High thermal conductivity of chain-oriented amorphous ... · XRD pattern of PT films and an array of PT nanofibers (diameter ~ 200 nm) on substrates fabricated by electropolymerization

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NNANO.2014.44

NATURE NANOTECHNOLOGY | www.nature.com/naturenanotechnology 1

High Thermal Conductivity of Chain-Oriented Amorphous Polythiophene

Virendra Singh†, Thomas L. Bougher†, Annie Weathers, Ye Cai, Kedong Bi, Michael T. Pettes, Sally A. McMenamin, Wei Lv, Daniel P. Resler, Todd R. Gattuso, David H. Altman, Kenneth H. Sandhage, Li Shi, Asegun Henry, Baratunde A. Cola *

*Correspondence to: [email protected] † These authors contributed equally

High thermal conductivity of chain-oriented amorphous polythiophene

© 2014 Macmillan Publishers Limited. All rights reserved.

http://www.nature.com/doifinder/10.1038/nnano.2014.44

This PDF file contains the materials and methods with supplementary figures S1-S20 and

supplementary table S1 and table S2.

Materials and Methods:

Materials. Nanoporous anodic aluminum oxide (AAO) were purchased from Whatman Co

(Anodisc 13, 200 nm nominal pore diameter) and Synkera Nanotechnologies Inc (Unikera, 100,

55, 18 nm nominal pore diameter). Gold sputtering source (Au, 99.9999%) were purchased from

Kurt J. Lesker Co. Unless otherwise noted all the chemicals were purchased from Sigma-Aldrich

and used as received. Boron trifluoride ethyl ether (BF3.Et2O) was freshly distilled before use.

One surface of the AAO templates must be converted into electrode to synthesize polythiophene

(PT) in the nanochannels. We sputter-coated ~500 nm of gold on one side of template and used

the gold layer as the working electrode for electropolymerization.

Polythiophene nanofiber fabrication and isolation

A simple and reproducible process using thermal diffusion bonding through a gold layer

was developed to grow PT nanofibers directly on metal substrates. We found that excellent

bonding occurred using a hydraulic pressure of about 45 MPa at 250 °C for 6 hours. PT

nanofibers were fabricated directly on metal substrates by electrochemical oxidation at constant

potential (1.3V vs Ag/AgCl) in a three-electrode one-compartment cell using a computer-

controlled potentiostat-galvanostat (Epsilon electrochemical system). The sketch of

electrochemical cell used for preparing the PT nanofiber arrays is shown in Fig. S1.

Supplementary Fig. S1. Cross-sectional view of three-electrode one-compartment

electrochemical cell used for template guided electrochemical synthesis of PT nanofibers.

The anodic potential is measured versus Ag/AgCl reference electrode. The AAO template

bonded to metal was used as the working electrode and a Kapton mask defined the active area.

Clean and polished stainless steel foil was used as counter electrode. All solutions were de-

aerated with argon and a slight overpressure of argon was maintained during nanofiber growth.

The nanofibers were grown at constant potential. To dissolve the AAO template and liberate the

vertically aligned array of PT nanofibers, we treated the template with potassium hydroxide for

24 hours. Isolated arrays were neutralized with 0.1 M hydrochloric acid and extensively washed


with de-ionized water before attachment to the substrates. The neutral state of the PT nanofibers

was confirmed with Raman spectroscopy as discussed below. The typical fabrication process is

outlined in Fig. S2.

Supplementary Fig. S2. Illustration of typical process used to fabricate PT nanofibers on variety

of substrates, suggesting the diverse applicability of process.

The chronoamperogram of potentiostatic electropolymerization of thiophene within

template nanochannels allows monitoring of nanofiber growth. Figure S3a shows a typical

current-time profile for thiophene in the nanochannels. One can note successive steps: (1) double

layer charging and nucleation (part A-B of curve) and (2) polymer growth (part B-C of curve).

General aspects of chronoamperogram (current-time profile) in AAO nanotemplate are

comparable with that of typical smooth metal electrodes. However, for nanoporous electrodes the

current reaches a plateau at longer times, which suggests that the formation of polymer

nanofibers occurs by instantaneous nucleation and subsequent two-dimensional growth for

shorter period of time1. A detailed analysis is required to further analyze the growth mechanism

within nanochannels. The scanning electron microscopy (SEM) images (inset of Fig. S3a) for

different samples show that the length of the nanofibers increases with total time of deposition.

The length and morphology (i.e., tubular versus solid fiber) of nanofibers were controlled by

pore diameter and the total charge passed through the electrochemical cell. The conditions used

to produce specific samples are shown in Tables S1 and S2. This growth technique causes

preferential chain growth up the wall of the nanopore in the direction of the tube axis (Fig. S3b).


Supplementary Table S1. Controlling the length of PT nanofibers through the total charge

passed through the electrochemical cell during the electropolymerization of 50 mM thiophene at

constant potential (1.3 V).

Total charge (Coulomb) Array height (µm)

0.2 2.9 ± 0.8

0.5 3.9 ± 1

1.0 15.6 ± 2

1.5 19.9 ± 2

Supplementary Table S2. Role of pore diameter on the morphology of PT nanofibers prepared

at constant potential (1.3 V) and 1.0 coulomb charge using 50 mM of thiophene.

Pore diameter (nm) Morphology

200 Mostly tubes

100 Solid fibers

55 Solid fibers

18 Solid fibers


Supplementary Fig. S3. (a) Current-time curve for electro-oxidation of thiophene in AAO with

~200-nm diameter pores at 1.3 V (versus Ag/AgCl). Insets depict different stages of

electropolymerization. (b) Illustration comparing molecular chain orientation in bulk polymer

film and electropolymerized polymer nanofiber.

SEM images of as prepared samples are shown in Fig. S4; a 90° tilt angle was used for

side views. The top view shows the tips of the nanofibers clumping together due to capillary

forces while drying, but the side view confirms that the majority of the tube length maintains

nominal vertical alignment.

Supplementary Fig. S4. SEM images of PT nanotubes fabricated at various amounts of total

charge passed through the electrochemical cell. (a) Top view of PT nanotubes synthesized with

total charge 0.2, 0.5 and 1.0 coulombs; from left to right; scale bars correspond to 2 µm. (b) Side

view of PT nanotube synthesized with total charge 0.2, 0.5 and 1.0 coulombs; from left to right;

scale bars correspond to 1 µm. The nanofibers tend to aggregate due to strong capillary forces

and their large aspect ratios.


A number of transmission electron microscopy (TEM), selected area electron diffraction

(SEAD) images and high-resolution TEM images of smaller diameter (100, 55, and 18 nm) PT

nanofibers are shown in Fig. S5. In total, more than 30 fibers were examined in detail in TEM

for each diameter range. The electron diffraction pattern in SEAD images (middle part of Fig.

S5) of NFs contains a broader ring and no bright spackles suggesting the amorphous nature of PT

nanofibers2. We also examined these fibers with standard powder x-ray diffraction (XRD). In

prior work, we have observed increased crystallinity in PT films electropolymerized at constant

current3, which shows sharp peaks associated with in-plane (d1) and cross-plane (d2) spacing of

PT chains in the film. Others4 have also observed crystallinity in PT films created through

electrochemical deposition at constant current. However, we only observed a broad hump,

similar to other amorphous materials5, in the XRD pattern (Fig. S6) of PT films and ~200 nm PT

nanofibers electropolymerized at constant potential. The XRD patterns for ~100, ~55, and ~18

nm PT nanofibers were flat with no peaks or significant humps (not shown). This suggests that

all PT nanofibers were amorphous. We also performed HR-TEM, as it provides the highest

resolution of structural details, at various locations on different nanofibers, which confirmed the

absence of long-range ordering in the electropolymerized nanofibers (Fig. S5 bottom).


Supplementary Fig. S5. TEM images (upper), selected area electron diffraction (SAED) pattern

(middle), suggest the amorphous nature of the fibers, and respective HR-TEM image (lower);

confirms the absence of nano-crystallites. All PT nanofibers of were synthesized with a total

charge 0.5 coulombs. (a) 18 nm template; scale bar is 400 nm. (b) 55 nm template; scale bar is

100 nm. (c) 100 nm template; scale bar is 100 nm. The scale bars in the HR-TEM images

indicate 2 nm.


Supplementary Fig. S6. XRD pattern of PT films and an array of PT nanofibers (diameter ~ 200

nm) on substrates fabricated by electropolymerization using 50 mM thiophene and boron

trifluoride ethyl ether as electrolyte. The peaks associated with in-plane (d1) and cross-plane

(d2) spacing are marked on XRD pattern of the semi-crystalline film for reference. The semi-

crystalline film was electropolymerized at constant current3, and the amorphous film and

nanofibers were electropolymerized at constant potential.

Raman spectroscopic analysis

PT nanofibers were analyzed with Raman spectroscopy to investigate the charge state of

polymer. The Raman spectrum shown in Fig. S7 was recorded by focusing the excitation laser

beam on the surface of the PT nanofibers. The most intense band of this spectrum is located at

ca. 1455 cm-1

, which is assigned to the symmetric stretching mode of the aromatic C=C bond

ring. This band is associated with neutral conjugated polythiophene segments6. The bands

associated with the oxidized polythiophene or structural defects at around 1180 cm-1

(C-C

stretching) and 690 cm-1

(C-S-C ring deformation) are weak.


Supplementary Fig. S7. Raman Spectrum of the surface of PT nanofibers excited by a 785-nm

laser beam.

Polarized infrared absorption spectroscopy measurements

Polarized infrared absorption spectroscopy (PIRAS) is a well-established method for

studying the degree of chain orientation in polymers7, 8

. A PIRAS-microscope (FTS7000-

UMA600, Agilent) with Perkin-Elmer wire grid polarizer (186-0243) was used for this purpose

with samples oriented 10° parallel from the IR beam using grazing angle attachment (Pike

Technologies 80 Spec) shown in Fig. S8.

Supplementary Fig. S8. Illustration of PIRAS experimental setup.

The freestanding PT nanofibers on metal foils were planarized in one direction by a

“knock-down” process using a Teflon-based roller9. The planarized PT nanofibers (Fig. S9a and

c) are mounted in the controlled atmosphere sample chamber of the PIRAS system. PIRAS

spectra of the PT nanofibers surfaces were recoded with KBr as the beam splitter and a liquid

nitrogen cooled MCT detector in the 400-4000 cm-1

frequency range. It should be noted that any

100

IR

beam

Polarizer Flattened PT nanofibers

To detector


misalignment of the fibers from the knock-down procedure (i.e., if they do not all lay in the same

direction) would only lessen the selective absorbance and hence lead to a lower orientation

function.

Supplementary Fig. S9. Representative SEM image of PT nanofiber arrays planarized by

knock-down technique and corresponding PIRAS spectra of PT nanofibers: from ~200 nm

template (a and b), and from ~100 nm template (c and d).


Supplementary Fig. S10. Illustration of polarized probe rays whose polarization plane is either

on the x-y plane (A║) or on the z-x plane (A┴). (a) Molecular structure of polythiophene,

highlighted parts showed the Cα

-Cα

inter-ring stretching band along the polymer backbone, and

(b) molecular orientation of polythiophene chain in fibers.

The intensities of light polarized orthogonal and at 10° to the axes of the nanofibers are I┴

and I10 with absorbances A┴ and A10, respectively. The parallel-polarized absorbance, A║ is a

component of the absorbance from the beam labeled I10, which is oriented at an angle of 10°

with respect to the fiber axis, as described by eq. S1.

(S1)

A qualitative measure of chain orientation is the dichroic ratio, R, defined as the ratio of A║ to

A┴. Deviation of this value from unity is indicative of selective orientation of the bond associated

with the absorption band8. Dividing eq. S1 through by A┴ allows the dichroic ratio to be solved

for from the measured infrared absorbances, as shown in eq. S2.

(S2)

To further quantify the chain orientation, we calculate the average orientation distribution8, 10

function (f)avg from eq. S3,

(S3)

10sin10cos 22

||10 AAA

210

||

2

sin (10)

cos (10)

A

A AR

A

0

0

( 1)( 2)

( 2)( 1)avg

R Rf

R R


Where R is dichroic ratio and R0 = 2 cot2 α, α being the angle between the transition moment

associated with the considered absorption band and the molecular axis (illustrated in Fig. S9b).

By assuming the angle between the transition moment associated with in-plane stretching

vibration and molecular axis remain unaltered during vibration, R0 is taken as zero, which sets

(R0+2) /(R0-1) to unity10, 11

. Several different locations on representative PT nanofibers samples

fabricated with the ~200 and ~100 nm templates were tested and the standard deviation of three

measurements was used to determine the experimental uncertainty for the reported orientation

parameters and dichroic ratios. Orientation parameter is a fraction of chain alignment varied

between zero for random chain orientation and one for complete orientation. PIRAS

measurement suggest that ~200 nm nanotubes and ~ 100 nm nanofibres have 25% and 42%

preferential chain orientation along the axis respectively.

Microbridge technique

The thermal conductivity measurement of individual PT nanofibers with a suspended

microbridge is described in detail elsewhere12

. In short, the measurement device consists of two

adjacent SiNx membranes each patterned with a serpentine platinum resistance thermometer

(PRT) and two electrodes, and supported by six, long, thin beams. An individual PT nanofiber

was placed across the gap between the two membranes. The measurements were carried out in an

evacuated cryostat with pressure on the order of 10-6

torr. A DC current supplied to one PRT

raises its temperature by ΔTh, and heat conduction through the sample causes a temperature rise

in the adjacent, sensing membrane of ΔTs. The temperature rise in the heating and sensing

membranes was measured from the temperature coefficient of resistance of the PRTs, and the

thermal conductance of the nanofiber was determined from the total Joule heating and

temperature difference between the heating and sensing membranes.

Due to the low thermal conductance of some of the nanofiber samples, on the order of 1

nW K-1

, it is necessary to account for the background heat transfer between the two PRTs via

residual gas molecules and radiation. Neglecting this background conductance, which is

comparable to the sample conductance, can lead to an overestimate of the thermal conductivity.

To eliminate the background conductance, the temperature rise on the sensing membrane was

measured relative to the temperature rise on the sensing membrane of a blank device with no

nanostructure. Such background elimination is carried out either with a separate background

conductance measurement of a blank reference device13

, or simultaneously with a new

differential measurement method. Details of this differential measurement are found elsewhere14

.

The background thermal conductance makes a relative contribution of 5% for the nanofibers

with diameter greater than 200 nm, and between 15 and 50% for the smaller diameter nanofibers.

The uncertainty in the thermal conductivity contains a contribution from uncertainty in

the diameter and suspended length measured by TEM, which ranges between 2-17% for the

samples studied in this work, as well as a contribution from the measured thermal conductance,

which correspondingly depends on the uncertainty in the Joule heating supplied to the heating

membrane, the uncertainty that results from background subtraction, and the uncertainty in the

measured temperature rise in the heating and sensing membranes, which combined can

contribute between 1 – 11% for the samples studied here12, 14

. The uncertainty in the sample


temperature is taken as the difference in temperature between the heating and sensing membrane,

which is typically 2-6 K.

The measured thermal resistance of the sample is expected to contain a contribution from

the contact resistance between the nanofiber and the SiNx membranes. This contact resistance is

inversely proportional to the contact width, which is proportional to the diameter. In addition, the

ratio between the contact resistance and the intrinsic diffusive resistance of the nanofiber is

proportional to the diameter and inversely proportional to the suspended length of the nanofiber.

Fig. S11 shows the measured thermal resistance normalized by cross sectional area versus

suspended length for diameters in the range of 71 nm and 245 nm at 250 K.

Supplementary Fig. S11. Resistance normalized by cross sectional area versus length for

individual PT nanofiber thermal conductivity measurements. The labels for the data points refer

to the diameter of the nanofibers in nm. The colored lines represent linear fits to the data.

For each of the two groups of nanofiber samples with diameter close to 200 nm and 100

nm respectively, the measured thermal resistance normalized by the cross section area increases

generally with the suspended length. A linear fitting to the data for each group extrapolates to a

residual resistance value at zero suspended length that is much smaller in absolute value than the

resistances measured for all fibers except the ones with diameter 145 and 71 nm. Hence, the

contact thermal resistance is small for all fibers excluding these two.

In addition to background heat transfer between the membranes, parasitic heat loss from

the circumference of the nanofibers is expected to result in an underestimate of the thermal

conductance. The thermal resistance of the nanofiber, considering radiation heat loss from the

circumference and assuming low thermal conductance such that , can be expressed

as15


(S4)

where , and ε, σ, κ, d, L, and T are the surface emissivity, Stefan-Boltzmann

constant, thermal conductivity, diameter, suspended length, and average temperature of the

sample. The limit of gives the limit of diffusive thermal resistance, Rs = 4L / pkd2 .

Therefore, the error in the thermal conductance due to radiation heat loss is found to be

(S5)

Considering a bulk emissivity of approximately 0.3, δ is found to be negligible – smaller than

0.1% for all nanofibers studied here.

TEM analysis of the PT nanofiber on the suspended device shows solid nanofibers with

Au particles dispersed on the surface. The Au particles are expected to originate from the Au

electrodes in the electropolymerization process. Figure S12 shows TEM images from the 71 and

204 nm samples suspended across the device membranes. All TEM results (i.e., high resolution

TEM and electron diffraction patterns) indicate that the measured nanofibers are amorphous.

Supplementary Fig. S12. (a) TEM of 71 nm PT nanofiber suspended across microbridge. (b)

TEM of 204 nm PT nanofiber suspended across microbridge.

b = 16esT 3 /kd

d =bLcoshbL

sinhbL-1


Gold particles were observed on the surface of some of the PT nanofibers, which is a

result of Au deposition on the template prior to electropolymerization. When present, the surface

area covered by Au particles was estimated to be 11% based on five different TEM images.

Assuming that the average diameter of the Au particles is 10 nm and the contact thermal

resistance between the Au particles and the PT fiber is negligible, the effective thermal

conductivity of the 10 nm surface layer of the PT fiber can be calculated using the Maxwell-

Garnett expression to be no more than 40% higher than the PT thermal conductivity.

Consequently, the average thermal conductivity of the entire PT fiber is increased by less than

10% with the presence of the Au nanoparticles on the surface. We note, however, that most of

the Au particles protrude from the PT surface so the effective surface layer is likely less than 10

nm thick, which would reduce the contribution of the Au particles further.

Molecular dynamics simulations

Molecular dynamics (MD) simulations of individual Pth chains were conducted using the

Large Atomic/Molecular Massively Parallel Simulator (LAMMPS)16

, a freely available code

developed at Sandia National Laboratories. The Reax force field was used to describe the atomic

interactions, via the parameterization described by Chenoweth, van Duin and Goddard.17

Equilibrium MD simulations with a time step of 0.15 fs were carried out for 3 ns in the

microcanonical ensemble at 300 K. Five independent simulations were conducted for improved

phase space averaging. At each time step the heat flux vector was calculated according to

Hardy’s derivation18

. The simulations employed periodic boundaries at the chain ends to mimic

the behavior of an infinitely long chain, allowing us to determine an upper limiting estimate for

the thermal conductivity. We simulated chains with lengths of 40 unit cells ~ 32 nm and the heat

flux autocorrelations of each independent simulation were averaged together. The resulting heat

flux autocorrelation function was then used in the Green-Kubo formula to calculate the thermal

conductivity19, 20, 21

.

Photoacoustic technique

The photoacoustic technique has been demonstrated as a method to determine the thermal

properties of thin films22, 23

, multi-layer samples24

, liquids25

, gases26

, and most relevant to this

work: nano-structured thermal interface materials27, 28, 29

. Photoacoustic is a non-destructive

method to resolve individual component resistances in a multi-layer sample. The photoacoustic

measurement consists of a modulated laser beam entering a closed cell and impinging upon the

top layer of the sample material. The laser energy is absorbed by the sample causing periodic

heating of the sample. The heat is conducted downwards into the sample as well as up into the

gas layer of the enclosed photoacoustic chamber. The periodic heating of the fix gas volume

causes periodic pressure fluctuations, which are detected by a sensitive microphone in the wall of

the chamber. Helium is used as the gas in the chamber, which will increase the sensitivity of the

measurement, given its thermal conductivity is five times higher than air. A schematic of the

experimental setup is shown in Fig. S13.


Supplementary Fig. S13. Photoacoustic experimental setup.

The output from an 1100 nm continuous-wave fiber laser passes through an acousto-optic

modulator, which is maintained at modulation frequencies between 300 and 4000 Hz by a

function generator. The beam is focused through a polished quartz window on the top of

photoacoustic cell and onto the surface of the sample. The gas in the photoacoustic cell is He that

is pressurized to 7, 70, or 140 kPa. The fully assembled sample consists of 80 nm of Ti on a 25-

µm Ag foil and 1 µm of gold on the backside. The Au-coated Ag foil is the growth substrate as

previously mentioned in the fabrication description; the Ti layer is deposited on the Ag foil to

absorb the laser energy. The array conductivity sample stack (Fig. S14 on the right) is created by

flipping the PT nanofiber array over and placing it on top of the quartz. The PT nanofiber array

is attached to the Au (growth substrate) on one side and to a 3 mm quartz disc on the other side.

The 80 nm layer of Ti on top of the silver foil absorbs the laser energy and introduces the

periodic heating into the sample; the sample configuration is shown in Fig. S14.


Supplementary Fig. S14. Sample configurations for photoacoustic measurement. The sample

diagram on the left is used to measure the total thermal resistance of a thermal interface material

and the sample diagram on the right is used to measure the thermal conductivity of the PT

nanofiber array.

The modulation frequencies used for testing allow the heat to penetrate the PT nanofiber

array and back contact fully, without passing completely through the quartz backing. The phase

and amplitude from the microphone are detected by a lock-in amplifier, and recorded by a

LabVIEW data acquisition system. In conjunction with measurements of the sample, a reference

material is measured to correct for the contribution to the phase shift from the cell geometry,

microphone response, and other details of the experimental setup. A 3 mm quartz slide with 80

nm of Ti is used as the reference sample.

The heat flow in the material is modeled to be one dimensional conduction following the

method of Hu et al. who developed a generalized solution for a multilayer material23

. Fitting for

unknown thermal properties can be done with either the amplitude or phase data; however, prior

experience has shown that the fitting is more robust when the phase shift is used27

.

The Levenberg-Marquardt method is the non-linear algorithm used to simultaneously fit

for multiple unknown parameters30

. The initial guess values are perturbed multiple times in an

attempt to ensure that the final values reached are a global rather than a local minimum. The

unknown properties in data fitting model are the contact resistance between the quartz and the

polythiophene (Rc1), the layer resistance of the PT nanofiber array, the contact resistance

between the polythiophene and the gold (Rc2), the thermal diffusivity of the PT nanofiber array,

and the contact resistance between the Ti and Ag foil. The contact resistance between the Ti and

Ag is very small and does not contribute significantly to the bulk resistance of the sample. The

thermal diffusivity of the PT nanofiber array is allowed to vary to achieve the best match

between the theoretical and experimental phase shift, but the value is not reported. It has been

shown that the total resistance of the sample is relatively independent of the buried layer thermal

diffusivity27

. Only the total thermal resistance values (Rtotal = Rc1 + Rlayer + Rc2) are reported for

the array when attached to the quartz and silver foil. Fig. S15 shows an example of the


photoacoustic experimental data for the PT nanofiber array (L = 1.9 µm) along with the best-fit

theoretical curve. This data represents a fairly typical data fit with a residual or goodness of fit

near the middle of all data sets. The error bars represent ± 0.5 degree of phase shift. The total

resistance of the sample was 17.1 mm²KW-1

, the array thermal diffusivity was found to be 0.3

mm²s-1

, and the interface resistance between the Ti and Ag was 0.2 mm²KW-1

.

Supplementary Fig. S15. Representative photoacoustic data for a PT nanofiber array thermal

interface material, height = 1.9 µm , Rtotal = 17.1 mm²KW-1

.

A number of calibration samples with known thermal properties were measured to verify

the photoacoustic system including SiO2, stainless steel, bronze, brass, and photoresist. Each

sample was found to be within 5% of published values, except photoresist, which was within 8%.

The 95% confidence interval for experimental uncertainty is 1.0 degrees or about 0.5 degrees for

one standard deviation30, 31

.

Bare array thermal conductivity. In this work, we introduce a new method to directly

determine the thermal conductivity of nanostructured arrays using the photoacoustic technique.

Traditionally, the photoacoustic technique is used with the laser energy absorbed by a solid

continuous layer23, 27, 32, 33, 34

, although it has been used for liquids25, 35

and gases26

in some cases.

While Bein et al. measured rough graphite samples36

, and Kozlov et al. measured the sound from

carbon nanotubes (CNTs), we are unaware of any work where thermal properties are determined

from a nanostructured array in which the laser energy is deposited directly into the material and

the photoacoustic response is measured. Feser et al. filled an array of Si nanowires with spin on

glass to create a continuous solid layer for time-domain thermoreflectance measurements26

,

however their top down etch technique and lower fill fraction (17-29%) both lend to easier

penetration of the array with a filler. In addition, this method is ideal for samples with much

higher conductivity so that there is a large difference between the thermal conductivity of the

filler and matrix. Panzer et al. measured the thermal conductivity of CNTs using a similar pump-


probe thermoreflectance technique by depositing a metal coating directly onto the tips of the

nanotubes37

. While the authors acknowledged that the metal layer was not continuous, the

thermal model used in their case necessitated a surface heat flux so it was important to absorb as

much of the laser energy as possible above the nanotubes. The photoacoustic thermal model

allows for volumetric heat generation from the absorption of laser energy23

so creating a surface

heat flux is not critical in this case. While volumetric absorption within the PT nanofiber layer

does not present a problem, any energy that passes through the array and reflects off the

underlying metallic substrate would introduce some error. The high fill fraction of nanofibers

(60%) will aid in the complete absorption of the laser energy for the longer arrays, however it is

likely that some of the laser energy reaches the substrate for the shortest arrays (height ~ 2 µm).

The main motivation in removing the metal foil on top of the PT nanofiber array is to increase

the sensitivity of the measurement to the thermal properties of the array so that a more accurate

measurement of the thermal conductivity is possible. We define the sensitivity as:

(S6)

where p is the value of property i, and ϕ is the phase shift37

. The partial derivative is calculated

numerically by perturbing the value pi by ± 1 percent and recalculating the phase. To

demonstrate the increased sensitivity of the bare array, the 11.6 µm array is considered as it was

measured in both scenarios. For the bulk thermal resistance measurement the layers above the PT

nanofiber array are 80 nm of Ti, 25 µm of Ag, and 1 µm of Au. In addition, the contact

resistance between the Au and PT nanofiber array is estimated to be about 1 mm²KW-1

based

upon the photoacoustic measurement. In the case of the bare array, the PT nanofibers are directly

exposed to the He gas with no additional thermal resistance in between. The sensitivity for each

case is plotted in Fig. S16.

i

iip

pS


Supplementary Fig. S16. Sensitivity of array thermal conductivity with and without top foil

layer for the photoacoustic technique.

The sensitivity of the measurement to the thermal conductivity of the PT nanofiber array

is three times higher for the bare array. Since the metal foil is the growth substrate for the array

in this case, the contact resistance is not extremely high. For samples with higher contact

resistance, the sensitivity to the array properties would be even lower. The main drawback of

measuring the bare array is the less predictable interaction between the laser beam and sample.

For a smooth layer of Ti on Ag foil the behavior of the incident light can easily be predicted. The

optical absorption length (OAL) of Ti at 1100 nm is approximately 26 nm38

, which means that

95% of the laser energy will be absorbed in the Ti layer. The OAL of PT is not well documented

and additional difficulties lie in understanding how the nanostructure will affect the absorption

length. Transmission measurements were performed on the arrays to estimate the effective

absorption length assuming the layer obeys the Beer-Lambert law: , where P is the

transmitted power, Po is the initial power, and t is the sample thickness. The transmitted power

was measured with a power meter using the same laser as the photoacoustic system (λ=1100 nm)

and a 1 mm spot size. The OALs were measured to be 2.0, 2.2, 4.2, and 6.0 for arrays of heights

2.9, 3.9, 15.6, and 19.9 μm, respectively. The difference in OAL for different array heights is

caused by changes in morphology, which is consistent with previous studies performed on CNT

arrays that found the OAL in vertically-aligned arrays increased with array height.39

The

amplitude of the photoacoustic signal was much stronger for the bare array compared to the foil-

covered array, which would seem to indicate that a majority of the laser energy was absorbed in

the top layer. If the heat generation was occurring in the buried metal layers, it would result in

lower signal amplitudes. One of the advantages of using photoacoustic for nanostructured

materials is the ability to use large spot sizes. In this work, we use a 1 mm beam diameter, which

is able to probe ~1.5x107 fibers in a single measurement. In contrast, a 10 μm beam diameter

would probe ~1.5x103 fibers, or four orders of magnitude fewer fibers. Fig. S17 depicts the

sensitivity of the unknown parameters in the bare array photoacoustic measurement.

P = Poe-t/OAL


Supplementary Fig. S17. Sensitivity of unknown parameters in photoacoustic measurement of

array thermal conductivity.

The measurement is most sensitive to the density and thermal conductivity of the PT

nanofiber array. To capture the uncertainty in the data fit associated with the unknown array

density, the unknown sample property values were perturbed by factors of 5, 20, 1/5, and 1/20.

The range of thermal conductivity values resulting from data fits with similarly low residuals

was used as the uncertainty associated with data fitting. The measurement uncertainty is

conservatively 1 degree of phase shift31

; to calculate the resulting uncertainty in thermal

conductivity associated with the measurement, the experimental phase shift was changed by plus

and minus 1 degree and then the data fitting was performed for each case. The difference

between the measured and adjusted phase shift was considered the uncertainty due to the

measurement. The total uncertainty in the thermal conductivity was found by:

, where Δmeas is the measurement uncertainty and Δfit is the data fitting

uncertainty. This results in an average uncertainty of 14%.

In comparison, the uncertainty for the calibration samples that use metal transducer layers

is between 4 and 8%. Although any convective heat transfer would be due to steady state

temperature rise and not alter the periodic photoacoustic signal, the convective heat loss was

estimated for completeness. For a laser power of 500 mW and a 1 mm beam diameter the steady

state surface temperature rise was approximately 7 °C at 300 Hz based upon a 3D photothermal

model40

. The convective heat transfer coefficient for a single 200 nm fiber was estimated to be

3000 W m-2

K-1 41

assuming the fiber is isolated far away from other fibers, which would result in

a heat loss of 3% to natural convection. This is considered an upper bound, since the convective

heat transfer coefficient of each individual fiber would be less when in a dense vertical array. To

assess the validity of the bare array measurement, several PT films (each ~3 µm thick) on quartz

were measured using the photoacoustic technique without a metal transducer layer. The average

Dtotal = Dmeas

2 + D fit

2


measured thermal conductivity of the PT film was 0.19 Wm-1

K-1

which is within the expected

range; the only previous measurement of thermal conductivity of a PT film we could find

reported a value of 0.17 Wm-1

K-1

42

. Further validation was found by using the array

conductivity to estimate the single fiber conductivity and compare with the value that was

measured by McMenamin et al. as collaboration for this work43

. They measured the single fiber

conductivity to be between 0.36 and 0.64 W m-1

K-1

for three fibers made with the 50 mM, 1.5 C

recipe. Our data for an array using the same recipe indicated single fiber conductivity of 0.62 ±

0.08 Wm-1

K-1

, which was in good agreement. An example of photoacoustic data from a bare

array thermal conductivity measurement is shown Fig. S18.

Supplementary Fig. S18. Representative data fit for array thermal conductivity measurement

using the photoacoustic technique. This data is for an array of height 12 µm, which has an

effective layer thermal conductivity of 0.76 Wm-1

K-1

.

The measured effective array thermal conductivity values were used to estimate the

thermal conductivity of individual fibers within the array. The generalized form of the effective

thermal conductivity of a composite with uniform sized ellipsoidal particles is44

:

(S7)

where is the effective through-plane conductivity of the film, is the fill fraction of the

particles, and given by:

(S8)

and

2

3333

2

1111

2

3333

2

1111*

33coscos12

cos11cos111

LLf

LLfKK m

*

33K f

ii

m

c

iiiim

m

c

iiii

KKLK

KK


(S9)

where θ is the angle between the axis of the film layer and the local particle axis, and ρ(θ) is the

distribution function of the particle orientation. are the geometrical shape factors given by:

(S10)

where p is the aspect ratio of the ellipsoid, a3/a1. In the limit where the aspect ratio is very large

and the fibers are perfectly vertically aligned, and p ∞ so and

which reduces eq. S7 to

, (S11)

which is identical to the rule of mixtures. While Feser et al. used the simplified form (equation

S11) for a uniform array of Si nanowires in a matrix of spin on glass43

, Marconnet et al. used the

more general version to predict the effective thermal conductivity of arrays of nominally aligned

CNTs44

. While our PT nanofibers are not as well aligned as an etched Si nanowire array, they are

significantly more aligned than CNTs. We use the eq. S11 to estimate the individual fiber

thermal conductivity as a lower bound. Introducing an orientation distribution will increase the

predicted single tube conductivity ( ) for the same measured effective thermal conductivity (

). The fill fraction of PT nanofibers was 60% based upon a template pore density of 1.9x109

cm-2

and a fiber diameter of 200 nm. Based upon the average film conductivity of 0.9 ± 0.1 Wm-

1K

-1 the solid fiber thermal conductivity would be 1.4 ± 0.2 Wm

-1K

-1. Many of the fibers in the

200 nm array were found to be tubes from TEM, with wall thicknesses from 40 to 80 nm (Fig.

1c). Based upon the same pore density and tube diameter, and a tube wall thickness of 40 nm, the

overall polymer fill fraction could be as low as 38%. If we assume that all the fibers in the array

are actually tubes, the thermal conductivity of the polymer portion of the tube would be 2.2 ± 0.6

Wm-1

K-1

. The range of 1.4 to 2.2 Wm-1

K-1

gives an estimate of the thermal conductivity

enhancement in the polythiophene material within the array. The single fiber thermal

conductivity values, extracted from the array measurements, are shown in Fig. S19. The thermal

conductivity of short fibers was less than that of long fibers, but not by a significant amount.

d

d

sin

sincoscos

2

2

iiL

1for,cosh1212

1for,cosh1212

1

2/322

2

1

2/322

2

2211

ppp

p

p

p

ppp

p

p

p

LL

1133 21 LL

1cos 2 033 L 5.011 L

pm fKKfK 1*

33

pK

*

33K


Supplementary Fig. S19. Individual fiber thermal conductivity as a function of fiber length

measured by photoacoustic. The values are extracted from array measurements using effective

medium theory assuming solid fibers, which is an underestimate because most fibers are tubes.

All measurements are performed on arrays with nominal fiber diameters of 200 nm. Each circle

represents a group of data that is different spots on the same sample.

Minimum thermal conductivity model

The modified expression for the minimum thermal conductivity is given by 45

:

(S12)

where vi is speed of sound of the ith

mode (two transverse and one longitudinal), n is the number

density of atoms, and is the Debye cut-off frequency in units of

temperature. The longitudinal speed of sound is 2800 ms-1

for bulk polythiophene46

, and the

transverse speed of sound was estimated to be 1200 ms-1

based on ratios the ratio of longitudinal

to transverse speed for a number of other polymers.47

The atomic number density was estimated

to be 5.1x1028

m-3

based upon atomic masses of the monomer unit and the amorphous polymer

bulk density of 1 gcm-3

48

. Equation S12 was numerically integrated over a range of temperatures

with constant speed of sound and atomic density to produce the κmin-PT line in Fig. 2b. In

addition to the existence of long mean free path phonons present in disordered solids49

, the likely

deviation from the Debye density of states for polymers will cause additional errors. There is

also the possibility that phonon-assisted fracton hopping in disordered solids could contribute to

thermal conductivity50

.

3

10 2

32

32

31

min

16 i

Ti

x

x

i

iB dxe

exTvnk

qi = 6p 2n( )1 3

/ kB( )vi


Mechanical adhesion

To investigate the normal adhesion force, a PT nanofiber array in the wet state was

collected by a clean surface with its aligned nanofiber surface in contact with the quartz surface.

After the drying on a target surface, a pin was glued on the Ag foil by 5 min epoxy. The epoxy

adhesive was coated on the center of the sample with an area smaller than that of the Ag foil. To

further exclude the possibility of the epoxy adhesive creeping up to the stalks of the specimen,

we pre-cured the epoxy gel for about 1 min before applying it to the specimen. Then, another pin

was glued to the backside of the substrate glass to measure the normal pull-off force (i.e., normal

adhesion force). The sample sizes were 0.5−0.8 cm2.

Supplementary Fig. S20. Experimental set-up used for adhesion force measurements.

The normal adhesion strength was tested using a standard tensile test machine (Fig. S20).

The samples were tested at a displacement rate of 1.0 mm.min

-1 The 1.9 µm array failed at 85

Ncm-² and the 11.6 µm array failed at 87 Ncm

-², while both 4.9 and 15.9 µm failed at the epoxy

interface used for testing, indicating a normal force of greater than 100 Ncm-² in both cases. Lu

et al. observed normal strength for similar PT nanofiber arrays of between 40 and 80 Ncm-² for

array heights between 5 and 20 µm51

. The larger normal pull-off forces observed in this work

could be due to the applied pressure of 225 kPa used during bonding, since Lu et al. bonded

under no applied pressure. Additional discrepancies could be introduced by the quality and

smoothness of their glass surface compared to our quartz surface. In any case, it is likely that

their estimate of 79% of nanotubes in contact with the surface is an over prediction since the

same analysis would predict numbers above 100% for our 4.9 and 15.9 um height arrays.

Impact of enhanced thermal conductivity on resistance of thermal interface material

The impact of enhanced thermal conductivity on the total thermal interface material

(TIM) resistance can be examined by estimating component resistances within the system. The

intrinsic layer resistance, Rlayer, is given by L/κ, where L is the array height (~ 2.5 µm) and is

the layer thermal conductivity (0.8 Wm-1

K-1

) for Rlayer ~ 3.1 mm2KW

-1. The total TIM resistance

of one sample was 17.1 mm2KW

-1 indicating that the combined contact resistance was


approximately 14 mm2KW

-1. To compare our material to a scenario where the amorphous PT

nanofibers would have no enhancement of thermal conductivity, we estimate the layer resistance

to be 21.9 mm2KW

-1 (κ = 0.19 Wm

-1K

-1, solid fibers with 60% fill fraction). If we assume that

the contact resistance is independent of the layer thermal conductivity, we can estimate the total

resistance of a PT nanofiber TIM with no enhancement to be approximately 34 mm2KW

-1. A

doubling of the total resistance is a conservative estimate since the fibers are tubes with a hollow

core, which will create an even higher layer resistance. For the device operated at about 100

Wcm-2

this increase in resistance would cause the device to operate at least 17 °C hotter,

reducing long-term reliability, or at reduced power to maintain equivalent operation temperature.

This demonstrates the practical necessity of using polymer nanofibers with enhanced thermal

conductivity for a TIM.

Description of commercial thermal interface materials (from52

)

Solders. Solder joints are solid metal TIMs that are made of low melting point metals

such as indium and tin that are melted and allowed to cool in between the heat source and sink to

provide a rigid interface.

Thermal grease. Thermal grease is a thick paste made of either silicone or hydrocarbon

oil that has a conductive filler to improve thermal conductivity. The main types of fillers used are

metals, ceramics, and carbon.

Phase change material (PCM). PCMs are a composite comprised of a paraffin or

polymer matrix and a thermally conductive filler such as a metal oxide. PCMs typically have a

melting temperature of around 50-90 °C and behave much like a highly viscous grease above this

temperature.

Gels. Gels are typically a silicone polymer with a thermally-conductive filler that can be

cured. Prior to curing they behave much like a thermal grease, and after curing they are similar to

a low modulus polymer.

Adhesives. Thermally conductive adhesives are essentially a double-sided tape with low

thermal resistance.

Device testing

Thermal measurements were performed using custom SiC Pt resistor-thermometer chip

affixed to a Cu block heat sunk to a temperature-controlled stage. Thermal coefficient of

resistance calibration data for each platinum resistor was obtained by varying the temperature of

the stage and recording resistance while supplying a low current level of less than 4.2 mA.

During calibration the heat dissipated through the resistor was negligible (<0.32 mW).

Temperature data from a Type-T thermocouple inserted into the Cu block was used to establish

the relationship between temperature and resistance, which was essentially linear. Thermal

resistance testing was then performed by varying the power dissipation of the resistor while

performing a 4-wire resistance measurement and measuring the block temperature. Thermal

resistance was computed as the temperature difference between the resistor and thermocouple

divided by the power input to the resistor. Voltage and current measurements were performed


with an HP 34401A multimeter capable of resolving input power to within approximately 0.1%.

Heat loss to the environment was assessed using numerical modeling assuming a natural

convection coefficient of 10 Wm-²K

-1 and was found to be negligible. Thermal interface

resistance was obtained through numerical modeling of the configuration in ANSYS TAS v11.0.

In this model, the thermal conductivity of Al was taken as 167 Wm-1

K-1

, Cu alloy C14500 as 355

Wm-1

K-1

, AuSn solder as 57 Wm-1

K-1

and Mo as 140 Wm-1

K-1

. The thermal conductivity of SiC

was taken as a function of temperature as measured via laser flash. Uncertainty in reported

thermal resistance assumes +/-2 °C temperature measurement error and +/-7% on SiC

conductivity. Thermal cycling was performed by applying and removing ~100 W of heat to the

Pt resistor on 300 s intervals for 80 cycles, or until the sensed resistor temperature reached a cut-

out limit of 250 °C. A common Ag-filled epoxy purchased from Epoxy Technology

(http://www.epotek.com/site/) was cycled to compare its reliability to that of the PT nanofiber

TIMs under similar conditions. The resistance of the epoxy increased by 354% from 13

mm2K/W to 46 mm

2K/W in only 36 cycles.

Based on the coefficient of thermal expansion (CTE) mismatch between SiC and Cu (1.2x10-5

K-

1), a temperature change of 180 °C would cause the outer edge of the Cu heat sink to expand

approximately 6 µm relative to the SiC chip. The total length of the PT nanofibers in the device

were only 2-3 µm, but they stayed well adhered indicating that the tips of the fibers must slide

along the surface while maintaining contact51

.


http://www.epotek.com/site/

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Documents

High thermal conductivity of chain-oriented amorphous ... · XRD pattern of PT films and an array of PT nanofibers (diameter ~ 200 nm) on substrates fabricated by electropolymerization