A statistical theory of interfacial thermal conductivity
Interfacial thermal conductivity model based on statistical features of two faces in contact, discussing surface roughness and heat flow
Burkhard, D. G.↗
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Effect of HIPing on the effective thermal conductivity/diffusivity and the interfacial thermal conductance of uniaxial SiC fibre-reinforced RBSN
Hot isostatic pressing (HIPing) was found to increase the thermal diffusivity/conductivity of uniaxial silicon carbide fiber-reinforced reaction-bonded silicon nitride (RBSN) matrix composites, as the result of the densification of the matrix, the increase in the grain size of the silicon carbide and the improved thermal contact between the fibers and the matrix. Transverse to the fiber direction the thermal diffusivity/conductivity was found to be a function of the surrounding gaseous atmosphere due to the access of the gas phase to the fiber-matrix interface, which was facilitated by the existence of an interfacial gap due to the thermal expansion mismatch between the fibers and the matrix. The interfacial conductance was found to exhibit a strong positive temperature dependence as the result of the closure of the interfacial gap with increasing temperature.
Bhatt, H.↗
On the theory of interfacial conductivity
Thermal and electric conductivities for interface separating two parts of system with different temperature and chemical and electrical potential
Narnhofer, H.↗
Statistical study of thermal contact conductance
A theoretical analysis of the principles of interfacial thermal conductance between two heated metal surfaces in mutual contact is presented. It was determined that when heat flows from one metal to the other, the flow lines converge toward the actual contact points since the thermal conductivities of the metals are much greater than any intervening medium such as air or fluids. The converging lines cause contact resistance, which is usually high compared to the resistances offered to heat flow by metals. The resultant variation in resistance can produce unreliable equipment for aerospace and industrial applications unless the conductance can be determined accurately.
Nejat, V. T.↗
Study of interfacial conductivity Final report
Statistical theory of interfacial thermal conductivity and crystal growth under weightlessness
Burkhard, D. G.↗
Role of the interfacial thermal barrier in the effective thermal diffusivity/conductivity of SiC-fiber-reinforced reaction-bonded silicon nitride
Experimental thermal diffusivity data transverse to the fiber direction for composites composed of a reaction bonded silicon nitride matrix reinforced with uniaxially aligned carbon-coated silicon carbide fibers indicate the existence of a significant thermal barrier at the matrix-fiber interface. Calculations of the interfacial thermal conductances indicate that at 300 C and 1-atm N2, more than 90 percent of the heat conduction across the interface occurs by gaseous conduction. Good agreement is obtained between thermal conductance values for the oxidized composite at 1 atm calculated from the thermal conductivity of the N2 gas and those inferred from the data for the effective composite thermal conductivity.
Bhatt, Hemanshu↗
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.↗
Role of interfacial thermal barrier in the transverse thermal conductivity of uniaxial SiC fiber-reinforced reaction bonded silicon nitride
The transverse thermal conductivity of reaction-bonded Si3N4 is significantly affected by an interfacial barrier at the interface formed with SiC reinforcing fibers. A comparative study of composites with and without reinforcing-fiber carbon coatings found the coating to reduce effective thermal conductivity by a factor of about 2; this, however, is partially due to a thermal expansion-mismatch gap between fiber and matrix. HIPing of composites with coated fibers led to an enhancement of thermal conductivity via improved interfacial thermal contact and greater grain size and crystallinity of the fibers.
Bhatt, H.↗
Challenges and Opportunities in Gen3 Embedded Cooling with High-Quality Microgap Flow
Gen3, Embedded Cooling, promises to revolutionize thermal management of advanced microelectronic systems by eliminating the sequential conductive and interfacial thermal resistances which dominate the present 'remote cooling' paradigm. Single-phase interchip microfluidic flow with high thermal conductivity chips and substrates has been used successfully to cool single transistors dissipating more than 40kW/sq cm, but efficient heat removal from transistor arrays, larger chips, and chip stacks operating at these prodigious heat fluxes would require the use of high vapor fraction (quality), two-phase cooling in intra- and inter-chip microgap channels. The motivation, as well as the challenges and opportunities associated with evaporative embedded cooling in realistic form factors, is the focus of this paper. The paper will begin with a brief review of the history of thermal packaging, reflecting the 70-year 'inward migration' of cooling technology from the computer-room, to the rack, and then to the single chip and multichip module with 'remote' or attached air- and liquid-cooled coldplates. Discussion of the limitations of this approach and recent results from single-phase embedded cooling will follow. This will set the stage for discussion of the development challenges associated with application of this Gen3 thermal management paradigm to commercial semiconductor hardware, including dealing with the effects of channel length, orientation, and manifold-driven centrifugal acceleration on the governing behavior.
microchannel↗
A numerical and analytical study of nonlinear bifurcations associated with the morphological stability of two-dimensional single crystals
The nonlinear stability of a two-dimensional single crystal of pure material in an undercooled melt is studied both analytically and numerically. The quasi-steady state approximation is used for the thermal fields, and the effects of different solid and liquid thermal conductivities, isotropic interfacial growth kinetics, and isotropic surface tension are included. The bifurcation analysis is performed by calculating the instantaneous value of the fundamental component of the local normal growth speed for an interface perturbed by a single Fourier shape component. Numerically, the fundamental component of the interfacial growth speed is found by Fourier analysis of the solution to an integrodifferential equation obeyed at the interface. Analytically, an expansion technique is used to derive a solvability condition defining each of these bifurcation points. The analytical and numerical results are in very close agreement. Almost all of the bifurcations are subcritical, and the results are presented by giving values of the Landau coefficient as a function of the different dimensionless parameters used in the model.
Brush, L. N.↗
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.↗
Nano-engineered Multiwall Carbon Nanotube-copper Composite Thermal Interface Material for Efficient Heat Conduction
Efforts in integrated circuit (IC) packaging technologies have recently been focused on management of increasing heat density associated with high frequency and high density circuit designs. While current flip-chip package designs can accommodate relatively high amounts of heat density, new materials need to be developed to manage thermal effects of next-generation integrated circuits. Multiwall carbon nanotubes (MWNT) have been shown to significantly enhance thermal conduction in the axial direction and thus can be considered to be a candidate for future thermal interface materials by facilitating efficient thermal transport. This work focuses on fabrication and characterization of a robust MWNT-copper composite material as an element in IC package designs. We show that using vertically aligned MWNT arrays reduces interfacial thermal resistance by increasing conduction surface area, and furthermore, the embedded copper acts as a lateral heat spreader to efficiently disperse heat, a necessary function for packaging materials. In addition, we demonstrate reusability of the material, and the absence of residue on the contacting material, both novel features of the MWNT-copper composite that are not found in most state-of-the-art thermal interface materials. Electrochemical methods such as metal deposition and etch are discussed for the creation of the MWNT-Cu composite, detailing issues and observations with using such methods. We show that precise engineering of the composite surface affects the ability of this material to act as an efficient thermal interface material. A thermal contact resistance measurement has been designed to obtain a value of thermal contact resistance for a variety of different thermal contact materials.
Ngo, Quoc↗
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.↗
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↗
Role of interfacial carbon layer in the thermal diffusivity/conductivity of silicon carbide fiber-reinforced reaction-bonded silicon nitride matrix composites
Experiments were carried out on samples of reaction-bonded silicon nitride uniaxially reinforced by SiC monofilaments with and without a 3-micron-thick carbon-rich coating. It is found that a combination of a carbon coatings on the fibers and an interfacial gap due to the thermal expansion mismatch in the composite can significantly (by a factor of 2) lower the effective thermal diffusivity in the direction transverse to the fiber. At atmospheric pressure, gaseous conduction across the interfacial gap makes a significant contribution to the heat transfer across the interface, indicated by significantly lower values of the effective thermal diffusivity under vacuum than in nitrogen or helium at atmospheric pressure.
Bhatt, Hemanshu↗
Thin Interface Asymptotics for an Energy/Entropy Approach to Phase-Field Models with Unequal Conductivities
Karma and Rapped recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp-interface solidification models, as discussed further by Almgren. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The additional degrees of freedom associated with the generalized phased-field equations can be chosen to eliminate the anomalous terms that arise for unequal conductivities.
McFadden, G. B.↗
SAGE III on ISS Lessons Learned on Thermal Interface Design
The Stratospheric Aerosol and Gas Experiment III (SAGE III) instrument - the fifth in a series of instruments developed for monitoring vertical distribution of aerosols, ozone, and other trace gases in the Earth's stratosphere and troposphere - is currently scheduled for delivery to the International Space Station (ISS) via the SpaceX Dragon vehicle in 2016. The Instrument Adapter Module (IAM), one of many SAGE III subsystems, continuously dissipates a considerable amount of thermal energy during mission operations. Although a portion of this energy is transferred via its large radiator surface area, the majority must be conductively transferred to the ExPRESS Payload Adapter (ExPA) to satisfy thermal mitigation requirements. The baseline IAM-ExPA mechanical interface did not afford the thermal conductance necessary to prevent the IAM from overheating in hot on-orbit cases, and high interfacial conductance was difficult to achieve given the large span between mechanical fasteners, less than stringent flatness specifications, and material usage constraints due to strict contamination requirements. This paper will examine the evolution of the IAM-ExPA thermal interface over the course of three design iterations and will include discussion on design challenges, material selection, testing successes and failures, and lessons learned.
Davis, Warren↗