A note on the Kapitza resistance.
Kinetic theory model for heat transfer across liquid He 2 boundary in contact with metal, noting agreement with Kapitza thermal resistance theory
Abbe, W. J.↗
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Understanding Thermal Transport in Polymer –Silver Nanowire Composites
Understanding thermal transport across filler-polymer interfaces and filler-filler contacts within polymer composites is of great importance for better thermal design of the composites that are widely used in high-performance heat exchangers, energy storage devices, and flexible electronics. Over the past several decades, considerable progress has been made in improving the thermal conductivity of polymer composites, but several key questions concerning the influence of interfacial thermal resistance, or Kapitza resistance, still remain. Firstly, the thermal properties of these composites are highly dependent on thermal transport through the filler network and its contacts. For metallic nanofillers, the thermal conductivity is often estimated using the Wiedemann-Franz law based on electrical conductivity; however, it remains a question whether the Wiedemann-Franz law still holds at nanoscale contacts. Through investigation of silver nanowires of varying sizes, we were able to demonstrate that the Lorenz number for silver nanowire increases with decreasing nanowire diameter. Examination of the corresponding electrical and thermal conductivities indicate that these changes are due to that the relative contribution of phonons becomes more significant as a result of elastic stiffening. Furthermore, we show that for silver nanowires, the contact thermal resistance is ~8 times lower than that of multi-walled carbon nanotube (MWCNT) of similar diameters. Additionally, through systematic studies of electrospun polymer-silver nanowire composite nanofibers, we investigated the impact of interface morphology on the thermal conductivity enhancement of the composite system and probed the value of the Kapitza resistance for individual polymer-filler interfaces. For polymer nanofibers containing continuous, single silver nanowires, the thermal conductivity increases linearly with increasing volume fraction of silver, which is consistent with the prediction of percolation theory for samples above the percolation limit. By comparing this linear trend to the measured thermal conductivities of composite nanofibers with more complex structures, we were able to determine the resistance associated with any additional polymer-filler boundaries. In doing so we find that the thermal boundary resistance for polyvinylpyrrolidone (PVP)–silver interfaces is significantly lower than that of comparable polymer-MWCNT composite systems.Together our studies provide new insights into thermal transport in polymer nanocomposites and should help facilitate the design of high performance polymeric thermal interface material.
Thermal transport↗
Understanding Thermal Transport in Polymer - Silver Nanowire Composites
Understanding thermal transport across filler-polymer interfaces and filler-filler contacts within polymer composites is of great importance for better thermal design of the composites that are widely used in high-performance heat exchangers, energy storage devices, and flexible electronics. Over the past several decades, considerable progress has been made in improving the thermal conductivity of polymer composites, but several key questions concerning the influence of interfacial thermal resistance, or Kapitza resistance, still remain. Firstly, the thermal properties of these composites are highly dependent on thermal transport through the filler network and its contacts. For metallic nanofillers, the thermal conductivity is often estimated using the Wiedemann-Franz law based on electrical conductivity; however, it remains a question whether the Wiedemann-Franz law still holds at nanoscale contacts. Through investigation of silver nanowires of varying sizes, we were able to demonstrate that the Lorenz number for silver nanowire increases with decreasing nanowire diameter. Examination of the corresponding electrical and thermal conductivities indicate that these changes are due to that the relative contribution of phonons becomes more significant as a result of elastic stiffening. Furthermore, we show that for silver nanowires, the contact thermal resistance is ~8 times lower than that of multi-walled carbon nanotube (MWCNT) of similar diameters. Additionally, through systematic studies of electrospun polymer-silver nanowire composite nanofibers, we investigated the impact of interface morphology on the thermal conductivity enhancement of the composite system and probed the value of the Kapitza resistance for individual polymer-filler interfaces. For polymer nanofibers containing continuous, single silver nanowires, the thermal conductivity increases linearly with increasing volume fraction of silver, which is consistent with the prediction of percolation theory for samples above the percolation limit. By comparing this linear trend to the measured thermal conductivities of composite nanofibers with more complex structures, we were able to determine the resistance associated with any additional polymer-filler boundaries. In doing so we find that the thermal boundary resistance for polyvinylpyrrolidone (PVP)–silver interfaces is significantly lower than that of comparable polymer-MWCNT composite systems. Together our studies provide new insights into thermal transport in polymer nanocomposites and should help facilitate the design of high performance polymeric thermal interface material.
Matthew L. Fitzgerald↗
Thermal conductivity and Kapitza boundary resistance of He-4 near T(gamma)
The preliminary results of high resolution measurements of the thermal conductivity of He-4 in a cell with a nominal 1 mm gap are reported and compared with previous results obtained with a 2 mm gap. The temperature dependence of the conductivity was found to be similar for both cells, indicating that size and boundary effects are well controlled. The detailed behavior of the Kapitza resistance just below T(gamma) is also reported.
Chui, T. C. P.↗
Modeling of Interfacial Modification Effects on Thermal Conductivity of Carbon Nanotube Composites
The effect of functionalization of carbon nanotubes on the thermal conductivity of nanocomposites has been studied using a multi-scale modeling approach. These results predict that grafting linear hydrocarbon chains to the surface of a single wall carbon nanotube with covalent chemical bonds should result in a significant increase in the thermal conductivity of these nanocomposites. This is due to the decrease in the interfacial thermal (Kapitza) resistance between the single wall carbon nanotube and the surrounding polymer matrix upon chemical functionalization. The nanocomposites studied here consist of single wall carbon nanotubes in a bulk poly(ethylene vinyl acetate) matrix. The nanotubes are functionalized by end-grafting linear hydrocarbon chains of varying length to the surface of the nanotube. The effect which this functionalization has on the interfacial thermal resistance is studied by molecular dynamics simulation. Interfacial thermal resistance values are calculated for a range of chemical grafting densities and with several chain lengths. These results are subsequently used in an analytical model to predict the resulting effect on the bulk thermal conductivity of the nanocomposite.
Clancy, Thomas C.↗
Prediction of Material Properties of Nanostructured Polymer Composites Using Atomistic Simulations
Atomistic models of epoxy polymers were built in order to assess the effect of structure at the nanometer scale on the resulting bulk properties such as elastic modulus and thermal conductivity. Atomistic models of both bulk polymer and carbon nanotube polymer composites were built. For the bulk models, the effect of moisture content and temperature on the resulting elastic constants was calculated. A relatively consistent decrease in modulus was seen with increasing temperature. The dependence of modulus on moisture content was less consistent. This behavior was seen for two different epoxy systems, one containing a difunctional epoxy molecule and the other a tetrafunctional epoxy molecule. Both epoxy structures were crosslinked with diamine curing agents. Multifunctional properties were calculated with the nanocomposite models. Molecular dynamics simulation was used to estimate the interfacial thermal (Kapitza) resistance between the carbon nanotube and the surrounding epoxy matrix. These estimated values were used in a multiscale model in order to predict the thermal conductivity of a nanocomposite as a function of the nanometer scaled molecular structure.
Hinkley, J.A.↗
Multiscale Modeling of Thermal Conductivity of Polymer/Carbon Nanocomposites
Molecular dynamics simulation was used to estimate the interfacial thermal (Kapitza) resistance between nanoparticles and amorphous and crystalline polymer matrices. Bulk thermal conductivities of the nanocomposites were then estimated using an established effective medium approach. To study functionalization, oligomeric ethylene-vinyl alcohol copolymers were chemically bonded to a single wall carbon nanotube. The results, in a poly(ethylene-vinyl acetate) matrix, are similar to those obtained previously for grafted linear hydrocarbon chains. To study the effect of noncovalent functionalization, two types of polyethylene matrices. -- aligned (extended-chain crystalline) vs. amorphous (random coils) were modeled. Both matrices produced the same interfacial thermal resistance values. Finally, functionalization of edges and faces of plate-like graphite nanoparticles was found to be only modestly effective in reducing the interfacial thermal resistance and improving the composite thermal conductivity
Clancy, Thomas C.↗
Measurement of the Heat Capacity of He-II Under a Heat Current Near the Lambda Transition
We present preliminary measurements of the heat capacity of superfluid helium-4 under an applied heat current near the lambda transition. The calorimeter is a standard cylindrical thermal conductivity cell with a 0.6 mm gap between two copper endplates. The sidewall is made of stainless steel. A heat current density in the range of 1 to 4 microW/sq cm is applied through the helium sample while a pulse method is used to measure the heat capacity. Temperature changes are recorded with high-resolution thermometers (HRTs) located on the top and bottom endplates. Corrections are made to the readings of the HRTs to account for the Kapitza boundary resistance and the anomalous Kapitza boundary resistance. After the corrections, both the top and the bottom HRTs. give the same heat capacity values. The heat capacity is found to be much larger than the prediction of recent theories. We also plotted our data on a scaled plot to test the prediction of scaling by the theories. The result and its interpretation will be presented. The cell height was deliberately made to be thin to reduce the effects of gravity. Nonetheless, gravity is expected to have significant effects on the heat capacity data in the temperature range of our measurement. A space experiment would remove this unwanted gravity effect and allow the true physics to be examined. Moreover, in the absence of gravity, a deeper cell can be used allowing HRTs to be mounted on to the sidewall providing direct measurements of the helium temperature, unaffected by the anomalous Kapitza boundary resistance.
Harter, Alexa W.↗
Passive Gas-Gap Heat Switches for Use in Adiabatic Demagnetization Refrigerators
We have designed, built, and tested a gas gap heat switch that works passively, without the need for a separate, thermally activated getter. This switch uses He-3 condensed as a thin film on alternating plates of copper. The switch is thermally conductive at temperatures above about 0.2 K, and is insulating if either end of the switch is below about 0.15 K. The "on" conductance (7 mW/K at 0.25K) is limited by the surface area and gap between the copper leaves, the saturated vapor pressure of the He-3, and the Kapitza boundary resistance between the He-3 and the copper. The "off" conductance is determined by the helium containment shell which physically supports the two conductive ends. We have also designed and are building passive gas gap heat switches which will passively turn off near 1 K and 4 K. For these switches we rely on the rapidly changing vapor pressure of He-4 above neon or copper substrates, respectively, when the coverage is less than one monolayer. The different binding energies of the He-4 to the neon or copper give rise to the different temperatures where the switches transition between the on and off states.
Shirron, P. J.↗
Multiscale Modeling of Grain Boundaries in ZrB2: Structure, Energetics, and Thermal Resistance
A combination of ab initio, atomistic and finite element methods (FEM) were used to investigate the structures, energetics and lattice thermal conductance of grain boundaries for the ultra high temperature ceramic ZrB2. Atomic models of idealized boundaries were relaxed using density functional theory. Information about bonding across the interfaces was determined from the electron localization function. The Kapitza conductance of larger scale versions of the boundary models were computed using non-equilibrium molecular dynamics. The interfacial thermal parameters together with single crystal thermal conductivities were used as parameters in microstructural computations. FEM meshes were constructed on top of microstructural images. From these computations, the effective thermal conductivity of the polycrystalline structure was determined.
Lawson, John W.↗