pubs.acs.org/NanoLett
Water Nanoconfinement Induced Thermal Enhancement at Hydrophilic Quartz Interfaces Ming Hu,*,†,‡ Javier V. Goicochea,‡ Bruno Michel,‡ and Dimos Poulikakos*,† †
Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, Sonneggstrasse 3, ETH Zurich, 8092 Zurich, Switzerland, and ‡ IBM Research GmbH, Zurich Research Laboratory, Sa¨umerstrasse 4, 8803 Ru¨schlikon, Switzerland ABSTRACT We report the effect of water nanoconfinement on the thermal transport properties of two neighbor hydrophilic quartz interfaces. A significant increase and a nonintuitive, nonmonotonic dependence of the overall interfacial thermal conductance between the quartz surfaces on the water layer thickness were found. By probing the interfacial structure and vibrational properties of the connected components, we demonstrated that the mechanism of the peak occurring at submonolayer water originates from the freezing of water molecules at extremely confined conditions and the excellent match of vibrational states between trapped water and hydrophilic headgroups on the two contact surfaces. Our results show that incorporation of polar molecules into hydrophilic interfaces is very promising to enhance the thermal transport through thermally smooth connection of these interfaces. KEYWORDS Water, confinement, thermal transport, quartz, molecular dynamics
E
termined the heat conduction of such thermal interfaces that employ carbon nanotube (CNT) arrays. In their work, the addition of the CNT array to phase change materials (PCMs) reduced the overall resistance of the Cu-PCM-Si interface by a factor of 4. The mechanism has been studied in the theoretical model of Hu et al.,4 who employed molecular dynamics (MD) simulations and an analysis of individual phonon scattering on Si-CNT interfaces and demonstrated a strong effect (2 orders of magnitude enhancement) of chemical bonding on the thermal transport across Si-CNT interfaces. Another effective method to reduce RK is replacing the interfacial gap by a highly conducting material. These materials are typically referred as thermal interface materials (TIMs). Typical TIMs involved in experiments include greases, PCMs, gels, and adhesives.5 All these TIMs have advantages and disadvantages.5,6 However, no matter what kind of TIM is incorporated, the physics becomes complicated, since two additional resistances are involved: the contact resistance between TIM and the substrates confining them, Rc, and the bulk resistance of TIM, Rbulk. For most greases, the bulk resistance of TIMs is of the same order as the contact resistance, while for PCMs and gels Rbulk is much larger than Rc.5 Thus, for traditional TIMs, it is almost impossible to reduce Rc and Rbulk simultaneously. In this Letter, we report results of nonequilibrium molecular dynamics simulations predicting a large increase of interfacial thermal conductance between two hydrophilic quartz surfaces in contact, by simply introducing an ultrathin water layer between the interfaces, which, due to the nature of water, achieves a high conductance between water and the hydrophilic surface
fficient heat dissipation is one of the crucial challenges that limits the development of disruptive microelectronic device technologies. The International Technology Roadmap for Semiconductors (ITRS) 20081 estimates that an 8 nm feature-size device may generate local heat fluxes as high as 100000 W/cm2 that would need to be dissipated efficiently to preserve device integrity, reliability, and performance. The anticipated heat fluxes at the die level are 1000 W/cm2, which is 10-fold higher than present complementary metal oxide semiconductor (CMOS) devices, making power dissipation perhaps the most important factor that eventually limits the device density on each chip. One of the keys to enhance the heat dissipation efficiency is to decrease the mismatch in the thermal properties of adjacent substrates as much as possible. This mismatch produces the interfacial thermal resistance, RK, known as Kapitza resistance.2 The Kapitza resistance occurs due to the scattering of phonons at dissimilar interfaces. Low values of interfacial thermal resistance are needed to effectively dissipate the heat from the Si die or chip surface to the heat spreader or heat sink. A commonly used method to reduce the interfacial thermal resistance is to directly modify the interfacial properties, e.g., by introducing interfacial bonding to connect materials in thermal contact. Recent experiments clearly established the importance of interfacial bonding on the thermal resistance. Xu and Fisher3 fabricated and de-
* To whom correspondence should be ethz.ch (M.H.) and
[email protected] (D.P.). Received for review: 10/16/2009 Published on Web: 12/03/2009 © 2010 American Chemical Society
addressed,
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and negligible bulk resistance of water. Although in recent years a considerable amount of interest has been dedicated to the investigation of dynamic properties of liquid water under spatially restricted conditions,7-17 to the best of our knowledge, the effect of such confined water on the thermal transport properties of the system of interest has not been investigated so far. We demonstrate that the overall interfacial thermal conductance between two quartz surfaces first steeply increases with increasing the water thickness, and subsequently decreases rather rapidly upon further increasing the water thickness. To this end, an optimal water layer thickness can be identified, corresponding to maximum overall thermal conductance. The peak occurs at the water layer thickness of around 2 Å, which is mainly attributed to the freezing of water molecules at extremely confined conditions and the excellent match of vibrational states between the trapped water and the hydrophilic headgroups on quartz surfaces. Our results show that an ultrathin water layer is an excellent TIM connecting hydrophilic interfaces for high heat fluxes. Our model structure consists of two silica slabs with water confined between two surfaces. The silica structure taken from ref 18 is R-quartz crystal and is composed of 3776 SiO2 atoms with (001)-type surface fully hydroxylated, resulting in two silanol (-Si-OH) headgroups for each Si surface atom. The entire system is contained within a rectangular simulation box with a cross section of 48.8 × 44.4 Å2, as shown at the top panel of Figure 1. Periodic boundary conditions are used in all directions, resulting in four planar silanol-water interfaces normal to the z direction. For validation purposes of the obtained results, we also performed calculations with a larger domain of cross section of ∼72 × 67 Å for selected cases. All molecular dynamics simulations were performed with the LAMMPS.19 A time step of 0.5 fs was used throughout the simulation. van der Waals forces were truncated at 12 Å with long-range Coulombic interactions computed using the particle-particle particle-mesh (PPPM) algorithm.20 In this study, we used a CHARMM interaction form to model a quartz crystal and its hydroxyl-terminated group with parameters taken from ref 18. The transferable intermolecular potential 3 point (TIP3P)21 with the SHAKE22 model was used to simulate water. The εij values in nonbonded interactions between different atom types, e(r) ) 4ε[(σ/r)12 - (σ/ r)6], are obtained via the geometric mean εij ) (εiεj)1/2 and σij via the arithmetic mean σij ) (σi + σj)/2. With regard to the validation of the interaction potential, no potential known to us after a thorough review of the literature has been specifically designed for use in nanoconfinement. The TIP3P model is widely used in previous studies to determine the transport properties of water confined in different kinds of nanotubes.23-26 In those studies the typical size of the nanoconfinement is less than 10 Å, which is of the same order as in our simulations. On the basis of our experience © 2010 American Chemical Society
FIGURE 1. Top panel: a snapshot of quartz-confined water model structure. The two quartz slabs are in the middle and on two sides. Water is confined between quartz slabs. Bottom panel: steady-state temperature profiles for JQ ) 6400 MW/m2 for four selected fully hydrophilic cases at 300 K. The solid squares are for quartz and the open diamonds are for water.
and that of other workers, we believe that the TIP3P model is capable of predicting thermal transport properties of water at such small scale. Having said that, it is also hoped that future experiments (indeed very difficult to conduct) will become available and be compared with simulations to shed more light on this issue. In the first stage of MD simulations, the system was equilibrated at a constant pressure of 1 atm and a constant temperature of T ) 300 K for 3 ns using a Nose/Hoover temperature thermostat and pressure barostat.27,28 After the NPT (constant pressure and temperature) relaxation, we continued to relax the system with a NVE (constant volume and no thermostat) ensemble for 500 ps. During this stage we monitored the total energy and temperature of the system. We found that the total energy was conserved very well and the temperature of the entire system remained constant with fluctuations around 300 K, which meant that the system had reached the equilibrium state. Following equilibration, we computed the system with nonequilibrium MD. The heat source and heat sink were placed at the center of the two quartz slabs, respectively, and were realized using the algorithm proposed by Jund and Jullien.29 At each time step, the algorithm scaled up/down the velocity of atoms in heat source/sink slices and eliminated the tendency of the center of mass to drift as well. 280
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The thermal energy was delivered to the heat source and was removed from the heat sink at an equal rate dQ/dt. Thus, once steady state is reached, a constant heat flux perpendicular to the quartz/water interface
JQ )
cases with numbers of water molecules ranging from a single molecule to 2720 molecules (∼50 Å thickness), which correspond to the areal densities of water in a wide range from 0.046 to 125.1 molecules/nm2. A separate system composed of two pure quartz slabs with hydrophilic surfaces but without water serves as a base of the thermal conductance. For comparison, we also run these cases with heat current magnitude decreased and increased by 50%. At the bottom panel of Figure 1, we show typical steadystate temperature profiles using JQ ) 6400 MW/m2. All temperature profiles in Figure 1 are characterized by monotonic temperature decreases, from ∼325 K at the heat source located at the center of the middle quartz slab, to ∼280 K at the center of the other quartz slab, where the heat sink is located. The temperature profiles for the quartz regions show well-defined slopes from which we estimated the bulk conductivity of quartz to be about 0.87 ( 0.25 W/mK, which is in good agreement with previous MD results using the same model.30 Note that size effects are less significant for the interfacial thermal conductance. After increasing the lateral system size by 50%, we obtained nearly the same value GK. This indicates that the size of the simulation cell is sufficient to avoid finite-size effects. The temperature profiles shown in Figure 1 are dominated by large temperature drops at the quartz-water interfaces, from which we can calculate the interfacial thermal conductance for each interface using eq 1. Since the scope of this paper is on the effect of water confinement on the thermal transport at the solid-solid interface, we focus our results and discussion on the overall thermal conductance between two contact quartz surfaces. As clearly seen in Figure 1, the water layer thickness has a marked effect on the temperature difference between the two quartz surfaces. Note that for 2.21 molecules/nm2 the position of the adjacent quartz surfaces is almost the same as that without water. This is because in this case the water has only 48 molecules for each gap and its thickness is negligible. To expose the water layer effect, in Figure 2, we present a plot of the overall thermal conductance between two quartz surfaces for different water thickness, i.e., as a function of areal density of confined water. To investigate the dependence of the results on the heat current, we also show the results with 50% smaller and larger heat current magnitude. To mimic a more realistic condition for the application of chip cooling, we run two additional sets of simulations. For that purpose, on one hand we raised the system temperature to 350 K and rerun the cases for all lengths of water. The results are reported in Figure 2. As expected, the overall thermal conductance as the water layer thickness shows the same trend as that at room temperature, except that the enhancement magnitude is about 20% less. This is expected because the coupling (hydrogen bonds) between water molecules and hydroxyl headgroups on the quartz surface becomes weaker with increasing temperature.31 On the
dQ/dt 2A
was established, where A is the cross-sectional area of the simulation cell. The factor of 2 accounts for the fact that with periodic boundary conditions the heat current JQ propagates in two directions away from the hot reservoir. To obtain the temperature profile, we divide the simulation box into slices of thickness of about 3.6 Å along the heat current direction (z direction). In order to obtain correct thermal conductance between two adjacent quartz surfaces, we calculated the temperature profiles of water and two quartz slabs separately especially at quartz/water interfaces. Each slice contains around 200-400 atoms to ensure that the fluctuation of the local temperature is not too large. The local temperature in each slice was calculated from the kinetic energy and was averaged over 500 ps. In this manner, 20 temperature profiles were obtained during the production run of 10 ns. After 3-4 ns we observed that the temperature profile does not change significantly. The reported data shown in Figures 1 and 2 correspond to the last 6 ns of each production run. The temperature drop ∆T at the interface was obtained from the temperatures of the two adjacent quartz surfaces near the interface. From the computed value of ∆T for a given heat flux JQ, the interfacial thermal conductance GK can be quantified via the relationship2
GK ) JQ /∆T
(1)
In order to study the effect of water thickness on the overall interfacial thermal conductance, we run different
FIGURE 2. Overall thermal conductance between quartz surfaces as a function of areal density of confined water. For hydrophilic (fully -OH terminated) surface cases, results at 300 K with different heat current are reported. For comparison, results for hydrophilic surface at 350 K and bare (fully oxygen terminated) surface at 300 K are also shown. © 2010 American Chemical Society
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other hand, we modified the quartz surface from hydrophilic (fully -OH terminated) to bare (fully oxygen terminated). As shown in Figure 2, the nonmonotonic change in the overall thermal conductance as the water layer thickens is less evident (only 15% enhancement was found) but the peak still occurs at the areal density of water of 2.21 molecules/nm2, because even for a bare surface there is still weak hydrogen bonding between the confined water and the oxygen-terminated quartz. The most prominent features of Figure 2 are the nonmonotonic change in the overall thermal conductance as the water layer thickens and that both the conductance value and the trend are independent of heat current magnitude. Two counterintuitive phenomena occur in the quartz/ confined water system. First, generally speaking, comparing to the base system (pure quartz/quartz without water), the overall thermal conductance is increased when a thin water is introduced. This is quite different from the general belief on common TIMs that interface materials always produce additional bulk thermal resistance, thus reducing the overall thermal conductance of the entire system. Second, the overall thermal conductance first steeply increases with increasing the water layer thickness and then decreases quickly when further increasing the water layer thickness. It is interesting to note that for pure quartz/quartz the interfacial thermal conductance is about 448 ( 20 MW/m2 K. This value is almost the same as the conductance between silica and self-assembled monolayers31 but 4 times larger than that between silica and water vapor32 and 2 orders of magnitude larger than that between silicon and amorphous polyethylene.33,34 Here, the high value of thermal conductance is primarily due to the strong coupling through hydrogen bonding of the hydroxyl headgroups on quartz surfaces. When water is confined between hydrophilic surfaces, increasing the number of water molecules first steeply increases the conductance up to the value of 836 ( 33 MW/ m2 K for areal density of water of 2.21 molecules/nm2, which corresponds to only 48 water molecules confined. Further increase of the water thickness leads to a fast decrease of the overall conductance. For water areal density of more than 34.4 molecules/nm2, which corresponds to a water layer thickness ∼ 15 Å, the overall conductance drops below the level of the pure quartz/quartz case. This is understandable considering that for thicker water slabs the water physically and markedly separates the adjacent quartz surfaces (the water layer thickness is not negligible) resulting in a reduction of the overall conductance. Nevertheless, an instinctive question is raised: what causes the behavior of the 2.21 molecules/nm2 system? Why does a sharp peak in the thermal conductance occur in this system? Next, we analyze these effects by investigating how the confinement of water is distinctive at this particular areal density and by providing the evidence how the water molecules connect the two quartz surfaces “smoothly” and serve as a bridge for the heat transmission across the interface. © 2010 American Chemical Society
FIGURE 3. Density profiles of water and quartz for different water states: (a) submonolayer (2.21 molecules/nm2); (b) monolayer (8.37 molecules/nm2); (c) bilayer (47.4 molecules/nm2). The red and blue lines are for left and right water slabs, respectively. The dotted and solid black lines are for the middle and side quartz slabs, respectively. The water density uses the left labels and the quartz density uses the right labels. Arrows show the heat current direction from heat source to heat sink. All figures have break ticks in the range of [-10, 10] in z position.
It is well-known that when water molecules are adjacent to solid surfaces their properties are often altered relative to the bulk state.18 The effect may result purely from restrictions on the diffusion of water or may be caused by physical/chemical interactions between the solid and water molecules, for example, hydrogen bond interactions, or may be the result of a combination of both. To study the mechanism behind the significant change of overall conductance, we begin with the layering effects of the water slabs, which are provided by the density profiles along the heat current direction. Figure 3 shows steady-state density profiles for some typical water states. We calculated the density profiles of water and quartz separately by computing the average number of atoms present in 0.5 Å thin planar slices parallel to the interface during the last 2 ns period of a production run. The series of results in Figure 3 illustrates the transition from submonolayer to monolayer to bilayer geometries, when the water slab becomes thicker, as observed in previous studies.11,18,35 Systems with fewer than 15.4 water molecules/nm2 form a monolayer, which is quite close to the transition value of 12.3 molecules/nm2 for water confined between hydrophilic self-assembled monolayers.11 In systems with more water, bilayers are seen. All density profiles of water in Figure 3 are characterized by the main peaks centered around the quartz/water interfaces, with some 282
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FIGURE 4. Three-dimensional mean-square displacement for different water thicknesses showing a liquid-like linear increase with time for monolayer and bilayer of water, while a solid-like behavior is shown for submonolayer water. All curves are for water confined between hydrophilic quartz surfaces at 300 K.
FIGURE 5. Low-frequency VDOS of water confined between hydrophilic quartz slabs at 300 K. The solid and dotted lines are for water near to cold and hot quartz surfaces, respectively. We also show the VDOS of cold and hot hydroxyl headgroups in black lines.
water molecules penetrating the surfaces and density oscillations continuing into the water layer. For thicker water, the water density at the center matches that of bulk water. However, there are some significant differences, especially between the submonolayer case and the other two cases, i.e., the remarkable asymmetry in the case of the submonolayer, while for monolayer and bilayer cases the density profiles are almost symmetric. This asymmetry is attributed to the fact that a small amount of water molecules is likely to be strongly affected by the different temperature of quartz surfaces confining them, resulting in lower densities near the hot quartz surfaces. More importantly, for the monolayer and bilayer cases, there is a gap between the two quartz surfaces (Figure 3, panels b and c), where the water fills this region and tends to form bulk liquid. The gap becomes wider when water layer thickens. However, the density profiles of the submonolayer water and quartz match very well, indicating that all the water molecules penetrate into the hydroxyl headgroups on the quartz surface and connect two quartz surfaces smoothly (Figure 3a). Thus, water molecules serve as a bridge between the two neighbor quartz surfaces, which enhances the heat transfer of the entire system (we will further discuss this later). Furthermore, when the water is extremely confined (submonolayer case), its behavior becomes quite different. This is illustrated by the direct measure of freezing of water molecules. Figure 4 shows the three-dimensional meansquare displacement (MSD) measurements of the water molecules. For comparison, we also show the measurements for bulk liquid water at 300 K. The results indicate a longtime linear increase with time for systems with areal density more than 15.4 water molecules/nm2, implying liquid-like molecular mobility. With a decrease of the water thickness, the system exhibits suppression of molecular mobility. The
estimated diffusion coefficient of a submonolayer water is about 1 and 3 orders of magnitude less than that of monolayer/bilayer and bulk water, respectively. This is a sign of freezing. Such freezing is attributed to the special landscape of potential formed by the surface silanol headgroups. On quartz (001) the distribution of surface headgroups allows for sufficiently large areas into which water molecules can adsorb onto the surface. Water is able to occupy the void spaces bounded by the protruding silanols. Interstitial water molecules are then stabilized by water-water and silanolwater hydrogen bonds and behave like a solid. The connection of the enhancement in heat transfer with such strong confinement can be qualitatively examined by the excellent match of vibrational density of states (VDOS) between ultrathin water and quartz surfaces. To analyze the vibrational properties of confined water, we calculated the density of states of water on both sides of the cold and hot quartz surfaces via a Fourier transform of the atomic velocity autocorrelation function. The measured VDOS for the selected water cases is shown in Figure 5. The results exhibit some specific features. The attenuation and down-shifting of the translational peak is evident as the thickness of the water slab decreases, which is in good agreement with a previous study.18 Figure 5 clearly shows that the VDOS match between submonolayer water and hydroxyl headgroups is much better than that of monolayer and bilayer water. Since low-frequency modes dominate heat transmission across an interface, we show the details of the lowfrequency part of VDOS in Figure 5. For monolayer and bilayer water, the VDOS of water departs from that of hydroxyl headgroups, while for submonolayer water, the match is excellent. Therefore, we conclude that the peak of overall thermal conductance occurring in the submonolayer case in Figure 2 results from the perfect match of VDOS
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tially constrained. Although the occurrence of water molecules changes the local order of the perfect tetrahedral structure, it provides much stronger silanol-water hydrogen bonds at the interface. In fact, following the procedure in ref 36 to determine the formation of hydrogen bonds (HBs), we checked the average number of water-water and silanol-water hydrogen bonds per water molecule and found that almost all of water molecules form hydrogen bonds with one or more silanol headgroups on both surfaces. Such hydrogen bond network functions like glue sticking two hydrophilic surfaces together. Combined with the vibrational analysis of the three connected parts in Figure 5, the reason that the peak of overall thermal conductance occurs in the 2.21 molecules/nm2 system (Figure 2) is underpinned. In conclusion, using nonequilibrium molecular dynamics simulations, we have studied the effect of nanoconfined water on the thermal transport properties of hydrophilic quartz interfaces, which is measured in terms of overall thermal conductance between two neighbor quartz surfaces, by imposing a one-dimensional heat flux across the simulation domain. A significant increase and a nonintuitive, nonmonotonic dependence of the overall interfacial thermal conductance on the water layer thickness were found. The mechanism of the peak occurring at submonolayer water stems from the freezing of water molecules at extremely confined conditions and the excellent match of vibrational states between trapped water and hydrophilic headgroups on the two contact surfaces. It should be noted that such an enhancement is very sensitive to the water thickness. Nevertheless, our findings point toward the direction of incorporating polar molecules into hydrophilic interfaces to enhance the thermal transport through thermally smooth connection of these interfaces. Therefore, even if it appears to be difficult to precisely control the water thickness, engineers can seek other polar substances for substitution.
FIGURE 6. Snapshot of silanol/water/silanol interfacial structure for the last frame of the nonequilibrium MD simulations: (a) pure quartz/ quartz without water, (b) water areal density of 2.21 molecules/nm2 (48 water molecules); magenta and yellow, Si in silanol headgroups at the two neighbor hot and cold quartz surfaces, respectively; silver, O in silanol headgroups; red, O atoms in water; white, H in water and silanol headgroups. The view is taken along the heat current direction.
Acknowledgment. This work was supported by KTI/CTI under Project No. P. 8074.1 NMPP-N and in part by the Swiss NanoTera NTF Project CMOSAIC. M.H. is thankful for the computation support from Brutus Cluster at ETHZ. This work was supported by a grant from the Swiss National Supercomputing Centre-CSCS under project ID s243.
between the water molecules and the hydroxyl headgroups on the quartz surfaces. Further insight into such strong coupling is provided by the view of the interfacial structure. Figure 6 illustrates the view of the water molecules residing on the quartz surfaces. For pure quartz without water (Figure 6a), a perfect tetrahedral structure is formed between four protruding silanol headgroups at two neighbor quartz surfaces. All the silicon atoms in one silanol surface are residing right above the center of a square grid formed by the silicon atoms in the other silanol surface. For water confined between quartz surfaces (Figure 6b), the interfacial structure follows a different pattern. Diffusion of water into the interstitial spaces on both faces of quartz (001), supplemented by formation of silanol-water hydrogen bonds, causes water to be spa© 2010 American Chemical Society
REFERENCES AND NOTES (1) (2) (3) (4) (5) (6) (7) (8)
284
Emerging Research Devices, International Technology Roadmap for Semiconductors, 2008 (http://www.itrs.net/Links/2008ITRS/ Update/2008_Update.pdf). Swartz, E. T.; Pohl, R. O. Rev. Mod. Phys. 1989, 61 (3), 605–668. Xu, J.; Fisher, T. S. Int. J. Heat Mass Transfer 2006, 49 (9-10), 1658–1666. Hu, M.; Keblinski, P.; Wang, J.-S.; Raravikar, N. J. Appl. Phys. 2008, 104 (8), No. 083503. Mahajan, R.; Chiu, C. P.; Prasher, R. Electron. Cooling [online] 2004, 10 (http://electronics-cooling.com/articles/2004/2004_ february_a1.php). Prasher, R. Proc. IEEE 2006, 94 (8), 1571–1586. Arcidiacono, S.; Bieri, N. R.; Poulikakos, D.; Grigoropoulos, C. P. Int. J. Multiphase Flow 2004, 30 (7-8), 979–994. Arcidiacono, S.; Walther, J. H.; Poulikakos, D.; Passerone, D.; Koumoutsakos, P. Phys. Rev. Lett. 2005, 94 (10), 105502. DOI: 10.1021/nl9034658 | Nano Lett. 2010, 10, 279-285
(9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)
(22) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 197723 (3), 327–341. (23) Kalra, A.; Garde, S.; Hummer, G. Proc. Natl. Acad. Sci. U.S.A. 2003, 100 (18), 10175–10180. (24) Hilder, T. A.; Gordon, D.; Chung, S. H. Small 2009, 5 (19), 2183– 2190. (25) Carvajal-Diaz, J. A.; Liu, L. J.; Cagin, T. J. Comput. Theor. Nanosci. 2009, 6 (4), 894–902. (26) Portella, G.; Groot, B. L. Biophys. J. 2009, 96 (3), 925–938. (27) Hoover, W. G. Phys. Rev. A 1985, 31 (3), 1695–1697. (28) Hoover, W. G. Phys. Rev. A 1986, 34 (3), 2499–2500. (29) Jund, P.; Jullien, R. Phys. Rev. B 1999, 59 (21), 13707–13711. (30) Schoen, P. A. E.; Michel, B.; Curioni, A.; Poulikakos, D. Chem. Phys. Lett. 2009, 476 (4-6), 271–276. (31) Hu, M.; Goicochea, J. V.; Michel, B.; Poulikakos, D. Appl. Phys. Lett. 2009, 95 (15), 151903. (32) Murad, S.; Puri, I. K. Chem. Phys. Lett. 2008, 467 (1-3), 110–113. (33) Hu, M.; Shenogin, S.; Keblinski, P. Appl. Phys. Lett. 2007, 91 (24), 241910. (34) Hu, M.; Keblinski, P.; Schelling, P. K. Phys. Rev. B 2009, 79 (10), 104305. (35) Cole, D. J.; Payne, M. C.; Csa´nyi, G.; Spearing, S. M.; Ciacchi, L. C. J. Chem. Phys. 2007, 127 (20), 204704. (36) Luzar, A.; Chandler, D. J. Chem. Phys. 1993, 98 (10), 8160–8173.
Li, T. D.; Gao, J. P.; Szoszkiewicz, R.; Landman, U.; Riedo, E. Phys. Rev. B 2007, 75 (11), 115415. Adeagbo, W. A.; Doltsinis, N. L.; Klevakina, K.; Renner, J. ChemPhysChem 2008, 9 (7), 994–1002. Lane, J. M. D.; Chandross, M.; Stevens, M. J.; Grest, G. S. Langmuir 2008, 24 (10), 5209–5212. Wang, H. J.; Xi, X. K.; Kleinhammes, A.; Wu, Y. Science 2008, 322 (5898), 80–83. Han, S.; Kumar, P.; Stanley, H. E. Phys. Rev. E 2009, 79 (4), No. 041202. Castrillo´n, S. R. V.; Giovambattista, N.; Aksay, I. A.; Debenedetti, P. G. J. Phys. Chem. B 2009, 113 (5), 1438–1446. Lee, S. H.; Rossky, P. J. J. Chem. Phys. 1994, 100 (4), 3334–3345. Koga1, K.; Zeng, X. C.; Tanaka, H. Phys. Rev. Lett. 1997, 79 (26), 5262–5265. Zangi, R.; Mark, A. E. Phys. Rev. Lett. 2003, 91 (2), No. 025502. Lopes, P. E. M.; Murashov, V.; Tazi, M.; Demchuk, E.; MacKerell, A. D. J. Phys. Chem. B 2006, 110 (6), 2782–2792. Plimpton, S. J. Comput. Phys. 1995, 117 (1), 1–19. Crozier, P. S.; Rowley, R. L.; Henderson, D. J. Chem. Phys. 2001, 114 (17), 7513–7517. Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79 (2), 926–935.
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