Thermal transport across SiC-water interfaces - ACS Applied Materials

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Thermal transport across SiC-water interfaces C. Ulises Gonzalez-Valle, Satish Kumar, and Bladimir Ramos-Alvarado ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b10307 • Publication Date (Web): 31 Jul 2018 Downloaded from http://pubs.acs.org on August 4, 2018

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ACS Applied Materials & Interfaces

Thermal transport across SiC-water interfaces C. Ulises Gonzalez-Valleα‡, Satish Kumarβ‡, Bladimir Ramos-Alvaradoα‡* α

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, State

College, Pennsylvania, 16801, USA. β

The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology,

Atlanta, Georgia, 30332, USA. * Corresponding author: [email protected]

ABSTRACT Thermal transport across interfaces made of 3C-type silicon carbide (SiC) and water was investigated by means of nonequilibrium classical molecular dynamics (NEMD). The effects of different crystallographic planes and atomic surface terminations were studied, as it pertains to interfacial heat transfer. Hydrophilic and hydrophobic conditions were analyzed by modifying the interfacial bonding strength between the solid and liquid phases. The formation of structures in the liquid molecules close to the solid substrate was observed and found that such structures are sensitive to the uppermost atomic layer termination, the wettability condition, and the temperature of the system. It was found that the interfacial heat transfer and the wetting properties are not universally related and in order to obtain a more comprehensive description, it is required to include the structuring observed in the liquid phase at the interface. A reconciliation of the thermal boundary conductance calculations was found after the density depletion length was utilized as the descripting parameter. KEYWORDS: molecular dynamics; silicon carbide; thermal boundary conductance; wettability; heat transfer; thermal boundary resistance.

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1. Introduction An inherent resistance to the transport of thermal energy exists when heat travels between different materials due to the abrupt change in properties at the interface. This resistance is commonly known as the thermal boundary resistance (TBR); however, it is also common to use its inverse, the thermal boundary conductance (TBC), which is defined as J=G∆Tint, where J is the heat flux, G is the TBC, and ∆Tint is the temperature discontinuity observed at the interface. Heat transfer across solid-solid interfaces at room temperature has received significant attention due to the large number of applications where these interfaces can be found.1-5 Alternatively, solid-liquid interfaces have received significantly less attention by the community. Cahill et al.6 presented a seminal review on nanoscale heat transfer where solid-liquid heat transfer was not fully addressed; however, in a consecutive comprehensive nanoscale heat transfer review, Cahill et al.7 reported a rising interest for heat transfer across solid-liquid interfaces during the decade of 2002-2012. Besides the revisions of Cahill et al.6-7 the importance of solid-liquid interfaces has been summarized by other researchers; Lu and Chen8 discussed the importance of solidliquid interfaces, as it pertains to finding them in multiple biomedical applications, electronics cooling, catalysis, energy generation systems, colloidal suspensions, and nanocomposites. In previous investigations, the wetting properties of a surface have been directly related with the TBC as a means to characterize the relationship between the solid-liquid affinity and interfacial heat transfer. Recent numerical and experimental findings seem to indicate that the bonding strength between solid and liquid atoms at interfaces is not sufficient to describe energy transport across dissimilar materials. After years of research, experimental and numerical investigations have helped to elucidate the main parameters that dictate nanoscale interfacial thermal transport; these parameters have been identified as 1) interfacial bonding9, 2) the


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mismatch of vibrational energy carriers10, 3) surface roughness5, and 4) the interfacial liquid structuring (solid-liquid interfaces)11. Despite the identification of these main mechanisms, the uncertainty of the complex interplay between the aforementioned parameters still exists. It has been observed that hydrophilic surfaces (strong solid-liquid affinity) present higher TBC than hydrophobic surfaces (weak solid-liquid affinity).12 Moreover, it has been reported that the TBC scales linearly with the work of adhesion (Wa), where Wa ~ 1+cos(θ) and θ is the contact angle.1314

However, this trend is not followed by complex systems, i.e., interfaces made of liquid

hydrocarbons and self-assembled monolayers (SAM).15-16 In Ref

15

, a bare gold surface had a

higher solid-liquid affinity energy than SAM-coated gold, but the TBC for the SAM-coated surfaces was significantly higher. This is mainly because SAM and some liquid hydrocarbons share the same molecular backbone; thus, similar energy carrier modes availability is expected on both sides of the interface (vibrational modes overlap) and consequently, heat transfer is facilitated. This indicates that a good overlap of the vibration modes can mediate weak interfacial bonding. The idea of explaining the TBC through the overlap of phonon modes has been challenged in SAM-coated surfaces in contact with water when different temperatures are considered.17 The higher the temperature, the higher the value of the TBC calculated within the system will be, as more interfacial scattering events occur; however, Hung et al.17 reported that the modes overlap did not show a major increase while the temperature of the system increased; conversely, it was indicated that the TBC depicted a significant dependence on the interfacial liquid structuring. Thus, the liquid structuring could be the missing piece in the description of the TBC at solid-liquid interfaces. The structuring of liquids at the interface with solids has been suggested as a driver of heat transfer behavior and this idea helped to explain wall temperature effects on the TBC


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through interfacial liquid concentration17 and different pressure and wettability effects on the TBC were reconciled using the peak density in the first hydration layer10. Another interfacial structure feature affecting the TBC is the formation of high-density zones observed at the interstitial spaces of crystals.18-19 These high-density zones are of considerable importance to the thermal transport mechanisms because of a possible enhancement produced by the presence of ice-like structures within the vicinity of the solid phase. As the solid state of water presents larger thermal conductivity in comparison with the liquid, substrates favoring the formation of these highly-order water cluster (due to greater interfacial spaces) are expected to have a larger TBC. The modification of the interfacial liquid properties calls for a description of not only the interfacial bonding but also, the liquid structuring. In Ref.20, a reconciliation of the anisotropic TBC calculations in different silicon planes and graphene-coated silicon exhibiting wettability transparency was achieved using the density depletion length. This parameter accounts for layering, concentration, and the equilibrium distance between phases due to steric repulsion indicating to be reliable for the characterization of the interface. Additional findings indicate that pure crystal structures do not follow the relation established for the TBC and the surface affinity as well as it was observed for SAM-coated surfaces; thus, interfacial structuring is not a particular feature for this type of complex systems. In this investigation, thermal transport across 3C-SiC-water interfaces was studied; due to its chemically passive nature, these types of interfaces can be found in biomedical devices, such as blood-contacting implants and lab-on-achip devices. The effects of the crystallographic planes and atomic surface terminations, as well as the wetting conditions (strength of interfacial bonding) were analyzed. The presence of liquid structuring and the formation of high-density zones was observed and correlated with the TBC and interfacial vibrational density of states calculations. The existence of highly ordered ice-like


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structures within subnanometer dimensions was formulated as an enhancing mechanism of thermal transport across solid-liquid interfaces. Pristine crystallographic 3C-SiC surfaces followed the relation G ~ 1+cos(θ) reported in previous investigations, but unlike previous analyses, a single scaling relation was observed per atomic plane independent of the atomic surface termination, while anisotropy of interfacial heat transfer was observed per atomic plane. The density depletion length was found to reconcile the anisotropic TBC behavior and the TBC for different atomic surface terminations for a crystalline compound, extending and validating the previous findings for single-atom crystals.20 However, the fitting function was found to be different between Si and SiC, suggesting a lack of generality of the TBC-depletion relation previously found.

2. Molecular Dynamics Modelling In MD simulations, the dynamics of the atoms are governed by classical laws and the atomic interactions are determined through empirical potentials or force fields; this empirical nature reduces the transferability of the potentials throughout different applications and requires validation before its implementation. The system under analysis consists of a water cluster confined between two SiC slabs; thus, it is required to evaluate the descriptive capabilities of the implemented models for water and SiC. During the simulation procedure, the MEAM21 potential was implemented to describe the solid phase utilizing the calibrated parameters for SiC. The thermal conductivity of SiC was calculated using the approach described by Schelling et al.22, where the thermal conductivity is computed for three-dimensional slabs of different length. Computationally affordable MD simulations are not able to capture the bulk behavior of SiC, but


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this method allows to estimate the bulk thermal conductivity by extrapolation of the trend computed for smaller systems. The thermal conductivity was calculated for three dimensional slabs of 2.6 x 2.6 nm2 transversal area and nine different lengths, from 15.5 to 80.2 nm; after this calculation a linear fit was applied to the inverses of the thermal conductivity and the length of the systems, the fitting function was λ-1=0.589586L-1+0.002714 (see Figure 1), where λ is the thermal conductivity and L is the length of the system. If L∞, which will represent the bulk, the value of the thermal conductivity will be given by the inverse of the constant term.

Figure 1. Calculation of the thermal conductivity in a SiC nanowire. The thermal conductivity of SiC was found to be 368.46 W/m K which is only about 5% overestimated in comparison with the experimental value reported for cubic SiC by Levinshtein et al.23, indicating that the MEAM potential with the implemented parameters is suitable to describe the properties of interest in the present analysis. For water the SPC/E24 model was implemented due to its computational affordability, large acceptance and utilization among the community (for comparison purposes), and its relatively good accuracy to predict the thermal conductivity in comparison with other water models25. One of the features of the SPC/E model is its rigidity which was enforced using the SHAKE26 algorithm while the long-range electrostatic


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interactions were handled using the PPPM27 method with an accuracy of 1 × 10–6. These two models will help to describe each phase; however, the interaction between the solid and liquid poses a challenging scenario. As it was indicated in the previous section, several unanswered question can be found within the analysis of solid-liquid interfaces, from the dynamics28 and the chemistry of the surface29 to the interfacial layering of the liquid phase11,

30-31

, all these

phenomena require deep exploration to characterize the complex interactions intrinsic for these systems. In this investigation, the solid-liquid interactions were modeled as van der Waals forces utilizing a 12-6 Lennard-Jones potential where only the interacting pairs Si–O and C-O were considered, where the interaction potential was calibrated through size-independent wettability simulations. The C-O parameters for the LJ potential were σC-O=3.19 Å, εC-O=0.005 eV, and a cutoff of 13 Å, which were optimized to obtain a contact angle of 64° for water over a pristine graphitic surface.32 The Si-O interactions are slightly more complex due to the lack of consistent values for the contact angle reported for pristine silicon surfaces; in order to overcome this issue one of the LJ parameters was maintained constant, σSi-O=2.63 Å with a cutoff of 13 Å, while different wettability conditions were emulated by varying the εSi-O parameter as described in Ref 33

. Once all the interactions for the analyzed system are described, the TBC was calculated

by means of NEMD simulations of the system depicted in Figure 2 a). The endmost atoms were kept fixed in order to restrain the system size, two adjacent regions were also defined, where thermal energy is added or rejected at the same rate. The addition/rejection of heat within the system produces a temperature gradient along the z-direction, as well as a temperature-jump where the transition between the two phases occurs, and then the temperature discontinuity and the heat flux can be used to calculate the TBC, see Figure 2b). The crystallographic orientation


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of the solid slabs was modified, such that the crystallographic planes (100) or (111) would face the water molecules. The nature of the 3C-type SiC allows for the presence of different surface terminations (carbon or silicon) for these crystallographic planes facing water, this effect was also considered. In order to verify the absence of any size effect, the length and the transversal area of the solid slabs were varied. It was found that a solid slab length of 10 nm and transversal areas of 2.62 x 2.62 nm2 and 2.78 x 2.67 nm2 for the (100) and (111) planes respectively, sufficed to not show any size effect on the TBC. Periodic boundary conditions were set in the xand y-directions of the system, while the ends in the z-direction were kept fixed by freezing the atoms of the outermost layer of each slab. The addition/rejection zones were 1.5 nm thick (encompassing the transversal area of the solid slabs) and were located right after the position of the fixed atoms (see Figure 2 a)). The space between the solid slabs was 6 nm where the water cluster was located and the number of water molecules was varied depending on the wettability condition in order to remove any compressibility effects34. The wettability condition changes the capillary pressure inside the confinement, thus the number of molecules or the size of the gap needs to be modified to keep the bulk pressure constant; thus, we varied the number of water molecules between 1000 and 1100.


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Figure 2. a) Snapshot of the analyzed system and b) temperature profile along the z-direction. The simulations were performed using the LAMMPS35 code along with VMD36 for visualization purposes. The simulation procedure consists of multiple stages: (1) energy minimization to remove any excess in potential energy due to the initial configuration, (2) equilibration at 300 K for 1 ns under a canonical ensemble (NVT) implementing the Nosé– Hoover37-38 thermostat with a time constant of 100 fs, (3) verification of the system stability and equilibration applying a microcanonical ensemble (NVE) for 1 ns, (4) thermal energy addition/rejection35 in the heat input and output regions for 5 ns, and (5) the final step is the harvesting run in which the kinetic energy (KE) and the coordinates of the atoms were sampled every 10 ps during 7.5 ns. All the aforementioned simulations were run with a time step of 1 fs. For the solid slabs, the temperature profiles depicted in Figure 2 b) were calculated by timeaveraging the KE per atomic plane of the SiC applying the equipartition theorem, which relates the temperature and the KE as T=KE/1.5kB. For the liquid molecules, the process is slightly


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different due to the mobile nature of water. The temperature profile was obtained by dividing the water confinement into 50 bins and performing a time-averaging and particle-count averaging of the KE per bin. Once the KE was averaged the temperature was calculated as T=KE/3kB since the SPCE water model only has 6 degrees of freedom due to its rigid nature. After the calculation of the temperature profiles, the temperature discontinuity ∆Tint was calculated by extrapolation of the linear fitting applied to the profiles at the interfaces (see Figure 2b)). In order to verify the linear response of these systems (J= G∆Tint) different heat transfer rates were utilized, varying from 5 to 15 nW, and the TBC (G) was calculated from the slope of the linear fit to the data. The same process was performed for each crystallographic plane (100 and 111), surface termination (carbon and silicon), and a wide range of wetting condition. 3. Results and Discussions 3.1 The Effect of the Wetting Condition on the Thermal Boundary Conductance Once the simulation procedure was established, the TBC was calculated for the different interfaces. As it was reported by Murad and Puri39, the temperature of the interface plays an important role in the TBC; thus, higher values of the TBC are observed for walls at higher temperature, for our particular system, the largest TBC difference between hot and cold walls was below 30%. The reported TBC values in Figure 3 are the average of the cold and hot walls calculations for different wetting conditions. Figure 3 a) presents the direct dependence of the TBC on the contact angle for different planes and atomic surface terminations in contact with water. As it was expected9,

11

, the wetting condition plays a significant role in the TBC. An

increase in the TBC can be observed while the surfaces become more hydrophilic (low contact angle, θ < 90°) and this behavior is captured by the relation G ~ 180°-θ. The TBC clearly shows


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a crystallographic plane dependence or anisotropy, as illustrated in Figure 3. Therefore, the contact angle, as a parameter used to characterize the solid-liquid affinity, describes the TBC for the same crystallographic plane and different atomic surface termination, but it does not represent a universal parameter to correlate the TBC.

Figure 3. Thermal boundary conductance relationships for different silicon carbide surfaces. (a) Thermal boundary conductance vs 180° - θ, where θ is the contact angle; and (b) thermal boundary conductance vs 1 + cos(θ), where 1 + cos(θ) is proportional to the work of adhesion. Other investigations have suggested the utilization of the work of adhesion as the parameter correlating the solid-liquid affinity with the TBC13-14. Figure 3b) depicts the dependence of the TBC on the relationship 1+cosθ, which is directly proportional to the work of


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adhesion. Apparently, the scaling relation G ~ 1+cosθ is able to predict the increment in the TBC when the wetting condition tends to be more hydrophilic; however, no universal description is observed, as two different scaling relations, one for each plane, are observed. In our previous investigation33, we demonstrated that the SiC(111) Si-terminated surface was the most hydrophilic among the studied surfaces. Ramos-Alvarado et al.20, 40, previously showed that the TBC followed a scaling relation G ~ εSL, where εSL is the energy parameter of the Lennard-Jones potential commonly used to model solid-liquid interactions at interfaces. Likewise, it has been previously demonstrated that εSL ~ 1 + cosθ and εSL ~ 180° - θ; thus, based on the direct relationship of the interfacial bonding strength and the TBC, it could be expected that the SiC(111) Si-terminated surface was the most conductive. Nonetheless, as it can be seen in Figure 3 the SiC(100) plane, irrespective of the atomic surface termination, is the one reporting the highest TBC. These results, in conjunction with previous findings, support the idea that the interfacial bonding, characterized by the surface wettability, does not provide a full description of the thermal transport across solid-liquid interfaces, calling for further analysis in order to fully describe the interplay of the mechanisms leading the thermal transport governing the TBC. It is noteworthy that unlike previous investigations, we are analyzing interfacial heat transfer across solid-water interfaces, where the solid is a crystal compound. The solid-liquid interactions and consequent modification of the interfacial liquid properties are reported in Ref.33 We observed that after implementing our interfacial modeling approach, the contact angle calculations on surfaces having either Si or C termination, existed in two different regions. Figure 3 depicts this observation, but more importantly, the data points overlap on a single TBC relationship as long as the crystallographic plane is the same regardless of the atomic surface


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termination. To the best of our knowledge, this is the first time that such an observation has been reported. 3.2 Liquid Structuring and Interface Modification Since the contact angle and the work of adhesion did not provide a unified description of the TBC of the different interfaces presented earlier, it is required to explore the additional mechanisms that have been formulated as governing parameters of heat transfer across solidliquid interfaces. It has been suggested that the interfacial liquid structuring plays a significant role in the transport of energy across solid-liquid interfaces, based on this idea, we can analyze the liquid side of the interface in order to identify any structuring; then, another issue looms, the definition of the interface. In this investigation, the interface was defined near the uppermost layer of the solid slabs in contact with the water cluster, depending on the surface termination. A 1 Å thick interface was defined about 3 Å above the substrate for C-terminated surfaces and for Si-terminated surfaces the interface started at 2.5 Å away from the uppermost Si layer. These distances correspond to the location of the first hydration layer at the interface. After defining the interfacial region, the coordinates of the atoms were sampled and the density contours were computed by a particle-count, time-averaging process. The density contours of the interfacial region are depicted in Figures 4 and 5. In Figure 4 the density contours of water over the SiC(100) crystallographic plane are illustrated, the black dots represent the location of the uppermost layer of carbon atoms and the yellow dots are the silicon atoms located on the Si-terminated surface; additionally, hydrophilic and hydrophobic wetting conditions are depicted for both terminations (lower and upper panels respectively). The unrestricted mobility of the liquid molecules allows them to arrange in periodic structures


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determined by the underneath solid substrate. Patterns are formed where the presence of highdensity zones is observed; these patterns and the high-density zones have been reported in previous investigations41-43. The formation of the patterns is independent of the atomic surface termination and the wettability condition, but their shape is determined by the crystallographic orientation of the solid substrate.


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Figure 4. Liquid structuring over SiC(100) surface, a) and c) carbon-terminated and b) and d) silicon-terminated, upper panels hydrophobic and lower panels hydrophilic conditions. The scale is in g/cm

3

.

A strong bonding (hydrophilic condition) will increase the number of molecules trapped within the high-density zones, i.e., larger concentrations when strong interfacial bonding is observed, compare Figure 4a) to 4c) and Figure 4b) to 4d). The crystallographic structure determines the configuration that the liquid takes and the formation of high-density zones are promoted if larger interstitial spaces are present within the solid substrate, see the diagonal alignment of the high-density zones caused by the large spaces between atoms in Figure 4. Finally, having a C or Si-terminated surface will affect the equilibrium distance at which the molecules will be sitting, this could modify the concentration of the molecules at the interface affecting the high-density zones. The Si-terminated surfaces showed a higher affinity with the liquid phase in comparison with C-terminated surfaces, this can be thought as a larger hydrophilicity.33 Figure 4 d) depicts the density contours computed for a SiC(100) Si-terminated surface, in this configuration the presence of the high-density zones is more noticeable in comparison with the other cases. The existence of the high-density zones in this surface can be the key to understand the results depicted in Figure 3 (larger TBC for lower contact angle compared to SiC(111)). Previous investigations have reported that these regions had similar properties as the solid state of water.44-45 If these regions had ice-like behavior, the thermal transport across these surfaces could be enhanced independently of the interfacial affinity between the solid and liquid phases.


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Similar to the SiC(100) surfaces, the Si-terminated surfaces depict larger concentration of water molecules in comparison with C-terminated for SiC(111), see Figure 5. The presence of a pattern over these surfaces was also observed, where two main difference can be highlighted for this crystallographic plane, the pattern shape and the high-density zones. The pattern differs from the one observed for the SiC(100) plane due the different atomic arrangement. Moreover, the size of the high-density zones has been reduced due to the higher packing factor observed for the SiC(111) plane. Figures 4 d) and 5 d) share the same wettability condition and surface termination, however, it is clear that the high-density zones are diluted for the SiC(111) crystallographic plane; this could be the first clue to explain the higher conductivity depicted by the SiC(100) Si-terminated surface. In order to explore this as the possible reason for the higher thermal performance of this surface, it is necessary to study the nature of the structures formed in the high-density zones.


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Figure 5. Liquid structuring over SiC(111) surface, a) and c) carbon-terminated and b) and d) silicon-terminated, upper panels hydrophobic and lower panels hydrophilic conditions. The scale is in g/cm

3

.

The simplest way to prove the presence of ice-like structures within the interfacial liquid region is to compute known properties of the interface and compare them with the properties of the different states of water, in this case, we used the vibrational density of states (DOS). The


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DOS for liquid and solid water was calculated and compared with the DOS obtained for the interfacial water with different atomic surface terminations, see Figure 6. The DOS was calculated as

DOS ~ FFT v i ( t ) ⋅ v i ( 0 )

(1)

where the DOS is proportional to the Fourier transform of the velocity-autocorrelation function of the i atoms. All of the calculations were performed for the same 1 Å thick interface described before and for the most hydrophilic case of each surface. Figure 6 a) illustrates that for the SiC(100) crystallographic plane the water molecules at the interface behave as pure ice, as seen in the DOS overlap of ice and interfacial water. This behavior showed to be independent of the surface termination (C or Si). Alternatively, the behavior of the water molecules at the interface on the SiC(111) plane is modified with respect to the bulk, but the properties are not similar to the solid state of water. Unlike the behavior observed for the SiC(100), Figure 6 b) presents an increase in the available vibrational modes for the water molecules located at the interface above this plane. As a larger number of vibrational states are available it could be expected an enhancement in the thermal transport across these specific cases; however, as it was reported by Ref.17, the vibrational states do not describe the thermal transport as a whole. Based on these findings, it is notorious that the interfacial liquid structuring plays a fundamental role in the thermal transport mechanisms at solid-liquid interfaces and its inclusion in the characterization of the TBC across solid-liquid interfaces is necessary.


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Figure 6. Modification of the vibrational density of states for the water molecules over a) SiC(100) and b) SiC(111).

3.3 Reconciliation of the Thermal Boundary Conductance Unlike the previous reports10,

13-14

, the affinity between the phases or the vibrational

modes could not describe the thermal behavior of SiC-water interfaces. In order to consider the possible contribution of the liquid structuring as a part of the thermal transport mechanisms, the density depletion length was selected as the parameter describing the interfacial liquid structuring; the density depletion length is defined in Eq. (2)20, 34.


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∞



δ = ∫ 1− 0



ρ S (z) ρ L (z)  −  dz ρ Sb ρ Lb 

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(2)

where δ is the depletion length, ρ is the mass density, S and L stand for solid or liquid respectively, and b indicates the value of the bulk property. The definition of this property considers the fluctuations of the mass density at the interface (as high-density zones or infiltrations46) and the equilibrium distance between solid and liquid atoms, providing a description which involves the structuring of the liquid molecules as well as the interfacial affinity. Figure 7 illustrates how the depletion length reconciles the calculations of the TBC for all the studied cases. Correlating the TBC with the depletion length makes all the data points to collapse onto a single curve. We have fitted the data using G = Ae-nδ, where A = 100.2 MW/m2K, n = 14.98 nm-1, and the quality of the fit was given by an R2 = 0.975. When δ→0, the maximum TBC value for this system could be expected, physically, such a situation could be given when liquid infiltration exists into the solid substrate. However, we observed that this was impossible due to the compactness of the SiC structure.33 Ramos-Alvarado et al.20 previously reported that the anisotropic behavior of the TBC on crystalline Si and graphene-coated Si in contact with water also followed the same scaling relation. It was left as an open question whether or not the given parameters of the functional fit could be universal. For the previous analysis20, A = 195 MW/m2K and n = 11.59 nm-1; hence, these new findings suggest that G = Ae-nδ is not a universal law and its parameters may depend upon the solid substrate and the wettability characterization performed on it.


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Figure 7. Reconciliation of the thermal boundary conductance calculated for different surfaces in contact with water using the density depletion length. Almost at the same time as Ramos-Alvarado et. al.20, Alexeev et al.10 found a similar relation as the one we are presenting here, in which the effects of wettability and pressure on interfacial heat transfer in a graphite-water interface, collapsed onto a single curve. The differences are that Alexeev et. al.10 characterized the TBR instead of the TBC and that the parameter used for the single-curve relation was the ratio of the maximum to bulk density obtained from the interfacial liquid layering. The equation used by Alexeev et. al.10 to fit the data was formulated based on the known effect of compressibility on the TBR. In our case, the density depletion length is not only a function of the first hydration layer peak, but also of the penetration of the liquid layering into the bulk liquid and the equilibrium distance between the solid and liquid atoms. Hung et al.17 found a scattered linear relation between the TBC and the integral of the pair distribution function of liquid molecules at the interface for a variety of interfaces showing different wetting conditions, which may seem similar to our analysis, but unlike the density depletion length, the pair distribution function is a real-space structuring parameter. More recently Han et al.47 found that the relationship suggested by Alexeev et. al.10


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breaks down at high pressures, in this work we are showing that the depletion length function suggested by Ramos-Alvarado et al. is not universal; hence, indicating that more work is still necessary before establishing a unique relationship between the interfacial liquid properties and heat transfer across solid-liquid interfaces. 4. Conclusions MD simulation were implemented to characterize the thermal transport across 3C-SiC and water interfaces. Two different crystallographic planes were analyzed (100 and 111), allowing to have different surface terminations (C or Si) in order to capture the nature of 3C-SiC. A wide range of wetting conditions were artificially generated and it was verified that the wettability of the surface plays an important role in the transport of energy across solid-liquid interfaces. It was observed that the TBC data points aligned onto a single scaling relation per atomic plane despite of the atomic surface termination, while the crystallographic plane dictated the TBC trends in two different linear scaling relations based on the contact angle and the work of adhesion. Based on the sole effect of the interfacial bonding, it could be expected to see the most hydrophilic case as the most conductive; however, the SiC(100) Si-terminated interface showed the highest TBC values despite of not being the most hydrophilic. This indicates that the interfacial bonding strength does not fully describe the thermal transport and additional mechanisms should be included. Previous investigations suggest that the interfacial liquid layering is a major contributor among the mechanisms involved in the thermal transport at solid-liquid interfaces. The presence of a structure within the liquid phase close to the solid substrate was observed; the pattern showed to be independent of the surface termination and the wettability condition but it is


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strongly affected by the crystallographic plane. The formation of high-density zones was observed for SiC(100) surfaces and the DOS corroborated the ice-like behavior of these small water clusters. The formation of ice-like structures helped to explain the larger conductance of the SiC(100) plane and posed the initial clue to involve the liquid structuring in the description of the TBC. Finally, the density depletion length, which involves the interfacial bonding strength and the liquid structuring, was used to characterize the thermal behavior of the interface and it was found that this parameter reconciled the TBC data points following an exponential relationship. Acknowledgements C. Ulises Gonzalez-Valle was partly supported by CONACyT (National Council on Science and Technology, Mexico) under the Mixed Scholarship Program No. 659146. Corresponding Author * Email: [email protected] Author Contributions ‡These authors contributed equally. REFERENCES (1) Pop, E., Energy Dissipation and Transport in Nanoscale Devices. Nano Research 2010, 3, 147-169. (2) Rotkin, S. V.; Perebeinos, V.; Petrov, A. G.; Avouris, P., An Essential Mechanism of Heat Dissipation in Carbon Nanotube Electronics. Nano Letters 2009, 9, 1850-1855. (3) Yu-Jia, Z.; Yue-Yang, L.; Wu-Xing, Z.; Ke-Qiu, C., Nanoscale Thermal Transport: Theoretical Method and Application. Chinese Physics B 2018, 27, 036304. (4) Balasubramanian, G.; Banerjee, S.; Puri, I. K., Unsteady Nanoscale Thermal Transport across a Solid-Fluid Interface. Journal of Applied Physics 2008, 104, 064306.


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Thermal transport across SiC-water interfaces - ACS Applied Materials

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