Ultrafast Flash Thermal Conductance of Molecular Chains

Zhaohui Wang,^1* Jeffrey A. Carter,^1* Alexei Lagutchev,^1* Yee Kan Koh,² Nak-Hyun Seong,^1* David G. Cahill,^2,3 Dana D. Dlott^1,3

At the level of individual molecules, familiar concepts of heat transport no longer apply. When large amounts of heat are transported through a molecule, a crucial process in molecular electronic devices, energy is carried by discrete molecular vibrational excitations. We studied heat transport through self-assembled monolayers of long-chain hydrocarbon molecules anchored to a gold substrate by ultrafast heating of the gold with a femtosecond laser pulse. When the heat reached the methyl groups at the chain ends, a nonlinear coherent vibrational spectroscopy technique detected the resulting thermally induced disorder. The flow of heat into the chains was limited by the interface conductance. The leading edge of the heat burst traveled ballistically along the chains at a velocity of 1 kilometer per second. The molecular conductance per chain was 50 picowatts per kelvin.

¹ School of Chemical Sciences, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
² Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
³ Fredrick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.

^* These authors contributed equally to this work.

To whom correspondence should be addressed. E-mail: dlott{at}scs.uiuc.edu

Heat transport is central to the operation of mechanical and electronic machinery, but at the level of individual molecules, the familiar concepts of heat diffusion by phonons in bulk materials no longer apply. Heat is transported through a molecule by discrete molecular vibrations. An emerging area in which vibrational energy transfer becomes crucial is the field of molecular electronics, where long-chain molecules attached to tiny electrodes are used to transport and switch electrons. When an electron is transported through a molecule, a portion of the electron's kinetic energy can be lost, appearing as molecular vibrational energy (1). In studies such as this one, in which molecular energy levels are not individually resolved, it is conventional to call such processes "heat dissipation" or "nanoscale thermal transport" (2), even though an equilibrium Boltzmann distribution is not necessarily achieved. Nitzan and co-workers (3) have estimated that 10 to 50% of the electron energies could be converted to heat, so that a power of 10¹¹ eV/s may be dissipated on a molecular electronic bridge carrying 10 nA under a bias of 1 eV. Using classical and quantum mechanical methods, they and others (1) have calculated steady-state temperatures resulting from such dissipation. Steady-state calculations, however, do not entirely capture the essence of this phenomenon. The energy lost when electrons are transported through a molecular wire in a fraction of a picosecond appears as staccato bursts, up to 1 eV per burst. On a 10-carbon alkane molecule, for instance, 1 eV is enough energy to produce a transient temperature jump T 225 K. At the temperatures associated with these ultrafast energy bursts, Nitzan and co-workers (3) suggest that, instead of the usual phonon mechanisms prevalent in ordinary thermal conduction processes (1), much of the heat is carried by higher-energy molecular vibrations such as carbon-carbon bending and stretching and carbon-hydrogen bending, which are delocalized over a few carbon segments (3).

To study molecular energy transport in the regime of short distances, short time intervals, and large temperature bursts, we have used an ultrafast flash thermal conductance apparatus to study densely packed self-assembled monolayers (SAMs) of long-chain hydrocarbon molecules anchored to metal substrates. Laser flash-heating increased the temperature of the metal substrate to 800°C in 1 ps. Heat flowed from the metal layer into the base of the molecular chains and then through the chains. A vibrational spectroscopy method was used that selectively probed the thermal-induced disorder of the methyl groups at the ends of the chains. The alkane chain lengths yielded a ballistic velocity for heat flow through the chains, and the measured thermal conductance plus the area per chain yielded a molecular thermal conductance.

The concept of the thermal conductance apparatus is illustrated in Fig. 1A. A femtosecond laser pulse flash-heated an 300-µm-diameter region of an Au layer crafted for a fast time response of 1 ps. The SAMs were formed from n-alkanethiol molecules HS-(CH₂)_n-CH₃ with an even number of carbon atoms from C6 to C24 (i.e., n from 5 to 23). A nonlinear coherent spectroscopic method (4) termed broadband multiplex vibrational sum-frequency generation spectroscopy (SFG) probed an ensemble of 10¹¹ alkane chains at the center of the heated region. We determined an overall rate for heat transport from Au into the alkane chains, and a time for heat to propagate from the base to the ends of the chains, as a function of the length h of the alkane molecules.

Fig. 1. (A) Concept of the ultrafast flash thermal conductance measurements. IR and visible pulses combine to generate SFG in an 200-µm-diameter region containing 1011 alkane chains. SFG is sensitive to thermal disordering of the alkane terminal methyl groups of SAMs, which occurs when heat propagates from the Au surface to the ends of the alkane chains. (B) Alkanethiol molecule of length h bound to Au surface. (C) Ultrafast thermal reflectance measurements show that the Au layer heats up to 80% of its final temperature in 1 ps. (D) SFG spectra of alkane thiol (n = 17) SAM at ambient temperature (blue) and after an ultrafast temperature increase to 800°C (red). [View Larger Version of this Image (37K GIF file)]

An 800-nm, 500-fs-duration laser pulse from an amplified titanium-doped–sapphire laser (5) incident on the Au/glass interface (the back side) of the 50-nm-thick Au layer generated hot electrons within a skin depth of 15 nm (6). Because the hot electrons have a large diffusion coefficient, the electron temperatures at the front and back of the Au layer equalized even before electron-phonon coupling brought the hot electrons into equilibrium with the lattice (6). Within 1 ps, the Au layer was in thermal equilibrium and uniformly heated throughout (6). To improve the adhesion of Au to glass it was necessary to add a Cr layer beneath the Au. Unfortunately, heat transfer from a Cr layer to Au is relatively slow; to minimize this effect, we made the Cr layer just 0.8 nm thick. An ultrafast thermoreflectance apparatus (2, 7) was used to characterize the temperature rise of the Au layer. As shown in Fig. 1C, there is a fast increase of the Au surface temperature to 80% of the final temperature within 1 ps. There is also a slower (1.5 ps time constant) rise to the final temperature due to the Cr layer. The same transient response was observed with either front-side or back-side flash-heating and with or without a SAM. The Au layer remained at an approximately constant high temperature for several nanoseconds, subsequently cooling by heat diffusion into the glass. In the SFG experiments, the intensity of the heating pulse was varied to locate the threshold for melting the Au, and then the pulse was attenuated by 20%. Because the melting temperature of Au T_m = 1064°C, this procedure resulted in flash-heating of the Au layer to 800°C.

SAMs have been studied extensively by SFG since 1991 (8), but ultrafast probing of a flash-heated SAM requires some elaboration. In the SFG technique we used, a femtosecond infrared (IR) pulse at 3.3 µm with a bandwidth of 150 cm^–1 is incident on the SAM, coherently exciting all the alkane CH-stretch transitions in the 2850 to 3000 cm^–1 range, along with electrons in the Au skin layer, producing an oscillating polarization in both the Au and the SAM layers. At the same time, a picosecond-duration 800-nm pulse ("visible") with a bandwidth of 7 cm^–1 is incident on the sample. The visible pulse interacts with this oscillating polarization through coherent Raman scattering to create a coherent output pulse at the IR + visible frequency. This combined IR-Raman interaction is forbidden (in the dipole approximation) in centrosymmetric media because the second-order susceptibility ⁽²⁾ vanishes in such media. Because the methylene –CH₂- groups of the alkane SAM form a nearly centrosymmetric solid, the SFG signal that we observed originated predominantly from the Au surface and the terminal methyl –CH₃ groups. The well-known SFG spectrum obtained in ppp polarization (4), from a SAM with n = 17 (i.e., an 18-carbon or C18 SAM), is shown in Fig. 1D. Molecular vibrational transitions appear as dips against a broad nonresonant background from Au. These methyl transitions have a spectral width = 15 cm^–1, corresponding to a coherence decay time constant T₂ = 0.7 ps, which indicates that SFG signals are emitted during an 1 ps time window. Thus the time resolution of these SFG measurements is 1 ps.

Three intense vibrational transitions were observed, originating from the symmetric _sCH₃ and antisymmetric _aCH₃ methyl stretching vibrations and from the CH₃ bending overtone transition, which draws intensity from a 2:1 Fermi resonance with the CH stretches (4, 8). All methylene transitions are weak, which is indicative of a high degree of order (4). Figure 1D shows the spectrum of a C18 SAM 400 ps after flash-heating, where the SAM is in equilibrium with Au at 800°C. All three methyl transitions have lost intensity as a result of thermal disordering of the methyl groups. The 2CH₃ band evidences a red shift. The red shift is caused by thermal excitation of the 1500 cm^–1 v = 1 state, which introduces an additional contribution from the anharmonically red-shifted v = 1 v = 3 transition. It is notable that methylene transitions remain weak at high temperature and that the transient intensity loss is reversible once the SAM returns to ambient temperature. This indicates that chains remain upright and remain bonded to their original sites. Under ordinary circumstances, alkane SAMs on Au desorb to form the disulfide CH₃-(CH₂)_n-S-S-(CH₂)_n-CH₃ at 175 to 225°C (9, 10), which displays enhanced methylene SFG transitions, so the unexpected stability of these SAMs at 800°C must be attributed to the brief duration of the temperature increase.

We performed molecular simulations of a C16 SAM on Au (27 molecules with periodic boundary conditions) to better understand thermal disordering of the terminal methyl groups. When the SAM was equilibrated at 300 K, the well-known (11) all-trans structure with a chain tilt of 35° and a zenith angle (angle between surface normal and final C-C bond) of 25° was obtained. The _sCH₃ transition has an IR transition dipole moment of magnitude, µ_IR, which is parallel to this final C-C bond. Because polarized Raman scattering from a methyl group is not very sensitive to methyl orientation, the SFG intensity of the _sCH₃ transition would be expected to be approximately proportional to the square of the normalized ensemble-averaged IR transition dipole moment, . As temperature was increased in the simulation, the methyl groups became orientationally disordered, which decreased the magnitude of µ². As shown in Fig. 2B, the SFG intensity in the 300 K > T > 600 K regime can be used as a molecular thermometer, and this molecular thermometer is approximately 1.5 Å thick, the width of a single CH₃ group. Above 600 K, SFG becomes insensitive to T; in our experiments, this helped to smooth out the effects of nonuniformity in laser heating. Figure 2, A and C, shows how thermal disordering progresses after a simulated fast temperature increase to 1100 K. On the <1-ps time scale, the labile terminal methyl groups undergo orientational fluctuations. On the 2-ps time scale, multiple gauche defects are created below the surface (12, 13). On a metal surface in ppp polarization, these gauche defects do not enhance methylene SFG intensities significantly as long as the chains remain upright (12, 13).

Fig. 2. Results of molecular simulations of alkanethiol SAMs. (A) Structure of alkanethiol SAM (n = 15). Simulations were performed on a unit cell of 27 alkanes with periodic boundary conditions. When T is increased to a high temperature, the methyl head groups become orientationally disordered. (B) The SFG intensity for the sCH3 transition is approximately proportional to the square of the normalized ensemble–average IR dipole moment (µ/µIR)2, which is temperature dependent. (C) With an instantaneous temperature jump to 1100 K, the methyl head groups become orientationally disordered in less than 2 ps. [View Larger Version of this Image (63K GIF file)]

Figure 3A shows a time series of SFG spectra after flash-heating of the Au to 800°C for C8 and C18 chains. SFG intensity loss is clearly faster with the shorter chains. The intensity-loss time dependence was similar for all three methyl vibrational transitions, so we now consider only _sCH₃, the most intense transition. To quantify the intensity loss, we define a normalized vibrational response function (VRF) (5, 13) as VRF(t) = [I(T_cold) – I(t)]/[I(T_cold) – I(T_hot)], where I(T_cold) is the _sCH₃ vibrational intensity at ambient temperature and I(T_hot) the intensity after a few hundred picoseconds when Au and SAM have equilibrated. The VRFs for C8 and C18 chains are shown in Fig. 3, B and C, where t = 0 denotes arrival of the flash-heating pulse. Near t = 0, there is a coherent artifact caused by interactions between the SFG pulses and the small portion of flash-heating pulse that leaks through the Au layer. This artifact is a fiducial time marker that locates t = 0. For all alkane chains, the VRFs increased exponentially toward unity with time constant . However, the VRF increase did not begin at t = 0. There was a time delay t₀ before this buildup. As a result of the delayed buildup, we fit the data to the function, VRF(t) = 0 for t < t₀ and VRF(t) = {1 – exp[–(t – t₀)/]} for t t₀. To extract the parameters t₀ and from the data, we plotted ln(1 – VRF) versus t as in Fig. 3, B and C, and used linear least-squares fitting in the t > t₀ region. The slope gave , and the abscissa intercept gave t₀. In Fig. 4, A and B, we plot t₀ and versus chain length. The chain length h, based on conventional molecular bonding parameters (11), obeys the relation h(nm) = 0.127 n + 0.4. Both t₀ and increased linearly with chain length.

Fig. 3. (A) SFG spectra of C8 (n = 7) and C18 (n = 17) SAMs without heating pulses (blue) and with flash-heating to 800°C (red). (B) VRF for a C8 monolayer. (C) VRF for a C18 monolayer. [View Larger Version of this Image (36K GIF file)]

Fig. 4. (A) Dependence on chain length of the delay time t0 between the flash-heating pulse and the arrival of the initial burst of heat at the methyl head groups. (B) Dependence on chain length of the time constant for thermal equilibration between flash-heated Au and alkane chains. [View Larger Version of this Image (16K GIF file)]

The delay time t₀ emerges from the ability of SFG to selectively probe alkanes at the terminal methyl groups. The heat burst from the Au substrate travels along the chains, but only after the leading edge of this heat burst reaches the terminal methyl groups does the SFG optical thermometer begin to register an effect. Thus, t₀ is interpreted as the time for heat to travel from the Au surface to the ends of the alkane chains. The linear dependence of t₀ on chain length indicates that the leading edge of the heat burst propagates ballistically along the chains, and the slope of the data in Fig. 4A gives a velocity of 0.95 (±0.1) nm/ps = 0.95 km/s.

The parameter is the time constant for SAM thermal disordering. Our simulations with infinitely fast heating indicate that thermal disorder can be created in about 2 ps, much faster than observed values of . Figure 2B indicates that the VRF stops increasing after the SAM reaches a temperature of 600 K. Thus we interpret as the time for a SAM in contact with a hot surface to attain a temperature of 600 K.

In Fig. 4, both t₀ and go to zero at a finite chain length of 0.8 nm. This indicates that the hot Au layer does not transfer its heat to an individual atom at the base of the SAM, but instead Au transfers energy to a region at the base of the SAM 0.8 nm in length, which is about four carbon segments. This result is in good agreement with the predictions of Segal et al. (3), which find that the heat-carrying vibrations of short-chain alkanes are delocalized over four to five carbon segments.

The linear dependence of on chain length h is indicative of a heat-transfer process dominated by interface thermal conductance (2, 14). In this case, heat transfer from Au to alkane chains is the rate-limiting step, the rate is controlled by the strength of coupling between Au phonons and alkane vibrations, and the interface thermal conductance G = hC_p/, where is the SAM density and C_p the SAM-specific heat. G is independent of chain length, but longer chains need more heat to reach the same temperature, so longer chains heat up more slowly. To estimate G, we need to correct the value of to account for the insensitivity of the SFG thermometer above 300°C and to estimate the specific heat C_p of the SAM layers up to 300°C, as described in the supporting online material. Because represents the time to heat to 300°C, a linear extrapolation would give the time to heat to 800°C as 2.8. We estimated an average specific heat _p = 3000 J Kg^–1 K^–1 in the 25 to 300°C range, based on a high-temperature extrapolation of low-density polyethylene data. Using the results in Fig. 4B, we obtained G = 220 (±100) MW m^–2 K^–1. This value of G is similar to what was previously obtained in studies of SAM-decorated nanoparticles in aqueous solutions (15).

The SFG probe technique can be seen to confer two important advantages. In the past, thermal conductance measurements of SAMs were based on measuring heat flow across two interfaces (16, 17); the ability to probe the SAM itself eliminates one interface. Even though the flow of energy into the SAM is determined largely by interface effects, the ability to selectively probe the atomic groups that terminate the chains, rather than the thermal expansion of the entire chain (18), allows us to investigate energy transport through the chain molecules themselves.

The quantum mechanical models of Nitzan and co-workers (1, 3) show that 700°C heat transport along alkane chains attached to a pair of metal electrodes involves molecular vibrations ranging up to 1500 cm^–1. The ballistic velocity of 1 km/s for heat transport along alkane chains should be understood as resulting not from acoustic phonons, which in polyethylene propagate at 2.3 km/s, but instead from a mix of intramolecular vibrations with slower velocities. The calculated values of thermal conductances at 700°C (3) were found to be approximately chain-length independent for n 7 and slightly less than 100 pW K^–1. Using our value of G and an area per alkane chain of 2.2 x 10^–19 m² (11), we obtain a single-molecule thermal conductance of 50 pW K^–1 = 0.3 eV ns^–1 K^–1. Thus, our measurements are in good agreement with quantum mechanical calculations that preceded our work.

References and Notes

Received for publication 16 May 2007. Accepted for publication 27 June 2007.

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