Mechanism of Temperature Dependent Thermal Transport across the

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Mechanism of Temperature Dependent Thermal Transport Across the Interface Between Self-Assembled Monolayer and Water Shih-Wei Hung, Gota Kikugawa, and Junichiro Shiomi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09516 • Publication Date (Web): 08 Nov 2016 Downloaded from http://pubs.acs.org on November 15, 2016

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The Journal of Physical Chemistry

Mechanism of Temperature Dependent Thermal Transport across the Interface between SelfAssembled Monolayer and Water Shih-Wei Hung1, Gota Kikugawa2, Junichiro Shiomi1,*

1

Department of Mechanical Engineering, The University of Tokyo, Tokyo, Japan

2

Institute of Fluid Science, Tohoku University, Sendai, Japan

AUTHOR INFORMATION Corresponding Author: [email protected]

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ABSTRACT

The thermal boundary conductance between water and self-assembled monolayer was studied using non-equilibrium molecular dynamics simulations. Different thermal transport behaviors were observed for hydrophobic and hydrophilic self-assembled monolayers. In the temperature range between 280 and 340 K, the thermal boundary conductance was found to depend on the temperature for hydrophobic self-assembled monolayers. On the contrary, the difference in thermal boundary conductance at different temperatures was slight for hydrophilic self-assembled monolayers. The correlations in velocity and density between terminal atoms of self-assembled monolayer and water molecules within the interface region were analyzed to understand the mechanism of thermal transport across the interface. The vibrational density of states calculation indicated that the temperature dependence does not originate from the overlap of phonon spectrum. The analysis of radial density distribution revealed that the temperature dependence is mainly attributed to the number of water molecules surrounding the terminal atoms of self-assembled monolayers.


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INTRODUCTION Interfaces between materials have become increasingly important due to the recent rapid development in nanoscle engineering.1 When the systems or their constituent length scales reach the nanometer scale, thermal boundary resistance (Kapitza resistance) of even atomistically flat interface can dominate the overall thermal transport because of significantly large specific surface area. Much effort has been directed toward understanding and controlling thermal transport across a solid/liquid interface, which is important in applications such as nanofluids. Nanofluids are fluid suspensions of nanometer-sized solid particles and fibers,2,3 proposed to enhance the thermal conductivity and convective heat transfer performance of the base liquids. Due to their large surface to volume ratio, the thermal boundary resistance at solid-liquid interface plays an important role in determining the thermal transport properties. One effective way to control the thermal boundary conductance (TBC), inverse of Kapitza resistance,4 is surface functionalization of the solid surface with self-assembled monolayers (SAMs).5–15 SAMs have been a promising surface-modification technique because they are stable, highly ordered, easy to prepare, and provide a wide range of organic functionality.16 The surface properties can be easily and flexibly modified by the



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designation of SAM molecules, enabling to tailor the thermal transport across the solidliquid interface. In-depth studies of the controllability of TBC have been reported on the basis of recent advances to access thermal transport properties at solid-liquid interfaces using molecular dynamics (MD) simulations5,11,12,17–22 or nanoscale heat conduction measurements such as the time-domain thermoreflectance (TDTR) method.23,24 Shenogina et al.13 quantified the TBC at SAM/water interface over a broad range of surface wettability by studying various terminal groups using MD simulations, and demonstrated a connection between TBC and the work of adhesion. Ge et al.14 measured the TBCs with hydrophilic and hydrophobic SAMs by using TDTR method, and found that the TBC of hydrophilic SAM is a factor of 2-3 larger than that of hydrophobic SAM. Harikrishna et al.8 showed that the TBC is proportional to the work of adhesion using TDTR method. Their results also indicated that the TBC is independent of the alkyl chain length in the range of 11-18 carbon units. The length-independence was also shown by Tian et al.9 for solid-ethanol interface using TDTR method. Acharya et al.10 performed MD simulation and showed that nanoscale roughness in addition to the hydrophilicity of SAM can enhance the TBC. Despite the great advance in understanding the influence of SAM wettability on TBC, one aspect with a practical importance that has not been explored well is the temperature


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dependence of TBC. Note that nanofluids for instance are most likely to be applied in a nonequilibrium setup with significant temperature variation in space if not also in time. In general, the thermal conductivity of nanofluid is more sensitive to temperature than that of the base fluid,2 in which the temperature dependence of TBC at SAM/liquid interface is expected to play a major role. However, the reported work on the temperature dependence is limited to that done by Goicochea et al.11 using MD simulation, where TBC between water and hydroxyl-terminated SAMs was observed to be almost independent of temperature. On the other hand, the studies of other solid-liquid systems have found that the temperature dependence of TBC depends on the wettability. Murad et al.25,26 demonstrated that the TBC increases with temperature for water/SiO2 and water/Si interfaces, and that the former interface with stronger hydrophilicity results in weaker temperature dependence. Song et al.27 reported a similar trend with respect to the wettability using a Lennard-Jones potential system, and explained that it is because the peak density of the liquid layer increases with temperature and the increment grows with wettability. It is of interest to quantify and understand in SAM/water system how the wettability influences the temperature dependence of TBC.



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Thus, this study aims to investigate the temperature dependence of TBC across SAM/water interface, with particular focus on the influence of SAM wettability and underlying mechanism from microscopic viewpoint. To that end, the non-equilibrium molecular dynamics (NEMD) simulations28 were performed to identify the effects of the chain length and terminal group on the temperature dependence of TBC. The correlations in velocity and density between SAMs and water molecules within the interface region were analyzed to understand the mechanism resulting in the differences in TBCs.

COMPUTATIONAL DETAILS This work seeks to study the interfacial heat transfer at the SAM/water interface. The model system consisted of a typical alkanethiolate SAM chemically adsorbed on the Au(111) surface with explicitly defined water molecules, as shown in Figure 1. Two different terminal groups were adopted to study the effect of wettability, methyl group for hydrophobic SAMs and hydroxyl group for hydrophilic SAMs, on interfacial thermal transport. The model system was a rectangular box with three-dimensional periodic boundary conditions. The solid gold substrates with face centered cubic lattice was placed at both ends (six layers on each side) of the simulation box. The SAMs were modeled by generating a 12×12 array of the single chain with a √3×√3R30°lattice structure and a sulfur−sulfur spacing of 0.497 nm29 to form a 5.19×5.99 nm2 cross-sectional area. In 6 ACS Paragon Plus Environment

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the middle of the simulation box, 2000 water molecules were introduced as solvent. Three alkanethiol molecules with different hydrocarbon chain lengths for each terminal groups, i.e., S(CH2)7CH3, S(CH2)10CH3, and S(CH2)16CH3 for methyl-terminated SAMs (CH3SAMs) and S(CH2)8OH, S(CH2)11OH, and S(CH2)17OH for hydroxyl-terminated SAMs (OH-SAMs), were chosen to study the influence of chain length. Hereafter, S(CH2)7CH3, S(CH2)10CH3, S(CH2)16CH3, S(CH2)8OH, S(CH2)11OH, and S(CH2)17OH were denoted briefly by C7CH3, C10CH3, C16CH3, C8OH, C11OH, and C17OH, respectively. The interaction potential between gold atoms in the solid substrate was modeled by the Morse potential.30 The force field proposed by Shevade et al. 31 was adopted for the alkanethiol molecules of SAM. However, this force field imposed bond constraint instead of bond stretching potential. In order to evaluate the heat transfer through the vibrational motion of bend stretching inside the SAM phase, the bond stretching potential32 was taken into account. For the hydroxyl group of OH-SAM, the NERD force field33 was adopted. The potential functions of SAM molecules were given by 𝑉tot = ∑bonds 𝑘𝑟 (𝑟 − 𝑟0 )2 + ∑angles 𝑘𝜃 (𝜃 − 𝜃0 )2 + ∑dihedrals ∑5𝑛=0 𝐶𝑛 cos 𝑛 𝜑 + 𝜎

12

∑nonbonded ∑𝑖 C7CH3 > C7CH3-k2. On the other hand, the dependence of stiffness of OH-SAMs is not significant. Because the terminal OH groups of OH-SAMs form a network structure in the surface plane due to hydrogen bonding,47 the behavior of molecules within the interface regime is sensitive to the potential models used. We found that the fluctuations of calculated TBCs and water molecule density distributions are too large to be reliable for OH-SAMs when doubling the force constants in the potential model. Thus, the C8OHk2 case was not included in the present study. The values of GSAM/Water of CH3-SAMs monotonically increase with the temperature, while that of OH-SAMs are not a strong function of temperature. To clarify the temperature dependence on TBC, the values of GSAM/Water were normalized to the values at 280 K, as shown in parts a and b of Figure 4. The temperature dependence of GSAM/Water is slight for OH-SAMs comparing with that for CH3-SAMs. The independence of GSAM/Water for OH-SAMs was also observed in the previous MD study11, where the conductance at OH-SAMs/water interface remains almost constant from 300 to 375 K. This observation is also in agreement with the previous studies43,44 that the temperature dependence of TBC at protein/water interface is slight for the temperatures from 280 to 320 K because most of the protein surface in contact with water is hydrophilic. On the


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other hand, the value of GSAM/Water is a strong function of temperature for CH3-SAMs. The value of GSAM/Water is 47% higher at 340 K than that at 280 K for C16CH3 SAMs. A previous MD study27 using Lennard-Jones potential system also showed that the temperature dependence of TBC at liquid/solid interface is related to the surface wettability, i.e., the temperature dependence is stronger for a more hydrophobic surface.

(a)

(b)

Figure 2. The temperature profile of (a) gold/C16CH3/water and (b) gold/C17OH/water systems at average temperature of 280 K. The shadow denotes the heat exchange regimes. The red dashed lines indicate the linear fit. The red squares represent the extrapolation of the linear fit at the interface. 13 ACS Paragon Plus Environment


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(a)

(b)

Figure 3. The TBCSAM/Water of (a) CH3-SAMs and (b) OH-SAMs as a function of average temperature of system.


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(a)

(b)

Figure 4. The normalized TBCSAM/Water of (a) CH3-SAMs and (b) OH-SAMs as a function of average temperature of system. Vibrational characteristics at the SAM/water interface The thermal transport across the interfaces is related to the vibrational characteristics of molecules forming interfaces. It has been proposed that the extent of overlap between 15 ACS Paragon Plus Environment


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the vibrational density of states (VDOS) of the molecules forming an interface can be taken as a qualitative measure of vibration coupling, which is related to the magnitude of the TBC.48 Therefore, the VDOS of molecules within the interface regime were analyzed to gain more details of the mechanism leading to the differences in TBCs at CH3SAM/water interface. The VDOS, S(f), was computed by the Fourier transform of the velocity autocorrelation function (VACF), C(t). The VACF is given by 𝐶(𝑡) = ∑𝑛𝑖=1〈𝑚𝑖 𝒗𝑖 (𝑡) ∙ 𝒗𝑖 (0)〉

(3)

where t is the time, n is the number of atoms calculated, 𝑚𝑖 and 𝒗𝑖 are the mass and velocity vector of the ith atom and 〈⋯ 〉 indicates an ensemble average. The VDOS is described as follows 𝜏

2

𝑆(𝑓) = 𝑘𝑇𝑁 lim ∫−𝜏 𝐶(𝑡) 𝑒 −𝑖2𝜋𝑓𝑡 𝑑𝑡 𝑓

𝜏→∞

(4)

where f is the frequency, k is the Boltzmann constant, T is the system temperature, Nf is the total degrees of freedom. To focus on the vibrational characteristics within the interface regime, only the water molecules of the first adsorption layer adjacent to the interface and the terminal atoms of SAM molecules, i.e. CH3, were evaluated. Figure 5 show the VDOS of CH3, SCH3(f), and water adjacent to the interface, SWater(f), of C7CH3, C7CH3-k0.5, and C7CH3-k2, respectively. The spectrum distributions of water molecules are almost the same for each system. On the other hand, the spectrum 16 ACS Paragon Plus Environment

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distributions of CH3 vary with different types of SAMs. The profiles of spectrum distribution of CH3 are similar in shape at different temperatures so that the changes in spectrum with temperature were insignificant. For different chain lengths, the frequency bands are similar, i.e. the low frequency band from 0 to 15 THz and the high frequency band from 32 to 42 THz. Meanwhile, the spectrum profiles change significantly by varying the force constants, as shown in Figure 5. For more flexible SAMs (smaller force constants), the low frequency band ranges from 0 to 10 THz and the high frequency band ranges from 22 to 30 THz. Whereas, the low frequency band ranges from 0 to 20 THz and the high frequency band ranges from 40 to 50 THz for stiffer SAMs (larger force constants). The overlap, O, of SCH3(f) and SWater(f) was calculated to qualitatively measure the vibration coupling. ∞

𝑂 = ∫0 𝑆𝐶𝐻3 (𝑓)𝑆𝑊𝑎𝑡𝑒𝑟 (𝑓)𝑑𝑓

(5)

As shown in Figure 6, the yielded overlaps change significantly with the different force constants, i.e. C7CH3, C7CH3-k0.5, and C7CH3-k2. The frequency band of water molecules only locates in the low frequency, 0-20 THz, so that the overlaps increase as the frequency band is shifted to the lower frequency, i.e. the more flexible SAMs. Thus, the enhancement of TBC with increasing flexibility of CH3-SAMs can be explained by



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the increasing overlap of VDOS. However, the yielded overlaps of C7CH3, C10CH3, and C16CH3 at different temperatures differ by less than 4%, i.e. the overlaps are independent of chain lengths and temperatures. Therefore, the results indicate that the temperature dependences of TBCSAM/water does not originate from the change in the vibrational coupling. Another possible mechanism of the temperature dependence in TBC is the role of anharmonic interactions at the interface,46 which increases with temperature and can enhance the thermal conductance by increasing the inelastic phonon transmission channels. However, as shown in Figure 5, both the line center and linewidth of VDOS are found to vary insignificantly with temperature, and hence, the current results suggest that the anharmonic interaction is not the key factor in the temperature dependence of TBC for the temperature range from 280 to 340 K.


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(a)

(b)



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(c)

Figure 5. VDOS profiles of heavy atoms CH3 and water molecules within the interface regime in (a) C7CH3, (b) C7CH3-k0.5, and (c) C7CH3-k2 system.

Figure 6. Overlap of SCH3(f) and SWater(f) for different CH3-SAMs at different average temperatures of system.


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Water behavior at interface It has been demonstrated that the thermal transport across solid/liquid interface is critically affected by the layering of water at the interface, i.e. the thermal conductance is strongly related to the value of the peak density of the first layer of water adjacent to the interface.22,27 Besides, the water layering structure is affected by the surface wettability and temperature. Accordingly, the density profiles of water and SAMs perpendicular to the interface were calculated to understand the microscopic structure within the interface regime. Parts a and b of Figure 7 show the density profiles of SAMs and water molecules within the SAM/water interface regime for CH3-SAMs and OH-SAMs, respectively. The oscillation in the water density adjacent to the interface can be observed for both CH3SAMs and OH-SAMs. The first peak of the density profiles are lower and broader for OH-SAMs than for CH3-SAMs. For OH-SAMs, the water molecules form hydrogen bonds with OH terminal groups of SAM surface, resulting in intercalation with the surface and degradation of layering structure.10 The difference between the CH3-SAMs and OHSAMs also manifests itself in the temperature dependences of the density profiles. In case of CH3-SAMs, the peak density of the terminal atoms of SAMs and the first peak of water layering structure decrease with temperature because of the higher mobility of the terminal atoms of SAMs and water at higher temperature. In case of OH-SAMs, the peak



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densities of the terminal atoms of SAMs also decrease with temperature as, however, the changes in the first peak densities of the water layering structure are minute. The fact that the temperature effect on the water density profiles is more obvious for the hydrophobic CH3-SAMs is consistent with the previous study.27 To gain more insight into the density correlation between the terminal atoms of SAMs and water molecules, we further calculate the inter-material radial density functions (RDFs). (a)

(b)

Figure 7. Density profiles in the direction perpendicular to the SAM/water interface of the (a) C7CH3 and (b) C8OH systems.

Figure 8 shows the RDFs, g(r), of water molecules at a distance r around the terminal atom of each SAM surfaces. The profiles of g(r) are similar in shape, i.e. the peak and


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valley positions are basically the same, for SAMs with the same terminal group. The widths and heights of the first peak vary with different chain lengths and temperatures for CH3-SAMs. On the other hand, the widths and heights of the first peak vary only with temperatures for OH-SAMs. The integral of g(r) to the first minimum, the gray dashed line in Figure 8, was calculated to present the average number of water molecules within the first shell around the terminal atoms of SAMs. Figure 9 summarize the integrals of the first layer of RDFs for different surfaces at different temperatures. The results clearly demonstrate that the integrals of the first layer of RDFs vary with the different SAMs and temperatures for CH3-SAMs, while the integrals are almost constant for OH-SAMs. For CH3-SAMs, the flexibility of SAM molecules and the mobility of water molecules both increase with temperature, resulting in more water molecules surrounding the terminal atoms of SAMs at higher temperature. As a result, the integrals of the first peak of RDF increase with temperature. For OH-SAMs, the strong adsorption between OH terminal and water molecules resulting in a stable value of number of water within the first shell around the OH terminal regardless of the lengths and stiffness of SAM molecules and temperatures. Thus, the average number of water molecules within the first shell surrounding the terminal atoms of OH-SAMs is independent of the chain lengths, stiffness, and temperatures.



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The relationship between TBCs of SAM/water interface and the integrals of the first peak of RDFs for CH3-SAMs is plotted in Figure 10. The TBCs of SAM/water interface are related to the integrals of the first peak of RDFs in a linear manner. The results suggest that the mechanism of the positive temperature dependence of TBC: larger temperature increases the number of water molecules that are in direct contact with the terminal atoms of CH3-SAMs, giving rise to more thermal transport channel between SAM and water. Moreover, the number of water molecules surrounding the terminal atoms is related to not only the temperature, but also the structure of SAM molecule. The stiffness dependence of CH3-SAMs on TBC can also be observed in Figure 10. It is proposed that the TBC at CH3-SAM/water interface can be tailored by adjusting the structure of SAM molecules, for example, the stiffness. For OH-SAMs, the independence of TBCs of SAM/water interface on temperature reflects the fact that the number of water molecules surrounding the terminal atoms of OH-SAMs is almost constant. This oberservation agrees well with the previous study49 of heat conduction of bulk alkane liquids, in which it was demonstrated that the efficiency of intermolecular heat path is sensitive to the structure of the first neighbor shell.


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(a)

(b)

Figure 8. Radial distribution functions between terminal atoms and water molecules at different average temperatures of system for (a)C7CH3, and (b)C8OH systems. Gray dashed line indicates the position of the first minimum.



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Figure 9. The integrals of the first layer of RDFs of water for different SAMs.

Figure 10. TBCSAM-Water as a function of the integral of the first layer of RDF of water for CH3-SAMs.


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CONCLUSIONS The NEMD simulations were implemented to investigate the mechanism of thermal transfer across the interface. The difference of thermal transfer characteristics was observed for the hydrophobic CH3-SAMs and the hydrophilic OH-SAMs. The length dependences of both CH3-SAMs and OH-SAMs are slight on local TBCs, GSAM/Water. The values of GSAM/Water for CH3-SAMs depend strongly on the stiffness of SAMs and temperature, while the values of GSAM/Water for OH-SAMs are almost constant regardless of the stiffness of SAMs and temperature. The correlations in velocity and density between SAMs and water molecules within the interface region were analyzed to further understand the mechanism. The results suggest that the thermal transport at the interface is not related directly to the vibrational characteristic of molecules forming interfaces. On the other hand, the thermal transport is promoted mainly due to the aggregation of more water molecules around the terminal atoms of CH3-SAMs. This finding suggests the thermal transport across the SAM/water interface can be tuned by changing the number of water molecules surrounding the terminal atoms, which can be achieved by varying the type of SAM molecules.



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Notes The authors declare no competing financial interests.

AKNOWLEDGEMENTS This work is partially supported by Japan Society for the Promotion of Science KAKENHI 2604364, 26289048, 16H04274, and the Collaborative Research Project of the Institute of Fluid Science, Tohoku University. S.-W. H. appreciates the financial support from Postdoctoral Fellowship for Overseas Researchers Program of the Japan Society for the Promotion of Science.


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Mechanism of Temperature Dependent Thermal Transport across the

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