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Megalitres of water with associated dissolved oxygen are injected into shale reservoirs during the hydraulic fracturing process. Pyrite oxidation, if it occurs in-situ, can generate extra H+, thereby dissolving calcite and increasing the salinity of flowback water. The process of calcite dissolution may soften the hydraulic fracture surfaces, resulting in proppants embedment and thus decreasing fracture conductivity for calcite-rich shales. Therefore, it is of vital importance to understand the impact of in-situ pyrite oxidation on fluid-shale interactions, particularly calcite dissolution, to help industry screen and design hydraulic fracturing fluids in shales. Spontaneous imbibition experiments were performed using Marcellus shale samples under three conditions: i) ambient conditions, where the fluid was in equilibrium with atmospheric air throughout the tests, ii) limited O2 condition, where the fluid was free equilibrated with air in a sealed cylinder and iii) vacuum condition, where the fluid in a sealed cylinder was degassed. The pH and ion concentrations were measured upon completion of the experiments. To further explore how pyrite oxidation affects fluid-rock interactions, we performed geochemical simulations with considerations of mineral dissolution (calcite, albite, quartz, chalcopyrite, pyrite and dolomite), surface complexation and the dissolved O2 on fluid salinity. The spontaneous imbibition tests show that the salinity of fluids in ambient conditions is higher than the limited or vacuumed saturation fluids, confirming that pyrite oxidation generates H+ which would dissolve minerals such as calcite and dolomite. This result is also supported by the observed pH and the concentration of dissolved Ca2+. The fluid fully saturated with O2 has the lowest pH and highest Ca2+ compared to limited O2 saturation condition and degassed condition. Scanning electron microscopy analyses show that brine saturation barely affects the morphology and elemental distribution of pyrite at ambient conditions, suggesting that pyrite oxidation plays a minor role in fluid salinity. Geochemical modelling also indicates that although pyrite oxidation can slightly increase fluid salinity, the salinity increment is less than 5% of reported flowback water salinity, confirming that the dissolved O2 in hydraulic fracturing fluids has a minor effect on fluid-rock interaction thus the salinity increment. This work demonstrates that pyrite dissolution at lab-scale would overestimate the impact of fluid-shale interactions and calcite dissolution in reservoir conditions. We prove that pyrite dissolution in in-situ conditions results in minor implications for fluid-shale interactions and calcite dissolution. Consequently, we limit intrinsic uncertainty of hydraulic fluid design associated with pyrite oxidization especially for calcite-rich shales.

The microseismicity associated with hydraulic fracturing in unconventional reservoir (i.e. shale gas play) has been investigated in the past several decades. Few experimental studies with respect to the focal mechanism and stress inversion was conducted, especially for Glutenite reservoir. In this study, the glutenite core was taken from the underground of 2600 m. Next, we performed scaled hydraulic fracturing tests on the cubic core (50×50×50mm) under geological principle stress condition in true tri-axial stress cell. Meanwhile, we monitored wellbore and pore pressure, and micro-seismic events during the fracture propagation from six faces of the cubic rock. Micro-seismic survey and events were interpreted to identify the induced fractures distribution in three dimension. Source mechanism and stress inversion were analyzed by moment tensor decomposition. The correlation of failure plane from microseismicity and tested sample implied that the microseismic events were accurately localized. The distribution of microseismic events from secondary and reopening tests indicated that the hydraulic fracturing induced microseismicity are mainly caused by significant tip effect (i.e. reactivate preexisting natural fractures). Based on source mechanism analysis, we found that the most of the failure are dominated by double-couple (DC). The correlation between original principle stress state and the one from STESI inversion indicated that the direction of principle stresses, especially for σ2 and σ3 inversed from reopening test, can be highly influenced by the hydraulic induced fracture or weak planes during secondary fracturing test.

A high-performance anion exchange membrane (AEM) is critical for the development of alkaline fuel cell. In this work, AEMs with an interpenetrating polymer network (IPN) are synthesized. An electron microscope clearly reveals a highly efficient “ion channel” network, which is constructed with a small amount of cation exchange groups. This specially designed ion channel leads to extraordinary hydroxide conductivity (e.g., 257.8 mS cm -1 at 80 °C) of IPN AEMs at moderate ion exchange capacity ( IEC = 1.75 mmol g − 1 ), as well as excellent long-term alkaline stability at harsh condition which showed that 81% of original conductivity can be retained after a long time for 1248 hours. Moreover, a remarkable peak power density of 1.20 W cm -2 (0.1 MPa backpressure) with nonprecious metal (FeNx-CNTs) as oxygen reduction reaction (ORR) catalyst in a fuel cell test was achieved. This work offers a general strategy to prepare high-performance AEMs based on IPN structure design.

Water uptake induced by fluid&ndash, rock interaction plays a significant role in the recovery of flowback water during hydraulic fracturing. However, the existing accounts fail to fully acknowledge the significance of shale anisotropy on water uptake typically under in situ reservoir temperature. Thus we investigated the shale-hydration anisotropy using two sets of shale samples from the Longmaxi Formation in Sichuan Basin, China, which are designated to imbibe water parallel and perpendicular to shale bedding planes. All the samples were immersed in distilled water for one to five days at 80 &deg, C or 120 &deg, C. Furthermore, samples&rsquo, topographical and elemental variations before and after hydration were quantified using energy-dispersive spectroscopy&ndash, field-emission scanning electron microscopy. Our results show that shale anisotropy and imbibition time strongly affect the width of pre-existing micro-fracture in hydrated samples. For imbibition parallel to lamination, the width of pre-existing micro-fracture initially decreases and leads to crack-healing. Subsequently, the crack surfaces slightly collapse and the micro-fracture width is enlarged. In contrast, imbibition perpendicular to lamination does not generate new micro-fracture. Our results imply that during the flowback process of hydraulic fracturing fluid, the shale permeability parallel to bedding planes likely decreases first then increases, thereby promoting the water uptake.

To reveal the enhanced oil recovery (EOR) potential of CO2 huff-n-puff in fractured tight conglomerate reservoirs, hydraulic fracturing combined with CO2 huff-n-puff experiments were conducted using a true triaxial stress cell core fracturing and displacement system. To better understand the potential mechanisms behind CO2 huff-n-puff, the change in rock properties and formation water properties caused by the interactions among supercritical CO2/formation water/oil/rock were investigated. Experimental results demonstrate that CO2 huff-n-puff is viable to boost oil recovery in tight conglomerate reservoirs with recovery factor of 23.2% after hydraulic fracturing and depletion process. Rock surface morphology, mineralogical composition and formation water composition analysis indicate that supercritical CO2 leads the water-oil-rock system to more water-wet by increasing rock surface roughness. Geochemical simulation results combining the surface complexation and ion-exchange shows that supercritical CO2 weakens the crude oil adsorption on rock surface, which also contributes to the oil recovery increment. These results reveal the EOR feasibility of CO2 huff-n-puff in fractured tight conglomerate reservoirs, and provide insights to characterize geochemical features of carbonated brine/oil/rock.

We reported an interface-induced synthesis of iron nitrogen (FeNx) enriched carbon nanotubes (FeNx-CNTs) with high activity in alkaline and acidic environment for oxygen reduction reaction (ORR) by coating polypyrrole (PPy) thin layers on iron-doped zeolitic imidazolate framework-8 (Fe-ZIF). The constructed polymer/metal-organic framework (MOF) interface suppresses the agglomeration of iron (Fe) atomic sites during the thermal activation, and thus facilitates carbon nanotubes (CNTs) formations with FeNx coordination in carbon matrix. The produced FeNx-CNTs catalyst shows excellent ORR activities with extremely high peak power density of 1.15 and 1.16 W cm−2 in anion and proton exchange membrane fuel cells, respectively.

Interpenetrating polymer network anion exchange membrane (IPN AEM) consists of cross-linked quaternized poly (vinylbenzyl chloride) and cross-linked poly (vinyl alcohol) is synthesized in this work. Electron microscope clearly reveals the IPN structure, and with this structural design, a highly efficient ion channel within IPN AEMs is constructed. This specially designed structure leads to high hydroxide (OH−) conductivity (e.g., 141.7 mS cm−1 at 80 °C) at a moderate ion exchange capacity (IEC) of 1.61 mmol g−1, and a remarkable peak power density of 0.64 W cm−2 with non-noble metal oxygen reduction reaction (ORR) catalyst in H2/Air (CO2-free) anion exchange membrane fuel cells (AEMFCs) test.

Super-insulating aerogels are promising materials to improve the energy efficiency of buildings. However, fabricating super-insulating yet mechanically robust and shape-memory aerogels remains challenging. Here, we integrate graphene oxide and a block copolymer to fabricate hybrid aerogels with triple networks and systematically study their mechanical and thermal properties. We show that the first network serves as sacrificial bonds and dissipates energy upon deformation, enabling the aerogels to have a high mechanical performance. The second network allows the aerogels to memorize the original permanent shape, and the third network is able to store strain energy and fix the aerogels in a temporary shape by vitrification. Remarkably, the strong phonon-scattering effect generated by the enormous interfaces between the three networks yields an ultra-low solid thermal conductivity of ∼8 mW m−1 K−1. The multi-functionality makes this class of hybrid aerogels particularly suitable for super-insulation applications on complex surfaces and in small spaces of buildings, industry and spacecrafts.

Fluid-shale interactions appear to significantly affect shale micromechanical properties, which regulate fracture network propagation during multistage hydraulic fracturing in shales and thus the gas production. While published works confirm that fluid-shale interactions can reduce Young's modulus and rock strength compared to dry shale samples, few attentions have been paid to unveil the nature of the physics with a combination of geochemical modelling and disjoining pressure isotherm, and fewer works have envisaged the effect of mineralogy (calcite-rich or quartz-rich rock) on shale weakening with presence of aqueous liquids. We hypothesize that fluid-mineral interactions likely generate electrical double layer force between mineral surfaces which would shift the disjoining pressure from strongly negative (mineral-air-mineral) to less negative or even positive (mineral-fluid-mineral) thus triggering Young's modulus reduction. To test the hypothesis, geochemical modellings including minerals dissolution (calcite, dolomite, quartz, pyrite and illite) and surface complexation were performed together with disjoining pressure isotherm using literature experimental data, accounting for the Young's modulus reduction induced by fluid-shale interactions. The geochemical modelling shows that the amount of mineral dissolution at in-situ condition is negligible, and thus may play a minor role in Young's modulus. Disjoining isotherm shows that both calcite and quartz (plane-plane geometry) give a strong negative disjoining pressure generated by van der Waals force and structural force in the presence of air, whereas the disjoining pressure can be shifted from strongly negative to less negative for calcite and even positive for quartz in presence of fluids due to the electrostatic force, suggesting a Young's modulus reduction due to the weaker adhesion in line with literature experimental data. This work provides an overall conceptual framework, which supports the hydraulic fracturing fluid design and treatment in shale reservoirs from geochemical and disjoining pressure isotherm perspectives.

CO2 huff-n-puff process appears to be important to unlock hydrocarbon resources from shale oil reservoirs after multi-stage hydraulic fracturing. While existing literature shows that CO2 diffusion plays a significant role in kinetics of oil recovery, few studies have been able to draw on any systematic research into fluid-shale interaction due to water uptake of CO2 in connate water (water carbonation), which governs fluids flow in fractures thus CO2 huff-n-puff performance. We therefore hypothesized that water carbonation would depress ion exchange process between oil and organic matter (OM) thus forming a more water-wet system. Moreover, water carbonation would also decrease the electrostatic forces between oil and edge charge on OM, thereby further promoting water-wet system. To test the hypothesis, we measured contact angles in non‑carbonated high salinity brine (HS), carbonated high salinity brine (CO2 HS) and carbonated low salinity brine (CO2 LS) at temperature of 25 °C and under pressure of 3000 psi. Moreover, a geochemical modelling was conducted to evaluate ion exchange and surface complexation reactions in three different brines. Our contact angle measurements showed that HS gave a contact angle of 130°, while CO2 HS and CO2 LS resulted a contact angle of 23.5° and 23.0°, suggesting a more water-wet system. Geochemical modelling shows that ion exchange reactions between oil and shale surfaces are dramatically depressed in carbonated brine. In particular, the bridges number between oil and shale surfaces decreases from 5.2 × 10−4 μmol/m2 to 5.3 × 10−6 μmol/m2 in carbonated brines, supporting the contact angle measurements. Moreover, the computed surface potential at oil and rock surfaces increases from around −40 mV to 150 mV, suggesting more repulsive forces in the presence of carbonated brine, further supporting contact angle results. This work reveals for the first time that water carbonation during CO2 huff-n-puff process likely triggers a hydrophilic shale surface, which may significantly affects multiphase flow in natural and hydraulic fractures in particular.

Subcritical crack growth in calcite-bearing reservoirs plays a vital role in rock deformation. Published experimental results show that fluid-rock interaction likely affects rock surface energy and triggers fracture propagation. However, much of research up to now has been only descriptive in nature, impairing a substantial interpretation to predict subcritical crack growth. In this study, we developed a physicochemical model to relate fluid-calcite interaction in particular surface potential to surface energy in light of capacitance theory. To test the model, we calculated calcite surface chemical species and surface potential as a function of pH, ion type and fluid salinity using surface complexation modeling. Moreover, we compared the predicted surface energy with Bergsaker et al.'s experimental measurements. Our results confirm that fluid chemistry would affect calcite surface species distribution and surface energy. At high acidic condition, lowering salinity increases surface potential of brine-calcite. At alkaline condition, lowering salinity decreases surface potential in the presence of MgSO4 and MgCl2 but increases that of Na2SO4. Furthermore, pH would affect the level of bonding-capable divalent such as Ca2+ through the equilibrium of calcite dissolution-precipitation, and thus indirectly influence surface energy. Our results unveil the importance of fluid-rock interaction on subcritical crack growth and shed light on hydrocarbon exploitation and CO2 capture and storage in carbonate reservoirs. These findings also delineate the inner connection between geochemical and geo-mechanical properties at subsurface.

Unlike conventional optics, plasmonics enables unrivaled concentration of optical energy well beyond the diffraction limit of light. However, a significant part of this energy is dissipated as heat. Plasmonic losses present a major hurdle in the development of plasmonic devices and circuits that can compete with other mature technologies. Until recently, they have largely kept the use of plasmonics to a few niche areas where loss is not a key factor, such as surface-enhanced Raman scattering and biochemical sensing. Here, we discuss the origin of plasmonic losses and various approaches to either minimize or mitigate them based on understanding of fundamental processes underlying surface plasmon modes excitation and decay. Along with the ongoing effort to find and synthesize better plasmonic materials, optical designs that modify the optical powerflow through plasmonic nanostructures can help in reducing both radiative damping and dissipative losses of surface plasmons. Another strategy relies on the development of hybrid photonic–plasmonic devices by coupling plasmonic nanostructures to resonant optical elements. Hybrid integration not only helps to reduce dissipative losses and radiative damping of surface plasmons, but also makes possible passive radiative cooling of nanodevices. Finally, we review emerging applications of thermoplasmonics that leverage Ohmic losses to achieve new enhanced functionalities. The most successful commercialized example of a loss-enabled novel application of plasmonics is heat-assisted magnetic recording. Other promising technological directions include thermal emission manipulation, cancer therapy, nanofabrication, nanomanipulation, plasmon-enabled material spectroscopy and thermo-catalysis, solar water treatment, and thermophotovoltaics., United States. Department of Energy. Office of Basic Energy Sciences (Grant DE-FG02-02ER45977), United States. Defense Advanced Research Projects Agency (Grant DE-AR0000471), Solid-State Solar-Thermal Energy Conversion Center (Award DE-SC0001299), Solid-State Solar-Thermal Energy Conversion Center (Award DE-FG02-09ER46577)

We demonstrate the agreement between first-principles calculations and experimental measurements of size effects in thermal transport in SiGe alloys without fitting parameters. Transient thermal grating (TTG) is used to measure the effect of the grating period on the temperature decay. The virtual crystal approximation under the density-functional-theory framework combined with impurity scattering is used to determine the phonon properties for the exact alloy composition of the measured samples. With these properties, classical size effects are calculated for the experimental geometry of reflection mode TTG using the recently developed variational solution to the phonon Boltzmann transport equation, which is verified against established Monte Carlo simulations. We find agreement between theoretical predictions and experimental measurements in the reduction of thermal conductivity (as much as fourfold of the bulk value) across grating periods spanning one order of magnitude. This paper provides a framework for the study of size effects in thermal transport in opaque materials.

Multi-stage hydraulic fracturing is an indispensable approach to enable shale oil available and affordable. However, a low flowback water recovery (usually Surface complexation modelling results show that the oil-brine-OM system wettability is primarily controlled by in-situ salinity and secondarily affected by pH and temperature. At a given pH, decreasing salinity triggers a greater positive surface potential for both oil and OM surfaces, implying a greater electrical double layer expansion thus hydrophilicity. Moreover, the surface potential for oil and OM decreases with increasing pH, which even would be shifted from positive to negative in the presence of low salinity water. Furthermore, the surface potential of both oil and OM decreases with increasing temperature at in-situ pH (from 3.5 to 7). The disjoining pressure results show that saturating sample from high salinity formation brine into the low salinity KCl solution will shift the disjoining pressure from negative values (attraction) to positive values (repulsion). Our results support the hypothesis that lowering salinity increases hydrophilicity of oil-brine-OM, which likely contributes to water uptake by shale. We also argue that geochemical modelling would be an effective tool to characterize the interaction of oil-brine-OM, providing insights into water uptake and enhanced oil recovery in shales.

Significance Thermoelectric technology can boost energy consumption efficiency by converting some of the waste heat into useful electricity. Heat-to-power conversion efficiency optimization is mainly achieved by decreasing the thermal conductivity in many materials. In comparison, there has been much less success in increasing the power factor. We report successful power factor enhancement by improving the carrier mobility. Our successful approach could suggest methods to improve the power factor in other materials. Using our approach, the highest power factor reaches ∼106 μW⋅cm −1 ⋅K −2 at room temperature. Such a high power factor further yields a record output power density in a single-leg device tested between 293 K and 868 K, thus demonstrating the importance of high power factor for power generation applications.

Tailoring the thermal conductivity of polymers is central to enlarge their applications in the thermal management of flexible integrated circuits. Progress has been made over the past decade by fabricating materials with various nanostructures, but a clear relationship between various functional groups and thermal properties of polymers remains to be established. Here, we numerically study the thermal conductivity of single-stranded carbon-chain polymers with multiple substituents of hydrogen atoms through atomic mass modification. We find that their thermal conductivity can be tuned by atomic mass modifications as revealed through molecular dynamics simulations. The simulation results suggest that heavy homogeneous substituents do not assist heat transport and trace amounts of heavy substituents can in fact hinder heat transport substantially. Our analysis indicates that carbon chain has the biggest contribution (over 80%) to the thermal conduction in single-stranded carbon-chain polymers. We further demonstrate that atomic mass modifications influence the phonon bands of bonding carbon atoms, and the discrepancies of phonon bands between carbon atoms are responsible for the remarkable drops in thermal conductivity and large thermal resistances in carbon chains. Our study provides fundamental insight into how to tailor the thermal conductivity of polymers through variable substituents., National Science Council (China) (51376069), National Key Basic Research Program of China (2013CB228302)

et al., Studying thermal transport at the nanoscale poses formidable experimental challenges due both to the physics of the measurement process and to the issues of accuracy and reproducibility. The laser-induced transient thermal grating (TTG) technique permits non-contact measurements on nanostructured samples without a need for metal heaters or any other extraneous structures, offering the advantage of inherently high absolute accuracy. We present a review of recent studies of thermal transport in nanoscale silicon membranes using the TTG technique. An overview of the methodology, including an analysis of measurements errors, is followed by a discussion of new findings obtained from measurements on both >solid> and nanopatterned membranes. The most important results have been a direct observation of non-diffusive phonon-mediated transport at room temperature and measurements of thickness-dependent thermal conductivity of suspended membranes across a wide thickness range, showing good agreement with first-principles-based theory assuming diffuse scattering at the boundaries. Measurements on a membrane with a periodic pattern of nanosized holes (135nm) indicated fully diffusive transport and yielded thermal diffusivity values in agreement with Monte Carlo simulations. Based on the results obtained to-date, we conclude that room-temperature thermal transport in membrane-based silicon nanostructures is now reasonably well understood., The work done at MIT was supported as part of the “Solid State Solar-Thermal Energy Conversion Center (S3TEC),” an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001299/DEFG02-09ER46577. The contribution by A.V.-F. and J. J. A.-G. was partially supported by Project 192 “Fronteras de la ciencia” and Project 251882 “Investigacion Científica Basica.” A. V.-F. also appreciates support from Conacyt through normal and mixed scholarships. MS and CMST acknowledge support from the Spanish program Severo Ochoa (Grant SEV-2013-0295), projects PHENTOM (FIS2015-70862-P) and nanoTHERM (CSD2010-00044), as well as from the EU project MERGING (309150). Z.L. and E.N.W. further acknowledge support and funding from the Air Force Office of Scientific Research (AFOSR), and are grateful to program manager Dr. Ali Sayir.

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring non-diffusive transport. By utilizing the known Fourier solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime., Comment: 17 pages, 2 figures

Superlattices are promising low-dimensional nanomaterials for thermoelectric technology that is capable of directly converting low-grade heat energy to useful electrical power. In this work, the thermal conductivities of GaAs/Ge superlattice nanostructures were investigated systematically in relation to their morphologies and interfaces. Thermal conductivities were measured using ultrafast time-domain thermoreflectance and were found to decrease with increasing interface densities, consistent with our understanding of microscopic phonon transport in the particle regime. Lower thermal conductivities were observed in (GaAs)0.77(Ge2)0.23 alloys; transmission electron microscopy study reveals phase separation in the alloys. These alloys can be interpreted as fine nanostructures, with length scales comparable to the periods of very thin superlattices. Our experimental findings help gain fundamental insight into nanoscale thermal transport in superlattices and are also useful for future improvement of thermoelectric performance using superlattice nanostructures., Comment: 11 pages, 5 figures

A single polyethylene chain was reported to have a high metal-like thermal conductivity (TC), which stands in sharp contrast to the thermally insulating feature of common bulk polyethylene materials. This work numerically investigates the impact of torsion and stretching on the TC of polyethylene strands by using equilibrium molecular dynamics simulations. The simulation results show that torsion slightly reduces the TC of a single polyethylene chain. In contrast, the heat conduction of polyethylene strands could be slightly enhanced under torsional loading with a specific torsional angle. Particularly, an apparent improvement of TC of polyethylene strands is achieved by combining torsion and stretching functions. It is found that the TC of torsional polyethylene strands is sensitive to torsional patterns. Our study proposes a specific torsional pattern of polyethylene strands that significantly enhances the heat conduction of the original counterpart. This study will play an essential role in guiding the...

The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path (MFP) distribution of materials via transient grating experiments., Comment: 19 pages, 4 figures

The impact of boundary scattering on non-diffusive thermal relaxation of a transient grating in thin membranes is rigorously analyzed using the multidimensional phonon Boltzmann equation. The gray Boltzmann simulation results indicate that approximating models derived from previously reported one-dimensional relaxation model and Fuchs-Sondheimer model fail to describe the thermal relaxation of membranes with thickness comparable with phonon mean free path. Effective thermal conductivities from spectral Boltzmann simulations completely free of any fitting parameters are shown to agree reasonably well with experimental results. These findings are important for improving our fundamental understanding of non-diffusive thermal transport in membranes and other nanostructures., Comment: 15 pages, 3 figures