Thermal Energy Transport across HardâSoft Interfaces - American

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Thermal Energy Transport across Hard-Soft Interfaces Xingfei Wei, Teng Zhang, and Tengfei Luo ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.7b00570 • Publication Date (Web): 31 Aug 2017 Downloaded from http://pubs.acs.org on September 2, 2017

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ACS Energy Letters

Thermal Energy Transport across Hard-Soft Interfaces Xingfei Wei 1), Teng Zhang1) and Tengfei Luo1,2),* 1) Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

2) Center for Sustainable Energy at Notre Dame (ND Energy), Notre Dame, IN 46556, USA *

Corresponding author: [email protected]

Abstract Interfacial thermal transport across hard-soft interfaces is of critical importance to a wide variety of energy applications, ranging from composite materials, batteries, thermoelectrics, photonic crystals to solar-thermal phase transition. In this perspective, we discuss major experimental and simulation tools used to study such interfacial thermal transport and summarize some new understanding attained. Most studies focus on the interfacial bonding effect, and the underlying relation between bond strength and thermal transport is recently understood from the molecular level: stronger bonds attract soft molecules closer to the hard surface, which leads to a more efficient energy communication across the interface. Recent studies have also demonstrated that the vibrational spectral coupling is another important factor that influences thermal transport across hard-soft interfaces – a factor that has long been under-appreciated for such interfaces. Despite the progress in this field, more research is needed to more deeply understand the physics and transfer the fundamental understanding into rational material design strategies.

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Table of content figure

*Left picture is modified from frontispiece of ref. (18)

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Thermal transport across hard and soft material interfaces is critical to a wide range of energy transfer and conversion applications, such as composites materials,(1,2) batteries, (3) nanofluids,(4) thermoelectrics,(5) photonic crystals(6) and solar-thermal phase transition,(7) to name a few. The thermal resistance presented by interfaces also becomes increasingly important and even dominates the thermal transport due to the large interface density when the characteristic dimensions of structures approach nanometer scale.(8,9) Actually, the first experimental observation of interfacial thermal resistance was on a hard-soft interfaces when Kapitza measured a non-zero temperature difference across a solid-liquid (copper-liquid helium) interface.(10) This quantity is later well known as the Kapitza resistance. The physical origin of the finite thermal conductance (i.e., the inverse of thermal resistance) across interface stems from the incomplete transmission of the thermal energy of heat carriers. While much experimental and theoretical advancement on thermal transport across hard-hard interfaces have been achieved,(9,11-13) the fundamental understanding of thermal transport across hard-soft interfaces lags behind significantly. Thermal transport across hard-hard interfaces are usually understood in the phonon gas picture, where phonons, as heat carriers, transmit through the interface with a given transmission coefficient. However, in soft materials, where atoms are usually disordered, even the definition of phonons become questionable because of the lack of periodicity and thus wavevector,(14) and traditional treatment of phonons transport picture in disordered materials has been challenged.(15) This makes thermal transport across hard-soft interfaces fundamentally different from that across hard-hard interfaces. The studies of hard-hard interfaces have focused on factors like phonon spectra mismatch (i.e., acoustic mismatch), surface roughness and inter-diffusion of species,(9,11-13) but for hard-soft interfaces, the central theme has almost always been the interfacial bonding effect. In this perspective, we strive to discuss two aspects of thermal 3


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transport across hard-soft interfaces including (1) the major experimental and simulation tools used to study interfacial thermal transport, and (2) some important fundamental new physics attained from recent studies. We also provide our perspectives on each of these aspects.

Experimental and Simulation Tools Pump-probe techniques: In the past two decades, the experimental tools used to study thermal transport across hard-soft interfaces have been dominated by laser pump-probe methods. These methods mainly include time-domain thermoreflectance (TDTR)(16) and transient absorption (TA).(17) In TDTR, a pump laser is directed to locally heat up the surface of a sample, and a temporally delayed probe laser is used to track the temperature evolution of the surface (through detecting the reflectance change) as the heat transfer cools down the surface (Fig. 1a). The decay curve, either in amplitude or phase delay, can be modeled by an appropriate heat transfer model to extract interfacial thermal conductance (Fig. 1c). Such a method has been used to measure the thermal conductance of metal-water(16) and metal-organic liquid(18) interfaces with the focus on how metal surface functionalization using self-assembled monolayers (SAM) impacts interfacial thermal conductance. The difficulty in TDTR measurement of hard-soft interfacial conductance mainly stems from the usually low thermal conductivity of the soft material. In general, the large thermal resistance of the bulk soft material dominates the total resistance and thus the measurement is not always sensitive to the changes in the hard-soft interfacial thermal conductance. Strategies like using a low thermal conductivity substrate or adding a thermal insulating layer (e.g., polymer) to force heat to transfer across the measured interface can help to some extent, but such measurements are still not sensitive enough to distinguish the 4


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difference between high thermal conductance values (e.g., >150 MW/m2K, see Fig. 1d). The measurement sensitivity also depends on the thermal conductivity of the specific soft material. For example, water, which has higher thermal conductivity than common organic liquids, will enable higher measurement sensitivity to the interfacial thermal conductance. Actually, there is also a larger number of studies of thermal transport across solid-solid interfaces bridged by SAM,(19-21) where solids, usually metals, have high thermal conductivity, making the measurements much more sensitive to the interfacial thermal conductance. These, however, are out of the scope of this perspective since SAM molecules between two metal surfaces are well ordered and behave more like crystals instead of amorphous soft materials.

Figure 1. Laser pump-probe methods to measure hard-soft interfacial thermal conductance. (a) Schematic of TDTR measurements where the metal in contact with the soft material is working as a transducer to absorb pump energy and sense temperature through reflectance change. (b) Schematic of TA measurements where the metal NPs dispersed in the soft material is working as the transducer. (c) A typical amplitude decay curve from the pump-probe experiment. (d) Comparison of the sensitivities of TA and TDTR measurements to the interfacial thermal conductance, G. TA apparently has higher sensitivity (i.e., curve shifts more when G changes) than TDTR due to larger interface-to-volume ratio.

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Increasing the overall interface area and thus the weight of interfacial thermal resistance among all resistances is an effective strategy to improve the measurement sensitivity to hard-soft interfaces. In this aspect, the TA method has been practiced by probing the thermal relaxation of nanoparticles (NPs) suspended in liquids.(17,22-24) Instead of probing a single interface in TDTR, the TA experiments usually detect the transient light absorption of an ensemble of NPs (Fig. 1b). Due to the larger interface-to-volume ratio in the suspension, the measurement sensitivity to interface can be improved significantly (Fig. 1d). The TA method is not without drawbacks. For example, the NPs can cluster and thus make the interpretation of data difficult (i.e., better heat conduction model is needed). The monodispersity of NP size, which influences the model setup for extracting conductance, is difficult to control. The selection of the size and shape of the NPs are usually constrained by the optical absorption peaks which need to match the laser wavelength for specific systems. Moreover, even with increased sensitivity, using TA to distinguish thermal conductance of different interfaces are still not trivial since the overall sensitivity is still low (Fig. 1d). To help interpret the observed experimental trend from TDTR or TA, techniques such as X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR) are often used, but they are mostly limited to characterizing hard surface functionalization (e.g., bonding and molecular coverage). Contact angle measurements provide an important method to infer the interfacial adhesion energy, which has been the most important focus for hard-soft interfacial thermal transport studies. In our opinion, other factors beyond interfacial adhesion energy can influence thermal transport as well. However, due to the difficulties in quantitative measurements, those factors have not been paid enough attention. For example, factors like molecular structure, local density and viscosity of the soft materials near the 6


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interface are currently not easily measureable experimentally, although they are sometimes called out to discuss hard-soft interfacial thermal conductance values.(16,18,25,26) In future studies, it is desirable to combine the pump-probe methods with other in-situ interface characterization techniques, such as sum frequency generation (SFG) vibrational spectroscopy (27) and FTIR-attenuated total reflection (FTIR-ATR) spectroscopy,(28) to detect the properties of the buried hard-soft interface in real time and link the above-mentioned other factors to thermal transport. The combination of SFG with pump-probe has been used to study thermal transport along molecules in SAM,(29) but here SFG was used as a tool to detect the behavior of SAM under a heat pulse instead of a tool to understand the interfacial characteristics of the hard-soft interface. Moreover, combining these in-situ interface characterization techniques with pump-probe can potentially mitigate the sensitivity problem if they can be directly used to detect the thermal response (hopefully temperature) of the soft molecules close to the interface. Here, we summarize some experimental hard-soft interfacial thermal conductance values measured by TDTR and TA collected from the literature in Table 1. This list is not meant to be all-inclusive but presented to show the orders of magnitude of hard-soft interfacial thermal conductance values. The readers are referred to a few other review articles(12,30,31) for thermal conductance of more interfaces including both hard-hard and hard-soft interfaces. Table 1. Summary of Interfacial Thermal Conductance Measured by TDTR and TA Methods. Hard-soft interface

Conductance -2

-1

(MWm K ) Spun-Cast PMMA/Si

9 – 100

Brush PMMA/Si

3 – 40

(a)

(a)

(b)

CNT- octane

~ 12

Pt/water

~ 130 (c)

Pt-Au alloy/toluene

~5

Au/hexadecane Au/paraffin wax

(c)

Measurement Method TDTR TDTR TA TA TA

~ 28

(d)

TDTR

~ 25

(d)

TDTR

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Au-SAM/hexadecane Au-SAM/paraffin wax

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~ 169 (d)

TDTR

(d)

TDTR

~ 165

Octadecyltrichlorosilane (OTS) functionalized Al/water

~60

(e)

TDTR

alkanethiol (C18) functionalized Au/water

~50 (e)

TDTR

Polyethylene glycol (PEG)-silane functionalized Al/water

~180 (e)

TDTR

C11OH functionalized Au/water

~100 (e)

hexadecyltrimethylammonium bromide (CTAB) functionalized Au/water Sapphire/Polystyrene (PS)

130-450 ~ 7.6

SAM with a -NH2 end group functionalized Sapphire/PS SAM with a -SH end group functionalized Sapphire/PS SAM with a -Cl end group functionalized Sapphire/PS

(g)

TDTR (f)

TA TDTR

~ 16.5

(g)

TDTR

~ 22.0

(g)

TDTR

~ 58.0

(g)

TDTR

(a) ref. (32); (b) ref. (17); (c) ref. (22); (d) ref. (18); (e) ref. (16); (f) ref. (23); (g) ref. (33).

Molecular dynamics (MD) simulations: Analytical models to predict thermal conductance at hard-soft interfaces have been rare and with limited success. For solid-solid interfaces, there have been acoustic mismatch and diffusive mismatch models. (11) These are based on the concept of phonon energy transmission and consider only the phonon properties of bulk materials. However, soft materials (e.g., liquids and polymers) are mostly disordered, and even the picture of phonon gas is questionable. Perhaps the most comprehensive tool to understand the detailed physics of thermal transport across hard-soft interfaces is molecular dynamics (MD) simulations. The maturity of MD software like LAMMPS (34) and the advancement of computing hardware have made such simulations routine tasks. However, details of simulating a hard-soft interface is highly non-trivial, especially when considering amorphous polymer molecules, since it has been found that the thermal transport in polymer is a strong function of the polymer density (35) and detailed chain conformation.(36,37) As a result, extreme care has to be taken to well equilibrate and relax the soft material structure and the interface configuration (e.g., interfacial distance).

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It is worth noting that MD simulations also have some inherent limitations. One is the availability and accuracy of interatomic potential models or force fields. There is a large selection of potential models available for organic molecules thanks to the long history of MD simulations in chemistry, biochemistry and materials fields. However, it should be noted that these potentials are mostly designed to describe the confirmation of the molecules, and none of them are specifically parameterized for thermal transport studies. Some of these potentials use united atom models or harmonic bonds, which will surely influence the accuracy in describing vibration modes, which are the heat carriers in common soft materials. However, recent study seems to suggest that it is not the accuracy of a certain potential model but the morphology of amorphous materials that dominantly impacts the accuracy of thermal conductivity prediction. (38) Moreover, the interaction across the interface involving solid atoms and soft material atoms are usually unknown. Universal force field (UFF) or other general purpose force fields are often used, but in many cases, it is necessary to fine-tune the potential parameters so as to match the experimental findings (e.g., the interfacial adhesion energy inferred from contact angles).(18) Another limitation of MD simulations is the lack of quantum effect. Quantum effect of a vibrating system limits the excitation of higher frequency modes at certain temperatures, but MD, as a classical tool, artificially has all modes equally excited disregard of the temperature. The good thing is that these high frequency modes are usually not significantly involved in thermal transport as they are more localized. Nevertheless, one should not expect very high accuracy of the predicted thermal conductance when using MD simulations given the above-mentioned limitations. However, MD is still the most valuable tool to understand the qualitative trend of conductance and explore the fundamental physics that cannot currently be achieved by experiments. There are three main methods to calculate the interfacial thermal conductance, including the steady-state non-equilibrium MD (NEMD), the transient heat pulse MD and the 9


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equilibrium MD (EMD). These are summarized in Fig. 2 where Au-SAM-hexylamine interfaces are studied as an example. In NEMD, a temperature gradient across the sample is applied and the steady state heat flux is extracted from the thermostats at heat sink and source to calculated thermal conductance (Fig. 2a). To obtain a good signal-to-noise ratio, relatively large temperature difference (~50-100 K) across the sample, which is usually a few tens of nanometers long, is usually needed. Such a high temperature gradient can lead to difference in polymer density along the temperature gradient, which may complicate the data analysis. Usually, the structural relaxation of the system is performed in the NPT (constant number of atoms, pressure and temperature) ensemble where temperature is uniform throughout the simulation cell. Then, when NEMD is performed, some part of the soft material will be squeezed while other parts will be expended due to the large temperature gradient, leading to artifacts in thermal conductance, since it is known that the interfacial distance is critical to thermal transport across hard-soft interfaces. (35,39) For example, the high temperature interface in Fig. 2a apparently has a larger temperature jump than the low temperature one, and this is due to the expansion-induced interface distance.(26,39) In such cases, one should set the temperature properly so that one interface can be close to the temperature of interest (e.g., 300 K, see Fig. 2a). It will also be beneficial to use NPH (constant number of atoms, pressure and enthalpy) ensemble, where system size is allowed to relax while a temperature gradient is applied, to equilibrate the structure with the temperature gradient already applied before transitioning to NEMD production runs.(40) Challenges also exist in how to define the temperature jump across the interface. However, since the simulation results should be regarded as qualitative to explore a trend, as long as a consistent criterion in extracting the temperature jump is applied, comparison between different interfaces can usually be fairly made. Normally, the interfacial temperature difference is calculated by extrapolating the linearly fitted temperature profiles of the hard and soft materials and taking the temperature 10


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difference right at the interface (Fig. 2a). Such a strategy may encounter difficulties if there is penetration of soft molecules into the solid surfaces or its functional molecules where the interface position is no longer well defined. (25)

Figure 2. MD methods used to calculate hard-soft interfacial thermal conductance. Here, the

Au-SAM-hexylamine interface is studied as an example. (a) A typical simulation setup in NEMD and the corresponding steady state temperature profile together with the definition of temperature jump across the interface. (b) A typical setup in heat pulse MD and the decay of temperature difference between Au and soft material. When assuming lumped capacitance, the decay should be exponential and the time constant can be fitted to back up thermal conductance (see inset equations). (c) Schematic of power exchange across interfaces due to interfacial interatomic forces (Eq. 2). The conductance shows better convergence behavior when large ensemble average is performed. The conductance values calculated from these three methods are shown in their respective panels. The values show reasonable agreement with one another.

Another method widely used for hard-soft interfaces is the heat pulse method. It is a transient method where the hard material is usually assumed to have much higher thermal conductivity than the soft material so that lumped heat capacitance and Newton’s law of cooling can be applied to extract an effective interfacial thermal conductance (Fig. 2b). In this method, a short-duration heat pulse is applied to the hard material to pump up its temperature, 11


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and the temperature difference between the hard and soft materials is monitored as a function of time (Fig. 2b). According to Newton’s law of cooling, the temperature difference should decay exponentially, and the extracted decay time constant can be used to calculate conductance (equation in Fig. 2b). This method is easy to implement and does not need a lot of computational time compared to NEMD. As can be seen in Fig. 2, it can also yield result within the error bar of that from NEMD. However, it has some critical limitations. First, the solid material needs to have much higher thermal conductivity than the soft material so that the lumped capacitance assumption is valid. This is usually valid. A more serious drawback is related to the internal phonon energy communication inside the hard material. When a thermostat is used to ramp up the temperature of the solid, the duration usually needs to be very short (normally a few hundred femtoseconds to a few picoseconds), and such a short time is insufficient for phonons in a solid to reach thermal equilibrium. This internal phonon equilibration will certainly influence the temperature decay curve. As a result, the decay time constant is not purely due to interfacial thermal transport but also partially due to the internal energy equilibration resistance among phonons in solids. This does not seem to be a problem for the case shown in Fig. 2b likely due to the fact that gold only has acoustic phonons and they exchange energy efficiently (i.e., the internal resistance is small). For materials with weak phonon scatterings, this can be a problem. For example, when a heat pulse is applied to a graphene or carbon nanotube (CNT) in contact with a soft material, the short heat pulse may effectively pump up the optical phonons. After the pulse, optical phonons will transfer heat to acoustic phonons which is more efficient in transferring heat across the graphene (or CNT)-soft material interface.(17,41) The cooling curve actual encompasses both of these two resistive processes. As a result, the heat pulse method may predict lower conductance values than NEMD methods for similar systems (e.g., compare results from Refs. (35) and (41)).

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Another emerging method is EMD based on the Green-Kubo formulation. It calculates thermal

conductance

utilizing

a

Green-Kubo

formulation

derived

from

the

fluctuation-dissipation theorem. (42) The conductance, G, can be expressed as the autocorrelation of the net power, Q, exchanged between atoms across the interface (Fig. 2c):

=

< 0 ∙ >

= ∑ ∈ ∙ − ∑ ∈ ∙ ∈

(1)

(2)

∈

where is force, is atomic velocity, and N1 and N2 are atoms at either side of the interface (Fig. 2c). This method is relatively new, but its application to interfaces has demonstrated success. (43) The obvious advantage is that there is no need for a temperature gradient, and thus related problems as previous discussed in NEMD can be avoided. The challenge of this method is mainly from the statistical nature of the Green-Kubo method, which leads to convergence problems of thermal conductance. Performing ensemble averaging with independent initial conditions (e.g., initial molecular configuration and velocities) can be effective to help sample the phase space more completely (i.e., maximize ergodicity) thus obtain converged thermal conductance values (Fig. 2c). For example, in Fig. 2c, after averaging data from 24 ensembles, a converged regime (black line) becomes more obvious, especially after 400 ps. We need to note that there is currently no standard criterion for defining the convergence. Some systems (such as simple crystal) will converge well, but some require large numbers of ensemble averaging. Since the autocorrelation of heat flux or net interfacial power is inherently related to the atomic movement, understanding the relation between the atom dynamics (e.g., vibrational frequency), decay of autocorrelation and thus the convergence of the transport property may help avoid any ambiguity in defining convergence. Such research, however, is currently lacking. The best strategy for now may be 13


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using large ensemble averaging and use the same time period to obtain converged thermal conductance values for all systems within one study. Of course, this increases the computational burden and sometimes defining convergence can be somewhat subjective. It should be noted that Eq. (2) is general and can also be used to extract the heat flux across interfaces in NEMD simulations. This helps decompose the contributions of different types of interactions (e.g., vdW and electrostatic) to thermal conductance, providing a tool to understand interfacial thermal transport in a greater depth.(26) In all, none of these three methods are perfect. However, when used with care and the understanding of their limitations, meaningful results, trends and, more importantly, physics can be extracted. As shown in Fig. 2, the three methods actually give similar thermal conductance values especially considering the many uncertainties discussed above. However, such comparison also depends on the nature of the system studied (e.g., Au-soft material vs. graphene-soft material) and the details in obtaining conductance values (e.g., defining interfacial temperature jump in NEMD and convergence in EMD). When comparing different interfaces, conductance values obtained from the same method should be used to minimize uncertainties from different methods. We believe that results from MD is more appropriate for obtaining a qualitative trend and exploring physics instead of offering quantitative predictions.

Fundamental Understanding of Thermal Transport Physics Interfacial bonding effects: Using the above discussed experimental and simulation tools, the fundamental physics of thermal transport across hard-soft interfaces are increasingly understood. Majority of the studies in this field have focused on how to promote stronger interfacial bonding across the interface to achieve higher thermal conductance. This is a 14


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natural strategy since solid surfaces have been historically functionalized to change the surface chemistry, which can influence the solid-liquid interfacial adhesion energy, although the initial purpose was not for thermal transport. Interfacial adhesion energy is generally changed by modifying the interfacial bonding. For example, more polar surface functionalization can lead to stronger electrostatic interaction across the interface. When met with highly polarized organic soft molecules, it is possible to functionalize hard surfaces with polar molecules to promote strong hydrogen bonds. Macroscopically, larger interfacial adhesion energy can usually be implied by better wettability. Recent studies by Zhang et al. 26 and Ramos-Alvarado et al.

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show that at the molecular level a larger interfacial adhesion

energy is manifested by the shorter interfacial distance as stronger bonds attract atoms from either side of the interface closer to each other, which also increases the local density and can potentially lead to local molecular structuring. Thermal transport across hard-soft interfaces can be greatly influenced by the interfacial adhesion energy according to both experimental and modeling studies. For metal-water interfaces, hydrophilic functionalization using SAM has led to as much as 3 times improvement in conductance from TDTR experiments. (16) Similar experiments also found or inferred a positive relation between the adhesion energy and interfacial thermal conductance between solids and soft materials (e.g., water and polymer). (33,45) MD studies of bonding effect are more widely seen than experimental studies likely due to the experimental difficulties discussed previously. Shenogina et al.(46) used MD simulations to investigate the wettability of differently functionalized surfaces and derived an almost linear relationship between the adhesion energy and conductance. A few other MD studies also investigated the relation between adhesion energy and thermal conductance of hard-soft interfaces,(35,41,47) and the conclusions are consistent. Figure 3 shows a compilation of conductance values of gold-organic liquid interfaces with different SAM functionalizations, 15


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and the data clearly show that a stronger interfacial bonding generally leads to higher thermal conductance.(26) However, the trend cannot be simply fit by a single linear line, because many other factors such as the vibrational nature of the soft material should also impact thermal transport.

Figure 3. Thermal conductance values of gold-organic liquid interfaces with different SAM functionalizations

plotted as a function of the interfacial adhesion energy, which is calculated by the summation of the vdW and electrostatic potential energy for all the atom pairs across the interface. Each color represents a different organic liquid, and each shape of the symbol represents a different type of SAM functionalization. In general, stronger interfacial adhesion energy leads to larger conductance.

When the interface is bonded by weak vdW interactions, the thermal conductance values are usually at the low end (< 50 MW/m2K). For example, one of the first experiments using TA to measure the thermal conductance across CNT-solvent interface showed that the thermal conductance is ~12 MW/m2K,(17) and similar values were found in MD simulations 16


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using the heat pulse method.(17,48) The good agreement between the experimental and simulation data, despite the aforementioned limitation of the heat pulse method, is likely because the TA experiment also heats up the CNT in a similar way as the heat pulse MD method. Chemical bonds (e.g., covalent bonds) establish the strongest interaction between two materials at the interface and thus can improve thermal conductance significantly.(35,47) However, forming covalent bonds is not always viable since the hard-soft interfaces are usually formed through physical means rather than chemical reactions. Within physical bonding, forming hydrogen bonds, which are 1-2 orders of magnitude stronger than vdW interaction, is the most versatile approach. In practice, hydrogen bonding can be established by functionalizing the hard surface using ligands with appropriate hydrogen bond acceptors/donors end groups to pair with those in the soft materials. For example, if the soft material features amine groups (-NH2), ligands with carboxyl groups (-COOH) can be used to functionalize the hard surface to promote interfacial hydrogen bonds. While fundamental research usually utilizes the simplest system to explore the physics (e.g., gold as the hard materials and SAM as functionalization ligands), practical applications need appropriate procedure to robustly functionalize the hard surfaces with ligands. Fortunately, there is a wide range of SAM molecules to be selected from for different categories of hard materials (e.g., thiols for metals and silanes for oxides), and their end groups can be tuned according to the nature of the soft materials.

Hydrogen bonding effect: Detailed MD studies have led to more in-depth understanding of the role of hydrogen bonding in interfacial thermal transport from a microscopic point of view beyond a simple relation between the adhesion energy and conductance values.(26) Hydrogen bond is the combination of strong electrostatic attraction between highly polarized 17


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groups and the vdW interactions existing between any non-bonded atom pairs. By separating these two, the electrostatic contribution is found to play a dominant role in enhancing the interfacial adhesion energy when the hydrogen bonds are present, which is intuitive (Fig. 4a). However, when decomposing thermal conductance into contributions from vdW and electrostatic interactions through Eq. (2), it is counter-intuitive to find that the vdW interaction, instead of the electrostatic force, dominates the actual increase in thermal conductance (Fig. 4b). Through further analysis, it has been concluded that there is a collaborative effect of vdW and electrostatic interactions in enhancing conductance across hydrogen-bonded interfaces: stronger electrostatic interactions will pull the soft molecules closer to the interface (Fig. 4c and 4d), and this shorter inter-molecular distance leads to increased interatomic forces across the interfaces (Eq. (2)), which results in larger interfacial heat flux and thus higher thermal conductance.(26)

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(a)

(c)

(b)

0 -100 -200 -300 -400 -500 -600 -700 -800

vdW Total

C6H13NH2

C6H13OH C5H11COOH

Organic Liquid

vdW

Interfacial Thermal Conductance (MW/m 2K)

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Interfacial Adhesion Energy (Kcal/mol)

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(d)

400 Total

vdW

300

200

100

0

C6H13NH2

C6H13OH C5H11COOH

Organic Liquid

Hexanoic acid

Interface

Au

Au higher atom density & stronger H-bond

vdW & H-bond

Au

Au

Interface Hexanoic acid

Figure 4. MD simulations provide more in-depth details of the mechanism of thermal transport across hydrogen-bonded hard-soft interfaces. (a) Decomposition of interfacial adhesion energy into contributions from vdW interaction (shaded portion) and electrostatic interaction. The latter is responsible for the increased adhesion energy due to stronger hydrogen bonds. (b) Decomposition of interfacial thermal conductance into contributions from vdW interaction (shaded portion) and electrostatic interaction. Surprisingly, the vdW interaction is responsible for the increased conductance after stronger hydrogen bonds formed. For panels (a) and (b), the interfaces presented here are between Au functionalized with the –COOH SAM and three organic liquids with increasingly polarized groups (i.e., -NH2 < -OH < -COOH). (c) Schematic of the collaborative effect of vdW and electrostatic interaction in enhancing conductance across hydrogen-bonded interfaces: stronger hydrogen bonds will pull the organic molecules closer to the interface, and this shorter interface distance leads to increased interatomic forces across the interfaces (Eq. (2)), which results in larger interfacial

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heat flux and thus higher thermal conductance. (d) Further confirmation of the closer hard-soft contact when there are stronger hydrogen bonds as demonstrated by the larger soft molecular density at the interface.

Vibrational spectra matching effect: Another factor that has been largely ignored when improving the thermal conductance of hard-soft interfaces is that interfacial thermal transport is also dictated by the phonon spectra matching (vibration matching), although earlier MD simulations have suggested such effects.(49) For hard materials, especially crystals, the atomic structures are well-ordered and the atoms are usually connected by strong covalent, ionic or metallic bonds. For soft materials, however, the structures are intrinsically disordered, and there exists a mixture of strong intra-molecular covalent bonds and weak inter-molecular non-bond interactions. Moreover, common soft materials are often organics consisting of elements that are usually much lighter than those in hard materials (i.e., metals, silicon and etc.). Due to such distinct compositions and bonding natures, the vibrational spectra of hard and soft materials usually have large mismatches, and the thermal conductance values are usually at the low end. Recently, a TDTR pump-probe experiment demonstrated a significant enhancement in thermal transport across hard-soft (Au-polyethylene (PE)) interfaces by coating the hard surfaces with SAM molecules (alkanethiols: HS(CH2)nCH3, see Fig. 5a). These SAM molecules have chemical compositions similar to the soft material (i.e., PE, see Fig. 5a).18 This results in a great increase by as much as 7 times in the thermal conductance compared to the un-functionalized interface (Fig. 5b). Counter-intuitively, such large increases in conductance after surface functionalization are realized despite the observed significant decrease in the interfacial adhesion energy illustrated by the smaller contact angle (Fig. 5c). Combining MD simulation and experimental data, it was found that the SAM chemically 20


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absorbed on the Au surface can act as a medium to bridge the vibrational spectral mismatch between Au and PE and thus enable efficient resonance-like thermal transport (Fig. 5d).(18) Of course, the prerequisite of the enhancement in conductance is the efficient thermal transport by the strong covalent bonds between SAM and Au and the small resistance of the thin SAM layer itself. A similar effect was also found by the TDTR experiments from Tian et al. (50) for functionalized Au-ethanol interfaces. Using SAM as a vibrational bridge should be widely applicable, since for common soft materials (e.g., organic liquids and polymers) one can often find SAM molecules with similar chemical composition as those of the soft materials.

(d)

Figure 5. Vibrational bridge effect of SAM in enhancing hard-soft interfacial thermal transport. (a) Schematic of the design of SAM to have similar backbone as the soft material (PE) so that it can have similar vibrational spectra as the soft material.(18)

(b) TDTR results showing alkanthiol-functionalized interfaces having larger

thermal conductance than the unfunctionalized bare interface. C6-C18 refer to alkanthiols with different length of backbones. (c) Contact angle measurements showing that after functionalization, the interfacial adhesion energy actually decreased as indicated by the increased contact angles. (d) Calculated vibrational power spectra of Au, C12 and hexadecane (HD) from MD indicating that C12 has almost identical vibrational feature compared to the HD.

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The aforementioned bonding effect can be easily combined with the vibrational bridging effect in practice. For example, for polar soft materials, such as decanoic acid, polyimide and nylon, the existence of highly polarized groups (i.e., -COOH, -C=O and -NH2) makes it possible to use polar SAM molecules (e.g., (HS(CH2)n-2COOH)) to coat the hard surface so as to form hydrogen bonds. At the meantime, the backbone of the SAM molecules can be tailored to be the same as or similar to that of the soft materials (e.g., SAM: HS(CH2)8COOH and decanoic acid: CH3(CH2)8COOH), and the combined strong hydrogen bond and vibration matching effect can further enhance interfacial thermal transport. Actually, the large conductance values of the interfaces studied in Fig. 3 all took advantage of such combined effects.

Molecularly heterogeneous interface: Beyond bonding and vibrational effects, molecular level surface heterogeneity can also improve the thermal conductance due to the increased effective contact area – a strategy similar to the fin structure used in conventional heat exchangers. Our recent EMD simulation results on Au-SAM-hexylamine interfaces find that SAM made up of short and long chain thiol molecules can allow soft molecules to penetrate into to the space between long thiols and thus increase the effective contact area compared to a flat SAM surface (Fig. 6). Due to such an effect, the conductance can be improved obviously (Table in Fig. 6). We note that for such an interface, where the soft material can penetrate into the SAM, it is difficult to define a temperature difference at the interface since it is subjective to determine the location of the interface. In this case, EMD is preferred over NEMD for calculating thermal conductance. The heterogeneous interface effect is essentially an interfacial bonding effect. Due to the penetration of soft molecules, there are more atoms from each side of the interface interacting 22


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with each other and the effective interfacial adhesion energy is enhanced (Table in Fig. 6). Another MD study also showed that the molecularly rough surface of SAM can enhance the thermal transport between SAM and toluene.(25) It is also worth noting that it has been proven that such heterogeneous SAMs can be experimentally synthesized,(51) so they are expected to have practical relevance beyond fundamental interests. Heterogeneous SAM

Flat SAM

Thermal conductance G=93±12 MW/m2 K

G=55±8 MW/m2 K

Effective contact area 2561±199 Å3

1836±29 Å3

Interface energy 150±30 kcal/mol

60±5 kcal/mol

Figure 6. Heterogeneous SAM functionalization increases effective contact area with soft material and thus increase thermal conductance. The enhanced contact area is due to the liquid molecule penetration into the space between long SAM chains. The table summarizes the calculated thermal conductance from EMD, the effective contact area from Voronoi tessellation and the interfacial adhesion energy.

Summary In this perspective, we reviewed and discussed recent activities in experimental and simulation studies of thermal transport across hard-soft interfaces. The advancements and drawbacks of both laser pump-probe experiments and MD simulations for studying interfacial thermal transport have been discussed. We believe that new experimental techniques (e.g., better sample design, direct temperature probing of soft molecules close to interface, and more realistic heat conduction model) need to be developed in order to resolve 23


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the low sensitivity issue of the existing pump-probe methods to hard-soft interfacial thermal conductance. MD simulation techniques are highly developed, but researchers need to understand the limitations of each methods and take them into account when analyzing obtained data. We believe that MD simulations are more appropriate for qualitative studies and exploring the fundamental physics of hard-soft interfacial thermal transport. Most studies in this field have focused on the interfacial bonding effect since it is a factor that can be relatively easily tuned through surface functionalization. Almost all of these studies point to a positive relation between the interfacial adhesion energy and thermal conductance. Hydrogen bonding has been a topic of interest, and MD simulations have provided some unprecedented details of the underlying relation between hydrogen bond strength and thermal transport. Recent experimental studies have also demonstrated that the vibrational spectral coupling is another important factor that influences thermal transport across hard-soft interfaces – a factor that has long been under-appreciated for such interfaces. While not intensively discussed in this paper, other factors, such as molecule penetration, liquid restructuring and the nature of heat carriers in soft and hard materials, are also topics of current and potential interests. Despite the progress in this field, further fundamental research is needed to achieve a more comprehensive understanding of the roles of different factors in interfacial thermal transport. Applied research is also needed to transfer the fundamental understanding into rational material design strategies.

Notes The authors declare no competing financial interest. 24


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Author Biographies Xingfei Wei is currently a Ph.D. student in the Department of Aerospace and Mechanical Engineering at the University of Notre Dame. He is studying thermal transport in polymers and at material interfaces. His research interests are transport processes, chemical reactions and sustainable energy development.

Teng Zhang received his B.S. in Polymer Materials and Engineering from University of Science and Technology of China in 2011 and Ph.D. degree in Mechanical Engineering from the University of Notre Dame in 2016. He joined Schrödinger Inc. in 2016, and is currently a senior scientist at the Materials Science Department. His research interest is focused on thermal transport, atomic-scale modeling, and amorphous builder for polymers and material interfaces.

Tengfei Luo completed his Ph.D. degree in Mechanical Engineering at Michigan State University. After postdoctoral research at Massachusetts Institute of Technology in the area of nanoscale heat transfer, he joined the faculty of the University of Notre Dame in 2012, where he is currently an Associate Professor and the Dorini Family Collegiate Chair in Energy Studies. His research interests span a broad spectrum in thermal transport in crystal materials, soft materials, across interfaces, photo-thermal liquid phase transition and water treatment.

Quotes to highlight in paper 25


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1. Thermal transport across hard-soft interfaces can be significantly enhanced by forming strong interfacial hydrogen bonds through proper surface functionalization. 2. Microscopically, stronger interfacial bonds attract atoms from either side of the interface closer to one another, leading to larger interatomic forces and thus more efficient thermal transport. 3. Self-assembled monolayer with proper molecular backbone can be used to functionalize hard surfaces to bridge the vibrational spectra gap between hard and soft materials, leading to unconventional enhancement in thermal conductance. 4. Heterogeneous self-assembled monolayer with non-uniform chain lengths can lead to larger effective contact area between hard and soft materials, enhancing thermal transport in a way similar to the fin structure in conventional heat exchangers.

Acknowledgements The authors acknowledge the financial support from the Army Research Office (W911NF-16-1-0267). T. L. also thanks the support from the DuPont Young Professor Award program. This research was supported in part by the Notre Dame Center for Research Computing and NSF through XSEDE resources provided by SDSC Trestles, Comet and TACC Stampede under grant number TG-CTS100078.

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