 0.7

An uncertainty analysis was completed for this study using Eq. (8). vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u j  2 uX MTIR UTIM ¼ t  dXn ð8Þ @ Xn n¼1 In Eq. (8), UTIM represents the uncertainty in the measured interface resistance across each mat, MTIR represents the measured interface resistance across the mat, rvn represents different measured properties within the system and dvn represents the uncertainty in those measurements. The measured properties within the system (and their associated uncertainties) include: the temperature recorded by the thermocouples (±0.2 K), the area of the reference bars (±0.004 cm2), the heat flow along the reference bars (±2 K/ m), the thickness of the sample (Table 3) and the thermal conductivity of the copper reference bars (±2 W/m K).

3.

Results and discussion

3.1.

Morphology of interwoven mats

As part of this study, a scanning electron microscope (SEM) is used to produce micrographs of each mat in order to make qualitative assessments of their morphologies. The micrographs allow for sufficient insight into the contact area between nanostructures in each mat, which can aid in our understanding of this effect on their thermal performance in application. In Fig. 3, micrographs of homogenous HGNF, MWCNT and SWCNT mats are shown. It can be seen in Fig. 3 that including cylindrical nanostructures with different diameters in each of the mats results in a variation of the contact area between them. In Fig. 3(a), a micrograph of the HGNF mat reveals that there is a wide distribution of nanofiber diameters that make up the mat. On average, the diameters of the herringbone nanofibers are significantly greater than the MWCNTs and SWCNTs used to fabricate the other two mats (Fig. 3(b and c)). The larger diameters result in nanostructures with larger mating contact areas. Thus, by comparing the thermal resistance across each mat, a determination of the dominant heat transfer mechanism within networks of nanostructures (the contact area between nanostructures versus the intrinsic thermal conductivity of each nanostructure versus the surface roughness of the mat itself) can be made. For instance, if the HGNF mats perform as well as either the SWCNT or MWNCT mats,

despite their much lower intrinsic thermal conductivity, then contact area is likely to be the dominant mechanism governing heat transfer, particularly if the average surface roughness of either the SWCNT or MWCNT mats is lower than the surface roughness of the HGNF mats. In order to greatly increase the contact area between nanostructures, high loading levels of xGnP are used to fabricate heterogeneous nanostructured mats. The large flat flakes of xGNP provide ample mating surface areas for the adjacent nanotubes or nanofibers. In Fig. 4(a–c), one can observe the presence of xGnP within each of the mats. In Fig. 4(a–c), the xGnP are shown to be ‘‘woven’’ into the nanostructured mats. In each case, the contact area between the xGnP and the cylindrical nanostructures is far greater than between the individual cylindrical nanostructures shown in Fig. 3(a–c). In many cases, a series of cylindrical nanotubes outlines each xGnP particle, providing numerous pathways for heat transfer to other xGnP. In this way, the xGnP are expected to act as ‘‘thermal highways’’ for the efficient transfer of heat between cylindrical nanostructures. This use of xGnP to manipulate and increase mating surface areas will provide significant insight into the effects of contact area on heat transfer in networks of nanostructures. In the homogenous mats, the nanostructures only contact one another along a line segment of atoms (or worse, at an individual atom) [47]. However, when xGnP are added to the now heterogeneous mats, they act as flexible ‘‘superhighways’’, conforming to the surface of the cylindrical nanostructures (in the form of a ‘‘well’’ shape, as shown in Fig. 5) to offer a greater area for phonon transport at interfacial regions. In most TIMs, it is not enough to use mats made of highly conductive nanoparticles alone because the mats do not effectively conform to the mating surfaces. Thus, conventional TIMs often utilize a wetting agent to aid in surface conformity. In order to determine whether the heterogeneous nanostructured mats developed here also require a wetting agent to improve their ability to conform to the surfaces of the copper reference bars, several mats are impregnated with a PCM wetting agent. The SEM is used to observe the impregnation effectiveness of each heterogeneous nanostructured mat. As an example, a HGNF/xGnP mat impregnated with a paraffin phase change material is shown in Fig. 6. In all cases, the PCM was able to effectively penetrate into the heterogeneous mats and coat the nanostructures, indicating a high affinity for this particular wetting agent.

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3.0 kV 16.6mm x 13.0k SE(M)

6 1 ( 2 0 1 3 ) 4 4 1 –4 5 7

4 µm

3.0 kV 16.8mm x 18.0k SE(M)

3 µm

5 µm

3.0 kV 16.8mm x 15.00k SE(M)

3 µm

(b)Heterogeneous MWCNT/xGnP Mat

(b) Homogenous MWCNT Mat

3.0 kV 14.8mm x 100k SE(M)

3.0 kV 16.8mm x 11.00k SE(M)

(a)Heterogeneous HGNF/xGnP Mat

(a)Homogenous HGNFMat

500 nm

(c) Homogenous SWCNT Mat Fig. 3 – SEM micrographs of homogenous nanostructured mats.

In order to qualitatively evaluate the intrinsic thermal transport within each mat, cross-section SEM images are given for MWCNT-based mats in Fig. 7(a–c). Here, the cross-section SEM views of the homogenous (MWCNT only) mat, the heterogeneous (MWCNT/xGnP) mat and the heterogeneous mat saturated with PCM are shown.

3.0 kV 16.8mm x 25.00k SE(M)

2 µm

(c)Heterogeneous SWCNT/xGnP Mat Fig. 4 – SEM micrographs of heterogeneous nanostructured mats.

The images in Fig. 7 provide a macroscopic perspective of the possible routes for phonon transport and boundary scattering within the nanostructure networks. In Fig. 7(a), the MWCNTs are shown to contact one another at discrete points, leading to a small region over which thermal transport can take place and thus significant phonon boundary scattering

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6 1 (2 0 1 3) 4 4 1–45 7

3.0 kV 9.9mm x 10.20k SE(M)

3.0 kV 10.3mm x 30.00k SE(M)

1 µm

6 µm

(a) Homogenous MWCNT mat

Fig. 5 – xGnP conforming to the surface of an HGNF.

xGnP HGNF PCM 3.0 kV 10.6mm x 800 SE(M)

30 µm

(b) Heterogeneous MWCNT/xGnP mat 3.0 kV 9.4mm x 4.00k SE(M)

10 µm

Fig. 6 – SEM micrograph of HGNF/xGnP mat saturated with PCM.

at the junction between nanostructures. Alternatively, Fig. 7(b) reveals that the xGnP dominate the overall structure despite accounting for only 54% of the total weight of the mat, yielding a network over which exists larger contact areas between nanostructures. It is expected that these larger contact areas result in less phonon boundary scattering at nanostructure junctions and thus a higher intrinsic thermal conductivity of the nanostructured mat. Finally, Fig. 7(c) shows the material in Fig. 7(b) saturated with a phase change material (PCM). Because the PCM constricts during solidification, it is expected that a moderate increase in contact area is achieved, resulting in a slightly higher intrinsic thermal conductivity than the material shown in Fig. 7(b). However, the primary purpose of the PCM is to act as a wetting agent in order to completely connect the surface asperities of the copper reference bars and is not expected to drastically enhance the intrinsic thermal conductivity of the material in Fig. 7(b).

3.2.

Surface topography and thermal interface resistance

The surface topography of each mat is measured using an Agilent 5500 AFM. In this study, a series of 3-dimensional,

3.0 kV 9.5mm x 1.20k SE(M)

40 µm

(c) Heterogeneous MWCNT/xGnP mat saturated with PCM Fig. 7 – Cross-section SEM view of MWCNT-based mats.

topographic images are qualitatively analyzed in order to determine how well each mat is likely to conform to the asperities of the copper reference bars. Fig. 8 shows the surface topography of each of the three homogenous, nanostructured mats. The maximum height of each surface deviates significantly from one mat to the next, indicating that the topography of each mat is statistically different. Thus it is highly likely the surface of each mat will conform differently to the asperities of each copper reference bar. A quantitative analysis reveals the magnitude of this discrepancy. The average surface roughness (Ra) and

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Fig. 8 – Surface topography of homogenous nanostructured mats.

the maximum average height of the surface profile (Rz) serve as a quantitative basis of comparison between the topographies of each mat. For optimal thermal performance, it is desirable to fabricate nanostructured mats with low surface roughness and highly flexible surfaces. A low surface roughness implies that the mat’s own surface asperities are significantly smaller than the surface asperities of the copper reference bars. This allows for a large portion of the mat’s surface to come in contact with the asperities of the copper materials. Similarly, a flexible mat surface is desired for good conformability to the copper asperities. Thus, both smooth and pliable surfaces are desirable from a thermal transport perspective. The statistical differences between the surface morphology of each mat are deduced using Ra and Rz in Fig. 9. In Fig. 9(a, c and e), the average height of the surface is used as a cut-plane in order to qualitatively assess the waviness of each mat surface as well as the nature of their peaks. This allows for sufficient differentiation between the surface roughness and pliability of each mat. Fig. 9 shows the peak topographies and the average roughness profiles for each of the mats in Fig. 8(a–c).

The average height, as seen in Fig. 9(a, c and e), is used to make relative comparisons between the mats (i.e. how rough each surface is relative to the average height of each mat’s asperities). By using this plane as a reference point for evaluation, the surface morphologies of each mat can be distinguished. A qualitative assessment of Fig. 9 reveals that the HGNF mats exhibit the roughest surface, while the MWCNT and SWCNT mats exhibit moderate to little surface roughness, respectively. A quantitative assessment of the average roughness parameters Ra and Rz confirms the topographical disparities between each of the mats; in descending order of average roughness and maximum profile height, the HGNFs exhibit the roughest surface (Ra = 71 nm, Rz = 405 nm), the MWCNTs have a moderate roughness in comparison to the HGNFs (Ra = 18 nm, Rz = 101 nm) and the SWCNTs have a substantially lower surface roughness than either the HGNFs or MWCNTs (Ra = 1.5 nm, Rz = 7.3 nm). The surface topography of the heterogeneous mats is shown in Fig. 10. Unlike the homogenous mats (Fig. 8(a–c)), the heterogeneous SWCNT nanostructured mat contains larger regions over which the surface is dominated by the more pliable xGnP particles. As a result, the xGnP provides for a more conformable surface for the heterogeneous SWCNT mat. This is not the case with the other two types of nanostructured mats (as confirmed by Fig. 4(a–c)). In order to compare the surface morphologies of the heterogeneous nanostructured mats in Fig. 10(a–c), the same set of parameters that defined the surface topographies in Fig. 9(a–f) are applied. When one qualitatively examines the nature of the topography in each of the xGnP mats, it is clear that the SWCNT/ xGnP mat is considerably better for heat transfer despite its rougher surface. In contrast to both the SWCNT and MWCNT heterogeneous mats, the HGNF in the HGNF/xGnP mat are large enough to fill in the majority of the valleys between xGnP, as shown in Fig. 11 a. This will be detrimental for heat transfer because the xGnP are pliable and thus able to conform better to the surface asperities at each reference bar; hence, filling in the valleys with less pliable HGNF is detrimental. Furthermore the HGNF have low conductivity and form a porous, air retaining network when bundled, further reducing effective transport conductivity. Thus, the xGnP are not expected to substantially enhance thermal transport across the HGNF mat from a surface conformability perspective. The difference in roughness between the SWCNT/xGnP and MWCNT/xGnP mats is less noticeable from a qualitative perspective. This is because the diameters of the SWCNTs and MWCNTs are more comparable than between SWCNTs or MWCNTs and HGNFs. However, one noticeable effect arises from the difference in volume between SWCNTs and MWCNTs which results in fewer MWCNTs in the MWCNT/ xGnP mixture than SWCNTs in the SWCNT/xGnP mixture when loading levels are held constant. More nanotubes result in a higher average surface roughness for the SWCNT/xGnP mat than for the MWCNT/xGnP mat. This higher surface roughness may be detrimental to heat transfer because the intrinsic thermal conductivities of SWCNTs and MWCNTs are much closer to each other than to the HGNF, leaving surface roughness as a dominant effect.

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451

Fig. 9 – Peak topography for homogenous mats.

A comparison between the interface resistances across each of the mats is provided to show the effect of nanostructure-nanostructure contact area, nanostructure intrinsic thermal conductivity and overall mat surface roughness on thermal performance in application. In order to test their surface conformity, the heterogeneous nanostructured mats are tested with and without a PCM wetting agent. The PCM is

used to evaluate whether a wetting agent is necessary to further enhance the thermal transport between the mat and the reference bars. All mats are compared to the commonly used commercial TIM Arctic Silver 5 in order to evaluate their performance against an industry standard. The initial and final in situ mat thicknesses are shown in Table 3 for all mats at the initial and final clamping pressures. The standard error

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Fig. 10 – Surface topography of heterogeneous nanostructured mats.

in measurement of the mat thickness is obtained by calculating the standard deviation of the measurements using SEM. Fig. 12 illustrates the difference in thermal interface resistance between SWCNT and MWCNT mats with and without xGnP. It can be seen that both with and without xGNP the thermal interface resistance across the SWCNT mat is substantially lower than the thermal interface resistance across the corresponding MWCNT mat. Although the MWCNTs have larger diameters and thus greater contact area, the SWCNT mat alone has a much lower surface roughness (Fig. 8(a–c)) and deforms at twice the rate (Table 3) as the MWCNT mat, indicating that the surface conformability provided by the SWCNT mat dominates thermal transport across the mat. However, when xGnP are embedded within SWCNT mats, the thermal interface resistance decreases by a factor of 2.64 (at 0.14 MPa). Because the two sets of nanostructures (SWCNTs and xGnP) have approximately the same thermal conductivity at room temperature (refer to Table 1), the substantial enhancement in thermal transmission across the mat is not an effect of the intrinsic thermal conductivity of the nanostructures. Additionally, the surface roughness of the SWCNT/xGnP mat is shown to be significantly higher than the SWCNT mat alone. The primary difference, then, between the SWCNT mats and the SWCNT/xGNP mats is the overall contact area between nanostructures. The solid–solid contact area is significantly larger between SWCNTs and xGnP than it

is between individual CNTs, as seen when comparing Figs. 3 and 4. This leads to a substantial increase in thermal transport and a corresponding decrease in thermal resistance from homogenous nanostructured mats to heterogeneous nanostructured mats containing xGnP. This is also the case in the MWCNT mats, whose CNT components have a slightly lower intrinsic thermal conductivity than the xGnP. If the thermal interface resistance across the mats were not sensitive to contact area, one would expect a slightly lower enhancement in thermal transport over the MWCNT/xGnP mat when compared to the SWCNT/xGNP mats. Instead, a 5.8-fold reduction in thermal interface resistance is seen at an interface pressure of 0.14 MPa. This represents a greater reduction in thermal interface resistance than the xGnP provides for the SWCNT mat, which indicates that the thermal transport across nanostructured mats is highly sensitive to contact area. Thus, the contact area between sets of nanostructures is clearly an important parameter in the design of nanostructured mats, which agrees well with the theoretical results presented in [47,54] for individual pairs of nanostructures. The effect of xGnP on the thermal interface resistance across HGNF mats is characterized against the MWCNT mats in Fig. 13. It can be seen that the thermal interface resistance across the HGNF mat is lower than it is across the MWCNT mat, despite the HGNFs having a significantly lower intrinsic thermal conductivity than MWCNTs. This indicates that the intrinsic thermal conductivity of contacting nanostructures has less effect on the thermal transport between them than does contact area, which agrees well with the results in Fig. 12. Additionally, the HGNF mat has a rougher surface topography per Fig. 9(a and b). Thus, the effect of contact area on thermal transport in nanostructured mats is magnified for this case given the low intrinsic thermal conductivity of the HGNF and the large surface roughness of the homogenous HGNF mat. Additionally, Fig. 13 reveals that the xGnP do not provide the same enhancement that they do in the MWCNT mats. This is due to the fact that the HGNF have a much higher contacting area than do the individual MWCNTs. In this case, the xGnP provide a higher contact area ratio for MWCNTs (i.e. xGnP area:MWCNT area) than they do for HGNF (i.e. xGnP area:HGNF area), thus confirming the importance of nanostructure-nanostructure contact area on thermal transport in nanostructure networks. In order to confirm that the contacting area between nanostructures is the material parameter that most affects thermal transport in networks of nanostructures, xGnP were embedded at increasing weight fractions from 9% to 54% in MWCNT mats. The results are displayed in Fig. 13. In Fig. 14, there is an exponential decrease in the thermal interface resistance with increasing weight fraction of xGnP. This is a clear indication that the contact area between nanostructures affects the thermal transport between them and is in strong support of the results given in Figs. 12 and 13. Finally, the mats are quantitatively evaluated for their ability to conform to the surface asperities of the reference bars by comparing their performance when fully saturated with a wetting agent (PCM) to the performance of the heterogeneous mats without any PCM. The heterogeneous mats are also compared against the commercial TIM Arctic Silver 5 in

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453

Fig. 11 – Peak topography for heterogeneous mats.

order to gauge their performance against an industry standard. Fig. 15 shows the thermal interface resistance across heterogeneous nanostructured mats with and without PCM. The HGNF/xGnP mat exhibits the largest thermal interface resistance across the copper reference bars. However, when the HGNF/xGnP mat is saturated with a PCM, the thermal interface resistance is reduced by a factor of 7.3 versus the HGNF mat alone. As a comparison, the PCM reduces the thermal interface resistance across the MWCNT/xGnP and SWCNT/xGnP mats by factors of 2.6 and 1.1, respectively, at

a pressure of 0.14 MPa (when the discrepancy is greatest). This confirms that the HGNF/xGnP mats are predominantly affected by their large surface roughness. Both the SWCNT/ xGnP and MWCNT/xGnP mats are shown to perform as well or better than the commercial TIM. Together, these results imply that both contact area and mat surface roughness can be engineered to produce highly reliable, high performance thermal interface materials that are competitive with state-of-the-art commercial TIMs [12]. Additionally, removing the need for a wetting agent substantially increases the reli-

CARBON

2.50E-05 2.25E-05 2.00E-05 1.75E-05 1.50E-05 1.25E-05 1.00E-05 7.50E-06 5.00E-06 2.50E-06 0.00E+00

6 1 ( 2 0 1 3 ) 4 4 1 –4 5 7

1.20E-05 1.00E-05

Rn (m2*K/W)

Rn (m2*K/W)

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8.00E-06 6.00E-06 4.00E-06 2.00E-06

0.00E+00

0

0.1

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0

0.6

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Clamping Pressure (MPa) SWCNT

MWCNT

SWCNT/xGnP

0.2 0.3 0.4 Clamping Pressure (MPa)

0.5

0.6

MWCNT/xGnP

Fig. 12 – Effect of xGnP inclusions on thermal interface resistance of SWCNT and MWCNT mats.

Fig. 15 – Effect of a wetting agent (PCM) on thermal interface resistance across heterogeneous nanostructured mats.

2.50E-05 0.0014 0.0012

RTIM (m2*K/W)

Rn (m2*K/W)

2.00E-05 1.50E-05 1.00E-05 5.00E-06

0.001 0.0008 0.0006 0.0004

0.00E+00

0

0.1

0.2

0.3

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Clamping Pressure (MPa) 0 0

Fig. 13 – Effect of xGnP inclusions on the thermal interface resistance of HGNF and MWCNT mats.

10

20

30

40

50

60

70

80

90

100

TIM Thickness (µm) HGNF

HGNF/xGnP

HGNF/xGnP/PCM

MWCNT

MWCNT/xGnP

MWCNT/xGnP/PCM

SWCNT

SWCNT/xGnP

SWCNT/xGnP/PCM

Arctic Silver 5

1.20E-05 MWCNT/xGnP

Fig. 16 – RTIM as a function of TIM thickness for homogenous and heterogeneous GNF- and CNT-based mats versus Arctic Silver 5 at 0.14 MPa.

Rn (m2*K/W)

1.00E-05 8.00E-06 6.00E-06 4.00E-06 2.00E-06 0.00E+00

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55%

Concentration of xGnP

Fig. 14 – Effect of weight fraction of xGnP on normalized thermal interface resistance across MWNT mat.

ability of the mats in application, as they are able to avoid the performance limitations (i.e. ‘‘pump out’’ and ‘‘dry out’’) that hinder conventional TIMs. In order to give the reader a sense of the performance of the above TIMs in application, RTIM is calculated as a function of TIM thickness for each of the TIMs analyzed in Figs. 12–15. In order to calculate RTIM, Rn is multiplied by thicknesses ranging from 1 to 100 lm and divided by the average RMS

roughness of the copper reference bars. The results are presented in Fig. 16. It is clear from Fig. 16 that at comparable thicknesses, only the HGNF, MWCNT and HGNF/xGnP mats do not perform as well as the commercial TIM Arctic Silver 5 in application. In addition to providing a practical way to compare the TIMs studied in this work, Fig. 16 can be used as a design guide for engineering the above mats to meet performance standards based on mat thickness and nanostructure mixture type at 0.14 MPa clamping pressure. A summary of the relative enhancement of the thermal interface resistance across each mat provided by xGnP and/ or PCM is shown in Table 4 for the initial (0.14 MPa) and final (0.56 MPa) loading pressures. Table 4 also includes the relative enhancement of the normalized thermal interface resistance of each mat versus the commercial TIM Arctic Silver 5. Those mats which exhibit a higher thermal interface resistance than Arctic Silver 5 under the same loading conditions are represented by negative values.

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Table 4 – Relative enhancement of normalized thermal interface resistance due to the presence of xGnP and/or PCM in nanostructured mats over Arctic Silver 5 at initial (0.14 MPa) and final (0.56 MPa) pressures. Material

Thermal interface resistance 0.14 MPa (m2 K/W 105)

Thermal interface resistance 0.56 MPa (m2 K/W 105)

Percent decrease versus base material 0.56 MPa (%)

Percent decrease versus Arctic Silver 5 0.56 MPa (%)

HGNF HGNF/xGnP HGNF/xGnP/PCM MWCNT MWCNT/xGnP MWCNT/xGnP/PCM SWCNT SWCNT/xGnP SWCNT/xGnP/PCM

1.29 1.06 0.18 2.03 0.35 0.13 0.47 0.18 0.16

0.82 0.57 0.12 1.14 0.16 0.07 0.32 0.12 0.10

– 31 85 – 86 94 – 61 67

128 58 66 220 54 81 11 66 71

4.

Conclusions

The results of this study show that nanostructure interfaces in composite, nanostructured mats can be geometrically engineered to reduce the thermal interface resistance. Results also show that these composite, nanostructured mats are potentially transformative as TIMs due to their high reliability and exceptional performance in application. The use of xGnP in HGNF, MWCNT and SWCNT mats revealed that the contact area between nanostructures plays a major role in thermal transport across nanostructure networks. In all cases, the xGnP reduced the thermal interface resistance across the mat by at least 31%, with much larger reductions occurring (61–86%) when the xGnP were added to mats whose primary nanostructures had small diameters (<100 nm). Additionally, the HGNF mat, whose individual nanostructures have much lower intrinsic thermal conductivity than the individual nanostructures in the MWCNT mat, outperformed the MWCNT mat at all pressures, indicating that contact area between nanostructures is the dominant thermal transport mechanism over intrinsic thermal conductivity when van der Waals bonding exists between individual pairs of nanostructures. Using this knowledge, nanostructured mats can be engineered to outperform current state-of-the-art TIMs. In this study, the MWCNT, MWCNT/xGnP, SWCNT and SWCNT/xGnP mats were shown to outperform the commercial TIM Arctic Silver 5 by as much as 81%. Finally, the heterogeneous mats are shown to conform well to the surfaces of the copper reference bars in this experiment, which resulted in nanostructured TIMs that did not require a wetting agent. This results in a highly reliable TIM that does not suffer from the issues that inhibit the longevity of current TIMs, namely ‘‘dry out’’, ‘‘pump out’’ and ‘‘hardening’’.

Acknowledgments The authors wish to recognize the work done by undergraduate lab assistants Rebecca Weigand and Lorelle Suriano in obtaining the SEM images. Their hard work is greatly appreciated. R.J.W. gratefully acknowledges support from the Environmental Protection Agency Science to Achieve Results (STAR) Fellowship.

This material is based upon work supported by the National Science Foundation under Grant No. 0931507. 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. The research described in this paper has also been funded in part by the United States Environmental Protection Agency (EPA) under the Science to Achieve Results (STAR) Graduate Fellowship Program. EPA has not officially endorsed this publication and the views expressed herein may not reflect the views of the EPA.

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