patrick(e.(hopkins( 0.2 si 0.8ge 0.2 with 2.0 at% b sample(preparaon(and(characterizaon(sample...

Patrick E. Hopkins Assistant Professor

Dept. Mech. & Aero. Eng. University of Virginia [email protected] patrickehopkins.com

ExcepAonally low thermal conducAviAes of fullerene derivaAve films and composites

John C. Duda University of Virginia **Now at Seagate Technologies, Minneapolis, MN Yang Shen and Mool Gupta Dept. of Electrical and Computer Engineering, University of Virginia

Extremes of heat conducAon

1022 10230.01

0.1

1

10

100

1000

Atomic Density (cm-3)

Ther

mal

Con

duct

ivity

(W m

-1 K

-1)

AmorphousCrystalline

DiamondCopper

AluminumSilicon

GermaniumLead

SiO2

Aerogels PCBM

C60/C70WSe2

:carbonP3HT

5000

0.005

Electrons and phonons

Localization/weak bonding

Structural disorder

Modified from Ken Goodsons plot (Science 315, 342 (2007))

Outline

Polymer samples and time domain thermoreflectance

Thermal conductivity of polymers: the rule of mixing

PCBM structure and sound speed (picosecond ultrasonics)

Ultralow thermal conductivity of PCBM

SemiconducAng polymers and fullerene derivaAves

PEDOT:PSS (poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate)

P3HT (poly(3-hexylthiophene-2,5-diyl)) PCBM ([6,6]-phenyl C61-butyric acid methyl ester) P3HT/PCBM blends Flexible electronics, light emitting diodes, photovoltaics, thermoelectric devices

Materials and ApplicationsSemiconducting polymers and fullerene derivatives PEDOT:PSS (poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate)) P3HT (poly(3-hexylthiophene-2,5-diyl)) PCBM ([6,6]-phenyl C61-butyric acid methyl ester)

Flexible electronics, light-emitting diodes, photovolatics, thermoelectric devices, ...

Why do their thermal properties matter? Thermoelectric efficiency as an example...

ZT = S2sTk

Dimensionless Figure of Merit

Ideally, ZT > 10 500 1000

0

0.5

1

1.5

Temperature (K)

ZT

PbTeSeTe/PbTe Quantum Dots

52 nm Si nanowire

Si0.8Ge0.2

Si0.8Ge0.2with 2.0 at% B

Sample preparaAon and characterizaAon Sample Preparation and Characterization of Morphology

I: Dissolve molecules in chlorobenzene at 1 wt. % 24 hours before fabrication II: Spin-coat ITO-coated glass slides or Si

wafers and use atomic force microscopy to characterize surface morphology

PCBM

P3HT

Blend

transducer

substrate

nanostructure

III: Evaporate 90 nm Al to serve as transducer for TDTR measurement

Cross plane electrical resistivities: 7.4x105 3.1x106 -cm

Shen et al. Solar Energy Materials 95, 2314 (2011)

Time domain thermoreflectance (TDTR)

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, -X/Y

TDTR data, 117 nm Al/Si

Pump-probe time delay (ns)

Can measure thermal conductivity of thin films and substrates () separately from thermal boundary conductance (hK)

Nanometer spatial resolution (~10s of nm) Femtosecond to nanosecond temporal resolution

Nuts and bolts details and advancements in afternoon session

Semi-infinite substrate

Nanostructure

Thin metal film transducer

Pump

Probe

Thermal penetration depth

Cahill RSI 75, 5119 (2004) Schmidt et al. RSI 79, 114902 (2008) Hopkins et al. J. Heat Trans. 132, 081302 (2010)

The temporal regimes during TDTR Project Description - EAGER - Solid-state thermal switching - Patrick E. Hopkins

SP#Tsunami#3.0#W,#80#MHz#90#fs#pulse#width#

Isolator#/4#

E.O.#Modulator#

BiBO#

/2#

Delay#line#(~7#ns)#

Red#filter#

Dichroic#

Blue#filter#

LockQin#amplifier#

Photodiode#

Camera#to#image#sample# Pump%

Probe%

1 10 100 1000 100000

2

4

6

8

10

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TDTR

sig

nal -

Vin/V

out

Pump-probe delay time (ps)

Picosecond ultrasonics

Thermal properties


Figure 3: (left) Schematic of optical layout for the TDTR measurement system in Hopkins laboratory at the Universityof Virginia. (right) Example TDTR data showing the two temporal regimes that will be utilized in this proposal toquantify the thermophysical properties of the complex oxides.

ously by slow lattice or joule heating,13,17 these previous approaches rely on global cooling of the materialvia "bulk" thermal diffusion. Here, we propose to use optical heating from an ultrashort pulsed laser systemto create a localized heating event in the VO2. This localized heating even will transform the VO2 from aninsulating state (off state, or open switch) to a conducting state facilitating charge flow (on state, or closedswitch). Utilizing a localized heating event driven by a laser allows for on/off heating, rapid thermal diffu-sion away from the localized heat source, and both DC and AC switching. With our laser system, we willdemonstrate AC switching up to 20 MHz, which is possible in VO2 due to the picosecond MIT relaxationtime.13 A schematic of this idea is shown in Fig. 4a in which the application of heating from a laser causesthe VO2 to switch to a electrically conducting state with a higher thermal conductivity, creating a closedcircuit and a potential difference. This will form the basis of the technology to power devices from heat.We will then optimize the switching magnitude and temperature by growing VO2 with different oxygenimpurities by changing the oxygen gas flow rate during VO2 synthesis.

5.2 Task 2: Electrically driven thermal switchThis goal of this task is to develop a thermal switch that is driven by an electrical current. As with Task

1, we will utilize the MIT in VO2 due to its fast relaxation time from the metal to the insulator state.13

We will apply a DC electrical current across a film of VO2 and measure the thermal conductivity of theVO2 with TDTR modified to give sub-millisecond measurements; to do this, we will monitor the thermore-flectance signal at a single delay time48,49 and record this signal change while the critical current is appliedto the VO2 (critical current density of 3104 A cm2).16 This will demonstrate the ability to rapidly turnon or off the thermal switch by changing the thermal properties via electrical current. Our preliminarymeasurements shown in Fig. 2 suggest that we will be able to switch the thermal conductivity by roughly afactor of 2, although we will tune this effect by varying both the current density and film thickness. We willthen demonstrate an AC electrically driven thermal switch by driving the MIT in VO2 with an AC current.As the switching time of VO2 is on the order of picoseconds,13 we will demonstrate AC thermal switchingon the order of 10s of GHz. This will form the basis of the technologies for thermal devices and logic. Aschematic illustrating this idea is shown in Fig. 4b.

5.3 Task 3: Electrically driven thermal storageThis goal of this task is to demonstrate the ability to permanently change the thermal state of a material

via an electric field. Although this technically is a thermal switch or thermal gate, this demonstration will

5

Semi-infinite substrate

Nanostructure

Thin metal film transducer

Pump

Probe

Thermal penetration depth

l r

fC

Can be ~50 nm for polymers

Thermal conducAvity of PCBM/P3HT blends

0 20 40 60 80 100

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P3HT Concentration (wt %)

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Unannealed

conductivity increases with thickness, we can safely say thatthe reduction is not due to film dislocations. Intriguingly,the thermal conductivities of the alloy thin films measuredin this Letter are among the lowest of any of the previousmeasurements on SiGe-based thin-film systems. We notethat the only previous data that approach our lowest mea-sured value are those in which the authors admit that themeasured samples have poor crystal quality (black filledsquares in Fig. 2) [2].

To quantify this effect, we turn to a model originallyproposed by Wang and Mingo [31], in which thermalconductivity ! is given by

! Z @!c=kBT0

k4BT3

2"2v@3 #T; yy4 expyexpy % 1&2 dy; (1)where kB is Boltzmanns constant, @ is Plancks constantdivided by 2", T is temperature, and y @!=kBTis a dimensionless parameter. The average velocity v iscalculated by v 1% xv%2Si xv%2Ge &%1=2, where x isthe Ge concentration and vSi and vGe are the averagespeeds of sound in Si and Ge, respectively, as calculatedby Wang and Mingo [31]. The scattering time for a givenfrequency, #, is related to the individual processes viaMattheissens rule # #%1U #%1a #%1b %1, where #U,

#a, and #b are the umklapp, alloy, and boundary scatteringtimes, respectively. These are given by

#U 1% x#%1U;Si x#%1U;Ge&%1; (2)

#a x1% xA!4&%1; (3)and

#b d=v; (4)where

#%1U;SiGe BSiGe!2 exp%CSiGe=T: (5)The constants A, B, andC are taken from Ref. [31], and d isthe film thickness.Our model is thus identical to that in Ref. [31] except

for the cutoff frequency, which we define as !c 2"v=a,with a being the lattice constant of the Si1%xGex filmapproximated by Vegards law: a 1% xaSi xaGe,where aSi and aGe are the lattice constants of silicon andgermanium, respectively. Equation (1) assumes a disper-sionless, Debye system. This is acceptable for Si1%xGexsystems with nondilute alloying compositions, since thedispersive phonons scatter strongly with the alloy atomsdue to their high frequencies. This assertion is substanti-ated by the reasonable agreement found between thismodel, our data, and previously reported measurementson thin-film alloys in Refs. [2,7,23] as shown in Fig. 2.To first assess the role of alloy composition, Fig. 3

shows the measured thermal conductivity versus Geconcentration and the predictions of the thermal conduc-tivity for bulk and thin-film Si1%xGex of three differentthicknesses at room temperature using Eq. (1). ForSi1%xGex with 0:2< x< 0:8, we found that the thermalconductivity is almost flat and in agreement with ourexperimental results. This lack of dependence on the Geconcentration is much more pronounced in thin films than

1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

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rmal

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-1K

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Period or Film Thickness (nm)

T = 300K

Si/Ge SL Ref. 2

Si0.85

Ge0.15

Ref. 2

Si/Ge SL Ref. 4Si/Ge SL Ref. 6

Si0.5

Ge0.5

Ref. 6

Si/Si0.71

Ge0.29

SL Ref. 7

Si0.84

Ge0.16

/Si0.74

Ge0.26

SL Ref. 7

Si0.9

Ge0.1

Ref. 7

Si/Si0.71

Ge0.29

SL Ref. 8

Si0.4

Ge0.6

Ref. 23

Si0.8

Ge0.2

(This Work)

Si0.8

Ge0.2

Model Eq. (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Total Sample Thickness (nm)

FIG. 2 (color online). Thermal conductivity measurements onSi0:8Ge0:2 of the thickness series along with previously reportedvalues of different Si/Ge superlattices, alloy-based superlattices,and alloy films at room temperature. Closed symbols representsuperlattices; open symbols represent Si1%xGex films. The ther-mal conductivity is plotted versus (a) period or film thicknessand (b) total sample thickness. The figure also shows the modelpresented in Eq. (1).

0.0 0.2 0.4 0.6 0.8 1.00

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5

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8

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Composition Series Thickness Series

T = 300K

The

rmal

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ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm

FIG. 3 (color online). Predictions of the thermal conductivityas a function of Ge composition for bulk and thin-film Si1%xGexof three different thicknesses calculated at room temperatureby using Eq. (1). The symbols correspond to experimental dataon the thickness series (down open triangles) and compositionseries (up filled triangles). With decreasing film thickness,alloying induces smaller and smaller changes in the thermalconductivity as size effects begin to dominate.

PRL 109, 195901 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

9 NOVEMBER 2012

195901-3

Cheaito et al. Phys. Rev. Lett. 109, 195901 (2012)

Thermal conductivity of mixtures Rule of mixtures holds

Thermal conductivity of thin films alloys

There is another model due to Burggeman, which isknown as the Burggeman asymmetric model (BAM) [42].Every et al. [37] modified the BAM to include Rb betweenthe particle and the matrix. This model is capable ofpredicting thermal conductivity of spherical particles forlarger volume fractions.

Recently Devpura et al. [40] proposed the use ofpercolation model for TIMs due to large contrast in theconductivities of the particles and the polymer matrix.Liang et al. [44] and Liang and Ji [45] used the percolationmodel to predict the thermal conductivity of thincomposites. Percolation is a geometrical phenomenon. Itbasically means that after some volume fraction, called thepercolation threshold !c, there is a continuous path forheat conduction trough the particles because the conduct-ing particles start to touch each other as shown in Fig. 5(a).The percolation model as given in Table 2 is strictly validonly near the percolation threshold. There are some veryimportant subtle points that have been overlooked inapplying the percolation-based models to predict thermalconductivity of composites [40], [44], [45]. The percolationphenomenon is strictly valid for kp=km ! 1. This ispossible in reality for electrical conductivity as perfectinsulators are possible. For thermal conductivity, this is notpossible in reality because for any solid there is a nonzerothermal conductivity. The percolation model was numer-ically evaluated [41] for planar geometries such as cubicalparticle. The percolation threshold for cubical particles pcis given in Table 3 for different arrangements of particles.Zallen [46] used pc and the maximum packaging fractionfor spherical particles to obtain !c for spherical particles,which is around 15% for all arrangements of particles asshown in Table 3. For two-dimensional composites madefrom aligned cylinders, !c is 0.45 [46]. If kp=km ! 1 thenthis scaling is all right and the percolation model can beused for spherical models; however, if kp=km 6 1, thenthere is a problem with spherical particles. For cubicalparticles, if kp=km 6 1 but if the ratio is still very large, acorrection to the percolation model has been proposed[47]. For spherical particles due to the curvature of thesurface, there will be constriction and spreading of heatflow lines near the particle and matrix interface. Thisconstriction/spreading of heat flow lines is not taken intoconsideration in the percolation model. This effect willincrease with decreasing contrast between kp and km. Thiswas recently shown by Ganpathy et al. [39]. This is not aproblem for planar geometry. Ganpathy et al. [39] alsoshowed that for kp=km 1 nonplanar results reduce to theplanar results which means that percolation model couldstrictly be used for spherical particles only in the limit ofkp=km 1. Therefore, percolation model has beensuccessful in the prediction of electrical conductivity ofcomposites made from spherical particles [48] and othernonplanar geometries [49]. Various modifications to thepercolation model has also been proposed [48]. Thepercolation model for kp=km ! 1 can also be used to

capture thin-film effects [50] which happens when thethickness of the composite is comparable to the dimensionsof the particles. Recently Devpura et al. [51] and Keblinskiand Cleri [52] considered the percolation model in thepresence of Rb and showed that percolation phenomenon isdiminished in the presence of Rb. The percolation modelhas been applied with some success in predicting thethermal conductivity of superconductors [53] and somecomplicated compounds [54].

Fig. 5. (a) The phenomenon of site percolation occurring with theformation of a continuous chain between the two surfaces by the

highly conductingparticles. (b)Thermal conductivityofTIMmade from

CNT and Ni particles (Hu et al. [29]). This figure indicates the presence

of percolation. Solid and dashed lines aremodel developed byHuet al.

[29] based on bond percolation. This figure shows a jump in thermal

conductivity near percolation threshold, which means that the CNT is

making contacts with different Ni particles.

Prasher: Thermal Interface Materials: Historical Perspective, Status, and Future Directions

Vol. 94, No. 8, August 2006 | Proceedings of the IEEE 1577


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Thermal conductivity of mixtures Rule of mixtures holds No evidence of percolation

Prasher, Proceedings of IEEE 94, 1571 (2006)


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Thermal conductivity of mixtures Rule of mixtures holds No evidence of percolation Annealing has variable effects

Temperature dependence on thermal conductivity in the PV

operating range

250 300 350 400 4500

0.1

0.2

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0.4

Temperature (K)

Ther

mal

Con

duct

ivity

(W m

-1 K

-1) PEDOT

P3HT45:55 Blend (annealed)45:55 Blend (unannealed) :carbon

P3HT

Open circle: Malen et al. J. Heat Trans. 133 081601 (2011)


0 20 40 60 80 100

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Unannealed

Thermal conductivity of mixtures Rule of mixtures holds No evidence of percolation Annealing has variable effects

Why is pure PCBM so low??

Size effects? Most likely not Already evidence that size effects dont play a role in polymers at these lengths

0 50 100 150 200 250

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al C

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PCBM

CuPc

CuPc: Jin et al. J. Appl. Phys. 112, 093503 (2012)

The data in Fig. 1!a" is fit to Eq. !2" with !polymer and Gas free parameters. A plot of !eff versus thickness with thebest-fit models is shown in Fig. 1!b". Values for the !polymerfitting parameter !0.22 and 0.21 W/m K" are within 10%error of the accepted bulk value for PMMA !0.20 W/m K".The interfacial conductance values of 300 MW /m2 Kand 420 MW /m2 K for the piranha treated and HF dippedsubstrates, respectively, are 6 to 14 times larger than previ-ous experimental values for alumina particles in a PMMAmatrix !30 MW /m2 K" Ref. 1 and calculated values forpolyethylene/silicon interfaces !50 MW /m2 K".12 We can-not preclude the possibility that this high G is a result ofpinholes or a reaction layer created during Al deposition.However, acoustic reflections observed in the in-phase signalallow us to confirm that films of "5 nm have the samespeed of sound as bulk PMMA, providing evidence thatthese films are not damaged.

The higher interfacial thermal conductance observedfor PMMA on HF dipped silicon compared to piranhatreated silicon results from the removal of the nativeoxide layer, which introduces an additional thermal barrier.To directly compare these data, the thermal conductance of a2 nm SiO2 layer !650 MW /m2 K" can be added in parallelwith the PMMA/HF interfacial thermal conductance!420 MW /m2 K" giving a value of 250 MW /m2 K. Thisvalue is lower than that measured for the PMMA/piranhatreated interface !300 MW /m2 K", suggesting that heat con-ducts faster across the PMMA/piranha treated interface. This

faster heat conduction may result from stronger hydrogenbonding between PMMA and the surface hydroxyls on thepiranha treated surface.13

Figure 2 compares the thermal transport of PMMAbrushes to spun-cast PMMA films. Surprisingly, the averagethermal conductivity for the brushes !0.215 W/m K" is only!10% higher than that measured for spun-cast PMMA films!0.190 W/m K" in the same thickness range. Drawn bulkPMMA shows a 50% increase in thermal conductivity alongthe draw direction,6,7 which is theorized to result from in-creased alignment of the CC backbone bonds along thethermal gradient direction.7,14,15 A similar increase was ex-pected for polymer brushes, which are known to exhibitchain extension when the spacing between grafted chains isshorter than the polymers radius of gyration !Rg".

1619 Weobserve grafting densities # !#=$NAt /Mn, where NA isAvogadros number and $=1.19 g /cm3 is the bulk densityof PMMA" of 0.350.65 chains /nm2, indicating sufficientoverlap to force the extension of polymer chains into thebrush regime.9,18,19

As a further check of polymer brush quality, swollenchain extension was evaluated. For a constant chain length,brush thickness versus grafting density follows a power lawrelation !t%#n". For chain spacing&Rg, n=0. For highergrafting densities, n has been reported to range between 1/3and 1/2,1719 implying that as the spacing between polymerchains reduces, chains extend away from the substrate to-ward the all-trans conformation !contour length, Lc". Liquidcell ellipsometric measurements on a separate series of

FIG. 1. !Color online" !a" Effective thermal conductance and !b" effectivethermal conductivity of Al/PMMA/Si stacks as a function of PMMA filmthickness for spun-cast PMMA on silicon with different surface treatments.Dotted lines in the inset show the best-fit models from Eq. !2" with !polymerand G as free parameters.

FIG. 2. !Color online" !a" Effective thermal conductance and !b" effectivethermal conductivity of Al/PMMA/Si stacks comparing spun cast PMMAlayers to PMMA brushes on piranha treated silicon substrates. Thermal con-ductivity is calculated by multiplying thermal conductance with the polymerlayer thickness; for the polymer brushes, this includes the thickness of theinitiator molecule.

011908-2 Losego et al. Appl. Phys. Lett. 97, 011908 "2010#

Downloaded 06 Oct 2010 to 134.253.26.4. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Losego et al. Appl. Phys. Lett.97, 011908 (2010)

Selected angle electron diffracAon

Determining Microstructure of PCBM Thin Films via SAED

Average dimension of individual PCBM nanocrystal in the range 5 to 50 nm [2].

[1] Chem. Commun., 2116 (2003) [2] Magn. Reson. Chem. 49, 242 (2011)

Unannealed Annealed

transport by three-dimensional hopping can be envisioned,while hopping in the third dimension is hampered in the case ofODCB due to the increased distance between the layers.

The increased hopping probability in three dimensions, i.e.,mobility in the fullerene phase, can be beneficial to theefficiency of the solar cell. We have not determined the electronmobility in the tiny crystals, let alone the anisotropy factors.

The hole mobility in a film of pristine MDMO-PPV increasedby an order of magnitude when spincoated from CB instead oftoluene.12 The dark current in MDMO-PPV:PCBM solar cells isproposed to be mainly an electron current on the fullerenephase, motivated by the difference in electron and hole mobility

in the pristine materials.13 If the phase separation in the blendwould be into domains of pure constituents (i.e. pure donor andacceptor domains), one could speculate about the influence ofthe solvent on the charge carrier mobility in the phases (throughdifferent molecular packing). However, there is no proof thatphase separation occurs in this way. More likely, phaseseparation takes place into domains with different ratios ofdonor and acceptor. This complicated phase separation ques-tions the comparison of single component mobilities with thoseobtained from composite bulk composites.

The surface morphology of the pristine MDMO-PPV films(PFM-AFM: pulsed force mode-AFM) cast from CB or xylenesshowed comparable roughness, although the one cast from CBappeared somewhat more homogeneous (Fig. 5). In contrast,blends (0.4 w/w % MDMO-PPV : PCBM = 1 : 4), spun fromODCB, CB, or xylenes, demonstrated strong dependence of thesurface roughness on the spincoat solvent (Fig. 6). ODCB gavemore homogeneous films (better fullerene-solvent) comparedto CB, whereas xylenes gave rise to large defects in the form ofdeep pinholes ( > 5 nm, bad solvent).

MDMO-PPV:PCBM photovoltaic devices, as depicted inFig. 1b, with the active layer spun from ODCB, CB, or xylenes,were constructed and measured (Table 1). The Voc (open circuitvoltage) obtained is identical within experimental error, asexpected.14 However, a dramatic increase in Isc (short circuitcurrent) and FF (fill factor) were observed for CB, whichresulted in an overall efficiency of 3.0% (uncorrected fortemperature and spectral mismatch), an increase of 30%compared to xylenes.15 Both Isc and FF are heavily influencedby the morphology of the photoactive blend, i.e., the formationof a proper interpenetrating network. It is expected that the scaleof phase separation is critical to the performance of the device.Spincoating from xylenes resulted in larger donor and acceptordomains compared to CB. Too large domains can hamper theformation of charge carriers (the exciton diffusion lengths inMDMO-PPV and PCBM are in the range of 10 nm). In theODCB case, smaller domains are observed compared to CB,thus generating a larger interface between donor and ac-ceptor.

In the case of highly intimate mixing, charge recombinationis expected to increase, reducing the overall conversion

Fig. 3 Crystal packing (ODCB). a. View along the [21,0,21]-direction, 2 3 2 3 2 unit cells; b. PCBM with neighbouring moieties (10.00 < d < 10.22 (d = C60 centre to centre distance)); c. PCBM with neighbouring moieties (d = 12.95, 13.15 and 13.76 ).

Fig. 4 Crystal packing (CB). a. View along the [0,0,1]-direction, 2 3 2 32 unit cells; b. PCBM with neighbouring moieties (9.85 < d < 10.13).

Fig. 5 PFM-AFM topography pictures spincast from 0.25% solutions. a. toluene, b. CB. c. surface profile from toluene (c1) and CB (c2).

2117CHEM. COMMUN. , 2003, 21162118

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Films processed via CB solution exhibit FCC-like lattice with 10 between fullerene moieties [1].

(a) (b)

PCBM films processed via CB solutions exhibit FCC-like lattice with ~1 nm between fullerene moieties

Nanocrystallites with average dimensions in the range of 5 50 nm (big rangebut does this matter?)

Magn. Reson. Chem. 49, 242 (2011)

Weakly bonded fullerenes

Diffusion(of(hot(electrons(

Phonon(propaga6on(

Einstein oscillations: Uncoupled vibrations of atoms with random

phases

When would this exist? Weak springs

Weakly bonded fullerenes

Diffusion(of(hot(electrons(

Phonon(propaga6on(

Einstein oscillations: Uncoupled vibrations of atoms with random

phases

When would this exist? Weak springs

produced in irradiation experiments andthe high grain abundances (for example,50% with respect to H20) predicted byinterstellar chemistry models. Given inter-stellar cloud lifetimes, slight warmingshould suffice to convert the H2CO to POMderivatives. These may be detectable assubstructure near 1000 cm` (10 gxm) onthe interstellar silicate feature at the precisepeak positions listed in Table 1. Further-more, the compounds produced could par-ticipate in other reactions, providing a newset of complex organics not previously con-sidered. In dense, hot cores where ice grainswould evaporate, some of the productsmight be observable in the gas phase (13).

There are already applications for theseresults to comet science. We can use theH2CO and NH3 abundances determined forComet Halley from ground-based and insitu measurements by Giotto and Vega toestimate that -3% of the organic in CometHalley are produced by thermal H2CO re-actions in the nucleus. These moleculeswould be very oxygen-rich (C/O - 1) andwould have alcohol-, ether-, and amine-type properties. The nature of the productsand their relative abundances strongly de-pend on the initial ice composition andwould therefore be a sensitive tracer of thechemical conditions inside the nucleus.Furthermore, these materials could contrib-ute to the IR emission already detectedfrom comets. Several of their CH stretchingbands peak at positions spanned by the"3.4-pm" cometary emission feature (14).

Chemical analysis of the products oflow-temperature H2CO reactions are nec-essary to better characterize the moleculesthat are expected under astrophysical con-ditions. Such studies are essential to under-stand the origin of the organic moleculesobserved in the interstellar medium and incomets as well as the processes and thechemical conditions in the ices where theywere formed.

REFERENCES AND NOTES

1. A. C. Danks, T. Encrenaz, P. Bouchet, T. le Bertre, A.Chalabaev, Astron. Astrophys. 184, 329 (1987).

2. M. J. Mumma and D. C. Reuter, Astrophys. J. 344,940 (1989).

3. L. E. Snyder, P. Palmer, I. de Pater, Astron. J. 97,246 (1989).

4. A. G. G. M. Tielens and W. Hagen, Astron. Astro-phys. 114, 245 (1982).

5. W. A. Schutte, thesis, University of Leiden, Lei-den, the Netherlands (1988).

6. L. J. Allamandola, S. A. Sandford, G. J. Valero,Icarus 76, 225 (1988).

7. J. F. Walker, Formaldehyde (Reinhold, New York,1964).

8. N-S. Zhao, thesis, University of Leiden, Leiden,the Netherlands (1990).

9. W. A. Schutte, L. J. Allamandola, S. A. Sandford,in preparation.

10. H. Tadokoro, M. Kobayashi, Y. Xawaguchi, A.Kobayashi, J. Chem. Phys. 38, 703 (1963).

1 1. L. J. Aflamandola, in Astrochemistry of Cosmic Phenomena, P. D. Singh, Ed. (Kluwer, Dordrecht, the

Netherlands, 1992), pp. 65-72; S. A. Sandford, inAstronomical Infrared Spectroscopy, S. Kwok, Ed.(Astronomical Society of the Pacific, San Francisco,in press).

12. V. U. Agarwal et al., Orig. Life 16, 21 (1985).13. C. Walmsley, in Interstellar Dust, L. J. Allamandola

and A. G. G. M. Tielens, Eds. (Kluwer, Dordrecht,the Netherlands, 1989), pp. 263-274.

14. T. Y. Brooke, A. T. Tokunaga, R. F. Knacke,Astron. J. 101, 268 (1991).

15. We thank M. de Groot and R. Grim (University ofLeiden), and S. Chang and C. Lerner (NASA/AmesResearch Center) for many valuable suggestionswhich were an essential contribution to this re-search. Supported by the National ResearchCouncil and NASA grant 199-52-12-04. W.A.S.was an NAS/NRC Resident Research Associatewhen this work was done.

28 October 1992; accepted 6 January 1993

Specific Heat and Thermal Conductivityof Solid Fullerenes

J. R. Olson, K. A. Topp, R. 0. Pohl*Evidence is presented that the lattice vibrations of compacted Cd/C7O fullerite micro-crystals consist predominantly of localized modes. Vibrational motions of the rigid mole-cules ("buckyballs") have been identified as well as their internal vibrations. Debye wavesplay only a relatively minor role, except below -4 kelvin. By comparison with othercrystalline materials, for these materials the Einstein model of the specific heat and thermalconductivity of solids, which is based on the assumption of atoms (in this case, buckyballs)vibrating with random phases, is in much better agreement with the measurements thanthe Debye model, which is based on collective excitations.

The first model for lattice vibrations ofsolids was proposed in 1907 by Einstein,who applied the quantum concept to themechanical motion of individual atoms in acrystal lattice that he assumed to be vibrat-ing with random phases (1). He subse-quently found that this model was inade-quate, its most drastic shortcoming beingthat it led to a thermal conductivity thatdisagreed with the observation on crystalsboth in magnitude and in temperature de-pendence (2). This disagreement was re-moved by Debye (3) and by Born and vonKarman (4), who demonstrated that incrystalline solids the atoms vibrate collec-tively as elastic waves. This picture hasbeen tested extensively and is now general-ly accepted. Exceptions have been noted,however. In amorphous solids and certaindisordered crystals, for example, the ther-mal conductivity above -50 K can be welldescribed with Einstein's picture (5, 6)(although the cause for the random phase ofvibration of the neighboring atoms, thecrucial assumption in Einstein's picture, isnot yet understood). Also, in some crystal-line polymeric solids, the specific heat hasbeen shown to be well described over a widetemperature range with a set of Einsteinmodes consisting of vibrational motions ofcertain molecular units (7). However, incrystal lattices of simple atomic constitu-ents, the model of collective wave motionhas always been found to be correct.We report here on a polycrystalline dis-

Laboratory of Atomic and Solid State Physics, CornellUniversity, Ithaca, NY 14853.*To whom correspondence should be addressed.

SCIENCE * VOL. 259 * 19 FEBRUARY 1993

ordered solid of a rather simple compositionin which the lattice vibrations are predom-inantly localized. Above -4 K, both itsspecific heat and its thermal conductivitycan be quantitatively described with Ein-stein's model, thus showing clearly the lim-itations of the commonly used picture thatis based on plane waves.

The starting material was microcrystal-line (-1 gm) commercial (8) fullerite pow-der containing -85% C60 and -15% C70molecules (buckyballs), which had beenextracted with toluene. Without any fur-ther treatment, the powder was compressedin a pellet press at 3000 atm, which resultedin pellets of a strength comparable to thatof soft pencil graphite. This procedure en-abled us to prepare samples of sufficient sizeto perform the measurements. Their massdensity p = 1.54 g cm-3 ( 10%) was closeto the theoretical density (Ptheor = 1.676 gcm-3) of the face-centered-cubic (fcc) lat-tice. From Debye-Scherrer x-ray diffractionmeasurements, an fcc lattice constant of a= 14.1 0.1 A was determined, near theaccepted value for pure C60 (a60 = 14.186A) (9). X-ray line shapes of the powder asreceived and of the compact solid werevirtually identical. We also investigated thethermal properties of compacts made of C60starting material and obtained similar re-sults (10). Thus, the presence of C70 ap-pears to be irrelevant as far as the observa-tions reported here and their interpretationare concemed. To avoid any ambiguity,however, we refer to the samples studiedhere as C,/C70 compacts. Small changes ofthe low-temperature specific heat were alsoobserved when the starting material or the

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specific heat can be calculated; see the solidcurve above ~10 K in Fig. 1, which agreeswell with our measurements.

Below -4 K, the specific heat decreasesless rapidly than predicted for Einstein os-cillators, and at the lowest temperatures ofour measurements the specific heat ap-proaches a linear temperature dependence.In this temperature range (

Thermal conducAvity of PCBM

100 200 300 400Temperature (K)

Ther

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Con

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ivity

(W m

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62 nm WSe2

39 nm PCBM74 nm PCBM

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Film Thickness (nm)10 100 7007

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PCBM

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Lower Extreme of Heat Conduction AmongFully Dense Solids

kE = 2k

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Qi = vi(h/kB)(6p2n)1/3

Duda et al. Phys. Rev. Lett. 110, 015902 (2013)

But still.why is this so low? Why lower than C60?


Ther

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PCBM, E = 22 K; E = 2.88e12 rad s1

vL = 3300 m s-1

vL = 2300 m s-1C60/C70, E = 35 K; E = 4.58e12 rad s1


Ther

mal

Con

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(W m

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-1)

0.01

0.1

1

C60/C70

min (C60/C70)

P:C60

24 nm WSe2

62 nm WSe2


:carbon2.1 g cm-3

:carbon0.9 g cm-3

min (PCBM)

50 450

0.1


0.2

0.02

WSe2

PCBM

(a)

(b)


kE = 2k

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x

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6

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3

i=1

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i

T

Qi

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0

x

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x

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PCBM, E = 22 K; E = 2.88e12 rad s1

vL = 3300 m s-1

vL = 2300 m s-1C60/C70, E = 35 K; E = 4.58e12 rad s1 100 200 300 400Temperature (K)

Ther

mal

Con

duct

ivity

(W m

-1 K

-1)

0.01

0.1

1

C60/C70

min (C60/C70)

P:C60

24 nm WSe2

62 nm WSe2


:carbon2.1 g cm-3

:carbon0.9 g cm-3

min (PCBM)

50 450

0.1


0.2

0.02

WSe2

PCBM

(a)

(b)


kE = 2k

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1/3

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x

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x

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3

i=1

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i

T

Qi

2 Z Qi

/T

0

x

3e

x

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PCBM, E = 22 K; E = 2.88e12 rad s1

vL = 3300 m s-1

vL = 2300 m s-1C60/C70, E = 35 K; E = 4.58e12 rad s1

Weakly bonded fullerenes in PCBM

PCBM adds an additional variable to C60: the tail

Picosecond ultrasonics sound speed in PCBM Project Description - EAGER - Solid-state thermal switching - Patrick E. Hopkins

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Thermal properties


Figure 3: (left) Schematic of optical layout for the TDTR measurement system in Hopkins laboratory at the Universityof Virginia. (right) Example TDTR data showing the two temporal regimes that will be utilized in this proposal toquantify the thermophysical properties of the complex oxides.

ously by slow lattice or joule heating,13,17 these previous approaches rely on global cooling of the materialvia "bulk" thermal diffusion. Here, we propose to use optical heating from an ultrashort pulsed laser systemto create a localized heating event in the VO2. This localized heating even will transform the VO2 from aninsulating state (off state, or open switch) to a conducting state facilitating charge flow (on state, or closedswitch). Utilizing a localized heating event driven by a laser allows for on/off heating, rapid thermal diffu-sion away from the localized heat source, and both DC and AC switching. With our laser system, we willdemonstrate AC switching up to 20 MHz, which is possible in VO2 due to the picosecond MIT relaxationtime.13 A schematic of this idea is shown in Fig. 4a in which the application of heating from a laser causesthe VO2 to switch to a electrically conducting state with a higher thermal conductivity, creating a closedcircuit and a potential difference. This will form the basis of the technology to power devices from heat.We will then optimize the switching magnitude and temperature by growing VO2 with different oxygenimpurities by changing the oxygen gas flow rate during VO2 synthesis.

5.2 Task 2: Electrically driven thermal switchThis goal of this task is to develop a thermal switch that is driven by an electrical current. As with Task

1, we will utilize the MIT in VO2 due to its fast relaxation time from the metal to the insulator state.13

We will apply a DC electrical current across a film of VO2 and measure the thermal conductivity of theVO2 with TDTR modified to give sub-millisecond measurements; to do this, we will monitor the thermore-flectance signal at a single delay time48,49 and record this signal change while the critical current is appliedto the VO2 (critical current density of 3104 A cm2).16 This will demonstrate the ability to rapidly turnon or off the thermal switch by changing the thermal properties via electrical current. Our preliminarymeasurements shown in Fig. 2 suggest that we will be able to switch the thermal conductivity by roughly afactor of 2, although we will tune this effect by varying both the current density and film thickness. We willthen demonstrate an AC electrically driven thermal switch by driving the MIT in VO2 with an AC current.As the switching time of VO2 is on the order of picoseconds,13 we will demonstrate AC thermal switchingon the order of 10s of GHz. This will form the basis of the technologies for thermal devices and logic. Aschematic illustrating this idea is shown in Fig. 4b.

5.3 Task 3: Electrically driven thermal storageThis goal of this task is to demonstrate the ability to permanently change the thermal state of a material

via an electric field. Although this technically is a thermal switch or thermal gate, this demonstration will

5

0 50 100Delay Time (ps)

Sign

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Al:PCBM

PCBM:Glass

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Sound speed in C60: 3,300 m/s Sound speed in PCBM: 2,300 m/s

Not enough to account for reduction we observe, but step

in the right direction indicating a change in

frequency of the fullerene

So what else could play a role? Functional tail in PCBM could cause additional scattering

via a similar interfacial mechanism as NCAs LETTERS

PUBLISHED ONLINE: 17 MARCH 2013 | DOI: 10.1038/NMAT3596

Surface chemistry mediates thermal transport inthree-dimensional nanocrystal arraysWee-Liat Ong1, Sara M. Rupich2, Dmitri V. Talapin2*, Alan J. H. McGaughey1,3and Jonathan A. Malen1,3*Arrays of ligand-stabilized colloidal nanocrystals with size-tunable electronic structure are promising alternatives tosingle-crystal semiconductors in electronic, optoelectronic andenergy-related applications15. Hard/soft interfaces in thesenanocrystal arrays (NCAs) create a complex and unchartedvibrational landscape for thermal energy transport that will in-fluence their technological feasibility. Here, we present thermalconductivity measurements of NCAs (CdSe, PbS, PbSe, PbTe,Fe3O4 and Au) and reveal that energy transport is mediated bythe density and chemistry of the organic/inorganic interfaces,and the volume fractions of nanocrystal cores and surfaceligands. NCA thermal conductivities are controllable withinthe range 0.10.3 W m1 K1, and only weakly depend on thethermal conductivity of the inorganic core material. This rangeis 1,000 times lower than the thermal conductivity of sili-con, presenting challenges for heat dissipation in NCA-basedelectronics and photonics. It is, however, 10 times smallerthan that of Bi2Te3, which is advantageous for NCA-basedthermoelectric materials.

Colloidal nanocrystals self-assemble into NCAs with electronicand optical properties that can be broadly tuned by nanocrystalcomposition and size14,68. To be considered as viable replacementsfor traditional semiconductors, NCA-based technologies mustalso meet thermal management demands as high operatingtemperatures degrade device performance and lifetime. Thermalconductivity (k) quantifies a materials ability to dissipate heat andrelates temperature gradient (rT ) to heat flux (q) through Fourierslaw, q=krT . Inmetals,most heat is carried by electrons, whereasin semiconductor and insulating crystals, thermal conductivityarises from the transport and scattering of quantized vibrationsthat are born from the periodic atomic lattice, that is, phonons.Our NCAs are non-metallic and have a vibrational structure thatis complicated by compositional heterogeneity and periodicityat two length scales: the atomic lattice within each core andthe array of periodic cores separated by ligand monolayers.Studies of planar self-assembled monolayer (SAM) junctionsshow that surface chemistry can control energy transport at theinterface between two solids9, but does it also influence thethermal conductivity of a bulk three-dimensional solid with acomplex network of internal interfaces? We herein report on thehitherto unknown thermal transport properties of NCAs, usingsystematic thermal conductivity measurements complemented byheat capacitymeasurements and atomistic simulations.

A series of NCAs was prepared with varying core diameters,core materials and ligand groups (Table 1) through spin-coatingconcentrated colloidal solutions onto silicon wafers6. During film

1Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA, 2Department of Chemistry, University ofChicago, Chicago, Illinois 60637, USA, 3Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213,USA. These authors contributed equally to this work. *e-mail: [email protected]; [email protected].

formation, the monodisperse nanocrystals self-assembled intoarrays, as seen in Fig. 1ac. For thermal conductivitymeasurements,the NCA films were coated with a gold transducer (150250 nmthick) by electron-beam evaporation.

The specific heat capacity (Cp) of the NCAs was determinedusing differential scanning calorimetry (DSC). The measuredCp varies with temperature and nanocrystal size as shown for adiameter series of PbSNCAs in Fig. 1d,e. The abrupt change in slopein Cp around 200K is the result of a glassy transition of the oleateligands10,11, as these unsaturated hydrocarbon tails do not crystallizeat the nanocrystal surface. In contrast, the CdSe NCAs capped withlong saturated hydrocarbon chains (that is, n-tetradecylphosphonicacid) can form ordered domains at the nanocrystal surface, indi-cated by sharp peaks in the DSC curves in Supplementary Fig. S1.We find that Cp can be estimated from a weighted average based onthe constituent mass fractions determined from thermogravimetricanalysis (TGA; Supplementary Fig. S2) and the bulk specific heatcapacities of the inorganic corematerial and the ligand (Fig. 1e).

Molecular dynamics simulations and harmonic lattice dynamicscalculations were performed to elucidate how the vibrationalstructure of a nanocrystal is related to its constituent core andligands (see Supplementary Information). The vibrational densityof states (vDOS) of a 2.8-nm-diameter Au nanocrystal and itsconstituent Au core and dodecanethiol ligands are shown in Fig. 2.The Cp of solids results from occupation of the vDOS accordingto BoseEinstein statistics. All core vibrational states overlap withligand states below the thermal activation frequency at 300K.Higher-frequency ligand states have no corresponding core statesto overlap with at higher temperatures. These two general featureswill be found for core materials with a similar Debye temperatureto Au (165K). Similarities in the vDOS of the nanocrystal and itscomponents thus explain why the measured Cp is consistent withthe estimate based on mass fraction. In this work, experimentalthermal conductivitymeasurements were carried out to understandhow this vibrational structure influences thermal transport.

To measure the thermal conductivity of the NCA thin films,we employed the frequency-domain thermal reflectance (FDTR)technique detailed in theMethods12. For CdSe NCAs, the measuredthermal conductivities are independent of film thickness attemperatures of 10, 77 and 300K, as shown in SupplementaryFig. S3a (room-temperature measurements for other NCAs areshown in Supplementary Fig. S3b). This result suggests that thermaltransport in NCAs is dominated by diffusive phonons with shortmean-free paths. Furthermore, the thickness invariance indicatesthat our measured values are bulk-like and not distorted by thermalresistances at the Au/NCA andNCA/Si boundaries.

NATURE MATERIALS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials 1

Figure S4 FDTR schematic and data. a, An intensity modulated pump laser (488 nm) is

periodically modulated by an electro-optic modulator and heats the sample periodically. An

unmodulated probe laser (532 nm), coincident with pump at the sample surface, senses the periodic

temperature change by thermoreflectance. The thermoreflectance signal is monitored by a lock-in

amplifier, measuring the phase lag of the temperature change relative to the heat flux as a function of

frequency. b, FDTR phase lag data and fits, plotted as a function of modulation frequency for bare

silicon and a NCA film on silicon. The differences in the signals indicate a high sensitivity to the

NCA thermal conductivity.

Figure S5 MD simulation model. The model used in the MD simulations simplifies a NCA into a

linear chain. In this case, eight cores (red spheres) with their tethered ligands (six yellow chains on

each core with two along each Cartesian direction) are shown. A typical simulated steady-state

temperature profile after a heat flux is applied is plotted below. Each point represents an average

temperature in one-half of a core, depicting a constant temperature profile in each core with

significant temperature drops across the ligand bridges between the cores.

NATURE MATERIALS | www.nature.com/naturematerials 17

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT3596

V8.03: Alan McGaughey This session: 8:30 AM (Invited)

Conclusion

New extremes in heat conduction can be realized through manipulating the bonds/frequencies of vibrations in weakly coupled systems

1022 10230.01

0.1

1

10

100

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AmorphousCrystalline

DiamondCopper

AluminumSilicon

GermaniumLead

SiO2

Aerogels PCBM

C60/C70WSe2

:carbonP3HT

5000

0.005

Exceptionally Low Thermal Conductivities of Films of the Fullerene Derivative PCBM

John C. Duda and Patrick E. Hopkins*

Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, Virginia 22904, USA

Yang Shen and Mool C. Gupta

Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904, USA(Received 25 May 2012; revised manuscript received 30 October 2012; published 2 January 2013)

We report on the thermal conductivities of microcrystalline [6,6]-phenyl C61-butyric acid methyl ester(PCBM) thin films from 135 to 387 K as measured by time domain thermoreflectance. Thermal

conductivities are independent of temperature above 180 K and less than 0:030! 0:003 Wm"1 K"1 atroom temperature. The longitudinal sound speed is determined via picosecond acoustics and is found to be

30% lower than that in C60=C70 fullerite compacts. Using Einsteins model of thermal conductivity, wefind the Einstein characteristic frequency of microcrystalline PCBM is 2:88# 1012 rad s"1. By comparingour data to previous reports on C60=C70 fullerite compacts, we argue that the molecular tails on thefullerene moieties in our PCBM films are responsible for lowering both the apparent sound speeds and

characteristic vibrational frequencies below those of fullerene films, thus yielding the exceptionally low

observed thermal conductivities.

DOI: 10.1103/PhysRevLett.110.015902 PACS numbers: 66.70."f, 63.22."m, 65.80."g

As a field of study, thermal transport is both ubiquitousand pervasive, as many technologies face a thermal man-agement challenge at some point in their lifetimes [1].Beyond application, the topic of thermal conductivity ofthe solid state has long been one of general scientificinterest [24], and a large and ongoing effort has beenset forth to expanding the limits of heat conduction [5,6].On one end of the spectrum, the so called lower limit ofthermal conductivity is typically observed in amorphousphases of materials, where conductivities are much lowercompared to that of their single crystalline counterparts [7].In these phases, heat conduction is described by a randomwalk of vibrational energy on the time and length scales ofatomic vibrations and interatomic spacing, respectively[2,8]. In addition, one can approach this lower limit bycreating multilayer, nano-crystalline, or porous films inwhich the spacing between interfaces, grain boundaries,or pores is on the order of several nanometers [916]. Inthese nanostructured materials, boundaries impede thermaltransport by scattering phonons, thereby shortening theirmean-free paths and yielding lower thermal conductivities.

Yet another advantage of nanostructuring is the possi-bility of creating an amorphouslike network of large,repeating unit cells. In such materials, low thermal con-ductivities can be realized not only by limiting phononmean-free paths, but also through the localization of vibra-tions. For example, the low thermal conductivities of com-pacted C60=C70 fullerite microcrystals reported by Olsonand Pohl [17] were attributed to the largely independentand poorly coupled oscillations within each of the fuller-enes. This explanation was further supported by low tem-perature heat capacity measurements that demonstratedEinstein-like behavior despite the microcrystallinity of

the compacts. More recently, Chiretescu et al. [18]reported a large reduction in the thermal conductivity ofa homogeneous solid through growth of layered WSe2, inwhich weak interlayer bonding led to a decrease in thermalconductivity below that of a single crystal of WSe2 alongthe c axis by a factor of thirty, and below the correspondingtheoretical minimum limit by a factor of six. There, too, theauthors noted that localization of vibrations could be partlyresponsible for the observed behavior.In this Letter, we report on thermal conductivities of the

fullerene derivative [6,6]-phenyl C61-butyric acid methylester (PCBM) from 135 to 387 K. Thermal conductivitiesof PCBM thin films were measured via time-domain ther-moreflectance (TDTR), a noncontact, pump-probe opticalthermometry technique. Above 180 K, thermal conductiv-ities were independent of temperature and less than0:030! 0:003 Wm"1 K"1, a factor of three less thanthat of C60=C70 fullerite microcrystals [17]. In addition,no significant dependence on the type of substrate onwhich the film was deposited, subsequent heat treatment,or film thickness over the range 22 to 106 nm was observed.Microcrystallinity was confirmed by transmission electronmicroscopy and electron beam diffraction. As with theaforementioned works, we attribute these exceptionallylow thermal conductivities to highly localized vibrationswith low characteristic frequencies, as well as low longitu-dinal sound speeds (2300! 100 m s"1 as measured bypicosecond acoustics, $ 30% lower than those measuredin compactedC60=C70 fullerite microcrystals). Last, we notethese films exhibit the lowest reported room-temperaturethermal conductivity of any fully dense solid [6,18].PCBM thin films were prepared according to the follow-

ing procedure: indium tin oxide (ITO) coated glass

PRL 110, 015902 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending

4 JANUARY 2013

0031-9007=13=110(1)=015902(5) 015902-1 ! 2013 American Physical Society

Surface characterizaAon

Weak bonding can go a long way in crystalline materials

Layered structures can exhibit ultralow thermal conductivity

intersection of (1 0 L) reflections with theEwald sphere probed the coherence of thecrystal structure along the direction normal tothe WSe2 sheets. The large line widths (Fig.1B) indicated that crystallographic orderingin the stacking of the WSe2 sheets was limitedto

patrick(e.(hopkins( 0.2 si 0.8ge 0.2 with 2.0 at% b sample(preparaon(and(characterizaon(sample...

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