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How Chemistry, Nanoscale Roughness, and the Direction of Heat Flow Affect Thermal Conductance of SolidWater Interfaces Hari Acharya,† Nicholas J. Mozdzierz,† Pawel Keblinski,‡ and Shekhar Garde*,† †
Howard P. Isermann Department of Chemical and Biological Engineering, and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, New York 12180, United States ‡ Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States ABSTRACT: We quantify the Kapitza thermal conductance of solidliquid interfaces between self-assembled monolayers (SAMs) and liquid water using nonequilibrium molecular dynamics simulations. We focus on understanding how surface chemistry, nanoscale roughness, and the direction of heat flow affect interfacial thermal conductance. In agreement with calculations by Shenogina et al. (Phys. Rev. Lett., 2009, 102, 156101) for SAMs with homogeneous headgroup chemistries, we find that for mixed CF3/OH SAMs, thermal conductance increases roughly linearly with the fraction of OH groups on the surface. Increasing nanoscale roughness increases solidwater contact area, and therefore the apparent thermal conductance. However, the inherent thermal conductance, which accounts for the increased contact area, shows only small and subtle variations. These variations are consistent with expectations based on recent work on the effects of nanoscale roughness on interfacial tension (Mittal and Hummer, Faraday Disc., 2010, 146, 341). Finally, we find that SAMwater interfaces show thermal rectification. Thermal conductance is larger when heat flows from the ordered SAM phase to the disordered liquid water phase, and the magnitude of rectification increases with surface hydrophilicity.
’ INTRODUCTION Heat transfer at the macroscale is a relatively mature subject where continuum equations are solved for the system of interest under appropriate boundary conditions.1 The temperature profile at a boundary between two materials is typically assumed to be continuous in such calculations. However, it is well-known that an interface offers resistance to heat transfer—the so-called Kapitza resistance2,3—which leads to a discontinuity in the temperature profile across the interface. When phases forming an interface are macroscopic in extent, the interfacial resistance can be neglected. In contrast, at the nanoscale or in materials containing a high density of interfaces, the interfacial resistance can be significant or even dominant. Interfaces involving liquids, especially water, are relatively sharp, with changes in order parameters (e.g., density, dielectric constant, etc.) occurring within a distance of one nanometer.4,5 Naturally, the nature of the interface—e.g., chemistry and/or topography—is expected to influence the interfacial resistance to heat transfer.6,7 Molecular simulations are ideally suited to vary these interfacial properties systematically and obtain insights into their effects on the thermal transport across the interface. Indeed, molecular dynamics (MD) simulations have been performed on liquidliquid as well as solidliquid interfaces to characterize their Kapitza resistance;6,8 remarkably the resistance values obtained from simulations of hydrophobic and hydrophilic interfaces are in good agreement with experimentally measured values.9 Using MD simulations, Patel et al. showed that the thermal conductance (the inverse of Kapitza resistance) of waterorganic liquidliquid interfaces is relatively high and can be further increased by adding surfactants with hydrophilic headgroups.6 At a waterphospholipid interface Nakano et al. did not observe a r 2011 American Chemical Society
temperature discontinuity indicating a very small interfacial thermal resistance.10 Recently, Shenogina et al. quantified the conductance of solidliquid interfaces comprising water (liquid phase) in contact with self-assembled monolayers (SAM, solid phase) presenting a range of headgroup chemistries from hydrophobic (CF3) to hydrophilic (OH).8 A correlation between wettability and conductance is expected.11,12 Shenogina et al. showed that Kapitza conductance, G, varies linearly with the macroscopic wettability of SAM interfaces, as measured by the cosine of droplet contact angle θ: G = B[1 + cos(θ)], where B is a constant of proportionality. This relationship can be thought of as an empirical connection between two ways to characterize interfacial coupling, one based on contact angle (i.e., wetting and adhesion) and the other based on heat transfer.13 There has been significant recent interest in understanding how chemical heterogeneities affect the wetting properties of solid surfaces.1417 Acharya et al. have pointed out an interesting asymmetry between the effects of adding hydrophilic sites into a hydrophobic background and adding hydrophobic sites into a hydrophilic background.16 Specifically, replacing only a few percent of the headgroups on a CH3 SAM with OH groups can significantly enhance the wettability of the surface. However, the converse effect (of replacing a few OH with CH3 groups) is less pronounced. Given the connection between contact angle Special Issue: Nigam Issue Received: May 13, 2011 Accepted: August 23, 2011 Revised: August 3, 2011 Published: August 24, 2011 1767
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Figure 2. Top views of pure CF3 and OH SAM surfaces as well as heterogeneous surfaces with 25%, 50%, and 75% OH groups. Figure 1. Snapshot of the molecular dynamics simulation setup shows the central bilayer and surrounding water (top panel). Alkane tails (cyan) are covalently attached to sulfur atoms (yellow) and present CF3 headgroups (green) to the water phase (red: oxygen, white: hydrogens). Heat sink and source regions are highlighted. The bottom panel shows a steady-state temperature profile for the CF3 SAMwater system. Interfacial temperature drop, ΔT, which is present on both sides, is shown by the arrow.
(i.e., wetting) and heat transfer implied by Shenogina et al., does the Kapitza conductance display a nonlinear dependence on the fraction of hydrophilic groups in mixed SAM systems presenting hydrophobic and hydrophilic headgroups? In addition to chemistry, the roughness of self-assembled monolayer interfaces can be manipulated systematically in simulations by organizing surfactant chains of varying lengths in different configurations. Roughness is typically expected to amplify the inherent wetting characteristics of the reference flat surface—that is, making a hydrophobic surface rougher will make it even more hydrophobic, and making a hydrophilic surface rougher will make it even more hydrophilic. Recently, Mittal and Hummer18 showed that this expectation may not hold when the roughness is nanoscopic in nature. How does nanoscale roughness affect the thermal transport properties of SAMwater interfaces? Here we perform nonequilibrium MD simulations of SAM water interfaces to quantify the dependence of Kapitza conductance on chemical heterogeneity and roughness. Specifically, we study SAMs presenting mixed hydrophobichydrophilic chemistries as well as nanoscale roughness. In addition, we study the dependence of the Kapitza conductance on the direction of heat flow for SAMs presenting a range of chemistries from hydrophobic to hydrophilic. These calculations highlight the possibility of observing thermal rectification in systems containing aqueous interfaces. Collectively, our simulation data offer a glimpse into the richness of heat transfer phenomena at the nanoscale and highlight the need for the development of new theories as well as experimental methods to test them.
’ SIMULATION DETAILS Our molecular dynamics system is 3-D periodic and contains a bilayer made of two SAMs in the center surrounded by a liquid water phase as shown in Figure 1. These bilayers comprise two alkane chains anchored to a central sulfur atom, one in the positive z direction and the other in the negative z direction. Each chain is terminated with a solvent exposed headgroup. The sulfur
atoms are position restrained consistent with the gold 111 lattice.19 The SAM bilayer has a cross-sectional area of 3.46 4.0 nm2 and contains a total of 128 surfactant chains. To study the effects of chemical heterogeneity, mixed SAMs presenting CF3 and OH headgroups at various compositions were used as shown in Figure 2. The dependence of thermal conductance on roughness was studied using homogeneous SAMs presenting CF3 headgroups. Chains spanning lengths from 7 to 13 carbons were arranged in various configurations to create four different rough surfaces as described later. To study the dependence of heat transfer on the direction of heat flow, we used SAMs presenting a range of headgroup chemistries from hydrophobic to hydrophilic (CF3, OCH3, CH2CN, OH, and CONH2). Alkane chains were represented by the united atom model.20 Headgroup chemistries OCH3, OH, and CONH2 were explicitly modeled with the AMBER force-field.21 The OPLS22,23 force-field was used for the headgroups CF3 and CH2CN. The TIP3P model was used to represent water molecules explicitly.24 All simulations were performed with GROMACS25,26 modified in-house to study heat transfer. Electrostatic interactions were handled using the particle mesh EWALD algorithm.27 MD simulations were first equilibrated in the NPT ensemble for 200 ps. Pressure and temperature were maintained at 1 bar and 325 K, respectively, using the Parrinello-Rahman barostat28 and the Nose-Hoover thermostat.29,30 We performed nonequilibrium MD simulations in the NVE ensemble to establish a steady-state temperature profile in the z direction following the procedure of Muller-Plathe.3133 This is achieved by removing kinetic energy from atoms within the “sink” slab and adding the same amount of kinetic energy to atoms in the “source” slab. Each simulation was run for 2.5 ns, with a time step of 1 fs, and a heat flux of 3000 MW/m2. Configurations were stored every 0.5 ps. A steady-state temperature profile was established after the first 250 ps. The remaining trajectory was used for the analysis presented below.
’ RESULTS AND DISCUSSION Effects of Chemical Heterogeneity on Thermal Transport. To quantify how chemical heterogeneity affects thermal conductance, we created SAM surfaces presenting a mixture of hydrophobic (CF3) and hydrophilic (OH) headgroups. We systematically explored five different compositions from pure CF3 to pure OH as shown in Figure 2. For mixed 1768
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Figure 3. Interfacial conductance of mixed CF3/OH SAM surfaces as a function of OH fraction (red). Points are simulation data and lines guide the eye. The free energy of hydration, μex, of a methane-like Lennard-Jonesium (σ = 0.373 nm, ε = 1.234 kJ/mol) is shown in blue. Black dashed line displays a linear expectation. Inset: Gex as a function of OH fraction.
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Figure 5. Variation of interfacial conductance with cos(θ) for mixed CF3/OH SAMs. The black dashed line is a linear fit to the data. The inset shows the variation of cos(θ) with OH fraction. The blue line is a guide to the eye.
similar, the overlap of the water density and SAM density profiles increases with increasing OH group fraction. That is, water molecules hydrogen bond with OH headgroups, resulting in greater intercalation with the surface (also shown pictorially in Figure 4), thus providing qualitative connections with the enhanced thermal conductance. Although the thermal conductance of mixed SAM surfaces increases with the fraction of OH groups, that increase is not precisely linear (red points in Figure 3). One may define excess conductance, Gex, as Gex ¼ G xGI ð1 xÞGJ
Figure 4. Density profiles for water (solid lines) and SAM heavy atoms (dashed lines) in three mixed SAMwater systems: 100% CF3, 25% OH, 100% OH. The origin, z = 0, defines the location where the SAM heavy atom density is 5% of its bulk value. The top panel shows a snapshot highlighting the intercalation of solvent water molecules with a SAM surface presenting 75% OH headgroups. Water molecules at the interface (oxygen red and hydrogen white spacefill) and the OH headgroups (oxygen blue and hydrogen white spacefill) are shown. The color scheme for other atoms is the same as in Figure 1.
surfaces, the CF3 and OH chemistries were arranged uniformly such that no segregation or patches were present on the surface; that is, they were fully mixed. Figure 3 shows the dependence of thermal conductance, G, of mixed SAMwater interfaces on the fraction of OH groups, obtained using G = Q_ /2A/ΔT, where Q_ is the thermal energy transfer per unit time, A is the cross-sectional area, the factor 2 accounts for heat transfer from two interfaces in the periodic box, and ΔT is the temperature jump at the interface. The addition of hydroxyl headgroups to a uniform CF3 surface leads to an increase in G, which is expected, and can be qualitatively understood from the behavior of water at the interface. Figure 4 shows heavy atom density profiles of water and SAM in the direction normal to the SAM surface. Water molecules layer near all surfaces, and the local density of water is high and bulk-like in all systems. Godawat and co-workers34 have shown previously that local density of water alone does not correlate well with the hydrophobicity of the underlying surface. Although the local densities (as quantified for example by the first peak value) are
ð1Þ
where G is the interfacial conductance of a mixed SAM surface, x is the fraction of headgroups of type I, and the subscripts I and J denote headgroup chemistries. Gex equals zero if the individual monolayer chains act as independent resistances in parallel, whereas nonzero values represent deviations from this ideal behavior, reflecting the influence of one headgroup on the thermal transport properties of the other. The conductance of mixed CF3 and OH surfaces shows small deviations from linearity, that is, Gex is small in magnitude (Figure 3, inset). In contrast, other measures of wettability display significantly nonlinear dependence on surface chemistry. For example, Acharya et al. showed that adding a small number of OH groups to a homogeneous CH3 surface can rapidly increase its wettability. Godawat et al.34 proposed the work of cavity formation near the surface (Δμex) as a molecular measure of hydrophilicity: the more hydrophilic the surface, the larger the work of cavity formation. Correspondingly, Figure 3 shows that Δμex for a methane-sized cavity depends nonlinearly on the fraction of OH groups, with higher slope for smaller OH fractions and lower slope for larger OH fractions. Figure 5 shows the variation of interfacial thermal conductance with wettability as measured by the cosine of the contact angle. We measured the contact angle by placing nanodroplets of water on various mixed surfaces as described previously.8,35 There are some uncertainties in the microscopic estimates of contact angles using simulations, especially at 50% OH fraction, because the contact lines are particularly jagged on such chemically heterogeneous surfaces. Nevertheless, Figure 5 shows an approximately linear dependence of thermal conductance on cos(θ). Because the adhesion energy between a liquid and a solid is proportional to [1 + cos(θ)], Figure 5 implies a connection between two different ways to characterize the solidliquid coupling as indicated previously by Shenogina et al.8 Figure 5 also highlights a limitation of the macroscopic contact angle based characterization of the 1769
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Figure 6. Schematic representation of grooved surface patterns with parameters depth, d, and width, w. See text for details.
Figure 7. Interfacial conductance for rough CF3 SAM surfaces calculated by normalizing the flux by the cross-sectional area (red) and the solvent-accessible surface area (blue).
solidliquid coupling at the interface. For sufficiently high OH fraction (J 75%), the surface is fully wetted by water, and the contact angle is zero. For these high OH fractions, contact angle measurements cannot resolve differences in hydrophilicity, but both the interfacial thermal conductance and the free energy of cavity formation can. As such, G and Δμex constitute more sensitive measures of solidliquid interfacial coupling. Effect of Surface Roughness on Interfacial Thermal Conductance. The SAM setup used in our simulations is ideally suited to introduce nanoscale roughness in a systematic manner. We used surfactants of different chain lengths and organized them to create four different types of rough surfaces as shown in Figures 6 and 7. For simplicity, we used only one type of headgroup chemistry, namely the CF3 group, in these simulations. We created grooves in a surface of width w and depth d, where w varied from 1 to 2 headgroup diameters, and d ranged from 2 to 4 carbon atoms. We denote the three grooved surfaces by w1d2, w2d2, and w2d4, which are shown in Figures 6 and 7. In these configurations, we did not use chains differing by more than four carbons in length because even at d = 4 the flexibility of the chains leads to their partial collapse and the groove loses some of its integrity. We also created a sinusoidal surface using surfactants of different chain lengths, all having a CF3 headgroup. One complete wave (trough to trough) included rows of alkane chains with lengths of 7, 9, 11, 13, 13, 11, 9, 7, respectively (see Figure 7). The periodic box included one wave with a wavelength of 3.5 nm and trough to peak vertical distance of 0.8 nm (i.e., amplitude of 0.4 nm). In this arrangement the smooth height gradient allows neighboring chains to support each other thereby preventing chain collapse.
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Figure 8. Water (solid lines) and SAM density profiles (dashed lines) for CF3 surfaces of different nanoscale roughness. Density profiles are translated horizontally such that SAM heavy atom densities are ∼5% of their bulk value at z = 0.
Figure 7 shows interfacial thermal conductance of rough surfaces calculated using two different areas for normalization of the heat flux. When the regular cross-sectional (CS) area is used, thermal conductance appears to increase with surface roughness consistent with the results of Shibahara et al. where they reported nanoscopic roughness enhancing interfacial conductance.36 However, when normalized by solvent-accessible surface area (SASA), the variation of thermal conductance with curvature is smaller and more subtle. As the contact area of the liquid with solid is increased upon introducing roughness, one expects better heat transfer, assuming that the roughness does not fundamentally change the nature of underlying thermal coupling. This is approximately true as reflected in the increase of apparent thermal conductance with a cross-sectional area normalization (red bars in Figure 7). On the other hand, many studies of interfacial wetting have shown that hydrophobicity or hydrophilicity of an interface can be affected by the extent and nature of surface roughness.13,18,37 Specifically, Mittal and Hummer have recently shown that introduction of nanoscale roughness (amplitude of 0.3 nm and wavelength of about 1.1 nm) leads to an increase in the interfacial energy of a reference hydrophilic surface making it hydrophobic.18 This increase was attributed to the cost of deforming the hydrogen bonded network of water to conform to the corrugations in the surface. They further found that when the wavelength of the sinusoidal surface becomes much larger, water is better able to conform to the surface and the interfacial energy actually decreases. Translating these ideas to our system would suggest a small decrease in the inherent thermal conductance for the rough grooved surface and a slight increase for the sinusoidal surface with larger wavelength. This expectation is qualitatively true for our system: thermal conductance normalized by the solvent-accessible area (which characterizes the nature of true thermal coupling at the interface) decreases somewhat for grooved surfaces relative to that for a flat surface (although that decrease is within the errorbars of our data; see the blue bars in Figure 7), and increases for the sinusoidal surface. Density profiles of water and SAM atoms in the rough surface, Figure 8, show penetration of water molecules into the grooves on the surfaces. For example, water resides ∼0.4 nm further inside the w2d4 pattern compared to the flat surface. Although water penetrates the grooves on the CF3 surface, it does not intercalate with the surface. Such intercalation and hydrogen bonding are required to enhance the inherent thermal coupling significantly. Thermal Rectification in SAMWater Systems As a Function of Surface Chemistry. Recent work using simulations38,39 1770
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Figure 9. (a) Temperature profiles for CONH2 SAMwater systems in two different heat flow configurations: hot-SAM/cold-water (red) and cold-SAM/hot-water (blue). (b) Hot-SAM/cold-water temperature profile is inverted and translated to show rectification clearly, as indicated by the arrow.
Figure 10. Temperature drop, ΔT, at the interface and its variation with heat flux, for two heat flow configurations in the CONH2 SAM water system. Lines guide the eye.
as well as experiments40 has shown that the thermal conductance of materials and interfaces can depend on the direction of heat flow.41 This dependence raises the possibility of designing thermal diodes with significant thermal rectification.42 We explored whether the self-assembled monolayer surfaces studied previously by Shenogina et al.8 display any rectification, and if so, how the extent of rectification depends on surface chemistry. To this end, we performed nonequilibrium MD simulations with heat flowing from SAM to water and vice versa for five different headgroup chemistries, namely CF3, OCH3, CH2CN, OH, and CONH2. Figure 9a shows temperature profiles obtained for a CONH2 SAMwater system in the two different heat transfer configurations with a flux of 3 103 MW/m2. To compare these two temperature profiles and to highlight rectification, we inverted the profile for the hot-SAM/cold-water configuration and plotted them on the same graph (Figure 9b). We note that the steady state temperatures at the interface are roughly the same for both configurations. It is clear that the temperature drop at the interface is smaller when heat flows from SAM to water than when it flows from water to SAM. This observation holds over a range of fluxes as shown in Figure 10, and highlights the thermal rectification at the CONH2 SAMwater interface. Following Roberts and Walker,42 we define rectification ε as ε¼
Gþ G Gþ þ G
ð2Þ
where G+ and G are the larger and smaller conductance, which for our systems are GSAMtowater and GwatertoSAM, respectively.
Figure 11. Dependence of thermal rectification, ε, on surface wettability [cos(θ)] for different surface chemistries.
Figure 11 shows that thermal rectification, ε, is small for a hydrophobic surface (εCF3 ≈ 0.01) and increases with increasing surface hydrophilicity, reaching a value of about 0.2 for the CONH2 SAM. To the best of our knowledge, ours are the first investigations of chemistry-dependent thermal rectification at solidwater interfaces. Given the ubiquity of aqueous interfaces in engineering and technological applications, a more detailed study of the origins of thermal rectification and ways to enhance it are warranted.
’ CONCLUSIONS We have presented results from MD simulations focused on quantifying the Kapitza thermal conductance of solidliquid SAMwater interfaces. Specifically, we explored the effects of surface chemistry, nanoscale roughness, and the direction of heat flow on the magnitude of interfacial thermal conductance. We found that increasing the hydrophilicity of SAM surfaces by replacing CF3 with OH headgroups results in an increase in thermal conductance that is slightly nonlinear with the fraction of OH groups. The magnitude of this nonlinearity is much smaller than that displayed by other molecular measures of interface wetting (e.g., free energy of cavity formation).16,34 We also found that increasing nanoscale roughness increases the solidwater contact area and thereby increases apparent thermal conductance. The inherent conductance as characterized by normalizing the heat flux by solvent-accessible surface area, however, varies subtly with surface roughness. Consistent with the calculations of Mittal and Hummer,18 which show an increase in hydrophobicity upon adding nanoscale roughness, the inherent thermal conductance decreases somewhat. In contrast, for surfaces with smooth sinusoidal character with long wavelength (= 3.5 nm), the inherent thermal conductance increases somewhat. Overall, the magnitude of change with nanoscale roughness is much smaller than that upon adding hydrophilic groups to the CF3 surface, indicating that surface chemistry provides a powerful handle for manipulating interfacial thermal conductance. This role of chemistry in influencing interfacial conductance may provide insights into the thermal properties of proteinwater interfaces43,44 where hydrophilic groups comprise a significant portion of the protein surface exposed to solvent. Finally, we find that SAMwater interfaces display some thermal rectification, i.e., dependence of thermal resistance on the direction of heat flow. Thermal conductance is higher when heat flows from the ordered SAM phase to the disordered liquid water phase and the extent of thermal rectification increases with surface hydrophilicity. We note that theories for interfacial thermal conductance are based typically on the mismatch in 1771
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT It is our pleasure to contribute this paper to the special issue honoring Prof. K. D. P. Nigam of Indian Institute of Technology, Delhi, India. Prof. Nigam has been instrumental in establishing close ties between Rensselaer and IIT-Delhi, and nurturing them over the past three decades. We thank Srivathsan Vembanur for his assistance with the surface area calculations. We also acknowledge the partial financial support of NSF-NSEC (DMR-0642573) and New York State NYSTAR program to Rensselaer Nanotechnology Center. ’ REFERENCES (1) Kern, D. Q. Process Heat Transfer; McGraw-Hill: New York, 1950. (2) Kapitza, P. L. The study of heat transfer in helium II. J. Phys. (U.S.S.R.) 1941, 4, 181. (3) Cahill, D. G.; Ford, W. K.; Goodson, K. E.; Mahan, G. D.; Majumdar, A.; Maris, H. J.; Merlin, R.; Phillpot, S. R. Nanoscale thermal transport. J. Appl. Phys. 2003, 93, 793–818. (4) Rowlinson, J.; Widom, B. Molecular Theory of Capillarity; Dover Publications, 2002. (5) Patel, H. A.; Nauman, E. B.; Garde, S. Molecular structure and hydrophobic solvation thermodynamics at an octane-water interface. J. Chem. Phys. 2003, 119, 9199–9206. (6) Patel, H. A.; Garde, S.; Keblinski, P. Thermal resistance of nanoscopic liquid-liquid interfaces: Dependence on chemistry and molecular architecture. Nano Lett. 2005, 5, 2225–2231. (7) Lervik, A.; Bresme, F.; Kjelstrup, S. Heat transfer in soft nanoscale interfaces: The influence of interface curvature. Soft Matter 2009, 5, 2407–2414. (8) Shenogina, N.; Godawat, R.; Keblinski, P.; Garde, S. How Wetting and Adhesion Affect Thermal Conductance of a Range of Hydrophobic to Hydrophilic Aqueous Interfaces. Phys. Rev. Lett. 2009, 102, 156101–156104. (9) Ge, Z. B.; Cahill, D. G.; Braun, P. V. Thermal conductance of hydrophilic and hydrophobic interfaces. Phys. Rev. Lett. 2006, 96, 186101–186104. (10) Nakano, T.; Kikugawa, G.; Ohara, T. A molecular dynamics study on heat conduction characteristics in DPPC lipid bilayer. J. Chem. Phys. 2010, 133, 1–9. (11) Murad, S.; Puri, I. K. Thermal transport across nanoscale solidfluid interfaces. Appl. Phys. Lett. 2008, 92, 133105–3. (12) Barrat, J.; Chiaruttini, F. Kapitza resistance at the liquid-solid interface. Mol. Phys. 2003, 101, 1605–1610. (13) Jamadagni, S. N.; Godawat, R.; Garde, S. Hydrophobicity of proteins and interfaces: Insights from density fluctuations. Ann. Rev. Chem. Biomol. Eng. 2011. (14) Giovambattista, N.; Debenedetti, P. G.; Rossky, P. J. Hydration behavior under confinement by nanoscale surfaces with patterned
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