Research Article www.acsami.org
Role of Hydrogen Bonds in Thermal Transport across Hard/Soft Material Interfaces Teng Zhang,† Ashley R. Gans-Forrest,‡ Eungkyu Lee,† Xueqiang Zhang,‡,⊥ Chen Qu,∥ Yunsong Pang,† Fangyuan Sun,¶ and Tengfei Luo*,†,# †
Department of Aerospace and Mechanical Engineering, ‡Department of Chemistry and Biochemistry, ⊥Radiation Laboratory, Department of Chemical and Biomolecular Engineering, and #Center for Sustainable Energy at Notre Dame, University of Notre Dame, Notre Dame, Indiana 46556, United States ¶ Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China ∥
S Supporting Information *
ABSTRACT: The nature of the bond is a dominant factor in determining the thermal transport across interfaces. In this paper, we study the role of the hydrogen bond in thermal transport across interfaces between hard and soft materials with different surface functionalizations around room temperature using molecular dynamics simulations. Gold (Au) is studied as the hard material, and four different types of organic liquids with different polarizations, including hexane (C5H11CH3), hexanamine (C6H13NH2), hexanol (C6H13OH), and hexanoic acid (C5H11COOH), are used to represent the soft materials. To study the hydrogen bonds at the Au/organic liquid interface, three types of thiol-terminated self-assembled monolayer (SAM) molecules, including 1-hexanethiol [HS(CH2)5CH3], 6-mercapto-1-hexanol [HS(CH2)6OH], and 6-mercaptohexanoic acid [HS(CH2)5COOH], are used to functionalize the Au surface. These SAM molecules form hydrogen bonds with the studied organic liquids with varying strengths, which are found to significantly improve efficient interfacial thermal transport. Detailed analyses on the molecular-level details reveal that such efficient thermal transport originates from the collaborative effects of the electrostatic and van der Waals portions in the hydrogen bonds. It is found that stronger hydrogen bonds will pull the organic molecules closer to the interface. This shorter intermolecular distance leads to increased interatomic forces across the interfaces, which result in larger interfacial heat flux and thus higher thermal conductance. These results can provide important insight into the design of hard/soft materials or structures for a wide range of applications. KEYWORDS: thermal transport, hard/soft material interface, hydrogen bond, molecular dynamics, surface functionalization, self-assembled monolayers
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INTRODUCTION
interfacial thermal conductance between solids and liquids from their experiments. A few molecular dynamics (MD) simulations have also studied the relationship between the interfacial energy and thermal conductance of hard/soft interfaces,11−13 and the findings are consistent with the experiments. Other MD simulations found that the surface functionalization can influence hard/soft interfacial thermal transport depending on the solvent penetration14 and surface ligand density.15 Although it is known that making the interface hydrophilic can improve thermal transport, the fundamental mechanism that links the stronger interfacial energy to thermal transport is still lacking. A common feature of the hydrophilic interfaces is the formation of hydrogen bonds. It is understandable that hydrogen bonds at the interface can significantly increase the
Thermal transport across hard and soft material interfaces is critical to a wide range of applications such as polymer composites,1,2 nanofluids,3 and nanoparticle-assisted hyperthermia therapeutics.4,5 The thermal resistance presented by interfaces also becomes increasingly important when the characteristic dimensions of the structures approach nanometer scale, where the interfacial thermal resistance can be similar to that of the component materials or even dominate thermal transport.6,7 Thermal transport across interfaces can be greatly influenced by the interfacial binding energy. For solid/liquid interfaces, hydrophilic functionalization has been an effective strategy to enhance interfacial thermal transport. Thermal conductance improvement by as much as three times was observed in experiments when a metal surface in contact with water was functionalized by hydrophilic self-assembled monolayers (SAMs).8 Tian et al.9 and Harikrishna et al.10 also found a positive relationship between the adhesion energy and © 2016 American Chemical Society
Received: September 22, 2016 Accepted: November 11, 2016 Published: November 11, 2016 33326
DOI: 10.1021/acsami.6b12073 ACS Appl. Mater. Interfaces 2016, 8, 33326−33334
Research Article
ACS Applied Materials & Interfaces
Figure 1. (a) Simulation setup for NEMD thermal conductance calculations: heat flows across the junction from source to sink. (b) Temperature profiles near the interface and the definition of the interfacial temperature difference. (c) Molecular structures of the SAM molecules and organic liquid molecules studied. From top to bottom, the functional groups of these molecules become more polarized.
thermal transport.16 With such sample designs, interfacial bonds can be isolated as the only determining factor responsible for the changes observed in thermal conductance. The interactions between Au atoms are simulated using a Morse potential. The Morse potential is also used to simulate the interaction between Au atoms and the sulfur (S) atoms in the thiol SAM molecules.17−19 The universal force field with slightly modified parameters is used for the nonbonding interactions between Au and other atoms.20,21 The parameter modification was found to be necessary to correctly describe the interfacial energy.20 The organic molecules, including the SAM molecules and organic liquid molecules, are modeled using the polymer consistent force field (PCFF).22 All simulations are performed using the large-scale atomic/ molecular massively parallel simulator.23 All components are arranged as shown in Figure 1a to form the hard/soft material interfaces. The two Au substrates each contain 25 layers of Au atoms arranged in the face-centeredcubic lattice. The Au(111) surfaces are exposed, and SAM molecules are placed on each surface, with the S atoms bonding to Au atoms using the Morse potential.17,24 A total of 400 organic liquid molecules are compacted into an amorphous phase and placed between the two substrates using Packmol,25,26 and then this block is annealed at 600 K to further optimize the conformation of the molecules. Nonequilibrium molecular dynamics (NEMD) simulations are performed to calculate interfacial thermal conductance (Figure 1a). The temperatures at the two thermostatted regions are set to 310 K for the heat source and 210 K for the heat sink using Langevin thermostats. The relatively large temperature difference is used to offer a better converged temperature profile near the interface because too small a temperature difference across the sample makes the interfacial temperature drop difficult to measure and thus makes it hard to calculate thermal conductance accurately. The reason for choosing the above-mentioned temperatures for the heat source and sink is that the temperature of the interface near the hot side is around 300 K, which is close to room temperature. Before the NEMD calculation, the whole system is first equilibrated at 260 K and 1 atm for 1 ns with periodic boundary conditions applied in all
interfacial binding energy, but how they are related to thermal transport at the molecular level is not completely clear. Moreover, the binding energy is a static property, but thermal transport across interfaces is due to the atomic motion (i.e., a dynamic property) and interatomic forces between the atoms at each side of the interface. In this work, we perform detailed MD simulations and analyses to study the role of hydrogen bonds in thermal transport across hard and soft material interfaces. A series of surface functionalizations and organic liquids (the soft materials) with different polarization groups are investigated to study different types of hydrogen bonds with different strengths. We decompose the thermal conductance into contributions from van der Waals (vdW) and electrostatic forces, and relate their contributions to the molecular distances of different hydrogen-bonded interfaces. It is found that stronger hydrogen bonds will pull the interfaces closer, whereas both vdW and electrostatic forces are stronger than weakly bonded interfaces. It is these increased forces that lead to larger heat flux at the interface and thus higher thermal conductance. These results, although fundamental in nature, can have important implications in the design of hard/soft materials or structures for different applications.
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SIMULATION METHODS In this work, gold (Au) is studied as the hard material, and four different types of organic liquids with varying polarizations, including hexane (C5H11CH3), hexanamine (C6H13NH2), hexanol (C6H13OH), and hexanoic acid (C5H11COOH), are studied as soft materials (Figure 1c). To study the hydrogen bonds at the Au/organic liquid interface, three types of thiolterminated SAM molecules, including 1-hexanethiol [HS(CH2)5CH3], 6-mercapto-1-hexanol [HS(CH2)6OH], and 6mercaptohexanoic acid [HS(CH2)5COOH], are used to functionalize the Au surface (Figure 1c). For brevity, they are denoted as −CH3 SAM, −OH SAM, and −COOH SAM, respectively, in the following text. We specifically choose all of the thiols to have the same type of backbone (−CH2−) and lengths of six carbon atoms so that all molecules have similar vibrational spectra, another factor that can influence interfacial 33327
DOI: 10.1021/acsami.6b12073 ACS Appl. Mater. Interfaces 2016, 8, 33326−33334
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Figure 2. Temperature profiles for Au/hexanol (C6H13OH) interfaces with different surface functionalizations under similar heat flux condition: (a) no functionalization; (b) −CH3 SAM; (c) −OH SAM. The temperature drop at the interface is significantly reduced by functionalizing the Au surface with SAMs, particularly for the system with hydrogen bonds (−OH SAM/C6H13OH).
Figure 3. (a) Thermal conductance values and (b) interfacial adhesion energies of different interfaces. Each bar is decomposed to the contributions from vdW and electrostatic interactions, with the former indicated by the grayed portions. The numbers shown in panel b are the numbers of hydrogen bonds at the corresponding interfaces.
type of surface functionalization is represented by one color and different organic liquids are labeled on the x axis. To link the thermal conductance enhancement to the interfacial energy, we calculate the interfacial adhesion energy in MD simulations (Figure 3b) by summing all interactions between the organic liquid and substrate (Au + SAM). For each type of organic liquid, as more polarized SAM molecules are used to functionalize the Au surface (i.e., −CH3 → −OH → −COOH SAMs), an increasing trend of interfacial thermal conductance is observed (Figure 3a). There are a few other key observations from Figure 3a. Compared to bare unfunctionalized Au surfaces, the functionalized interfaces all show larger conductance. Our previous study showed that such enhancements are due to the fact that the SAM molecules, which have the same carbon backbone as the organic liquids (see Figure 1c), can bridge the gap in vibrational spectra between Au and organic liquids and hence improve interfacial thermal transport (see Note 1 in the Supporting Information).20 As a result, even though the −CH3 thiol functionalized surfaces have lower interfacial energy compared to the bare Au (Figure 3b, yellow vs green bars), the thermal conductance values of these functionalized interfaces are larger than those of the bare Au interfaces (Figure 3a, yellow vs green bars). However, further enhancements in the thermal conductance shown in the −OH and −COOH SAM functionalized Au surfaces compared to the −CH3 SAM functionalized ones should be attributed to the improvement in the interfacial adhesion energy related to the hydrogen-bond formation (Figure 3b). Compared to the −CH3 SAM functionalized surfaces, the −OH SAM functionalized surfaces show increased interfacial adhesion energy for all types of organic liquids (Figure 3b, blue vs green bars). Such a rising trend is due to the stronger
three spatial directions. After the structures are fully relaxed, the last layer of Au atoms at each end is fixed and vacuum spaces at the ends are created by enlarging the simulation cell size in the z direction. This prevents heat leakage from the heat source to the heat sink through the Au blocks due to the periodic boundary condition, forcing all of the heat to transfer across the hard/soft interfaces. Simulations using NVE ensembles (constant volume and energy) for 8−10 ns are then performed to calculate thermal conductance. A typical steady-state temperature profile for the high-temperature interface is shown in Figure 1b. The heat flux (q) is calculated from the energy input and output rates from the Langevin thermostats for the heat source and sink. The temperature drop (ΔT) at the interface is calculated as a linear extrapolation of the bulk temperature to the edge of Au and the organic liquid (Figure 1b). Interfacial thermal conductance (G) is then calculated as G = q/ΔT. We note that only data from the interface at the hightemperature end is included in the following text because the temperature of this interface is close to room temperature (∼300 K).
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RESULTS AND DISCUSSION Interfacial Thermal Conductance and Interfacial Energy. Figure 2 shows representative temperature profiles at the steady state of the NEMD simulations for differently functionalized Au/C6H13OH interfaces. Qualitatively, we can see that the temperature drop at the interface is significantly reduced after functionalizing the Au surface with SAMs, particularly for the system with hydrogen bonds (Au/−OH SAM/C6H13OH). The calculated thermal conductance values for different Au/ SAM/liquid interfaces are shown in Figure 3a, in which each 33328
DOI: 10.1021/acsami.6b12073 ACS Appl. Mater. Interfaces 2016, 8, 33326−33334
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Figure 4. Thermal conductance as a function of the interface adhesion energy for different liquids contacting differently functionalized Au: (a) hexane (C5H11CH3); (b) hexanamine (C6H13NH2); (c) hexanol (C6H13OH); (d) hexanoic acid (C5H11COOH). The dashed lines are linear fits.
form one relatively weak hydrogen bond with a −OH group because of their weaker polarization. To further highlight the impact of hydrogen bonds on interfacial thermal transport, we compile the thermal conductance values from functionalized interfaces and plot them as a function of the corresponding adhesion energy separately for different liquids (Figure 4). The insets in these figures show the representative hydrogen-bonding structures visualized from VMD. For hexane (Figure 4a), when the SAM is changed from −CH3 to −COOH, the increase in interfacial adhesion energy is obvious. Such an increase can be attributed to the stronger polarity of the −OH and −COOH groups than that of the −CH3 group, and such stronger polarity gives rise to stronger electrostatic interaction between the SAM and hexane. On the other hand, for hexanamine (Figure 4b) and hexanol (Figure 4c), their −NH2 and −OH end groups can form hydrogen bonds with the −OH and −COOH groups in SAMs; hence, the thermal conductance enhancements are more pronounced compared to the hexane cases. For hexanoic acid (Figure 4d), the thermal conductance is distinctly higher for the −COOH SAM surface than the −OH SAM surface. The −COOH groups in SAM and those in hexanoic acid can actually form two hydrogen bonds per pair of molecules, which is very strong, making their interfacial adhesion even stronger (Figure 4d), and as a result, the thermal conductance is further increased.
interactions between the polar −OH group of the SAM molecules and the liquid molecules. Compared with surfaces functionalized by −COOH SAM, those functionalized by −OH SAM form weaker hydrogen bonds with the −NH2 group in hexanamine (C6H13NH2), the −OH group in hexanol (C6H13OH), and the −COOH group in hexanoic acid (C5H11COOH).27 When the surface is functionalized by −COOH SAM, the interfacial adhesion energies are further improved (pink bars in Figure 3b) because of the formation of stronger hydrogen bonds between the highly polarized −COOH group in SAM and the organic liquid molecules. To further link the interfacial adhesion energy to the role of hydrogen bonding at different interfaces, the number of hydrogen bonds is calculated using visual molecular dynamics (VMD)28 with the following criterion: donor−acceptor distance ≤ 3.0 Å and angle cutoff ≤ 20°. In Figure 3b, we indicate the number of hydrogen bonds corresponding to the blue and pink bars. For each organic liquid, larger numbers of hydrogen bonds are found to correspond well to larger interfacial adhesion energies (Figure 3b). It is worth noting that the numbers of hydrogen bonds do not necessarily correspond to the relative interfacial energy for different organic liquids because the strength of each type of hydrogen bond is not the same. For example, two −COOH groups can form very strong hydrogen bonds with each other, while −NH2 groups can only 33329
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Figure 5. Heat flux decomposition of (a) −CH3 SAM/hexane (C5H11CH3), (b) −COOH SAM/hexane (C5H11CH3), and (c) −COOH SAM/ hexanoic acid (C5H11COOH) interfaces. As the interacting molecules become more polarized, the contribution from the electrostatic forces to the total heat flux increases (red lines).
We also used linear lines to fit the data in each panel in Figure 4. It can be seen that the data generally agree well with a linear relationship for each liquid but the slopes differ. This is in agreement with the previous MD simulations and experimental results, showing that the interfacial thermal conductance changes linearly with the interface energy for solid/water interfaces.10,11 We note that the data for bare Au surfaces are not included in these linear fitting because they involve not only the interface adhesion energy effect but also the aforementioned vibrational spectral mismatching effects.20 It is worth mentioning that the calculated thermal conductance values are virtually contributed from three thermal conductance components, consisting of those from the Au/ SAM interface, the SAM layer, and the SAM/liquid interface. We can extract the SAM/liquid thermal conductance based on previously reported thermal conductance of the Au/SAM interfaces. A number of studies have estimated the thermal conductance of the Au/SAM interface, and values from 200 to 400 MW·m−2·K−1 have been reported.18,29,30 Several studies have also shown that thermal transport across the SAM layer made of short and well-aligned alkane chains is highly efficient, making their thermal resistance negligible.18,29,31,32 If a value of 400 MW·m−2·K−1 is assumed for thermal conductance of the Au/SAM interface18 and the thermal resistance of the SAM layer is neglected, we estimate the thermal conductance of the hydrogen-bonded SAM/liquid interface to be as high as ∼880 MW·m−2·K−1. Because of very large density of the polarized functional group and hydrogen bonds, we note that such values are much higher than those of common vdW interfaces, even most hydrogen bonds involving protein/water interfaces (100− 300 MW·m−2·K−1),33−35 and are comparable to those of covalent interfaces like epitaxial interfaces (∼700 MW·m−2· K−1)36 and anthracene/alkane interfaces (∼1000 MW·m−2· K−1).37 Role of Hydrogen Bonds in Interfacial Thermal Transport. It is known that the strength of the hydrogen bond is contributed by the electrostatic attraction between highly polarized functional groups and the vdW interactions existing between any nonbonded atom pairs. In fact, the hydrogen bonds are the result of the combined effect from different nonbonded interactions in the force field (PCFF) used in our study. Such a strategy is shown to be sufficient and also widely used in many other common force fields, like CVFF,38 AMBER,39,40 and OPLS.41 In these models, the electrostatic interaction between the hydrogen-bond donor and acceptor leads to the formation of hydrogen bonds,22,42 and thus a further decomposition of the interfacial adhesion energy
into the vdW and electrostatic portions can be carried out to further understand the role of hydrogen bonds in thermal transport. Here, we decompose the interfacial interaction for all interfaces. The grayed portion in Figure 3b indicates the portion of the interfacial energy contributed by vdW interactions, and the rest of the interfacial adhesion energy is attributed to electrostatic interactions. It is noted that, in some cases (e.g., some green and blue bars in Figure 3b), electrostatic interactions are repulsive, their contributions to the total interfacial energy are positive values, and thus the grayed area (vdW contribution) can be larger than the area of the total interfacial adhesion energy. There are some other key observations that indicate the role of hydrogen bonding: For interfaces consisting of nonpolarized functional groups (e.g., −CH3 SAM), the vdW interaction dominates the interfacial adhesion energy (e.g., yellow bars in Figure 3b), and the electrostatic contribution is negligible. On the other hand, for polarized molecules, especially SAM/organic liquid pairs that can form hydrogen bonds (e.g., −COOH SAM with C6H13NH2, C6H13OH, and C5H11COOH), the electrostatic interaction plays an important role (Figure 3b, pink bars). Especially in cases with a larger number of hydrogen bonds (−COOH SAM with C5H11COOH and C6H13OH), the electrostatic portion counts for more than half of the total interfacial adhesion energy (the last two pink bars in Figure 3b). Thus, for interfaces with strong hydrogen bonds, hydrogen bonding significantly increases the total interfacial adhesion energy via electrostatic interactions. To further understand the role of hydrogen bonds in thermal transport, the total heat flux at the interface is decomposed into vdW and electrostatic portions by calculating the heat flux via vdW and electrostatic forces separately. To perform such a decomposition, the total structure is first separated into to two parts: group hard (gh) and group soft (gs). The former includes atoms in the substrate and the SAM, while the latter includes atoms in the organic liquid. The power exchanged between gh and gs can be calculated as43,44 p=
⎛ 1⎜ ∑ Fij ·vj − 2 ⎜⎝ i ∈ gh/ j ∈ gs
⎞ Fji ·vi⎟⎟ ⎠ i ∈ gh/ j ∈ gs
∑
(1)
where Fij is the force on atom j from atom i and vj is velocity of atom j. Equation 1 describes the net power exchanged across the interface due to interatomic forces. The total force (Fij) at the interface consists of two components: force due to vdW interaction (FvdW ij ) and force due to electrostatic interaction 33330
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Figure 6. Force distribution of (a) vdW and (b) electrostatic interactions with a large y-axis view range to show the most highly populated force strengths. Force distribution of (c) vdW and (d) electrostatic interactions with a large x-axis view range to show the distribution of strong interactions.
(Fqij). Thus, during the NEMD simulation, the net power exchanged via vdW interaction (pvdW) and that via electrostatic interaction (pq) at the interface can be separated using the following equation: p = p vdW + pq ⎛ 1 = ⎜⎜ ∑ FijvdW ·vi − 2 ⎝ i ∈ gh/ j ∈ gs +
⎛ 1⎜ ∑ Fijq ·vj − 2 ⎜⎝ i ∈ gh/ j ∈ gs
In Figure 3a, the grayed areas of the bars indicate the interfacial thermal conductance contributed by vdW interactions (GvdW), and the rest of the total interfacial thermal conductance is due to electrostatic interactions (Gq). For all six pairs of SAM and organic liquid that can form hydrogen bonds (the last three blue and pink bars, Figure 3a), the electrostatic interactions contribute 25−40% of the total interfacial thermal conductance. Surprisingly, even for the SAM/organic liquid pair with the strongest hydrogen bond (−COOH SAM/ C 5 H 11 COOH), the portion of the interfacial thermal conductance due to vdW interaction still counts more than that of the electrostatic interactions (the last pink bar, Figure 3a). Interestingly, as stronger hydrogen bonds form between more polarized SAM and organic liquid, the vdW portion of the interfacial thermal conductance also increases (e.g., grayed portion of the last three pink bars, Figure 3a). Because heat flux across the interface is achieved through interatomic forces applied from atoms on one side of the interface to atoms on the other side, one possible explanation for larger GvdW in more polarized interfaces could be that the strength of vdW forces also increase as stronger hydrogen bonds are formed. In Figure 6, we plot the histograms of different forces across three types of representative interfaces, −CH3 SAM/C5H11CH3, −OH SAM/C6H13OH, and −COOH SAM/C5H11COOH, which have no hydrogen bonds, weak hydrogen bonds, and strong hydrogen bonds, respectively. The histograms describe the number distribution of pairwise interactions across the interface as a function of the magnitude of forces due to such interactions. Here, a negative force indicates the attraction between two atoms, and positive means repulsion. For both vdW and electrostatic forces, there is a large population around zero, corresponding to weak interactions
⎞ ⎟ FvdW v · ji j⎟ i ∈ gh/ j ∈ gs ⎠
∑
⎞ Fqji ·vi⎟⎟ i ∈ gh/ j ∈ gs ⎠
∑
(2)
Figure 5 shows the time integration of power exchanged across three representative interfaces via different types of interactions and their summation, which yield cumulative energies across the interfaces. What are also shown in the figure are the average cumulative energies into and out of the thermostatted regions in the NEMD simulations [(Qout − Qin)/2], which are derived from the Langevin thermostats. It is found that the time integration of the total power exchanged across the interface is the same as the average energy into and out of the thermostatted regions, validating our heat flux decomposition algorithm. From the most nonpolarized interfaces (−CH3 SAM/C5H11CH3 with no hydrogen bond) to the most polarized interfaces (−COOH SAM/C5H11COOH with the largest number of hydrogen bonds), pq significantly increases (slope of the red lines, Figure 5). The heat fluxes (JvdW or Jq) via vdW or electrostatic interactions can be further calculated as pvdW/S or pq/S, where S is the cross-sectional area, and thus the interfacial thermal conductance due to a certain type of interaction can be calculated as GvdW = JvdW/ΔT or Gq = Jq/ΔT. 33331
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numbers of pair interactions are also listed in Table 1, and more polarized molecules are found to establish more pair interactions across the interface. To explain the reason for the larger numbers of pair interactions in the hydrogen-bonded interfaces, the atom number density near the interface is calculated (Figure 7). The exact position of the interfaces between SAM and organic liquid is defined by the local minimum of the atom density at the interface, and the interface positions of different SAM/ organic liquid pairs are all placed at 0 Å (Figure 7). Along the normal direction of the interface, 0.1-Å-thick slabs are used to calculate the atom density as a function of the distance to the interface. −COOH SAM can form strong hydrogen bonds with organic liquids, such as C 6 H 13 NH 2 , C 6 H 13 OH, and C5H11COOH (black curves in Figure 7b−d, respectively), and it is found that the atom density local minima in these cases are much larger than those in the other cases. In addition, as the SAM molecules change to more polarized ones, the major peak near the interface of the organic liquid shifts closer to the interface (indicated by the orange arrows in the insets of Figure 7a−d), which is also an indication of closer contacts. We note that such effects share some similarity with the pressure-induced thermal-transport enhancement across interfaces19 and in bulk polymers as seen in other simulations. When high pressure is applied, the atoms are pushed closer, which enhances the energy transport efficiency from one to another. However, the hydrogen-bond effect is more localized at the interface, while the pressure effect is global (Note 2 in the Supporting Information). Moreover, from a practical point of view, applying high pressure can impose complications and inconvenience in many applications. Liquid Restructuring and Vibrational Spectral Matching Effects. Liquid restructuring was attributed as one possible reason for the high thermal conductance at solid/aqueous surfaces.45 However, there are still debates over such a mechanism,8,46−48 and its effect on interfacial thermal transport is estimated to be insignificant.8,48 Moreover, a recent study demonstrated that liquid restructuring at the solid surface is largely universal, disregarding the surface functionalization and solvent polarity.49 Our characterizations of the structures of the organic liquids near the interface also do not show any correlation between the structure and thermal conductance enhancement (Note 3 in the Supporting Information). As mentioned earlier, vibrational spectral matching (acoustic match) is another factor that can influence interfacial thermal transport.16 However, because the molecular structures of the SAMs and organic liquids studied are chosen to be the same, the vibrational spectral matching for different interfaces in this study should be the same (Note 1 in the Supporting Information), and hence it should also not be the reason for the observed thermal conductance enhancement among functionalized surfaces. These analyses reassure that the large difference in the thermal conductance originates from the hydrogen bonds at the interface.
between atoms that are relatively far apart from each other (Figure 6a,b). In addition, parts a and b of Figure 6 also show that the strength of the electrostatic forces has a much broader distribution compared with that of the vdW forces, which is related to the slower decaying nature of the electrostatic interactions. Parts a and b of Figure 6 show the same data but illustrate the distribution of strong interactions after the proper adjustment of the view range of both axes. For interfaces consisting of more polarized molecules (polarization: red > black > blue, Figure 6), the widths of the main peaks around zero become larger, indicating the increase of the number of atomic pairs that have strong interactions. Because of the formation of hydrogen bonds, which have strong electrostatic interactions between dipoles, the pair number distributions show peaks at −20 kcal/mol·Å, and the structures with stronger hydrogen bonds yield both more pairs (higher peak of the red line compared to the black line, Figure 6d) and stronger electrostatic interactions (peak position shifted to the left) around −20 kcal/mol·Å. Correspondingly, the calculated Gq for the −COOH SAM/C5H11COOH interface (69.5 MW·m−2· K−1) is larger than that for the −OH SAM/C6H13OH interface (46.4 MW·m−2·K−1). Besides larger contributions to the thermal conductance themselves, stronger electrostatic interactions will also increase the force strength from vdW interactions. Figure 6c shows that a larger population of stronger interactions occurs when molecules can form hydrogen bonds (red > black > blue). As shown in Figure 6c,d, from nonpolarized molecules to highly polarized molecules, there is an increase in the strong repulsive vdW interaction (positive forces) and an increase in the strong attractive electrostatic interactions (negative values). To qualitatively compare the magnitude of forces across the interfaces, Table 1 shows the total vdW and electrostatic force Table 1. Total vdW and Electrostatic Forces and Total Pair Number interface
total vdw
−CH3 SAM/ C5H11CH3 −OH SAM/C6H13OH −COOH SAM/ C5H11COOH
−8.5 ± 1.3
a
323.3 ± 56.3 1589.0 ± 32.0
total electrostatic 6.5 ± 0.2 −281.5 ± 44.7 −1424.0 ± 28.0
total pair number 140439 211254 218008
The force unit is kcal·mol−1·Å−1.
f total = ∑N·f, where N is the number of pairs and f is the magnitude of force between two atoms. Table 1 shows that, for the nonpolarized −CH3 SAM/C5H11CH3 interface, the vdW interactions provide the adhesive forces (negative values) that bind the two materials, while the electrostatic forces are repulsive. For the other two hydrogen-bonded interfaces, the electrostatic interactions provide the adhesive forces (negative values), and the vdW forces are repulsive. Moreover, hydrogen bonds not only lead to larger attractive electrostatic forces but also lead to stronger repulsive vdW forces. As suggested by eq 1, these stronger vdW forces in the hydrogen-bonded interface will lead to larger GvdW. Actually, besides the occurrence of stronger vdW interactions, parts a and c of Figure 6 also show that the total number of pair interactions is larger in the hydrogen-bonded interface: red and black lines are always higher than the blue line. Calculated from the pair number distribution, the total
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CONCLUSION In this work, our MD simulations found that hydrogen bonds at hard/soft material interfaces can significantly facilitate interfacial thermal transport. Molecular-level analyses show that such efficient thermal transport originates from the collaborative effect of the electrostatic and vdW portions in the hydrogen bonds. It is found that stronger hydrogen bonds will pull the organic molecules closer to the interface. The closer 33332
DOI: 10.1021/acsami.6b12073 ACS Appl. Mater. Interfaces 2016, 8, 33326−33334
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Figure 7. Atom number density profiles near the interfaces for (a) hexane (C5H11CH3), (b) hexanamine (C6H13NH2), (c) hexanol (C6H13OH), and (d) hexanoic acid (C5H11COOH). Different color lines correspond to different organic liquids, as indicated by the legend in panel a.
Energy Sciences, under Award DE-FC02-04ER15533 (NDRL no. 5074). F.S. thanks National Natural Science Foundation of China (Grant 51606193). T.L. thanks the useful discussion with Prof. S. Ptashiska, Prof. S. Alex Kandel, and Prof. Y. Elaine Zhu. 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 TG-CTS100078.
contact between the two materials and higher atom number density of the organic liquids near the interface leads to increased interatomic forces across the interface, which results in larger heat flux from not only the electrostatic forces but also the vdW forces at the interface. This is the root reason for the higher thermal conductance. These results can have important implications in the design of hard/soft materials or structures for different applications.
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ASSOCIATED CONTENT
S Supporting Information *
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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b12073. Vibrational power spectral calculation, pressure effect versus hydrogen-bond effect, liquid structure near the interface, and temperature effect on interfacial thermal conductance (PDF)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] ORCID
Tengfei Luo: 0000-0003-3940-8786 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS T.Z. and T.L. acknowledge financial support from the Army Research Office (Grant W911NF-16-1-0267). E.L. is supported by the DARPA project (D15AP00094). X.Z. acknowledges the U.S. Department of Energy Office of Science, Office of Basic 33333
DOI: 10.1021/acsami.6b12073 ACS Appl. Mater. Interfaces 2016, 8, 33326−33334
Research Article
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