Minimum Thermal Conductivity Model Research Articles

Structure and thermal conductivity of high-pressure-treated silica glass. A molecular dynamics study

High-pressure treatment of oxide glasses can lead to significant alteration of various material properties such as increased density, ductility, and elastic moduli. In this study, a model of melt-quenched bulk silica glass was subject to high-pressure treatments (up to 16 GPa) using molecular dynamics simulations. The thermal conductivity of such prepared glass structures was determined using the equilibrium Green–Kubo method. We observed that, up to the pressure treatments of ∼6 GPa, the structure exhibits moderate density increase and a much steeper increase between 6 and 16 GPa, with associated density increase of fivefold silicon atoms. We also observed a noticeable increase (up to 20%) of the thermal conductivity in samples subjected to high-pressure treatments. The observed increases are somewhat, but not significantly, larger than those predicted by the minimum thermal conductivity model, accounting for density and elastic moduli increase.

Effect of hydrogen bonds on the thermal transport in a precisely branched polyethylene with ordered and amorphous structures

Hydrogen bonds are considered to be bridges in forming networks for heat transfer in polymers. Nevertheless, a large number of polymer systems with hydrogen bonds have very low thermal conductivity (TC). The role of hydrogen bonds in regulating TC of polymers is still beyond fully understood. Herein, we systematically investigate the effect of hydrogen bonds on the intrinsic TC of polymers with ordered and amorphous structures by using molecular dynamics simulations. The ordered polymer (termed as ar-P21AA) has lamella structure with stacked layers alternatively composed of aligned polymer chains and hydrogen-bonded functional groups, which provides an ideal model for studying hydrogen-bond-mediated heat transfer. We find that significant ITR exists at the interface composed of hydrogen-bonded carboxyl groups; nevertheless, ITR of that hydrogen-bonded interface is about 2 times smaller than that of a typical VdWs interface. The Role of hydrogen bonds in enhancing the interfacial thermal transport is analyzed. As for the amorphous ar-P21AA, increasing the hydrogen-bonding strength does not change much TC due to the invariance of stiffness and packing density of the structure, in terms of the minimum thermal conductivity model. A consequent effect on the chain morphology when introducing hydrogen bonds may be a factor to be considered for improving the thermal conductivity. The work provides insight into the design of thermally conductive polymers by introducing hydrogen-bonding interaction.

Uniquely anisotropic mechanical and thermal responses of hybrid organic-inorganic perovskites under uniaxial strain.

The complete understanding of the mechanical and thermal responses to strain in hybrid organic-inorganic perovskites holds great potential for their proper functionalities in a range of applications, such as in photovoltaics, thermoelectrics, and flexible electronics. In this work, we conduct systematic atomistic simulations on methyl ammonium lead iodide, which is the prototypical hybrid inorganic-organic perovskite, to investigate the changes in their mechanical and thermal transport responses under uniaxial strain. We find that the mechanical response and the deformation mechanisms are highly dependent on the direction of the applied uniaxial strain with a characteristic ductile- or brittle-like failure accompanying uniaxial tension. Moreover, while most materials shrink in the two lateral directions when stretched, we find that the ductile behavior in hybrid perovskites can lead to a very unique mechanical response where negligible strain occurs along one lateral direction while the length contraction occurs in the other direction due to uniaxial tension. This anisotropy in the mechanical response is also shown to manifest in an anisotropic thermal response of the hybrid perovskite where the anisotropy in thermal conductivity increases by up to 30% compared to the unstrained case before plastic deformation occurs at higher strain levels. Along with the anisotropic responses of these physical properties, we find that uniaxial tension leads to ultralow thermal conductivities that are well below the value predicted with a minimum thermal conductivity model, which highlights the potential of strain engineering to tune the physical properties of hybrid organic-inorganic perovskites.

Effect of Linker Length and Temperature on the Thermal Conductivity of Ethylene Dynamic Networks.

Dynamic covalent networks are a class of polymers containing exchangeable bonds. The influence of the thermodynamics and kinetics of dynamic bond exchange on the thermal conductivity and mechanical properties of dynamic networks is important for understanding how they differ from thermoplastics and thermosets. In this work, a series of ethylene dynamic networks are synthesized from benzene diboronic acid and alkane diols with different precise ethylene linker lengths. The thermal conductivity of these ethylene dynamic networks at 40 °C decreases from 0.19 to 0.095 W/(m K) when the ethylene linker length increases from 4 to 12 carbons. The thermal conductivity also has a strong temperature dependence, decreasing by a factor of 3 over the temperature range from -80 °C to 100 °C. The minimum thermal conductivity model predicts these trends of the thermal conductivity with variations in ethylene linker length and temperature.

Effect of Aromatic/Aliphatic Structure and Cross-Linking Density on the Thermal Conductivity of Epoxy Resins

High thermal conductivity polymers are in great demand as thermal management materials. However, the thermal conductivity of polymers is typically low, ∼0.2 W/(m K), and a predictive understanding of the relationship between the thermal conductivity and the molecular structure of polymers is not yet established. In this work, 14 epoxy resin thermosets are synthesized from one aliphatic epoxide and one aromatic epoxide with seven amine hardeners. These thermosets are used to systematically examine the dependence of the thermal conductivity on the molecular structure of the epoxide and the hardener. In general, aromatic structures have a higher thermal conductivity than aliphatic structures. Moreover, naphthalene-based hardeners provide the highest thermal conductivity, 0.34 W/(m K), 230% higher than the lowest thermal conductivity among the 14 epoxy resin thermosets. The cross-linking density is controlled by mixing different molar ratios of diamine and triamine and does not influence the thermal conductivity, volumetric heat capacity, density, or longitudinal speed of sound. Measured thermal conductivities of 14 epoxy resins lie between 50 and 115% of the prediction of the minimum thermal conductivity model.

Elasticity and thermal transport of commodity plastics

Applications of commodity polymers are often hindered by their low thermal conductivity. In these systems, going from the standard polymers dictated by weak van der Waals interactions to biocompatible hydrogen bonded smart polymers, the thermal transport coefficient k varies between 0.1 - 0.4 W/Km. Combining all-atom molecular dynamics simulations with some experiments, we study thermal transport and its link to the elastic response of commodity plastics. We find that there exists a maximum attainable stiffness (or sound wave velocity), thus providing an upper bound of k for these solid polymers. The specific chemical structure and the glass transition temperature play no role in controlling k, especially when the microscopic interactions are hydrogen bonding based. Our results are consistent with the minimum thermal conductivity model and existing experiments. The effect of polymer stretching on k is also discussed.

Elimination of Extreme Boundary Scattering via Polymer Thermal Bridging in Silica Nanoparticle Packings: Implications for Thermal Management

Recent advances in our understanding of thermal transport in nanocrystalline systems are responsible for the integration of many technologies into advanced energy systems, including thermoelectric refrigeration systems and renewable energy platforms. However, there is little understanding of heat energy transport mechanisms that govern the thermal properties of disordered nanocomposites. In this work, we explore thermal transport mechanisms in disordered packings of amorphous nanoparticles with and without a polymer filling the interstices in order to quantify the impact of thermal boundary scattering introduced at nanoparticle edges in an already amorphous system and within the context of a minimum thermal conductivity approximation. By fitting a modified minimum thermal conductivity model to temperature-dependent measurements of thermal conductivity from 80 to 300 K, we find that the interstitial polymer eliminates boundary scattering in the disordered nanoparticle packing, which surprisingly leads to a...

Thermoelectric properties of inverse perovskites A3TtO (A = Mg, Ca; Tt = Si, Ge): Computational and experimental investigations

Oxygen-containing inverse perovskites represent one possible solution to reduce the cost and enhance the sustainability of thermoelectric materials. Although oxygen-containing compounds may be thought to reduce the electronic mobility and thus the thermoelectric performance, computational studies on A3TtO (A = Mg, Ca; Tt = Si, Ge) revealed that they exhibit high electrical conductivity originating from Dirac cones at valence and conduction bands. High Seebeck coefficients were predicted arising from multiple degenerate bands, leading to enhanced power factors, and low thermal conductivities were predicted using the minimum thermal conductivity model. These predictions were validated by experimental studies on Ca3SiO and Ca3GeO, which were synthesized through high-temperature methods. They adopt an orthorhombic structure (space group Imma). Transport measurements show high Seebeck coefficients and low thermal conductivities for these compounds, confirming their potential for high thermoelectric performance.

Low thermal conductivity of atomic layer deposition yttria-stabilized zirconia (YSZ) thin films for thermal insulation applications

Thermal insulation applications have long required materials with low thermal conductivity, and one example is yttria (Y2O3)-stabilized zirconia (ZrO2) (YSZ) as thermal barrier coatings used in gas turbine engines. Although porosity has been a route to the low thermal conductivity of YSZ coatings, nonporous and conformal coating of YSZ thin films with low thermal conductivity may find a great impact on various thermal insulation applications in nanostructured materials and nanoscale devices. Here, we report on measurements of the thermal conductivity of atomic layer deposition-grown, nonporous YSZ thin films of thickness down to 35nm using time-domain thermoreflectance. We find that the measured thermal conductivities are 1.35–1.5Wm−1K−1 and do not strongly vary with film thickness. Without any reduction in thermal conductivity associated with porosity, the conductivities we report approach the minimum, amorphous limit, 1.25Wm−1K−1, predicted by the minimum thermal conductivity model.

Thermal conductivity of methanol-ethanol mixture and silicone oil at high pressures

4:1 methanol-ethanol (ME) mixture and silicone oil are common, important pressure transmitting media used in high pressure diamond anvil cell (DAC) experiments. Their thermal conductivities and elastic properties are critical for modeling heat conduction in the DAC experiments and for determining thermal conductivity of measurement samples under extreme conditions. We used time-domain thermoreflectance and picosecond interferometry combined with the DAC to study the thermal conductivities and elastic constants C11 of the ME mixture and silicone oil at room temperature and to pressures as high as ≈23 GPa. We found that pressure dependence of the thermal conductivity of ME and silicone oil are both well described by the prediction of the minimum thermal conductivity model, confirming the diffusion of thermal energy between nonpropagating molecular vibrational modes is the dominant heat transport mechanism in a liquid and amorphous polymer. Our results not only provide new insights into the physics of thermal transport in these common pressure media for high pressure thermal measurements, but will also significantly extend the feasibility of using silicone fluid medium to much higher pressure and moderately high temperature conditions with higher measurement accuracy than other pressure media.

Thermal conductivity of sputtered amorphous Ge films

We measured the thermal conductivity of amorphous Ge films prepared by magnetron sputtering. The thermal conductivity was significantly higher than the value predicted by the minimum thermal conductivity model and increased with deposition temperature. We found that variations in sound velocity and Ge film density were not the main factors in the high thermal conductivity. Fast Fourier transform patterns of transmission electron micrographs revealed that short-range order in the Ge films was responsible for their high thermal conductivity. The results provide experimental evidences to understand the underlying nature of the variation of phonon mean free path in amorphous solids.

Ultralow thermal conductivity of fullerene derivatives

Recently, Duda et al. [J. C. Duda, P. E. Hopkins, Y. Shen, and M. C. Gupta, Phys. Rev. Lett. 110, 015902 (2013)] reported that the fullerene derivative [6,6]-phenyl-C${}_{61}$-butyric acid methyl ester (PCBM) has the lowest thermal conductivity \ensuremath{\Lambda} ever observed in a fully dense solid, \ensuremath{\Lambda} \ensuremath{\approx} 0.03 W m${}^{\ensuremath{-}1}$ K${}^{\ensuremath{-}1}$. We have investigated a variety of phases and microstructures of PCBM and the closely related compound [6,6]-phenyl-C${}_{61}$-butyric acid n-butyl ester (PCBNB) and find that the thermal conductivities of PCBM and PCBNB films are mostly limited to the range 0.05 \ensuremath{\Lambda} 0.06 W m${}^{\ensuremath{-}1}$ K${}^{\ensuremath{-}1}$ with a few samples having slightly higher \ensuremath{\Lambda}. The conductivities we observe are \ensuremath{\approx}70$%$ larger than reported by Duda et al. but are still ``ultralow'' in the sense that the thermal conductivity is a factor of \ensuremath{\approx}3 below the conductivity predicted by the minimum thermal conductivity model using an estimate of the thermally excited modes per molecule.

Effective thermal conductivity of the solid backbone of aerogel

Based on the superlattice nanowire model, a modified model to predict the effective thermal conductivity of aerogel solid backbone is presented. We study both the size effect and interfacial resistance effect on the thermal conductivity of interconnected particles of the aerogel backbone. The effective thermal conductivity of the aerogel backbone is significantly lower than that of the pure nanowire and the single particle due to the interfacial thermal resistance. The solid thermal conductivity of the aerogel calculated by the present model is in good agreement with that by the minimum thermal conductivity model, and also agrees well with available experimental data when the aerogel density is above 100kg/m3.

Ultralow Thermal Conductivity in Polycrystalline CdSe Thin Films with Controlled Grain Size

Polycrystallinity leads to increased phonon scattering at grain boundaries and is known to be an effective method to reduce thermal conductivity in thermoelectric materials. However, the fundamental limits of this approach are not fully understood, as it is difficult to form uniform sub-20 nm grain structures. We use colloidal nanocrystals treated with functional inorganic ligands to obtain nanograined films of CdSe with controlled characteristic grain size between 3 and 6 nm. Experimental measurements demonstrate that thermal conductivity in these composites can fall beneath the prediction of the so-called minimum thermal conductivity for disordered crystals. The measurements are consistent, however, with diffuse boundary scattering of acoustic phonons. This apparent paradox can be explained by an overattribution of transport to high-energy phonons in the minimum thermal conductivity model where, in compound semiconductors, optical and zone edge phonons have low group velocity and high scattering rates.

Thermal conductivity and refractive index of hafnia-alumina nanolaminates

Hafnia-alumina nanolaminates show improved smoothness and reduced crystallinity relative to pure hafnia in films formed by atomic layer deposition (ALD). However, typical nanolaminates also show reduced cross-plane thermal conductivity due to the much larger interface density relative to continuous films. We find that the interface thermal resistance in hafnia-alumina nanolaminates is very low and does not dominate the film thermal conductivity, which is 1.0 to 1.2 W/(m K) at room temperature in 100 nm thin films regardless of the interface density. Measured films had a number of interfaces ranging from 2 to 40, equivalent to interface spacing varying from about 40 to 2 nm. The degree of crystallinity of these films appears to have a much larger effect on thermal conductivity than that of interface density. Cryogenic measurements show good agreement with both the minimum thermal conductivity model for disordered solids and the diffuse mismatch model of interface resistance down to about 80 K before diverging. We find that the films are quite smooth through a 400:5 ratio of hafnia to alumina in terms of ALD cycles, and the refractive index scales as expected with increasing alumina concentration.

Testing the minimum thermal conductivity model for amorphous polymers using high pressure

Pressure dependence of thermal conductivity provides a critical test of the validity of the model of the minimum thermal conductivity for describing heat transport by molecular vibrations of an amorphous polymer. We measure the pressure dependence of the thermal conductivity \ensuremath{\Lambda}($P$) of poly(methyl methacrylate) using a combination of time-domain thermoreflectance and SiC anvil-cell techniques. We also determine \ensuremath{\Lambda}($P$) from a computational model of amorphous polystyrene. In both cases, \ensuremath{\Lambda}($P$) is accurately predicted by the minimum thermal conductivity model via the pressure dependence of the elastic constants and density.

Interfacial effects on the thermal conductivity of a-Ge thin films grown on Si substrates

We use the 3ω method to measure the effective thermal conductivity of thin films of a-Ge with thicknesses of 20–150 nm in the temperature range of 30–300 K. By using a moving shadow mask, the films are grown on the same Si (001) substrate in a single deposition run to minimize changes in the microstructure. We observe a reduction in the effective conductivity of the films with the decreasing layer thickness. From the measured data we estimate values for both the film thermal conductivity and the thermal boundary resistance (TBR) between SiO2/a-Ge/Si at the different temperatures. An experimental value of the interface resistance of 2×10−8 m2 K/W is obtained at 300 K. The temperature dependence of the TBR differs appreciably from calculations based on the diffusive mismatch model. The values derived for the intrinsic thermal conductivity of the films, kfilm(300 K)=0.64 W/mK, agree with predictions from the minimum thermal conductivity model and with values measured by Cahill and Pohl [Phys. Rev. B 37, 8773 (1988)] for thicker films.

Nanoscale Thermal Property of Amorphous SiC: A Molecular Dynamics Study

AbstractThermal properties of amorphous silicon carbide (a-SiC) at nanometric scales are studied by molecular dynamics (MD) simulations based on an empirical interatomic potential. A scalable parallel MD algorithm is used for studying systems as long as 30nm. To validate the potential, phonon density of states and specific heat of a-SiC are first calculated. Size effects are studied, and errors are estimated for the temperature profile for different system sizes. Simulation time required to achieve steady temperature profiles is also determined. Finally the thermal conductivities of a-SiC at various temperatures are calculated. The results show that thermal conductivities of a-SiC at nanometric scale also agree with Slack's minimum thermal conductivity model.

Thermal conductivity computed for vitreous silica and methyl-doped silica above the plateau

The thermal conductivity of carbon-doped silicon dioxide films, fabricated to potentially serve as interlayer materials with low dielectric permittivity in small circuits, has been recently measured [B. C. Daly et al., Physica B 316-317, 254 (2002)]. Trends in the results were found to be inconsistent with the minimum thermal conductivity model. We report computational results for the thermal conductivity of vitreous silica and two methyl-doped silica systems of different composition, which serve as models for vitreous silica with nanoscale defects, in terms of their vibrational modes. Addition of methyl groups to silica influences the nature of the vibrational modes, particularly in the THz region. These modes, while apparently not localized, exhibit enhanced amplitude around methyl groups and are better characterized as resonant modes. We find the thermal conductivity to decrease with increased methyl doping, corresponding to a decrease in the participation ratio of the heat-carrying modes.

Thermal conductivity decomposition and analysis using molecular dynamics simulations: Part II. Complex silica structures

Using molecular dynamics simulations, the thermal conductivity of silica-based crystals is found to be a result of two independent thermal transport mechanisms associated with atomic structure. The first mechanism is temperature independent, produces a thermal conductivity on the order of 1 W/m K, and is related to short length scale behavior. It is governed by the silicon coordination, which is unique to a given structure. The second mechanism is temperature dependent and is related to long length scale behavior. At a temperature of 300 K, the associated thermal conductivity ranges from 9 W/m K for the c-direction of quartz to 0.4 W/m K for zeolite-A. This mechanism is controlled by the atomic bond lengths and angles. Complex unit cells, notably cage structures, can distort the SiO 4 tetrahedra, leading to a shortening of the phonon mean free path and a spatial localization of energy. The results suggest that an alternative to the available minimum thermal conductivity model for amorphous materials is needed for the crystalline state.