Fully Organic Bulk Polymer with Metallic Thermal Conductivity and Tunable Thermal Pathways

Abstract Electrically insulating polymers are indispensable for electronic and energy applications, but their poor thermal conduction has increasingly become a bottleneck for high‐performance devices. Highly drawn low‐dimensional polymeric fibers and thin films can exhibit metallic conductivity. Extending this to bulk materials required by real world applications is prohibitive due to the additional interfacial thermal conduction barriers. It is demonstrated that highly aligned ultrahigh molecular weight polyethylene microfibers can be incorporated into a silicone matrix to yield a fully organic bulk polymer composite with a continuous vertical phonon pathway. This leads to a perpendicular thermal conductivity of 38.27 W m−1 K−1, at par with metals and two orders of magnitude higher than other bulk organic polymers. Taking further advantage of the mechanical flexibility of the microfibers, the processing method offers the freedom to tailor heat transfer pathways in a macroscopic 3D space. The material/process opens up opportunities for efficient thermal management in high‐performance devices.

PEMF (diameter of 15 m) fabricated via a gel spinning process was purchased from Shenzhen Teli Chemical Fiber Co., Ltd. PDMS precursors (SYLGARD TM 184) were obtained from Dow Chemical.

Preparation of PDMS/PEMF composites
The continuous and flexible PEMF bunches with suitable weight contents (0-68.85 wt%) were firstly placed in a metal mold. They were tightened with the help of the tunability of the dimension of the mold, and thus fixed to be the designed shape, such as simple cuboid, treelike shapes, complicated "SCU" shapes. The viscous PDMS precursors were vacuum infiltrated into the customized PEMF bunches and cured at 80 o C for at least 8 h to obtain PEMF-A, which was cut into desirable dimension/shape with a high-pressure water-cutting technique. PEMF-R material was prepared by mixing PDMS precursors and random PEMF in a mold followed by a similar thermal curing procedure.

Characterization
Field-emission scanning electron microscope (SEM) and its mapping characterization was conducted with a JSM-7500F machine by Jeol for morphological observations of PEMF and PDMS/PEMF materials. The extended nanocrystals in PEMF were verified by an atomic force microscope (AFM, 359 Marin Keys Bivd, Suite 20, USA). 2D wide-angle X-ray scattering (2D WAXS) characterization was performed at room temperature using a Bruker D8 Discover X-ray diffractometer equipped with a Vantec 500 detector to analyze the oriented information. Raman spectra were collected with Aramis machine made by HORIBA JOBIN YVON, in order to describe the molecular orientation and crystallinity of PEMF.
Laser flash analysis (LFA, NETZSCH, Germany) technique was used to quantify the thermal diffusivity at variable temperatures, and the testing voltage and pulse width were set to be 250 V and 600 µs, respectively. The different samples were tailored into the dimension of 10 mm*10 mm*x mm, where x is in the range from 2.5 mm to 4.0 mm. Anisotropic thermal conductivities of PDMS and various PDMS/PEMF composites were calculated according the equation κ = α*ρ*C p , where κ, α, ρ and C p respectively correspond to anisotropic thermal conductivity, thermal diffusivity, density and specific heat capacity. C p of PDMS and PEMF were respectively measured by differential scanning calorimetry (DSC, TA) using sapphire as the standard. Dielectric properties were measured by a broad-frequency dielectric spectrometer Concept 50 (Novocontrol, Germany) over the frequency range from 10 -1 to 10 6 Hz at room temperature.
To visualize the thermal management of various materials, infrared camera (FLIR-T600) was used to record the temperature distribution of the samples. For evaluating the thermal management capacity, the samples were coated by graphite to guarantee their similar surface optical properties, and then placed on the hot stage (65 o C, 85 o C or 100 o C). The surface temperatures were then recorded by infrared camera. For the demonstration in Figure S12, black graphite was coated onto the intended heating spot followed by laser light irradiation (LSR808H-FC-5W, LASEVER INC.). Again, videos were captured by the infrared camera.
The COB device was measured by the assembled equipment including high-precision power supply (Agilent E3640A), 30G random signal generator, BER tester (Keysight N4960A, N4951A), and high-speed sampling oscilloscope (Keysight DCA-X 86100D, 83484 and 86105D components). Because the large air gap ( 2.5 mm) exists between the heat source on the printed circuit board and the metal shell, our PDMS/PEMF was tailored into the suitable dimension. Before the test, a commercial thermal grease was coated at the bottom and up surface of PDMS/PEMF bulk sample, and therefore the interfacial thermal resistance with heat source or heat sink would be minimized.
Mechanical compression test was carried out on an Instron 5967 universal tester (USA) with a 1 mm min -1 stretching velocity at room temperature.

Statistical Analysis
Quantitative data were expressed in form of means ± standard deviation, as shown like the    Raman spectra were used to analyse the molecular orientation and crystallinity ( c ) of PE powder and PEMF, according to the peak intensity ratio of 1128 cm -1 and 1160 cm -1 (I 1128 /I 1160 ), and the ratio of integral intensity areas of 1414 cm -1 to 1293 cm -1 and 1305 cm -1 (A 1414 /A 1293+1305 ), respectively. It indicates that PEMF is provided with much higher molecular orientation after stretching due to a significant increase of I 1128 /I 1160 , at the same time that it also possesses higher  c than PE powder. The DSC results could also be utilized to calculate the  c of PE powder and PEMF. From the formula  c = ΔH/ΔH c , ΔH and ΔH c correspond to melting enthalpy of chosen materials and melting enthalpy of PE with complete crystallizations, respectively. ΔH could also be gained by integrating the areas of peaks from the image. It is commonly acknowledged that the ΔH c of PE material is 293 J/g as usual. According to DSC results, the PEMF (58.6%) behave higher  c than pure PE powder (49.1%), which is in accordance with the mentioned Raman spectra results.         Noted that the heat flux provided in Figure S10 was calculated based on the power input of hot plate, while ignoring the influence of heat convention and heat radiation with surroundings. With the help of 2D SAXS analysis and Fit 2D software packaging, we could obtain detailed structural information of PEMF samples, such as the curves of I (q), average diameter of shish crystals of PEMF and average length of shish crystals of PEMF ( Figure S11).

Curves of I (q) and I (ϕ):
The 2D SAXS analysis is often related to the scattering wave vector q (nm -1 ) and the scattering intensity I. As for the curves of I (q), with the help of Fit 2D software, we could integrate the patterns by meridian scan along the direction of q, in order to gain the results of scattering intensity distribution. Figure S11a shows the I(q) curve of PEMF, which clarifies the existence of long, oriented fibrillar, shish crystals.
Meanwhile, the curves of the scattering intensity I and the azimuth angle ϕ could also be obtained. As for the curves of I (ϕ), with the help of Fit 2D software, we could integrate the patterns with the whole range of azimuth angle ϕ (0-360º). Besides the obvious 2D SAXS scattering patterns of sample, the I (ϕ) curve of PEMF obviously shows the double peaks in Figure S11b, which gives a great assistance to manifest the highly oriented structures of PEMF.

Calculation of average diameters of shish crystals of PEMF:
From the previous research about shish-kebab structure, the specific shish structure could be considered as a collection of long and smooth extended-chain crystals, like a stick. [26] Thus, according to the "Guinier approximation", [27] the average diameters of fibrillar shish crystal (D crystal ) could be gained by Equation 5 as follows: According to scattering pattern of 2D SAXS, the Guniner approximation expansion could be gained by Equation 6: R g is the radius of gyration of rod-like crystals, I(q) and q could be attained by the above curves of I (q). At the same time, the shish structure is regarded as symmetrical cylinder, so the D crystal could be calculated as follows: From the fitting curve of Guniner approximation expansion, there are two parts of the fitting curves. In the first part (q < 0.015nm), the mentioned Equation 6 and 7 could be used to calculate the D crystal . The slope of Guniner approximation expansion could be easily gained and the R g , D crystal could also be attained. The fitting curve of Guniner approximation expansion of PEMF is in Figure S11c.
Calculation of average length of shish crystals of PEMF: According to Peter and Ruland method, [28] the average length of fibrillar shish crystals (L crystal ) of PEMF could be obtained.
In this method, the B obs means the integral width of one-dimensional azimuth at different q values along the direction of equator. The B obs could be calculated as follows: ϕ is the azimuth angle; I (q, ϕ) is the scattering intensity. If all the azimuthal distribution could be modeled by Lorentz functions, the relation of B obs and L crystal is as follows: b ϕ is the misorientation factors of shish. If the azimuthal distribution accord with Gaussian expressions, then the relation of B obs and L crystal is as follows: L crystal could be obtained from the slope of the equations. In this study, all azimuthal distributions were found to be better fit with Lorentz functions, thus the Equation 9 was determined to calculate the L crystal . The fitting curves of B obs and 1/q is shown in Figure S11d.
Modified EMT model analysis: R crystal-amorphous is quantified according to the modified EMT model [29] , in which PDMS with amorphous region of PEMF is taken as the matrix, while the crystalline region of PEMF is considered as the additive. Its value is fitted according to Equation 11 as follows: (11) where κ e is the κ of PEMF-A materials, κ m is the κ of PDMS/amorphous PEMF matrix, f is the volume content of fibrillar nanocrystal, p is the aspect ratio, D is the diameter of fibrillar nanocrystal. Herein, D and p were respectively measured by SAXS ( Figure S11). It was reported that an individual PE fibrillar nanocrystals could achieve an axial κ of 237 W/m K, in consideration of the crystalline size based on diffuse phonon scattering at boundaries. [30] Series Model was used to quantify the thermal conductivity of amorphous region of PEMF (30.89 W/m K) according to this literature (Equation 12), [31] as well as the κ m (Equation 13).
Based on these parameters, R crystal-amorphous is estimated to be 7.77*10 -9 m 2 K W -1 .
where f is the volume content of fibrillar nanocrystal in PEMF, , , and are the thermal conductivity of PEMF, fibrillar nanocrystal of PEMF, and amorphous region of PEMF, respectively.
where is the volume fraction of amorphous region of PEMF in PDMF/PEMF, , , and are the thermal conductivity of PDMS/amorphous PEMF matrix, amorphous region of PEMF and PDMS, respectively.

Nonlinear model (Foygel et al.) analysis:
The nonlinear model proposed by Foygel et al. [32] is used to fit the contact thermal resistance (R crystal-crystal ) (Figure 3b), where it is noteworthy that PDMS with amorphous region of PEMF is taken as the matrix, while the crystalline region of PEMF is considered as the additive. The equations are provided as Equation 14 and Equation 15 as follows: where κ 0 is a preexponential parameter that is the estimated contribution of fibrillar nanocrystal network alone, V f is the volume percentage of fibrillar nanocrystal, V c is the critical volume percentage of fibrillar nanocrystal, L is the length of fibrillar nanocrystal, S is the average contact area between adjacent two crystals, and is a conductivity exponent that is determined by the aspect ratio of fibrillar nanocrystal. Considering usually limited contact area from fibrous crystals due to the restricted linear overlap, thus <1/1000 of fibrillar crystal's surface area is assumed as S. Based on this, R crystal-crystal is determined to be 4.1*10 -11 m 2 K W -1 . This exceedingly low interfacial thermal resistance attributes to the contribution of amorphous regions of PEMF that have bridged adjacent fibrillar nanocrystals within the PDMS/PEMF material.

Additional performance of PEMF-A required in thermal managements
Figure S12. Schematic illustration of heating process of PEMF-A with "S" shape. In virtue of laser transmitter (heat source, 2.8 W) and infrared imaging camera, the thermoconductive performances could be obviously exhibited. To explore the thermal stability, anisotropic thermal conductivities at different temperatures were studied. Firstly, DSC analysis was used to confirm the critical melting points (T m ) of PEMF-A materials, which manifests a stable T m around 150 o C ( Figure S13a). Figure S13b and Figure S13c further verify this conclusion, as both anisotropic thermal conductivities of PEMF-A material behave a gradual variation as increase of the test temperature, and the small decrease in κ⊥, derived from the increase of specific heat capacity but the decrease of thermal diffusion coefficient ( Figure S14, Table S3 and Table S4). All of parameters could be in the stable state after 17 times of heating or cooling cycles. These excellent thermo-conductive characteristic at variable temperatures is ascribed to the highly efficient phonon highways, in which fibrillar nanocrystals, crystal-amorphous interfaces and crystal-crystal contacts could be durable at higher temperatures.        height, which could be better reflect noise margin of signal transmission. In virtue of combination with COB packed chips, our material with metal-like κ could directly exhibit a promising potential in the giant power devices in Figure S19.
Detailly, the working parameters, including node temperature, jitter, eye dimensions, and margin obtained from the eye diagram analysis were respectively studied at room temperature.
According to the eye diagrams, COB chip packed with our PEMF-A materials performs the lowest jitter in the time domain that reflects the excellent signal stability as shown in Figure   S20a. In addition, the eye dimensions ( Figure S20b As shown in Figure S21a (Supporting Information), PEMF-A material with 55 wt% PEMF could behave retained compressive properties, including relatively low modulus (1.6580.332 MPa) and compression strength (84058 kPa). Pristine PDMS material exhibits modulus of (0.5000.585 MPa) and compression strength of (19627 kPa). Moreover, images in Figure   S21b (Supporting Information) demonstrates the ability of PEMF-A to be bended without any breakage, indicating its good mechanical properties. In Figure S21c and S21d, we also provided the   of PEMF-A before and after bending or compression. It was found that bending procedure give rise to no obvious degradation of   , while after 10% compression, the   of PEMF-A has decreased by 14.8%. We think that vertically aligned PEMF bunches would be bended during the compression procedure, while they could not revert to the original configuration although the PDMS matrix could.