Thermal conductivity and interface thermal conductance• Thermal conductivity is a property of thecontinuum• Thermal conductance (per unit area) G is aproperty of an interface
Analyze ratio V in /V out using an exactsolution of the heat diffusion equation
Maximum pressure achieved in thermalconductivity measurements1 atm=bar1 bar=100 kPa1 Mbar=100 GPaDalton and Hsieh
I. Works well for homogeneous disorderedmaterials but is this model valid for glassypolymers?amorphousdisordered crystalfeldsparPMMA
Test the applicability of the model for glassypolymers• Polymers combine strongcovalent bonds along thebackbone (and within theside groups) and weak“non-bonded” interactionsbetween chains.• At high pressures, thisstrong inhomogeneity inbond strength is reduced.C 11 data for PMMA frompicosecond interferometry
Need thin (
Nanoscale polymer brushes “graftedfrom” the SiC anvil
Thermal conductivity of PMMA polymer isindependent of thickness and agrees well withthe predicted scaling with (C 11 ) 1/2Thermal Conductivity (W m -1 K -1 )10.50.20.1Andersson et al. 0 n 1/6 C 111/210 nm22 nm9 nm6 nm13 nm0 2 4 6 8 10 12Pressure (GPa)
II. Do optical phonons contribute to heatconduction or scatter acoustic phonons?• Leibfried-Schlömann equation– acoustic phonons dominant heatcarriers– three phonon anharmonic scatteringbetween acoustic modes controlsphonon mean-free-pathfV1/33D2TV molecular volume = Debye frequency Gruneisen parameter• Test using relative low modulus water ice thatis compressed by 33% at P=22 GPa.
Water ice has a remarkably rich phase diagramPetrenko and Whitworth (1999)
Ice VII, cubic with two interpenetrating but notinterconnected bcc sub-lattices• Hydrogen-bonding inice VII is disordered• Ice VIII is the protonordered form• Ice X is thought to be“polymeric”: H-bondis symmetricC.J. Knight, Ph.D. thesis (2009)
Use Al-coated mica as a substrate. Measure usingAr and then with ice.Diamond anvil cell
Measuring thermal conductivity of water ice VII• Experimental details are complicated1. coat thin mica substrate with Al2. measure mica with Ar pressure medium3. use published MD simulation of Ar thermalconductivity to analyze the data for mica4. measure again with H 2 O ice as thepressure medium5. use density functional theory to calculatechanges in H 2 O heat capacity per unitvolume6. analyze the data7. repeat...
Derive changes in Debye frequency ω D andGrüneisen parameter γ from equation of state V(P)• Data for V(P) are fitto a model (e.g.,Birch-Murnaghan)• Assume ω D scaleswith K 1/2• γ is derived from asecond derivative ofthe V(P) curve.V(P) of ice VII by synchrotronx-ray diffractionFrank et al., Geochimica et Cosmochimica Acta, 2004
Good agreement with LS equation overwide range of compression
III. What is the role of weak interfacialbonding in thermal transport at interfaces?• Elastic constants andphonon spectra oftypical materials do notchange much between0
Interface stiffness s is analogous tointerface thermal conductance Gapply pressure, Papply heat flux, Jdisplacement, dd1sP ( )PTemperature, TT1GJzz
Deposit Al on SiC with and without coating withmonolayer CVD graphene by transfer-printingDiamond anvil cell
Clean SiC anvil at high temperaturesand deposit Al film in-situ by sputtering
Compare clean interface with a layer ofCVD graphene inserted at the interface• Clean interface has theweak pressuredependence expectedfrom diffuse-mismatch(DMM) calculations.• Insert graphene: lowconductance andstrong pressuredependence.• At P>8 GPa, “weak”interface becomes“strong” andconductance is high.
Summary• Pressure dependence of PMMA polymer in good agreementwith the model of the minimum thermal conductivity– Polymers do not resemble the atomic solids the model wasoriginally intended for. Why is this model is so robust?• Pressure dependence of ice VII in good agreement withLeibfried-Schlömann equation– Optical phonons are not an important factor for thermalconductivity of water ice either as carriers or scatteringmechanisms. Will this be true for oxide minerals?• Pressure dependence of typical (dirty, weakly bonded)interfaces is in poor agreement with the diffuse mismatchmodel– Weak interfacial bonding suppresses heat conduction atinterfaces. Pressure can be used to vary the strength ofinterface bonding.