Temperature Effects on Water-Mediated Interactions at the Nanoscale

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Temperature Effects on Water-Mediated Interactions at the Nanoscale Justin Engstler, and Nicolas Giovambattista J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b05430 • Publication Date (Web): 04 Sep 2018 Downloaded from http://pubs.acs.org on September 5, 2018

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The Journal of Physical Chemistry

Temperature Effects on Water-Mediated Interactions at the Nanoscale Justin Engstler1 and Nicolas Giovambattista1,2∗ 1

Department of Physics, Brooklyn College of the City University of New York, Brooklyn, NY 11210, USA

2

Ph.D. Programs in Chemistry and Physics, The Graduate Center of the City University of New York, New York, NY 10016, USA E-mail: [email protected] Phone: (+1) (718) 951-5000 ext. 2859 Abstract We perform molecular dynamics simulations to study the effects of temperature on the water-mediated interactions between nanoscale apolar solutes. Specifically, we calculate the potential of mean force (PMF) between two graphene plates immersed in water at 240 ≤ T ≤ 400 K and P = 0.1 MPa. These are thermodynamic conditions relevant to cooling- and heating-induced protein denaturation. It is found that both cooling and heating have the effects of suppressing the attraction, and ultimate collapse, of the graphene plates. However, the underlying role played by water upon heating and cooling is different. Isobaric heating reduces the strength and range of the interactions between the plates. Instead, isobaric cooling stabilizes the plates separations that can accommodate an integer number of water layers between the graphene plates. In particular, the energy barriers separating these plate separations increase linearly with 1/T . We also explore the sensitivity of the plates PMF to the water model employed. In the case of the TIP4P/2005 model, water confined between the plates crystallizes

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into a defective bilayer ice at low temperatures while, in the case of the SPC/E model, water remains in the liquid state at same thermodynamic conditions. The effects of varying water-graphene interactions on the plates PMF is also studied.

1

Introduction

Water-mediated interactions (WMI) play a fundamental role in self-assembly processes in aqueous solutions (see, e.g., Refs. 1–3 ). Perhaps the most relevant of such interactions is the hydrophobic attraction among (hydrophobic) solutes (e.g., Refs. 4–10 ). For example, the selfassembly process of protein folding is driven by hydrophobic interactions (HIs) between the protein hydrophobic residues, most of these residues clustering into the protein’s core. 6,11 In the formation of cell membranes and micelles, 5,12,13 amphiphilic molecules (i.e., molecules characterized by a hydrophilic head and a hydrophobic tail) self-organize into specific structures such that their hydrophobic tails cluster together. A quantitative understanding of WMI in general, and HIs in particular, is also relevant in chemical engineering and material science. There is interest in these fields to build structures at the nanoscale, where traditional approaches to build target structures fail or are difficult to implement. 14 A promising tool to build at the nanoscale is to design particles that, once put together, self-organize into the desired structure. In this regard, understanding WMI at the quantitative level may help in the designing of nanoparticles or molecular structures with specific effective interactions so that they can self-assemble in an aqueous environment into the desired nanostructure. 14–16 Quantifying WMI has been challenging because of their complex dependence on numerous factors. For example, in the case of hydrophobic surfaces, WMI are sensitive to diverse properties of the interacting units, such as surface chemistry, 17,18 size, 19,20 and shape, 19,21 as well as thermodynamic conditions, such as pressure 22–26 and temperature. 27–29 Solution properties, such as ion concentration, also influence WMI. 30,31 In this work, we focus on the effects of temperature on the WMI between graphene plates, which serve as model apolar nanoscale solutes. Our work is partially motivated by the processes of cooling- and heating2


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induced protein denaturation, which are believed to be caused, at least in part, by changes in the strength of the WMI among the protein’s hydrophobic residues. 32 Protein denaturation upon heating is a well-known phenomenon but cooling-induced protein denaturation usually occurs at sub-zero temperatures (in cases where crystallization can be avoided) and is less understood. Most computer simulation studies have mainly focused on HIs at room temperature and standard pressure. In addition, many of these studies are based on idealized solutes, such as united atom representations of methane. In this work, we perform molecular dynamics (MD) simulations to quantify the effects of temperature on the WMI between realistic model solutes. Specifically, we calculate the potential of mean force (PMF) between two nanoscale graphene plates immersed in water, at different temperatures. We choose to use graphene plates for the present study because, contrary to other relatively smooth surfaces, such as silica, 33 crystallization of water confined by graphene has not been observed at normal pressure and temperature. 33,34 In addition, graphene 20,35–37 and similar C-based nanoparticles, such as fullerenes and single-wall carbon nanotubes, 21,38 have already been used as model systems to study HIs and confined water. 8,39 This work is organized as follows. In Sec. 2, we describe the computer simulation details. The temperature effects on the WMI between graphene plates are discussed in Sec. 3.1, for the case of SPC/E water, and Sec. 3.2, for the case of TIP4P/2005 water. A brief description of the thermodynamic properties of water confined between graphene plates is included in Sec. 3.3. In Sec. 3.4 we discuss the effects of tuning water-graphene interaction parameters (changing the hydrophilic/hydrophobic character of graphene) on the plates PMF. We summarize the results presented in this work in Sec. 4.

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2

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Computational Details

We perform molecular dynamics (MD) simulations of two graphene plates immersed in water at constant pressure and temperature. Each graphene plate is composed by 135 carbon atoms arranged in a single layer as shown in Fig. 1a. The C-C bond length is 0.141 nm and the plate’s area is A = dx × dy = 1.709 × 1.762 nm2 . The system box is orthorhombic with dimensions that fluctuate with time, with Lx > 4.7 nm, Lz > 4.7 nm, Ly > 7.5 nm at all temperatures considered. The graphene plates are immobile and are located symmetrically with respect to the center of the box, parallel to the xy-plane. The system contains N = 6541 water molecules, and periodic boundary conditions are applied along the three dimensions. A cross-section of the system is shown in Fig. 1b. Computer simulations are performed at P = 0.1 MPa and 240 ≤ T ≤ 400 K (T = 240, 260, 300, 360, 400 K for the case of SPC/E water and T = 240, 260, 280, 300, 320, 360, 400 K for the case of TIP4P/2005 water; see below). For a given T and P , a set of MD simulations are performed at fixed plates separations r = 0.24, 0.26, ...1.5 nm. All MD simulations are performed using the GROMACS computer simulations package. 40 The temperature and pressure are maintained constant by using a Nos´e-Hoover thermostat (with a time constant of 1 ps) and a Berendsen barostat (with a time constant of 1 ps). Electrostatic interactions are treated using a Particle Mesh Ewald (PME) solver with a reciprocal space griding of 0.12 nm and cubic polynomial interpolation. A cutoff rc = 1.1 nm is used for the real space force calculations of the PME solver as well as for the LJ short range interactions. In order to study the sensitivity of the results to the water model employed, we perform MD simulations using the SPC/E 41 and TIP4P/2005 42 water models. The SPC/E model is a three-interacting-sites water model commonly used to study liquid water as well as water in confinement and at interfaces (see, e.g., Refs. 33,43–47 ). The TIP4P/2005 model is a fourinteracting-sites water model that has been mostly used to study the properties of bulk liquid water (e.g., Refs. 48,49 ), ice (e.g., Ref. 50 ), and amorphous ice. 51,52 Both models reproduce relatively well the thermodynamic and dynamical properties of liquid water, however, the 4


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TIP4P/2005 model is remarkably superior to the SPC/E model in reproducing the phase diagram of ice. 53,54 Water molecules interact with the graphene plates via a Lennard-Jones pair potential between the water O and graphene C atoms; C atoms have no partial charges, resulting in apolar surfaces. The corresponding water O-graphene C Lennard-Jones (LJ) parameters are given in Table 1. Werder et al. 55 showed that when the LJ parameters of Table 1 are used with SPC/E water, the contact angle of a droplet composed of N = 2000 water molecules on graphite is θc ≈ 950 . We performed MD simulations of a water droplet in contact with large, extended graphene plates, as done in Refs., 56,57 and find that the contact angle of SPC/E water on graphene is θcSP CE ≈ 970 . In the case of TIP4P/2005 water T IP 4P/2005

droplets on graphene, we obtain θC

≈ 960 . Both values are consistent with previous

calculations 58 of water in contact with graphene suggesting that water contact angle on (free standing) graphene plates is somewhere in the range 950 − 1000 . We note that, strictly speaking, if hydrophobicity is defined in terms of water contact angle, then the (apolar) surfaces considered in this work are marginally hydrophobic. Indeed, it has been shown that graphene plates can be considered hydrophobic based on the density fluctuations of water at the interface. 39 Nanoscale graphene plates have also been used in the past as hydrophobic model solutes to study HIs. 20,35,36 We stress, however, that the hydrophobicity/hydrophilicity in model graphene surfaces is sensitive to the water-carbon interactions; see Ref. 59 MD simulations at a given temperature T and plates separations r are performed for 4 ns with a simulation time step dt = 0.002 ps. Data analysis is performed based on the last 2 − 3 ns of the simulation runs. The simulation time appears to be long enough to avoid non-equilibrium artifacts in our measurements at all temperatures. For comparison, we note that the structural relaxation times in bulk SPC/E water at ρ = 1.0 g/cm3 are τbulk ≈ 5, 17, 125 ps at 260, 240, 220 K, respectively, 47 so that even at our lowest temperature (240 K) the simulation time is about 235 τbulk . It is possible, however, that at very short graphene plates separations, the confined liquid is metastable relative to the vapor. 37

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2.1

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Mean Force and Potential of Mean Force

For a given (T, r) we extract directly from the MD simulation the average force acting on each C and calculate the force on each graphene plate, F~i (r); here i = 1 (i = 2) indicates the graphene plate on the left (right) side of Fig. 1b. Forces F~i (r) are calculated every 2 ps from the MD simulation and averaged over time. The magnitude of the average force acting on the plates is then

F (r) =

F~2 (r) · n ˆ 2 + F~1 (r) · n ˆ1 , 2

(1)

where n ˆ i is the unit vector perpendicular to graphene plate i that points away from the confined volume. It follows that F (r) > 0 (F (r) < 0) for repulsive (attractive) WMI between the graphene plates. By combining the results from our MD simulation for all values of r ≤ 1.5 nm, we obtain the average force F (r) at a given T . The PMF between the graphene plates is calculated as a function of the plate separation r by integration,

G(r) − G(r0 ) = −

Z

r

F (r)dr,

(2)

r0

where r0 is a reference separation and G(r0 ) is an arbitrary constant; in this work, r0 = 1.5 nm and G(r0 ) = 0.0. The expression above implies that the PMF between the graphene plates can be thought of as the effective average potential energy between the plates at fixed T (P = 0.1 MPa) in the presence of the solvent. Note that at the present conditions (T and P constant), the PMF for a given r is also the Gibbs free energy of the system. To show this we note that for a given plates separation r, the Gibbs free energy is defined as G(r) = U + P V − T S. If r → r + dr, the first law of thermodynamics states that dU = dwnon−P V − P dV + T dS, where dwnon−P V is the work done on the system (plates plus water) that is not due to a compression/expansion of the system. 60 For the system under study,

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dwnon−P V = −F (r)dr where F (r) is the mean force that one plate exerts on the other, in the presence of the solvent. It follows that, at constant T and P , dG(r) = dwnon−P V = −F (r)dr and hence,

G(r) = −

Z

r

F (r)dr + G(r0 ),

(3)

r0

which is identical to Eq. 2. This approach to calculate the PMF between a pair of solutes (including graphene plates) has been implemented in the past; see, e.g., Refs. 30,61

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Results

3.1 3.1.1

Two Graphene Sheets Immersed in SPC/E water Potential of Mean Force

The total PMF between the graphene plates in the presence of SPC/E water, G(r), is shown in the inset of Fig. 2a at selected temperatures. In order to compare the effective PMFs obtained at different temperatures, we show in the main panel of Fig. 2a the total PMF divided by the thermal energy kB T . The corresponding contribution to the total PMF due solely to water is Gw (r) ≡ G(r) − Gp (r), where Gp (r) is the total potential energy between the graphene plates in vacuum, separated by a distance r; see Fig. 2b. Fig. 2c shows the mean force on the plates obtained from the MD simulations. We estimate the error bars in the calculated PMF by performing two independent simulations at T = 240 K and P = 0.1 MPa; typical error bars in the total PMF are of the order of 8 kJ/mol. Figure 2a shows that at all temperatures, G(r) exhibits oscillations that become negligible at approximately r > 1.5 nm. At the lowest temperature studied (T = 240 K), three minima can be clearly identified at r1 = 0.30 − 0.32 nm, r2 = 0.65 − 0.70 nm, and r3 = 0.89 − 0.98 nm while a forth weak minimum occurs at r4 ≈ 1.30 nm. As shown in the supplementary information (SI), these minima indicate stable/metastable states corresponding to configurations 7



where the graphene plates are separated by zero (empty confined volume), one, two, and three water layers, respectively, in agreement with previous computer simulations performed at standard pressure and temperature

35,62

(see also Sec. 3.2). It follows that the energy

barriers separating these minima are associated to the expulsion of a single water layer in the confined volume as the plates move closer to each other, from ri+1 to ri (i = 1, 2, 3). The strong similarities between Figs. 2a,b for r > 0.60 nm indicate that the energy barriers separating the stable plate separations are indeed due to the presence of water. The effects of increasing the temperature from T = 240 K to 400 K is to weaken the oscillations in the graphene plates PMF. In particular, at approximately T = 360 − 400 K, the total PMF (Fig. 2a) at r > 0.9 − 1.0 nm is rather constant and approximately equal to zero. This means that at these temperatures and plate separations, the effective interactions between the plates vanish. Accordingly, heating has the effect of reducing the range of the interactions (forces) between the graphene plates, from ≈ 1.5 nm at T = 240 K to ≈ 0.9 − 1.0 nm at T ≈ 360 − 400 K. In addition, at r < 0.9 nm, heating reduces the depth of the minima in the total PMF/kB T at r1 and r2 , while decreasing the energy barriers separating these two minima. It follows from Fig. 2 that heating contributes towards the de-stabilization of those states where water molecules confined between the plates arrange into zero, one, two,... layers (an integer number of water monolayers), relative to the states where the plates are fully dissociated, r > 1.5 nm. Of particular interest are the effects of temperature on the first minimum of the total PMF (r = r1 = 0.30 − 0.32 nm). At this small separation, there is no space between the plates to accommodate water molecules and the graphene plates are in a ‘collapsed’ state. Interestingly, the local minimum at r = r1 in the total PMF is not altered upon heating (inset of Fig. 2a). However, heating does alter the corresponding value of the total PMF/kB T (main panel of Fig. 2a) from −210 kJ/mol at T = 240 K to −130 kJ/mol at T = 400 K (i.e., a 40% reduction). This means that the collapsed-plates state becomes less stable due to the increase in thermal energy (kB T ) upon heating while the water-induced PMF is not affected.

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We note that this conclusion holds only for the case r = r1 . For the cases r = r2 , r3 , r4 , the total PMF (inset of Fig. 2a) decreases upon heating and hence, the thermal energy further reduces the total PMF. We also note from the inset of Fig. 2a that the total PMF between the plates is, within error bars, approximately independent of temperature. This implies that the entropic cost of forming the plate-water interface is approximately zero (see also Ref. 28 ). As we will show below, this seems to be specific to SPC/E water, as the same conclusion does not hold for TIP4P/2005 water. 3.1.2

Activation Energies and Graphene Sheets Collapse

It follows from the discussion above that cooling has the effect of increasing the range of the WMI between the graphene plates. In particular, as shown in Fig. 2a, cooling towards T = 240 K leads to an increase in the energy barriers separating the states corresponding to r = r1 , r2 , r3 , r4 . Figure 3a shows the corresponding activation free energies, ∆Gact (T )/kB T , that the plates need to overcome in order to move from ri to ri+1 (dashed lines) and from ri+1 to ri (solid lines); i = 1, 2, 3. For given consecutive PMF minimum and maximum, with free energies Gmin and Gmax , the corresponding activation free energy is defined as ∆Gact (T )/kB T = (Gmax (T ) − Gmin (T )) /kB T . It follows from Fig. 3a that all activation energies increase linearly with 1/T . For example, for the plates to move from r = r2 to r = r1 (collapsed state), ∆Gact (T )/kB T varies from ≈ 5 at T = 400 K to 20 at T = 240 K (≈ 400 % increase). Microscopically, the increase of activation energies with decreasing temperature implies that, upon cooling, it becomes more difficult for the plates to expel or add a water layer in the confined volume. After all, decreasing the temperature strengthens the hydrogen bonds between water molecules, making more difficult for the water hydrogen-bond network to change configuration. Hence, lowering the temperature has the effect of increasingly trapping the graphene plates at separations r = r1 , r2 , r3 , r4 . It follows that cooling helps to disfavor (i.e., to kinetically frustrate) the collapse of the graphene plates. Accordingly,

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the repulsive mean forces between the plates in Fig. 2c, at approximately ri < r < ri+1 , increase upon cooling. A subtle point follows from Fig. 3a. The energy barrier that the plates need to overcome in order to move apart, from ri to ri+1 , and closer, from ri to ri−1 , to each other are different (i = 2 , 3, 4). For the case r = r2 , the energy barrier is lower for the transition r2 -to-r1 than for the case r2 -to-r3 . This means that, if r = r2 , thermal energy is more favorable to bring the plates together (while removing the water layer between the plates). However, if the plates separation is r = r3 , the energy barrier is lower for the transition r3 -to-r4 than for the case r3 -to-r2 . Hence, if r = r3 , thermal energy will most probably help the plates to move apart from one another (while adding an extra water layer in the confined volume). This asymmetric effect becomes more evident at low T. 3.1.3

Mean Force

Next, we discuss briefly the T -dependence of the mean force acting on the plates. Figure 2c shows F (r) at different pressures. Since F (r) = −(∂G(r)/∂r)P,T (see Eq. 2), it follows that F (r) > 0 (F (r) < 0) when the slope of G(r) in Fig. 2b is negative (positive), and that F (r) = 0 at the location of the maxima and minima of G(r). Perhaps the most interesting observation of Fig. 2c is the discontinuity of F (r) at r = 0.60 − 0.64 nm, which may be difficult to detect from Fig. 2a. This discontinuity occurs at r = dc (T ) where dc (T ) is the location of the first maximum of G(r). Interestingly, we find that dc (T ) coincides with the separation at which capillary drying occurs, i.e., the minimum separation at which water molecules are found in the confined space (see Sec. 3.4 and SI). dc (T ) is very small and increases slightly upon heating. In the present case, dc (T )/2 = 0.30 − 0.32 nm which is approximately the minimum distance between water O atoms and the plates found at all plates separations studied (see SI). Thus, the capillary drying at r = dc (T ) is due to steric effects (see also 20,35,63 ). As shown in Sec. 3.4, when the water-graphene interactions are weakened and the plates become more hydrophobic, drying occurs at much larger separations

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than those observed in Fig. 2. The discontinuity in F (r) at r = dc (T ) is reminiscent of a first-order phase transition since F (r) is a first-order derivative of the system free energy (Eq. 2). However, one must note that the confined volume is finite and thus, density fluctuations are bounded. Yet, in the limit of infinitely large graphene plates, the discontinuity in F (r) would correspond to a true first-order phase transition. 64 In this case, since F (r) is an extensive property, the change in F (r) as r → dc (T ) should increase with the plates area, A, while the pressure acting on the walls [F (r)/A] for r → dc (T ), should reach an asymptotic value as A → ∞.

3.2

Two Graphene Sheets Immersed in TIP4P/2005 water: Crystallization Effects

The total PMF between the graphene plates immersed in TIP4P/2005 water is shown in Fig. 4a. The contribution to the total PMF due solely to water and the mean force between graphene plates are included in Figs. 4b,c. At first sight, Figs. 2 and 4 may look qualitatively similar. For example, the location of the minima and maxima of the total PMF, in Figs. 2a and 4a, and the PMFwater , in Figs. 2b and 4b, are roughly the same. Indeed, as for the case of SPC/E water, the minima in the total PMF of Fig. 4 correspond to plates separations that can accommodate an integer numbers of water layers between the plates. For a closer look at the PMF between the graphene plates in SPC/E and TIP4P/2005 water, we include in Figs 5a-c and 5d-f the total PMF/kB T and mean forces between the plates when they are immersed in SPC/E and TIP4P/2005 water. At high temperatures, both water models induce practically the same graphene-graphene interactions (Figs. 5a,d). However, cooling results in pronounced differences in the PMF/kB T and F (r) at r ≈ 0.7 − 1.1 nm. In particular, as T → 240 K, the PMF between the plates in the presence of TIP4P/2005 water develops a deep minimum at r ≈ 0.9 nm, which is much milder in the case of SPC/E water. As we discuss below, this is because TIP4P/2005 water crystallizes into a defective bilayer-ice at r ≈ 0.9 nm while SPC/E water remains in the liquid state at 11



the same conditions. To show the crystallization of confined TIP4P/2005 at low temperatures, we focus on the total PMF between plates at T = 240 K; see inset of Fig. 6a. The main panel of Fig. 6a shows the mean-square displacement (MSD) of the water O atoms in the confined space at selected plates separations. The MSD is calculated over those molecules found between the plates at t = 1 ns that remain within the confined space (at all times) until time t. The corresponding number of molecules [that remain between the plates during the time interval (1 ns, t)], N (t), is shown in Figs. 6b. Fig. 6c shows the density profile of water at the selected plates separation and confirms, as discussed in Sec. 3.1, that water molecules arrange into monolayer (r = 0.62 − 0.72), bilayer (r = 0.86 − 1.00), and trilayer structures (r ≈ 1.20 − 1.45). At small plates separations, r = 0.62 − 0.72, the MSD(t) increases rapidly and, at t ≈ 2.5 ns, the MSD≈ 1 nm2 , implying that, in average, water molecules displace by > 0.3 nm (which is the OO distance between neighboring molecules in bulk water). It follows that water molecules are indeed diffusing at these plate separations and hence, that water confined between the plates is in the liquid state. We note that the MSD drops sharply to zero at approximately t > 3 ns because at these times N (t) = 0, i.e., all molecules that were between the plates at t = 1 ns have finally left the confined space. As the plates separation increases from r = 0.80 (magenta) to r = 0.92 nm (orange), the MSD(t) decreases considerably and in particular, MSD(t) ≈ 0 at r = 0.92 nm for all times. Simultaneously, N (t) seems to approach an asymptotic finite value for long times; this is particularly evident for the case r = 0.92 nm. These findings imply that water molecules do not diffuse at long times and that, instead, they get trapped within the confined space, i.e., confined TIP4P/2005 water is reaching a crystal or vitrified state. A snapshot of the system at r = 0.92 nm is included in Fig. 7a. With the present graphene plate size, it is apparent that the confined molecules form a crystal-like structure containing hydrogen-bonded molecules arranged in distorted pentagons, hexagons, and heptagons. In

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addition, water molecules are arranged in a bilayer structure with both layers being in registry with each other (AA stacking). The confined molecules form a single hydrogenbonded network as found, e.g., in hexagonal ice. We note that the ice-like structure found at r = 0.92 nm is very sensitive to the plates separations and it is not found at r = 0.86, 1.00 nm; see Figs. 7b,c. For comparison, we show in Fig. 7d a snapshot of SPC/E water at same conditions (T = 240 K and r = r3 ≈ 0.96 nm). Fig. 7d indicates that indeed, the structure of SPC/E water is amorphous, as expected for liquids. One may wonder if TIP4P/2005 water may crystallize at T > 240 K. To answer this question we show in Figs. 8a-c the MSD(t), N (t), and density profile at all temperatures studied, for the plates separation r = 0.92 nm, at which the bilayer ice forms. Fig. 8a shows that, at short times (e.g., t ≈ 1.1 ns), the MSD(t) increases with increasing temperature. In particular, the MSD(T ) seems to approach an asymptotic, non-zero value for long times only for approximately T < 260 K, consistent with liquid water reaching a crystalline state. That crystallization occurs only at approximately T < 260 K is also consistent with the behavior of N (t), which seems to saturate at long times at a finite value for T = 240 K but decays to zero for higher T (at T = 260 K, N (t) seems to decay to zero within ≈ 10 − 20 ns). Although the melting temperature of confined and bulk water are not necessarily related, we note that bulk TIP4P/2005 water has a melting temperature of Tm ≈ 252 K at normal pressures, 42 indicating the tendency of this water model to crystallize at the temperatures where we observe the bilayer ice.

3.3

Temperature Effects on Confined Water: Density, Thermal Expansion Coefficient, Compressibility, and Density Fluctuations

In this section, we discuss briefly the thermodynamic changes experienced by confined water itself as the temperature and plates separation vary. After all, it is the response of water to

13



changes in temperature and confining dimensions that leads to the WMI described in the previous sections. 3.3.1

Density and Thermal Expansion Coefficient

We focus, first, on the density of SPC/E and TIP4P/2005 water confined by the plates at r = 1.50 nm, at all temperatures studied. The density of confined water is defined as ρ = N m/Vconf where m = 18.016 g/mol is the mass of a water molecule. The confined volume is Vconf = A D where A is the plates area and D is the ‘effective’ separation between plates. It is known that Vconf is an ill-defined quantity (see, e.g., Ref. 33 ). The upper value of D is given by the true separation between plates, D = r = 1.50 nm. An alternative definition of D is to consider the thickness of the water film found between the plates, as determined from the density profile of water, ρslab (z). We find that ρslab (z) = 0 for approximately z = ±0.525 nm in all cases considered. This results in the lowest value for D, i.e. D = 1.05 nm. Since it is not evident what value of D and Vconf to consider, we will discuss the results for both cases D = 1.05 and 1.50 nm. Fig. 9a shows the density of confined water as function of temperature for both SPC/E and TIP4P/2005 water for D = 1.50 nm (up-triangles) and D = 1.05 nm (down-triangles). For comparison, we also show the density of bulk water at P = 0.1 MPa from experiments as well as for the SPC/E and TIP4P/2005 models. The main points of Fig. 9a are as follows. (i) The density of confined water ρconf (T ) is not sensitive to the water model employed. (ii) ρconf (T ) is very sensitive to the value of D considered and, depending on the value of D chosen, one may conclude that confined water has a larger (D = 1.05 nm) or lower (D = 1.50 nm) density than bulk water. However, we note that the maximum value of ρconf (T ) (D = 1.50 nm) is close to the density of bulk water, ρbulk (T ), while the minimum value of ρconf (T ) is much smaller than ρbulk (T ). (iii) Bulk water has a weak density maximum at 277 K. However, in agreement with previous simulation studies (e.g., 33,65 ), we find that ρconf (T ) increases monotonically upon cooling. In other words, under confinement, the

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density maximum of water is either removed or shifted to very low temperature. Computer simulations of a water-like monatomic liquid shows that both solvophobic and solvophilic confinement shift the phase diagram of the bulk liquid to lower temperatures. 66 In order to show the effect of confinement on the density of water, we include in Fig. 9b,c the average number of water molecules in the confined space as function of the plates separation, N (r), for all temperatures considered. N (r) is qualitatively independent of the water model employed. In particular, N (r) increases monotonically upon cooling at all separations studied. Accordingly, the behavior of ρconf (T ) shown is Fig. 9 for r = 1.50 nm holds, qualitatively, for all 0.62 < r < 1.50 nm. We also quantify the effects of temperature on the density of confined water by calculating the thermal expansion coefficient,

αPres

−1 ≡ ρ

∂ρ ∂T

Pres ,A,r

−1 = N

∂N ∂T

(4) Pres ,A,r

where Pres is the external or reservoir pressure (0.1 MPa). In order to calculate αPres , we first interpolate ρconf (T ) with a second order polynomial; this polynomial is then used to ∂ρ in Eq. 4. We stress that αPres is the thermal expansion coefficient at calculate ∂T Pres ,A,r

constant Pres (and constant r, A) and that Pres is not necessarily the same pressure acting on the confined liquid, e.g., along the direction perpendicular to the walls. In bulk liquids ∂ρ . the pressure is isotropic and the thermal expansion coefficient is just αP = −1 ρ ∂T P,N Fig. 10 shows αPres (r) for both water models at selected temperatures. In both cases,

the effect of temperature is rather negligible. The main point of Fig. 10 is the oscillatory behavior of αPres (r). Indeed, the behavior of αPres (r) is reminiscent of the behavior of F (r) shown Fig. 5. Such an oscillatory behavior in αPres (r) can be rationalized in terms of the changes in water structure, as confined water evolves from a tri-layer, to a bilayer and, finally, to a monolayer liquid.

15



3.3.2

Page 16 of 42

Compressibility and Density Fluctuations

The role of density fluctuations of nanoconfined and interfacial water has been the focus of previous computational studies (see e.g. 39,67,68 ) and it has been shown that density fluctuations (or local compressibility) at interfaces could be used to quantify the local hydrophobicity of a given surface. That water under hydrophobic (hydrophilic) confinement can exhibit enhanced (similar) compressibility relative to bulk water has been shown in Ref. 33 Next, we discuss the compressibility of water confined between the graphene plates as well as the effect of temperature and plates separations. Under the present conditions, water confined between the graphene plates corresponds to a system in the Grand Canonical Ensemble. For an (isotropic) system in such an ensemble the compressibility κT can be expressed as

κT =

V h∆N 2 i kB T hN i2

(5)

where h∆N 2 i = hN 2 i − hN i2 is the fluctuations in the number of molecules in the system. 69 Accordingly, we calculate the compressibility of confined water using Eq. 5. Fig. 11a shows κT as function of temperature for SPC/E and TIP4P/2005 water, for the case r = 1.50 nm. Included are the results for κT using the values D = 1.50 nm (up-triangles) and D = 1.05 nm (down-triangles) in Eq. 5. Within the noise of the data, it is apparent that (i) the results for both water models are comparable. In particular, (ii) the compressibility of confined water (r = 1.50 nm) is enhanced, relative to bulk water, at all temperatures studied. (iii) Consistent with Fig. 9a (where the density maximum of bulk water is shifted towards lower temperatures or removed at the nanoscale), the minimum of bulk water compressibility (at T ≈ 325 K) is either removed or shifted towards very low temperatures for the case of water confined by graphene plates. In order to show the effect of confinement on the compressibility of water, we include in Fig. 11b,c κT as function of the plates separation for all temperatures studied. At all

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separations, and for both water models considered, κT increases upon heating above T ≈ 320 K; at lower temperatures, variations in κT are within error bars. At least at T > 320 K, we also find that confinement at r < 1 nm largely increases water compressibility. This is evident in the limit r → dc (T ), i.e., as the water molecules are completely expelled from the confined space. Interestingly, within the noise of the data, we cannot identify an oscillatory behavior in κT as function of r. This may seem unexpected given that oscillations were observed in the plates PMF and αPres (r). If confirmed, this implies that the mean forces between plates, and the structure of confined water (i.e., trilayer, bilayer, monolayer) correlate with αPres (r) but not with κT (r).

3.4

Graphene plates with tuned hydrophobicity/hydrophilicity

Given that the water model plays a relevant role in the PMF between graphene plates, one may wonder what the effects are, if any, of altering the strength of water O-graphene C interactions. To address this question, we focus on the case of TIP4P/2005 water model at T = 300 K, and consider modified graphene plates with different water O-graphene C interaction strengths. Specifically, we re-scale the LJ ǫ-parameter of graphene C atoms, ǫC , by a constant k, i.e., ǫC → k × ǫ0C , where ǫ0C = 0.2363 kJ/mol is the corresponding value for the original graphene plates (see Table 1). We consider three modified graphene plates with k = 0.3, 0.7, 1.7 and list the resulting LJ parameters in Table 2. The contact angles of TIP4P/2005 water (at T = 300 K) in contact with these surfaces are θc = 1290 , 1080 , 730 for k = 0.3, 0.7, 1.7, respectively. It follows that, the graphene plates are hydrophobic for k = 0.3, 0.7 and hydrophilic (yet, apolar) for k = 1.7. The LJ pair potential between water O and graphene C is shown in the inset of Fig. 12a. Figs. 12a,b show the total PMF and water contribution to the total PMF at T = 300 K for all surfaces studied; the corresponding mean forces are shown in Fig. 12c. The effects of increasing the water O-graphene C attraction are as follows. Increasing k, (i) increases the depth of the PMF minima and height of the PMF maxima (Figs. 12a,b), i.e., tuning 17



the (apolar) surfaces more hydrophilic leads to the stabilization of those states where there is an integer number of water layers in the confined space. In addition, we find that (ii) dc changes considerably with increasing ǫCO . As shown in Fig. 13, dc shifts from dc ≈ 0.86 nm for the most hydrophobic surface (k = 0.3) to dc ≈ 0.58 nm for the most hydrophilic surface (k = 1.7). It follows from points (i) and (ii) that, as the surfaces become more hydrophilic, it is more difficult for the graphene plates to reach the collapse state. Regarding the formation of bilayer-ice at r ≈ 0.92 nm, it is found that (iii) the bilayer-ice is suppressed as the surface becomes more hydrophobic. This is indicated by the corresponding decrease in the PMF minimum at r = r2 = 0.92 nm. In particular, for our most hydrophobic surface (k = 0.3, θc = 1290 ), this PMF minimum becomes very shallow.

4

Conclusions

We characterized the effect of temperature on the water-mediated mean force and PMF between two nanoscale graphene plates at P = 0.1 MPa. Our MD simulations, based on two water models (TIP4P/2005 and SPC/E models), show that the PMF between graphene plates is an oscillatory function of the plates separation (Figs. 2 and 4) that is non-negligible for separations up to r ≈ 1.0−1.3 nm (240−400 K). The local minima of the PMF correspond to plates separations that accommodate zero (collapsed plates state), one, two, and three water layers. The energy barriers in the PMF that separate two stable states are associated to the expulsion of one water layer as the plates approach each other. The free energy barriers ∆Gact (T )/kB T were found to increase upon cooling linearly with 1/T . Similarly, the corresponding repulsive mean forces between the plates increase upon cooling (Figs.2c and 4c). Our results show that both isobaric cooling and heating tend to suppress the attraction and ultimate collapse of the graphene plates. However, the underlying mechanism that suppresses this attraction between the apolar plates depends on the specific (cooling- or

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heating-induced) process. Heating above ≈ 300 K flattens the plates PMF, i.e., it destabilizes the states that can accommodate an integer number of water layers between the graphene plates (including the collapse plates state) and reduces the range of interactions between the plates. Instead, cooling deepens local minima and increases the energy barriers in the PMF. As a result, cooling helps to kinetically trap the graphene plates at separations that can accommodate an integer number of water layers in the confined space. This is also consistent with the strengthening of water-water hydrogen bonds upon cooling, which leads to a hydrogen-bond network of water molecules more resistant to configurational changes. The range of temperatures studied are motivated by the well-known processes of coldand heating-induced protein denaturation, where the WMI between apolar domains (e.g., hydrophobic interactions) play a fundamental role. Although one must be cautious when extending results obtained with idealized surfaces, such as our graphene plates, to the case of biological surfaces, such as proteins, it is noteworthy that the present results may provide an explanation of the different role played by water during heating- and cooling-induced protein-denaturation (see, e.g., Ref. 70 ). Of particular interest is the role played by the water model in the WMI between graphene plates. Specifically, we found that at approximately T > 300 K, the PMF between plates is rather independent of the water model employed. However, at low temperatures the PMF may be affected by crystallization. Specifically, in the presence of TIP4P/2005 water, confined water crystallizes into a defective bilayer ice; crystallization occurs rapidly for plates separations of ≈ 0.92 nm. Instead, in the case of SPC/E water, confined water remains in the liquid state. It has been shown that the crystallization temperature of nanoconfined and bulk water may be considerably different (see, e.g., Ref. 71 ). Yet, the crystallization of nanoconfined TIP4P/2005 water, but not of nanoconfined SPC/E water, is consistent with the corresponding crystallization temperatures of T ≈ 252 K (TIP4P/2005) and T = 215 K (SPC/E) water. 72 It is difficult to imagine that bilayer ice (Fig. 7a) may form in the case of water confined by biological surfaces. After all, crystallization is very sensitive to surface

19



chemistry, surface curvature, and confining dimensions. However, we do not discard the possibility that bilayer water may reach some kind of vitrified or slow-diffusive liquid state. We also included in this work a brief description of the behavior of water confined between the graphene plates. In agreement with previous studies, nanoscale confinement eliminates many of water anomalous properties, such as the presence of a density maximum. In particular, we observe that some properties such as the thermal expansion coefficient of nanoconfined water αPres (r) exhibits an oscillatory dependence on the separation distance between the plates, in analogy to the oscillatory behavior of the plates PMF. Instead, such an oscillatory behavior is not evident in other thermodynamic properties, such as water compressibility, κT (r). Interestingly, we found that both αPres (r) and κT (r) increase sharply as r → dc (T ), i.e., as water is expelled between the plates (dewetting).

5

Supporting Information

Additional material is included showing the close relationship between the graphene plates PMF and the formation of water layers between the plates.

Acknowledgments Support for this project was provided by the National Science Foundation (CBS-1604504) and by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York. This research was supported, in part, by a grant of computer time from the City University of New York High Performance Computing Center under NSF Grants CNS-0855217, CNS-0958379 and ACI-1126113.

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References (1) Dill, K. A.; Bromberg, S. Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology; Garland Science: New York, 2003. (2) Ball, P. Water as a Biomolecule. ChemPhysChem 2008, 9, 2677-2685. (3) Levy, Y.; Onuchic, J. N. Water Mediation in Protein Folding and Molecular Recognition. Annu. Rev. Biophys. Biomol. Struct. 2006, 35, 389-415. (4) Rasaiah, J. C.; Garde, S.; Hummer, G. Water in Nonpolar Confinement: from Nanotubes to Proteins and Beyond. Annu. Rev. Phys. Chem. 2008, 59, 713-740. (5) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley: New York, 1980. (6) Kauzmann, W. Some Factors in the Interpretation of Protein Denaturation. Adv. Protein Chem. 1959, 14, 1-63. (7) Ben-Naim, A. Hydrophobic Interactions; Plenum: New York, 1980. (8) Berne, B. J.; Weeks, J. D.; Zhou, R. Dewetting and Hydrophobic Interaction in Physical and Biological Systems. Annu. Rev. Phys. Chem. 2009, 60, 85-103. (9) Ashbaugh, H. S.; Pratt, L. R. Scaled Particle Theory and the Length Scales of Hydrophobicity. Rev. Mod. Phys. 2006, 78, 159-178. (10) Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly. Nature 2005, 437, 640-647. (11) Brandem, C.; Tooze, J. Introduction to Protein Structure; Garland Publishing: New York, 1998. (12) Structure and Dynamics of Mambranes, Handbook of Biological Physics; Lipowsky, R., Sackmann, E., Eds.; Elsevier: Amsterdam, 1995. 21



(13) Harpham, M. R.; Ladanyi, B. M.; Levinger, N. E.; Herwig, K. W. J. Water Motion in Reverse Micelles Studied by Quasielastic Neutron Scattering and Molecular Dynamics Simulations. Chem. Phys. 2004, 121, 7855-7868. (14) Whitesides, G. M.; Grybowski, B. Self-assembly at all Scales. Science 2002, 295, 24182421. (15) Rabani, E.; Reichman, D. R.; Geissler, P. L.; Brus, L. E. Drying-Mediated SelfAssembly of Nanoparticles. Nature 2003, 436, 271-274. (16) Tirrel, M. Modular Materials by Self-Assembly. AIChE Journal 2005, 51, 2386-2390. (17) Giovambattista, N.; Debenedetti, P. G.; Rossky, P. J. Hydration Behavior under Confinement by Nanoscale Surfaces with Patterned Hydrophobicity and Hydrophilicity. J. Phys. Chem. C 2007, 111, 1323-1332. (18) Hua, L.; Zangi, R.; Berne, B. J. Hydrophobic Interactions and Dewetting between Plates with Hydrophobic and Hydrophilic Domains. J. Phys. Chem. C 2009, 113, 5244-5253. (19) Lum, K.; Chandler, D.; Weeks, J. D. Hydrophobicity at Small and Large Length Scales. J. Phys. Chem. B 1999, 103, 4570-4577. (20) Zangi, R. J. Driving Force for Hydrophobic Interaction at Different Length Scales. J. Phys. Chem. B 2011, 115, 2303-2311. (21) Li, L.; Bedrov, D.; Smith, G. D. Water-Induced Interactions between Carbon Nanoparticles. J. Phys. Chem. B 2006, 110, 10509-10513. (22) Hummer, G.; Garde, S.; Garc´ıa, A. E.; Paulaitis, M. E.; Pratt, L. R. The Pressure Dependence of Hydrophobic Interactions is Consistent with the Observed Pressure Denaturation of Proteins. Proc. Natl. Acad. Sci. USA 1998, 95, 1552-1555.

22


Page 22 of 42

Page 23 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(23) Ghosh, T.; Garc´ıa, A. E.; Garde, S. Enthalpy and Entropy Contributions to the Pressure Dependence of Hydrophobic Interactions. J. Chem. Phys. 2002, 116, 2480-2486. (24) Silva, J. L.; Foguel, D.; Royer, C. A. Pressure Provides New Insights into Protein Folding, Dynamics and Structure. Trends in Biochem. Sci. 2001, 26, 612-618. (25) Ghosh, T.; Garc´ıa, A. E.; Garde, S. J. Water-Mediated Three-Particle Interactions between Hydrophobic Solutes: Size, Pressure, and Salt Effects. J. Phys. Chem. B 2003, 107, 612-617. (26) Ghosh, T.; Garc´ıa, A. E.; Garde, S. Molecular Dynamics Simulations of Pressure Effects on Hydrophobic Interactions. J. Am. Chem. Soc. 2001, 123, 10997-11003. (27) Shimizu, S.; Chana, H. S. Temperature Dependence of Hydrophobic Interactions: A Mean Force Perspective, Effects of Water Density, and Nonadditivity of Thermodynamic Signatures. J. Chem. Phys. 2000, 113, 4683-4700. (28) Zangi, R.; Berne, B. J. Temperature Dependence of Dimerization and Dewetting of Large-Scale Hydrophobes: A Molecular Dynamics Study. J. Phys. Chem. B 2008, 112, 8634-8644. (29) Koishi, T.; Yoo, S.; Yasuoka, K.; Zeng, X. C.; Narumi, T.; Susukita, R.; Kawai, A.; Furusawa, H.; Suenaga, A.; Okimoto, N., et al.; Nanoscale Hydrophobic Interaction and Nanobubble Nucleation. Phys. Rev. Lett. 2004, 93, 185701. (30) Zangi, R.; Hagen, M.; Berne, B. J. Effect of Ions on the Hydrophobic Interaction between Two Plates. J. Am. Chem. Soc. 2007, 129, 4678-4686. (31) Lund, M.; Jungwirth, P.; Woodward, C. E. Ion Specific Protein Assembly and Hydrophobic Surface Forces. Phys. Rev. Lett. 2008, 100, 258105.

23



(32) Panick, G.; Vidugiris, G. J. A.; Malessa, R.; Rapp, G.; Winter, R.; Royer, C. A. Exploring the Temperature-Pressure Phase Diagram of Staphylococcal Nuclease. Biochemistry 1999, 38, 4157-4164. (33) Giovambattista, N.; Rossky, P. J.; Debenedetti, P. G. Effect of Pressure on the Phase Behavior and Structure of Water Confined between Nanoscale Hydrophobic and Hydrophilic Plates. Phys. Rev. E 2006, 73, 041604. (34) Giovambattista, N.; Rossky, P. J.; Debenedetti, P. G. Phase Transitions Induced by Nanoconfinement in Liquid Water. Phys. Rev. Lett. 2009, 102, 050603. (35) Choudhury, N.; Pettitt, M. On the Mechanism of Hydrophobic Association of Nanoscopic Solutes. J. Am. Chem. Soc. 2005, 127, 3556-3567. (36) Lu, L.; Berkowitz, M. L. Hydration Force between Model Hydrophilic Surfaces: Computer Simulations. J. Chem. Phys. 2006, 124, 101101. (37) Sharma, S.; Debenedetti, P. G. Evaporation Rate of Water in Hydrophobic Confinement. Proc. Natl. Acad. Sci. USA 2012, 109, 4365-4370. (38) Li, L.; Bedrov, D.; Smith, G. D. A Molecular-Dynamics Simulation Study of SolventInduced Repulsion between C60 Fullerenes in Water. J. Chem. Phys. 2005, 123, 204504. (39) Eun, C.; Berkowitz. M. L. Fluctuations in Number of Water Molecules Confined between Nanoparticles. J. Phys. Chem. B 2010, 114, 13410-13414. (40) Hess, B.; Kutzner, C.; Van Der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory and Computation 2008, 4, 435-447. (41) Berendsen, H. J. C.; Grigera, J. R.; Stroatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269-6271.

24


Page 24 of 42

Page 25 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(42) Abascal, J. L. F.; Vega, C. A General Purpose Model for the Condensed Phases of Water: TIP4P/2005. J. Chem. Phys. 2005, 123, 234505. (43) Willard, A. P.; Chandler, P. Instantaneous Liquid Interfaces. J. Phys. Chem. B 2010, 114, 1954-1958. (44) Godawat, R.; Jamadagni, S. N.; Garde, S. Characterizing Hydrophobicity of Interfaces by Using Cavity Formation, Solute Binding, and Water Correlations Proc. Natl. Acad. Sci. USA 2010, 106, 15119-15124. (45) Remsing, R. C.; Xia, E.; Vembanur, S.; Sharma, S.; Debenedetti, P. G.; Garde, S.; Patel, A. J. Pathways to Dewetting in Hydrophobic Confinement. Proc. Natl. Acad. Sci. USA 2015, 112, 8181-8186. (46) Vanzo, D.; Bratko, D.; Luzar, A. Dynamic Control of Nanopore Wetting in Water and Saline Solutions under an Electric Field. J. Phys. Chem. B 2015, 119, 8890-8899. (47) Starr, F. W.; Sciortino, F.; Stanley, H. E. Dynamics of Simulated Water under Pressure. Phys. Rev. E 1999, 60, 6757-6768. (48) Pathak, H.; Palmer, J. C.; Schlesinger, D.; Wikfeldt, K. T.; Sellberg, J. A.; Pettersson, L. G. M.; Nilsson, A. The Structural Validity of Various Thermodynamical Models of Supercooled Water. J. Chem. Phys. 2016, 145, 134507. (49) Biddle, J. W.; Singh, R. S.; Sparano, E. M.; Ricci, F.; Gonz´alez, M. A.; Valeriani, C.; Abascal, J. F.; Debenedetti, P. G.; Anisimov, M. A.; Caupin, F. Two-Structure Thermodynamics for the TIP4P/2005 Model of Water Covering Supercooled and Deeply Stretched Regions. J. Chem. Phys. 2017, 146, 034502. (50) Sanz, E.; Vega, C.; Espinosa, J. R.; Caballero-Bernal, R.; Abascal, J. L. F.; Valeriani, C. Homogeneous Ice Nucleation at Moderate Supercooling from Molecular Simulation. J. Am. Chem. Soc. 2013, 135, 15008-15017. 25



(51) Wong, J.; Jahn, D. A.; Giovambattista, N. Pressure-Induced Transformations in Glassy Water: A Computer Simulation Study Using the TIP4P/2005 Model. J. Chem. Phys. 2015, 143, 074501. (52) Engstler, J.; Giovambattista, N. Heating- and Pressure-Induced Transformations in Amorphous and Hexagonal Ice: A Computer Simulation Study Using the TIP4P/2005 Model. J. Chem. Phys. 2017, 147, 074505. (53) Abascal, J. L. F.; Vega, C. Dipole-Quadrupole Force Ratios Determine the Ability of Potential Models to Describe the Phase Diagram of Water. Phys. Rev. Lett. 2007, 98, 237801. (54) Sanz, E.; Vega, C.; Abascal, J. L. F.; MacDowell, L. G. Phase Diagram of Water from Computer Simulation. Phys. Rev. Lett. 2004, 92, 255701. (55) Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. J. On the Water-Carbon Interaction for Use in Molecular Dynamics Simulations of Graphite and Carbon Nanotubes. J. Phys. Chem. B 2003, 107, 1345-1352. (56) Giovambattista, N.; Almeida, A. B.; Alencar, A. M.; Buldyrev, S. V. Validation of Capillarity Theory at the Nanometer Scale by Atomistic Computer Simulations of Water Droplets and Bridges in Contact with Hydrophobic and Hydrophilic Surfaces. J. Phys. Chem. C 2016, 120, 1597-1608. (57) Giovambattista, N.; Debenedetti, P. G.; Rossky, P. J. Effect of Surface Polarity on Water Contact Angle and Interfacial Hydration Structure. J. Phys. Chem. B 2007, 111, 9581-9587. (58) Taherian, F.; Marcon, V.; van der Vegt, N. F. A. What Is the Contact Angle of Water on Graphene? Langmuir 2013, 29, 1457-1465.

26


Page 26 of 42

Page 27 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(59) Accordino, S. R.; Montes de Oca, J. M.; Rodriguez Fris, J. A. Appignanesi, G. A. Hydrophilic Behavior of Graphene and Graphene-Based Materials. J. Chem. Phys. 2015, 143, 154704. (60) Levine, I. N. Physical Chemistry; McGraw-Hill: New York, 2002. (61) Zangi, R. Driving Force for Hydrophobic Interaction at Different Length Scales. J. Phys. Chem. B 2011, 115, 2303-2311. (62) Walqvist, A.; Berne, B. J. Computer Simulation of Hydrophobic Hydration Forces on Stacked Plates at Short Range. J. Phys. Chem. 1995, 99, 2893-2899. (63) Choudhury, N.; Pettitt, M. The Dewetting Transition and the Hydrophobic Effect. J. Am. Chem. Soc. 2007, 129, 4847-4852. (64) Gao, Z.; Giovambattista, N.; Sahin, O. Phase Diagram of Water Confined by Graphene. Sci. Rep. 2018, 8, 6228. (65) Kumar, P.; Buldyrev, S. V.; Starr, F. W.; Giovambattista, N.; Stanley, H. E. Thermodynamics, Structure, and Dynamics of Water Confined between Hydrophobic Plates. Phys. Rev. E 2005, 72, 051503. (66) Sun, G.; Giovambattista, N.; Xu, L. Confinement Effects on the Liquid-Liquid Phase Transition and Anomalous Properties of a Monatomic Water-Like Liquid. J. Chem. Phys. 2015, 143, 244503. (67) Sarupria, S.; Garde, S.; Quantifying Water Density Fluctuations and Compressibility of Hydration Shells of Hydrophobic Solutes and Proteins. Phys. Rev. Lett. 2009, 103, 037803. (68) Patel, A. J.; Varilly, P.; Chandler, D. Fluctuations of Water near Extended Hydrophobic and Hydrophilic Surfaces. J. Phys. Chem. B 2010, 114, 1632-1637.

27



(69) Pathria, R. K.; Statistical Mechanics; Butterworth-Heinemann: Oxford, 2001. (70) Kim, S. B.; Palmer, J. C.; Debenedetti, P. G. Computational Investigation of Cold Denaturation in the Trp-Cage Miniprotein. Proc. Natl. Acad. Sci. 2016, 113, 89918996. (71) Giovambattista, N.; Rossky, P. J.; Debenedetti, P. G. Computational Studies of Pressure, Temperature, and Surface Effects on the Structure and Thermodynamics of Confined Water. Annu. Rev. Phys. Chem. 2012, 63, 179-200. (72) Vega, C.; Sanz, E.; Abascal, J. L. F. The Melting Temperature of the Most Common Models of Water. J. Phys. Chem. 2005, 122, 114507. (73) R. A. Fine and F. J. Millero, Compressibility of Water as a Function of Temperature and Pressure. J. Phys. Chem. 1973, 59, 5529-5536. (74) Speedy, R. J.; Angell, C. A. Isothermal Compressibility of Supercooled Water and Evidence for a Thermodynamic Singularity at −450 C. J. Chem. Phys. 1976, 65, 851858.

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Table 1: Lennard-Jones interaction parameters, σCO and ǫCO , between water O and graphene C atomsa . Water Model SPC/E TIP4P/2005

a

ǫ0C 0.2363 0.2363

σC0 0.3214 0.3214

ǫO 0.6500 0.7749

σO 0.3166 0.3159

ǫCO 0.3919 0.4279

Parameters are given by the Lorentz-Berthelot combination rules, ǫCO =

σCO 0.3190 0.3186

θc 970 960

p ǫ0C ǫO and σCO =

0 σC +σO , 2

0 where (ǫ0C , σC ) and (ǫO , σO ) are the LJ parameters of the graphene C atoms and water O atoms, respectively.

θc is the contact angle of water in contact with graphene at T = 300 K. Values of ǫ and σ are given in kJ/mol and nm, respectively.

Table 2: Lennard-Jones interaction parameters, σCO and ǫCO , between water O and C atoms of the modified graphene platesa . k 0.3 0.7 1.7

a

ǫC 0.0709 0.1654 0.4018

ǫCO 0.2344 0.3580 0.5580

θc 1290 1080 730

Parameters are given by the Lorentz-Berthelot combination rules, ǫCO =

√

ǫC ǫO and σCO =

σC +σO , 2

with ǫC = k × ǫ0C ; ǫ0C is the LJ parameters of the original graphene plates (see Table 1). In all modified 0 surfaces, σC = σC , as for the original graphene plates (see Table 1). (ǫO , σO ) are the LJ parameters of water

O atoms in the TIP4P/2005 model (see Table 1). θc is the contact angle of TIP4P/2005 water in contact with the modified graphene model surfaces at T = 300 K. Values of ǫ and σ are given in kJ/mol and nm, respectively.

29



Figure 1: (a) Top view of one of the graphene plates used in this work. (b) Snapshot of the system studied showing the two graphene plates immersed in an orthorhombic box filled with water molecules; the plates separation is 1.5 nm. The graphene plates are immobile and are located symmetrically with respect to the center of the box, parallel to the xy-plane.

30


Page 30 of 42

Page 31 of 42

50

(a) SPC/E

PMFTOTAL/kBT

0 PMFTOTAL [kJ/mol]

-50 -100 -150 -200 0.2

0.4

0 -100 -200 -300 -400 0.2 0.4 0.6 0.8

1

1.2 1.4

0.6

0.8 1 r [nm]

1.2

1.4

(b) SPC/E

0 -50 -100 -150 0.2

30

2

100

r [nm]

PMFWATER [kJ/mol]

PMFWATER/kBT

50

F(r) [10 kJ/mol/nm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

100 50 0 -50 -100

0.6

0.2 0.4 0.6 0.8 1 1.2 1.4 r [nm]

0.8 1 r [nm]

(c) SPC/E

1.2

1.4

T=240 K T=260 K T=300 K T=360 K T=400 K No Water

20 10 0 -10 -20 0.2

0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 2: (a) Total PMF between the graphene plates immersed in SPC/E water at different temperatures. For better comparison, the total PMF is divided by the thermal energy, kB T . The total PMF without the factor 1/kB T is shown in the inset and main panel (dashed-line). (b) Contribution to the total PMF due solely to water. (c) Mean force acting on the plates. Dashed-lines in (a) and (c) are the total PMF and mean force between the graphene plates in vacuum.

31



∆GBARRIER/kBT

200

(a) SPC/E 1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

150 100 50 0 2.5

200 ∆GBARRIER/kBT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 42

3

3.5 -1 1000/T [K ]

4

(b) TIP4P/2005 1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

150 100 50 0 2.5

3

3.5

4

-1

1000/T [K ]

Figure 3: (a) Temperature-dependence of the activation free energies obtained from the total PMFs shown in Fig. 2a for the case where the graphene plates are immersed in SPC/E water. (b) Activation energies for the plates immersed in TIP4P/2005 water taken from Fig. 4a. Activation free energies correspond to the process of changing the plates separation from ri to rj (j = i ± 1), where ri is the location of the i-th minima of the total PMF. i and j are given in the figure labels. In all cases, the energy barriers increase upon cooling, disfavoring (i.e., making kinetically more difficult) the collapse of the graphene plates.

32


Page 33 of 42

(a) TIP4P/2005

0 -50

PMFTOTAL [kJ/mol]

PMFTOTAL/kBT

50

-100 -150 -200 0.2

0.4

0 -100 -200 -300 -400 0.2 0.4 0.6 0.8

1

1.2 1.4

0.6

0.8 1 r [nm]

1.2

1.4

(b) TIP4P/2005

0 -50 -100 -150 0.2

30

2

100

r [nm]

PMFWATER [kJ/mol]

PMFWATER/kBT

50

F(r) [10 kJ/mol/nm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

100 0 -100 0.2 0.4 0.6 0.8 1 1.2 1.4 r [nm]

0.6

0.8 1 r [nm]

1.2

1.4

T=240 K T=260 K T=280 K T=300 K T=320 K T=360 K T=400 K No Water

(c) TIP4P/2005

20 10 0 -10 -20 0.2

0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 4: Same as Fig. 2 for the case where the graphene plates are immersed in TIP4P/2005 water.

33


0 -50 -100 -150 -200

Page 34 of 42

(a) T=400 K

0 -50 -100 -150 -200 0 -50 -100 -150 -200 0.2

(b) T=300 K

(c) T=240 K 0.4

0.6

0.8

1

1.2

1.4

r [nm]

2

F(r) [10 kJ/mol]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

PMFTOTAL/kBT


10 0 -10 -20

(d) T=400 K

10 0 -10 -20

(e) T=300 K

10 0 -10 -20

(f) T=240 K

0.2

0.4

0.6

0.8

1

1.2

1.4

r [nm]

Figure 5: Comparison of the (a)(b)(c) total PMF and (d)(e)(f) mean force between the graphene plates immersed in SPC/E (dashed lines) and TIP4P/2005 water (solid lines). Data is taken from Figs. 2 and 4. The minimum in the total PMF at r = 0.92 nm becomes more pronounced when the graphene plates are immersed in TIP4P/2005 water. At this plates separation, and for T = 240 K, TIP4P/2005 crystallizes between the plates while SPC/E water remains in the liquid state.

34


2.5

2

MSD [nm ]

2

100

(a) TIP4P/2005 T=240 K

0 -100 -200

1.5

0.3

0.6

0.9 r [nm]

1.2

1 0.5 0 1

1.5

2

2.5 t [ns]

N(t)

3

3.5

4

(b) TIP4P/2005

60

T=240 K

40

20

0 1

1.5

2

2.5 t [ns]

3

3.5

3

4

r=0.62nm r=0.66nm r=0.72nm r=0.80nm r=0.86nm r=0.92nm r=1.00nm r=1.12nm

4 (c) TIP4P/2005 T=240 K 3.5 ρslab(z) [g/cm ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PMFTOTAL [kJ/mol]

Page 35 of 42

3 2.5 2 1.5 1 0.5 0

-0.4

-0.2

0 z [nm]

0.2

0.4

Figure 6: (a) Mean-square displacement of TIP4P/2005 water confined between the graphene plates (see text) at different plates separations r and for T = 240 K. (b) The corresponding average number of molecules that remain between the plates during the time interval 1−4 ns, As the plates separation r → 0.92 nm, the MSD and N (t) approach an asymptotic finite value indicating that TIP4P/2005 water crystallizes. (c) Density profile of water confined between the graphene plates; at r = 0.92 nm confined water forms a defective bilayer ice (T = 240 K).

35



Figure 7: Snapshots of TIP4P/2005 water confined by graphene plates at T = 240 K and (a) r = 0.92, (b) r = 0.86 and (c) r = 1.00 nm. (d) Snapshots of SPC/E water confined by graphene plates at T = 240 K and r = 0.96 nm. Only TIP4P/2005 water confined at r = 0.92 nm forms a defective bilayer ice.

36


Page 36 of 42

Page 37 of 42

(a) TIP4P/2005 r=0.92nm

2

MSD [nm ]

2

T=240 K T=260 K T=280 K T=300 K T=320 K T=360 K T=400 K

1.5 1 0.5 0 1

1.5

2

2.5 t [ns]

3

3.5

4

(b) TIP4P/2005

N(t)

60

r=0.92 nm

40

20

0 1

3

ρslab(z) [g/cm ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

1.5

2

2.5 t [ns]

3

3.5

4

(c) TIP4P/2005 r=0.92 nm

-0.4

-0.2

0 z [nm]

0.2

0.4

Figure 8: Temperature effects on the crystallization of confined TIP4P/2005 water at plates separation r = 0.92 nm: (a) Mean-square displacement of TIP4P/2005 water, (b) average number of water molecules that remain between the plates during the time interval 1 − 4 ns. (c) Density profile of water confined between the graphene plates. Crystallization into a defective bilayer ice can be observed only at T < 260 K.

37



3

Density [g/m ]

1.2

(a) r=1.50 nm

1.1 1 0.9 0.8 0.7 0.6

250

300

350

400

T [K]

N(r)

100 50

T=240 K T=260 K T=300 K T=360 K T=400 K

(b) SPC/E 0 100 N(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 42

50

T=240 K T=260 K T=280 K T=300 K T=320 K T=360 K T=400 K

(c) TIP4P/2005 0

0.6

0.8

1 r [nm]

1.2

1.4

Figure 9: (a) Density of water confined between the graphene plates as function of temperature. The densities for SPC/E (blue triangles) and TIP4P/2005 water (black triangles) are identical within error bars. Down- and up-triangles are, respectively, the densities defined with an effective separation between the plates of D = 1.05 nm and D = r = 1.50 nm. For comparison, we also include the density of bulk water as measured in experiments (red circles), and in both TIP4P/2005 (dashed black circles) 42 and SPC/E water 47 (blue circles). (b)(c) Average number of molecules in the confined volume as function of the plates separation r, for all temperatures studied.

38


-4 -4

αPres [10 /K]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


αPres [10 /K]

Page 39 of 42

80

(a) SPC/E

60 40 20 0 80

T=240 K T=300 K

60

(b) TIP4P/2005

40 20 0

0.6

0.8

1 r [nm]

1.2

1.4

Figure 10: Thermal expansion coefficient of water confined between the graphene plates at constant external (reservoir) pressure (0.1 MPa) and as function of the plates separation. For comparison, we note that the standard isobaric thermal expansion coefficient for bulk water is αP = −1/ρ (∂ρ/∂T )P ≈ 3.0 × 10−4 1/K as measured in experiments, while αPres = 9.0 × 10−4 K−1 for r > 1.5 nm in both TIP4P/2005 and SPC/E water. The dashed-line indicates the smallest r below which no water is found between the graphene plates.

39



1.8

(a) r=1.50 nm

κT [1/GPa]

1.5 1.2 0.9 0.6 0.3

250

300

350

400

κT [1/GPa]

T [K]

κT [1/GPa]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 42

10 8 6 4 2 0 10 8 6 4 2 0

0.6

0.8

T=240 K T=260 K T=300 K T=360 K T=400 K

(b) SPC/E

T=240 K T=260 K T=280 K T=300 K T=320 K T=360 K T=400 K

(c) TIP4P/2005

1 r [nm]

1.2

1.4

Figure 11: (a) Compressibility of water confined between the graphene plates as function of temperature. The densities for SPC/E (blue triangles) and TIP4P/2005 water (black triangles) are comparable within the noise in the data. Down- and up-triangles are, respectively, the densities defined with an effective separation between the plates of D = 1.05 nm and D = r = 1.50 nm. For comparison, we also include κT for bulk water as measured in experiments (red circles 73 and line 74 ) and for TIP4P/2005 (black circle). 42 (b)(c) Compressibility of confined water as function of the plates separation r and for all temperatures studied.

40


Page 41 of 42

100

-100

(a) TIP4P/2005 T=300 K

-200

UCO(r) [kJ/mol]

PMFTOTAL [kJ/mol]

0

-300 -400 -500

PMFWATER [kJ/mol]

-600 0.2

1 0.5 0 -0.5 0.2

0.4

0.6

0.4

0.8 1 r [nm]

0.6 r [nm]

0.8

1.2

1.4

100

0

-100

(b) TIP4P/2005 T=300 K

-200 0.2

0.4

0.6

0.8

1

1.2

1.4

r [nm] 40

2

F(r) [10 kJ/mol/nm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30

k = 0.3 k = 0.7 k = 1.0 k = 1.7

20 10 0 -10 -20

(c) TIP4P/2005

-30

T=300 K

-40 0.2

0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 12: (a) Total PMF between modified graphene plates where the Lennard-Jones parameter ǫC for the graphene C atoms are re-scaled by a constant k (the corresponding water contact angles are θc = 1290 , 1080 , 960 , 730 for k = 0.3, 0.7, 1.0, 1.7, respectively; see Table 2). The LJ pair potential between water O atoms and graphene C atoms are included in the inset. (b) Water contribution to the total PMF and (c) mean force between the modified graphene plates. The original graphene plates correspond to the case k = 1. Dashed-lines in (a) and (c) are the PMF and mean force between the plates in vacuum.

41



120 100 k=0.3 k=0.7 k=1.0 k=1.7

80 N(r)

60 40 20 0.2

0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 13: Average number of molecules between the modified graphene plates of Fig. 12. The largest plates separation at which N (r) = 0 defines the critical distance dc at which water is expelled between the plates (dewetting). dc depends strongly on the the water Ographene C interaction or, alternatively, on the surface hydrophobicity/hydrophilicity, which is quantified by the parameter k; see Table 2.

(Potential of Mean Force)/kBT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 42

50 0 -50

T=400 K T=360 K T=320 K T=300 K T=280 K T=260 K T=240 K

Defective Ice

-100 -150 -200 0.2

0.4

0.6

0.8

1

1.2

Plates Separation [nm]

Figure 14: TOC graphic.

42


1.4

Temperature Effects on Water-Mediated Interactions at the Nanoscale

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