Nanostructured polymer films with metal-like thermal conductivity

Due to their unique properties, polymers – typically thermal insulators – can open up opportunities for advanced thermal management when they are transformed into thermal conductors. Recent studies have shown polymers can achieve high thermal conductivity, but the transport mechanisms have yet to be elucidated. Here we report polyethylene films with a high thermal conductivity of 62 Wm−1 K−1, over two orders-of-magnitude greater than that of typical polymers (~0.1 Wm−1 K−1) and exceeding that of many metals and ceramics. Structural studies and thermal modeling reveal that the film consists of nanofibers with crystalline and amorphous regions, and the amorphous region has a remarkably high thermal conductivity, over ~16 Wm−1 K−1. This work lays the foundation for rational design and synthesis of thermally conductive polymers for thermal management, particularly when flexible, lightweight, chemically inert, and electrically insulating thermal conductors are required.


Supplementary Note 2. Steady-state thermal conductivity measurements
Thermal conductivity measurement of the plastic films is very challenging because the samples are very thin at high draw ratio (~1-3 microns). A recent experimental study 2 of Dyneema, Zylon and Spectra fibers suggested that some previous work may have overestimated thermal conductivities by as much as a factor of 3. We explored numerous methods to measure thermal conductivity of the drawn films, and eventually decided to use an extensively validated home-built steady-state platform [3][4][5] . We calibrated the setup by measuring various control samples, including 304-stainless steel foils 6 , Dyneema fibres 2 and Zylon fibres 2 , Sn 7 and Al 7 films, and measured thermal conductivity 15.3 W m -1 K -1 , 22.6 W m -1 K -1 and 23.6 W m -1 K -1 , 64.4 W m -1 K -1 and 202.7 W m -1 K -1 for 304-stainless steel foils 6 , Dyneema fibres 2 and Zylon fibres 2 , Sn 7 and Al 7 films, respectively. These measured thermal conductivity is similar to those reported in previous references 2, 6,7 . We also used a transient pump-probe technique [8][9][10] to measure a thick laminate and the results are consistent with the steady-state method [3][4][5] . Each method is described in more detail below.
Thermal conductivity measurement principle of steady-state method: Direct measurement of the electrical heating power ( "# ) as a function of temperature difference ( % − ' ) across a sample film was performed 3 (Supplementary Figure 1). % (303 K) was kept constant via feedback control of "# , while ' was reduced to create a small temperature difference (up to 10 K) by systematically increasing the thermoelectric cooling power. Multiple measurements of "# were performed at a given temperature difference once the system had reached steady state (Supplementary Figure 1b). Subsequently, the slope of the linear fit yields, according to Fourier's law and after correction for thermal shunting (Supplementary Figure 1b). Convection and parasitic heat loss were minimized using high vacuum and a temperature-controlled copper shield, respectively. Special effort was taken to minimize the thermal radiation exchange and to ensure that the reported thermal conductivity is conservative even if any residual radiation exists. Thermal shunting was minimized and quantified after each experiment by removing the film sample and repeating the measurement.
We create a geometry such that the one-dimensional (1D) Fourier law of heat conduction is satisfied [3][4][5] , which is shown in Supplementary Equation 1.
where , , , % and ' , are the sample cross-sectional area, thermal conductivity, sample length, hot side temperature, cold side temperature and heat flow through the sample, respectively. Figure 1a show a schematic and some images of the experimental setup, respectively. The sample was suspended between a hot junction clamp and a cold junction clamp, all of which were guarded by a copper radiation shield. We maintained the hot clamp temperature % constant using a resistive electrical heater while the cold clamp temperature ' was systematically lowered by a thermoelectric cooler. We achieved this by feed-back controlling the electrical heating power "# into the heater as the cooling power increased (Figure 2a, Figure 2b and Supplementary Figure 1).

Analysis of the parasitic heat losses:
By keeping the hot clamp and copper radiation shield at the same constant temperature, parasitic heat losses such as through the electrical leads to the heater and thermocouples were effectively kept constant, which therefore did not affect the slope of "# versus the temperature differential ∆ . As shown in Fig. 2b  Analysis of the uncertainties due to thermal radiation: This method only leads to accurate results when the surrounding temperature is constant to ensure constant parasitic heat losses from the hot side and radiation loss is minimal. For these purposes, a temperature-controlled copper radiation shield guarded the heater clamp and the suspended sample. The radiation shield was constantly maintained at the hot side temperature, % , and all heater current leads and hot side thermocouple wires were thermally grounded to minimize parasitic heat losses which was especially important for samples with small thermal conductance.
Parasitic radiation heat transfer between the sample and the environment is of major concern for the accuracy of the thermal conductivity measurements. Two measures were taken to ensure the reliability of reported data. As already mentioned, the sample was surrounded by a temperature-controlled (at % ) radiation shield. This configuration led to an additional heat input from the shield into the suspended sample, which reduced the required electrical heating power "# for a given temperature difference and hence the reported thermal conductivity is a more CONSERVATIVE value. Second, the sample length was chosen to ensure that heat conduction along the sample is higher than the surface radiation loss (Supplementary Figure 2d). The ratio of radiation to conduction heat flow can be approximated as: where is the sample thickness, the thermal conductivity, the sample length, the emittance, the Stefan-Boltzmann constant, % and ' the hot and cold side temperatures of the sample.
We attempted to measure emittance based on reflectance and transmittance values, but the low emittance and experimental uncertainties sometimes led to negative values. Therefore, we decided to use emittance of the films at different draw ratios (different thickness) based on the following empirical formula found in literature 11 : = 2.51 × 10 ID − 3.12 × 10 IJ = + 4.55 × 10 IJ − 4.13 × 10 IL + 0.206 where is the film temperature in Celsius, and is the sample thickness in microns which were carefully measured using a micrometer and a profilometer, as detailed in the section below the measured films at different draw ratios. In general, radiation errors are less than 20%, and for the higher draw ratios, less than 10%.
We analyze the radiative thermal shunting loss here. We carefully considered thermal radiative shunting between the hot and cold side. We minimized radiative shunting by using polished copper ( < 0.05) for the hot and cold clamps (Supplementary Figure 1a). In addition, radiative thermal shunting calibration was performed (Supplementary Figure 1f). The same measurement procedure was used without a suspended sample allowing to obtain the radiation heat flow between the hot and the cold side. To ensure a large enough signal-to-noise ratio, the sample geometries were optimized such that the radiative thermal shunting is limited to less than 20% relative to heat conduction by the sample, and less than 10% for most samples Analysis of uncertainties due to sample geometry: error in determining the drawn film thickness was minimized by using a Bruker DektakXT stylus profilometer, which was first calibrated by a 45-nm step height standard from Bruker company. The drawn film was mounted on a silicon wafer, and the film thickness was obtained by the edge step. Supplementary Figure 2a shows film thicknesses at different draw ratios. Each film thickness was measured 10 times at different locations along the sample. Supplementary Figure 2b shows some representative thickness profiles for the 110× film.  Figure 3). The estimated radiation to conduction ratio for the measured Dyneema bundle was <2%.
Minimization of the thermal interface resistance: temperatures of the hot and cold sides were measured by thermocouples attached to the hot and cold clamps. Key to accurately measuring the temperatures is the use of proper thermal interface materials between the film and the copper clamps. Several thermal interface materials (TIM) were investigated using the 304-stainless steel foils 6 , Dyneema fibres 2 and Zylon fibres 2 as the reference samples, which has similar thermal conductance as our polymer films. We found that a certain type of unhardened silver epoxy paste provided a reliable contact and the smallest interface thermal resistance, as compared to other TIMs such as indium foil or silicone-based thermal paste. Using the unhardened silver epoxy paste also gave us the opportunity to disassemble the setup without damaging the sample and with some epoxy left on the clamped ends of the sample as marks. The distance between the marks corresponds to the length of the sample and allows us to double-check our initial length measurement (via the microscope image). We minimize thermal interface resistance by using thermal paste as much as possible (Supplementary Figure 1a). Because there is an effect of thermal contact resistance, our measurement tends to UNDERESTIMATED thermal conductivity of all the samples including drawn polyethylene films.
Effect of the anisotropic thermal conductivity of the films: one of the main characteristic properties of the drawn polymer films is the large anisotropy in thermal conductivity.
In the in-plane draw direction the thermal conductivity ( QR ) is drastically larger than the perpendicular directions such as the cross-plane thermal conductivity ( SR ). This inevitably affects the temperature profile in the clamped region as shown schematically in Supplementary Figure 4a.
Mean sample temperature to the left of the cold clamp can be significantly higher compared to the clamp temperature. In order to estimate the effect we approximate the two-dimensional (2D) fin conduction problem with a 1D fin problem by lumping the sample's cross-plane thermal resistance into an effective thermal contact resistance U%,' ≈ /4 SR (Supplementary Figure 4b). The resulting differential fin equation is with being the film thickness, and ' being the sample temperature along x-direction and the cold clamp temperature, respectively. The differential equation can be solved with a specified heat flux, , at the left side of the clamp and the sample temperature being ' at infinity as the two boundary conditions.

Supplementary Note 3. Time-domain thermoreflectance measurements
Sample preparation: One of the most challenging steps in the time-domain thermoreflectance (TDTR) experiments is sample preparation, whereby a flat and smooth crosssectional surface of the drawn film has to be created 12 . To this end, we hot pressed (Carver 4120) 100 layers of 50× films into a laminate (~150 µm thick, 1 mm wide and 2 cm long) at 120 °C for 40 minutes. We did not expect dramatic structural change due to the elevated temperature, since the film melting point was measured using differential scanning calorimetry (TA Instruments Discovery) to be ~140 °C (Supplementary Figure 5a), consistent with previously reported values (~144 °C) for UHMWPE 13 . We further embedded the laminated 50× film into an epoxy matrix, which was necessary for us to properly mount and cut the cross-section using a microtome (Leica Microsystems). This cutting procedure created a flat and smooth cross-section surface of the laminate and the surrounding epoxy. Using atomic force microscope characterization, the rootman-square roughness of the cross-section surface was measured to be ~10 nm in a 15 µm × 15 µm region (Supplementary Figure 6). It is quite challenging to obtain such ultra-smooth (rootmean-square roughness ~ 10 nm) and aligned polymeric films without altering the sample. The difficulty in sample preparation for TDTR is further complicated by the fact that the yield of our drawing platform is not very uniform at higher draw ratio. We thus only prepared one thick sample for the TDTR experiment.
Measured thermoreflectance signals were fitted to a standard two-dimensional, 3-layer heat conduction model considering the aluminum (Al) transducer, the laminate and in-between interface. Both the out-of-plane (film draw direction) and in-plane thermal conductivity of the UHMWPE laminate were explicitly modeled to account for the expected anisotropy.
Laser parameters: a 100-fs-wide pump laser pulse (~400 nm center wavelength) was used to instantly heat up the surface of an aluminum-coated sample (Supplementary Figure 6), the cooling of which was then monitored using a probe pulse (800 nm) as a function of delay time between the pulses ( Fig. 2c) 9,10 . Subsequently, the cooling curves were fitted to a standard twodimensional heat transfer model to get the sample thermal conductivity ( Fig. 2c and Fig. 2d). In order to increase the signal-to-noise ratio, modulated heating was applied by electro-optical modulation of pump power, which resulted in a complex signal with its amplitude and phase recorded by a lock-in amplifier. Both the amplitude and phase signals were used for model fitting.
The excellent agreement between amplitude and phase fitting confirmed the measurement reliability ( Fig µm, respectively, using a scanning slit beam profiler. Such a configuration ensures that the thermoreflectance signal essentially captures a 1D heat conduction process perpendicular to the sample surface, or equivalently, parallel to the draw direction (Fig. 2c). This setup also helps minimize any uncertainty associated with inaccurate measurement of laser beam size. Finally, multiple pump modulation frequencies (3 MHz and 6 MHz) were used to see if there is any frequency dependence.
Aluminum transducer layer thickness: the Al layer thickness was set as 90 nm during electron-beam evaporation and was subsequently measured using a profilometer as 88 ± 3 nm.
Thickness was further verified by performing TDTR measurement of a standard sapphire sample, which was Al-coated together with the UHMWPE sample.
Heat capacity of 50× films: differential scanning calorimetry measurement of the heat capacity of the 50× films was performed using a TA Instruments Discovery. The calorimeter was calibrated with a standard sapphire sample prior to measurement of the films. The sample temperature was cycled 3 times between 180 K and 340 K at a heating rate of 5 K/min. The

Supplementary Note 4. Structural characterization with synchrotron X-ray
Synchrotron X-ray scattering measurements were carried out at Sector 8-ID-E of Advanced Photon Source (APS), Argonne National Laboratory, with an unfocused and collimated 10.91 keV X-ray beam of cross-section 200´200 µm 2 (V´H). Samples were measured in a vacuum chamber in order to minimize radiation damage and scattering background from air and X-ray windows.
Single-photon-counting area detector Pilatus 1MF was mounted 137 mm and 2153 mm downstream away from the sample for wide-angle X-ray scattering (WAXS) and small-angle Xray scattering (SAXS), respectively. Each sample was translated for multiple examination to ensure macroscopic structural homogeneity. Raw WAXS and SAXS patterns were processed with various corrections with MATLAB-based GIXSGUI software before quantitative structural analysis. The film surface was perpendicular to the incident beam as shown Fig. 4a.

WAXS and SAXS data corrections: intensity of the 2D WAXS and SAXS images was
corrected on a pixel-by-pixel basis 16 : where ikl is the raw data, n is the air gap absorption correction, j is the detector efficiency correction, is the detector's flat-field correction at the operation energy of 10.91 keV, q is the solid angle correction, is the polarization correction, is the Lorentz correction.

WAXS analysis:
We identified an orthorhombic cell with lattice constants a = 7.42 Å, b = 4.95 Å and c = 2.54 Å, which agreed well with reference values 17 .
Effective crystallinity: X-ray diffraction (XRD), or WAXS, is routinely employed to measure the percentage of crystallinity of materials consisting of crystalline and amorphous components 18 . It is based on the assumption that the number of elastically scattered photons by one phase is proportional to the amount of that phase in the scattering volume. This leads to another requirement for this method to work, i.e. tagging each scattered photon to the corresponding phase (crystalline or amorphous). The tagging of photons can be readily achieved provided a known crystalline lattice type and structure 18 . As given in the Supplementary Equation 8, the crystallinity is calculated as the ratio of the integrated intensity from the crystalline peaks to the sum of the crystalline and amorphous intensities 18 .
Most samples for crystallinity analysis often take the form of powders. It is quite a challenge to obtain the true value of crystallinity from polymer fiber or sheet samples using this method 19 . This is because while the amorphous components are isotropic, ordered polymer chains and crystalline components often adopt certain orientations, nullifying the isotropy assumption of the method.
In this work, we introduce a concept of "effective crystallinity" which attempts to approximate the true crystallinity. It was calculated with the same Supplementary  for the 2.5× films, and the amorphous fraction of 0.08 for 110× films (Fig 4f). We note that on high draw-ratio samples, for example, as in the 110× sample, while unprocessed 2D pattern does not reveal significant amorphous contribution, sufficient photon statistics can be seen after the data is converted to 1D XRD curve and thus a high confident estimation of the crystallinity is warranted.
We note that considerable improvements have been achieved over the years both in the film quality and in our X-ray scattering measurements and analysis 1 .
Crystallite orientation: the degree of orientation was quantified by orientation order parameters defined as the intensity-weighted moments of cos , where is the tilt angle between the c-axis and draw direction (Fig. 4a) 20 . The orientation orders can be calculated directly from the Here ⊗ denotes the convolution. The structure factor is defined as the Fourier transform of ( ) and thus given by For lamellar superlattice stacking, = , and the distance of successive units along the drawing direction is coupled with the unit lengths, rather than being independent as in the pure 1D para-crystal model. We therefore adopt the size-spacing coupling approximation (SSCA) 24  We first discuss the extraction of the structural parameters used in the equation. As mentioned above, the SAXS measurement characterizes periodicity of the lamellar superlattice.
One can first obtain the period length from SAXS structure factor analysis. The lengths (and ratios) of different regions (amorphous / crystalline) can be further estimated by studying the electron density distribution. In Fig. 4f inset, we show the electron density profile with respect to the draw ratio measured on different samples. The middle region (Fig. 4f inset, electron density ~1) becomes larger and larger as draw ratio increases, and can be identified as the crystalline region, while the two sides where the electron density is close to zero are the amorphous regions. We take the amorphous region as the part where the electron density is less than 0.05 (corresponding to a length › ). The remaining part ( − › ) is taken as the effective crystallite size S . The ratio between the amorphous region and the total length › / gives the amorphous fraction (Fig. 4f, circles).
Due to the uncertainties involved in estimating the lengths from the SAXS measurement data, we do not directly use the experimental data points for and S in the thermal model. Instead, Finally, we mention that though one-dimensional heat conduction model has been adopted, there is still possibility that the heat may flow across different polyethylene nanofibers. Here we justify our 1D model by showing that the thermal resistance of this curved heat flow is too large to explain our experimentally measured thermal conductivity.
In Supplementary Figure 14c, we show the schematic of the heat flow along a curved path across two different nanofibers. We will focus on one single fiber (fiber A), and estimate the thermal resistance of heat flow from fiber A to the surrounding fibers and then back to fiber A.
We consider path starting at red dashed line and ends at blue dashed line, with a total length corresponding to one repeated unit.
For estimation, we take geometry data for the 50× drawn sample (crystalline thermal conductivity kc ~ 70 W m -1 K -1 , repeated unit length Ltot ~ 22 nm, crystalline domain length Lc ~ 20 nm) and take the nanofiber diameter D to be 10 nm. It is important to note that the nanofibers assemble into bundles mostly via van der Waals interactions, which creates large interfacial thermal resistance. We estimate the interfacial thermal conductance h to be around 3 × 10 Ü W m I= K I• based on literature data 28 for clean interface with van der Waals bonding.
Because the interface in our case is not atomically flat, the actual thermal conductance can be even lower. We also neglect the thermal resistance in the surrounding fibers, effectively treating them to be at uniform temperatures. These simplifications represent the worst scenario which will only underestimate the total thermal resistance.
If the curved path were the dominant heat conduction channel, the corresponding thermal conductivity based on the area and repeated unit length of the nanofiber should match our experimental measurement. However, the corresponding thermal conductivity for the heat flow along the curved path is which is much smaller than the measured thermal conductivity (~ 30 W m -1 K -1 at 50×). The above analysis depends on the interfacial thermal conductance h, for which we have assumed a small value (3 × 10 7 W m -2 K -1 ). Even if h takes a larger value, e.g. h =1 × 10 8 W m -2 K -1 , the corresponding thermal conductivity along the curved path will only see a modest increase (ktot ~ 4.3 W m -1 K -1 ), which is still far from being able to explain our data. Considering all these, we conclude that the curved path has negligible contribution to the total heat conduction.
Sensitivity analysis: here we provide a sensitivity analysis for the relevant parameters (crystalline state thermal conductivity kc, and amorphous fraction ), to show that our conclusion of amorphous phase developing a large thermal conductivity is unaltered by the uncertainties involved in determining the structural parameters. We use the 50× drawn sample as an example.
We first evaluate the sensitivity of the estimated amorphous thermal conductivity ka to kc. In Supplementary Figure 16a, we plot the variation of ka with different values of kc. As stated above, the value of kc is determined by combining our measured crystallite size and the literature reported size-dependent single chain polyethylene thermal conductivity. At 50× we obtained kc ~ 70 W m -Of course, if the fraction of the amorphous region is zero, then it is unnecessary to invoke a large amorphous phase thermal conductivity to explain our measured total thermal conductivity because a large crystalline thermal conductivity itself suffices. However, we believe our structural characterization has provided sufficient evidence to show that the fraction of the amorphous region is not zero (Fig. 4, Supplementary Figure 12 and Supplementary Figure 13). As stated above, the amorphous fraction is estimated from SAXS measurement. For the 50 × drawn sample, the sensitivity of ka to the amorphous fraction parameter ( ) is shown in Supplementary Figure 16b.
At 50×, our estimated amorphous fraction is ~ 11% (Fig. 4f), corresponding to ka ~ 5 W m -1 K -1 . This amorphous fraction is consistent with the crystallinity measured for 50× drawn sample which is ~ 84% (Fig. 4d). We have estimated the amorphous fraction based on SAXS rather than crystallinity because we believe SAXS provides a more quantitative measure. Nonetheless, if we instead inferred the amorphous fraction based on crystallinity to give ~ 16%, ka will be even higher (~7 W m -1 K -1 , Supplementary Figure 16b). The uncertainty involved in determining the amorphous fraction has been taken into account, as shown by the shaded area in Fig. 4f. In case that the actual amorphous fraction is 50% less than the current value ( ~ 6%), ka will be ~ 2.5 W m -1 K -1 (Supplementary Figure 16b), still significantly larger than its bulk situation. Therefore, we have shown that within the possible range of the amorphous fraction , ka could vary but is always significantly larger than its bulk value.
Furthermore, as we mentioned in the manuscript, reference 27 also gave simulated thermal conductivity of different polyethylene crystallites assuming diffuse boundary scattering. Under this assumption, the thermal conductivity of a 30 nm crystallite at room temperature is ~ 40 W m -1 K -1 , which is even smaller than the total thermal conductivity we measured. As explained in the manuscript, we believe that the diffuse boundary scattering maybe too conservative since the interface between the crystalline and amorphous regions is of van der Waals in nature and also some molecules may extend from the crystalline to the amorphous regions. A smaller thermal conductivity of the crystalline region only leads to a larger amorphous region thermal conductivity.
Hence, we believe that the stated thermal conductivity of the amorphous region represents conservative lower limits.  Table 2). The error bars take into account the uncertainties in the measurement of the Sn film geometry, the uncertainty in the estimation of the radiation contribution (Sn emissivity at room temperature takes 0.04 with 50% uncertainty considered) and the uncertainty in the thermal shunting measurement. h Measured thermal conductivity for Al films with different geometry (Supplementary Table 2). The error bars represents the uncertainties in the measurement of the Al film geometry, the uncertainty in the estimation of the radiation contribution (Al emissivity at room temperature takes 0.07 respectively with 50% uncertainty considered) and the uncertainty in the thermal shunting measurement. Detailed analysis of geometric uncertainties is discussed in Supplementary 2. Blue curve represents expected thermal conductivity of aluminum from measurement with respect to the sample length, considering the contact resistance, following the analysis given in Supplementary Equation 5 and Supplementary Equation 6 but replacing kCP by t/2RC, where RC is the contact resistance. An RC value of 4.2×10 -5 m 2 K W -1 gives thermal conductivities matching our experiments, and this RC value corresponds to a 42 µm layer thick silver epoxy paste if the uncured silver epoxy has a thermal conductivity of 1 W m -1 K -1 and it is reasonable. The cross-sectional area takes the sample geometry (width is 0.51mm, and thickness is 25µm). The contact resistance value is within reasonable range for interfaces between metals, explaining the lower value of our measured thermal conductivity for the highly conductive reference samples. Compared with reference value for Al thermal conductivity 7 , we always underestimate the Al thermal conductivity by our steady-state method. i Geometrically scaled electrical heating power (Pels) as a function of the temperature difference (Th-Tc) across films. Representative data (10×, 90×, 110×, Dyneema and S. Steel 304) are scaled to the geometry of a 50Å~ film (Pels = Pel •(A/L)50×/ (A/L)). A larger slope indicates a higher thermal conductivity.

Draw ratio Length
Supplementary Figure 2. Polyethylene film thickness and radiation error analysis. a Drawn polyethylene film thickness is in the range of ~ 1-8 , as measured by a stylus profilometer. b Representative profiles for 110× film at 10 different locations along the sample. c Computed emittance for various polyethylene films at 298 K. d Radiation error as a function of draw ratio. In general, radiation errors are less than 25%, and for the higher draw ratios, less than 10%. Figure 3. SEM images. a Average Dyneema fiber diameter is ~17

Supplementary
. Scale bar indicates 50 . b Zylon fiber diameter is ~11.7 . Scale bar indicates 10 . c Images of a torn 70× polyethylene film in this work, the interior nanofiber diameters is ~ 8 nanometers. Scale bar indicates 100 .
Supplementary Figure 6. Images across multiple length scales of a TDTR sample. The sample features a UHMWPE laminate embedded in an epoxy matrix, and was carefully cut with a microtome at room temperature in order to reveal a flat and smooth cross-section for TDTR measurement. a Photo of the sample mounted in front of a long-working-distance 10× microscope objective. Inset is a zoom-in view of the microtomed cross-section partially coated with an 88 nmthick aluminum layer. b Dark-field optical micrograph of the sample cross-section obtained during a TDTR measurement. The UHMWPE laminate cross-section is ~1 mm × 150 µm and consists of 100 layers of as-drawn 50× films hot pressed together. It separated into two halves during sample preparation. Smooth and dark regions generally indicate good sample surface quality. The blue and red circles show the pump (53 µm in diameter) and probe (11 µm) spots, respectively. Scale bar indicates 100 . c Bright-field optical micrograph of the cross-section prior to e-beam evaporation of aluminum. Scale bar indicates 200 . d AFM image of the UHMWPE laminate cross-section. The root-mean-square surface roughness is ~10 nm. Scale bar indicates 5 .

Supplementary Figure 7. Measured and fitted complex thermoreflectance signals.
The measured data is the average of 10 individual runs using a modulation frequency of 6 MHz. a-b Real and imaginary parts of the complex signal, respectively. c-d Amplitude (normalized) and phase representation of the same signal, respectively. Phase fitting was performed to obtain the sample thermal conductivity together with the aluminum/sample interface thermal conductance, which were subsequently used to compute all the red curves. The reliability of the experimental results is demonstrated by the fact that fitting to phase alone leads to excellent agreement between modeled and measured data in all four panels. As expected, fitting of the amplitude yields equally good results (see Fig. 2d). Figure 8. Sensitivity analysis of the TDTR experiment. a Sensitivity 9,10 of the amplitude of the complex thermoreflectance signal to the aluminum/substrate (UHMWPE laminate) interface thermal conductance (GAl/Substrate) and substrate thermal conductivity (kSubstrate). b Sensitivity when fitting to the phase of the thermoreflectance signal. Although amplitude fitting and phase fitting offer different relative sensitivity to the substrate conductivity and the interface conductance, both are sufficiently sensitive considering the relatively small experimental noise and more importantly the excellent agreement between results from phase and amplitude fitting.  Figure 10. Schematic of the lamellar superlattice structure and electron density profile. a Each repeating unit of the lamellar superlattice is of a total length , which includes three phases: a crystal phase of length S , an amorphous phase of length › , and two transition layers of length è in between to represent an electron density change from crystalline to amorphous. b

Supplementary
Step-like three phase model describing the electron density profile of the unit is simplified by a two-phase model with a continuous density profile. In the two-phase model, the transition is modeled by an error function profile (whose derivative is a Gaussian of standard deviation of s). Figure 11. The structure factor and size distribution analyzed by SAXS. a The structure factor ( ) is modeled using the 1D para-crystal model, and describes how the units are stacked to form a lamellar superlattice. The curves are vertically shifted for clarity (except 1×). As draw ratio increases, the humps move to smaller q, suggesting larger length scales in the higher draw ratio films. The humps become less significant at higher draw ratios, suggesting more structural disordering as shown in Supplementary Figure 11b Figure 10. b Modeled variation of thermal conductivity along chain direction in one unit cell, noting that the transition region has been included into the crystalline part by assuming that the former has a thermal conductivity equal to that of the latter. c Schematic for heat flow along the curved path (start at fiber A, flow into surrounding fibers, and then back to fiber A). While the path is drawn for one fiber in the surrounding, in reality multiple fibers can exist and has been taken into account in the analysis.