Comparative Study of the Effects of Temperature ... - ACS Publications

Subscriber access provided by UNIV OF BARCELONA

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

A Comparative Study of the Effects of Temperature and Pressure on the Water-Mediated Interactions between Apolar Nanoscale Solutes Justin Engstler, and Nicolas Giovambattista J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b10296 • Publication Date (Web): 28 Dec 2018 Downloaded from http://pubs.acs.org on January 5, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 44 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

The Journal of Physical Chemistry

A Comparative Study of the Effects of Temperature and Pressure on the Water-Mediated Interactions between Apolar Nanoscale Solutes 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 (MD) simulations to study the effects of temperature and pressure on the water-mediated interaction (WMI) between two nanoscale (apolar) graphene plates at 240 ≤ T ≤ 400 K and −100 ≤ P ≤ 1200MPa. These are thermodynamic conditions relevant to, e.g., cooling-, heating-, compression-, and decompression-induced protein denaturation. We find that at all (T, P ) studied, the potential of mean force (PMF) between the graphene plates, as function of the plates separations r, exhibits local minima at specific plates separations r = rn that can accommodate n water layers (n = 0, 1, 2, 3). In particular, our results show that isobaric cooling and isothermal compression have a similar effect on the WMI between

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

the plates; both processes tend to suppress the attraction and ultimate collapse of the graphene plates by kinetically trapping the plates at the metastable states with r = rn (n > 0). In addition, isobaric heating and isothermal decompression also have a similar effect; both processes tend to reduce the range and strength of the interactions between the graphene plates. Interestingly, at low temperatures, the WMI between the plates are affected by crystallization. However, crystallization depends deeply on the water model considered, SPC/E and TIP4P/2005 water models, with crystallization occurring at different (T, P ) conditions, into different forms of ice.

1

Introduction

Self-assembly processes in aqueous solutions play a critical role in nature as well as in many scientific and engineering applications (see, e.g., Refs. 1–6 ). Examples include protein aggregation, 7 protein folding/misfolding, 8–10 micelles and cell membrane formation, 4 and the assembly of nanoparticles and colloids into specific structures. 11–13 These processes are driven by water-mediated interactions (WMI) between the corresponding interacting units, e.g., nanoparticles and biomolecules. Accordingly, changes in the aqueous environment, such as the addition of salt 14,15 or variations in the working conditions (e.g., changes in pH, T , P ), 16–23 can profoundly affect the effective forces between the interacting units and the corresponding final arrangement. The effects of temperature and pressure are particularly relevant in self-assembly processes in aqueous solutions as well as in the aggregation of biomolecules and phase separation processes. For example, proteins can remain in their functional, native (folded) state only at relatively low pressures and small range of temperatures. 24–26 Excessive isobaric heating or cooling, and isothermal compression or decompression can induce the denaturation of the protein, affecting its biological function. 27,28 Fig. 1 is a schematic phase diagram for proteins proposed by Hawley 29 based on the assumption that proteins have only two different states, folded and unfolded. The ‘elliptical’ solid line in the figure separates the thermody2


Page 2 of 44

Page 3 of 44 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


namic states where the protein is in its native state from the non-native, unfolded states. The four arrows in the figure represent thermodynamic paths that have been followed in experiments to study protein denaturation. The red and green arrows represent, respectively, the well-known processes of heating- and compression-induced protein denaturation, which are rather expected phenomena and have been studied extensively in the past (see, e.g., Refs. 16,17,28,30–32 ). The process of cooling-induced protein denaturation, indicated by the blue arrow, is less intuitive and it is still not fully understood. 26 The magenta arrow in the figure represents the process of decompression-induced protein denaturation at negative pressure (tension), which has been observed for the case of the protein ubiquitin. 33 Phase diagrams consistent with the phase diagram of Fig. 1 are found in many globular proteins (see, e.g., Refs. 27–29 ). It may not be surprising that such a protein phase diagram is indeed intimately related to the effects of T and P on the WMI among the protein residues. 25,31 For example, an important contribution to cold protein denaturation is the weakening of the effective attraction between buried hydrophobic residues and the associated penetration of water between hydrophobic contacts. 34–36 Evidence that water plays a fundamental role in protein-denaturation is provided by protein-like lattice 37–39 and coarse-grained models 40 that include explicitly a water-like solvent. 37–39 These model systems, while simple, can exhibit a phase diagram consistent with the phase diagram of Fig. 1. Protein phase diagrams with parabolic shape (at positive pressures) have been obtained in coarse-grained models of proteins with implicit WMI taken into consideration. Specifically, in Ref. 41 the coarse-grained ‘associative memory, water mediated, structure and energy model’ (AWSEM) is employed to study the stability of two different proteins, ubiquitin and λ-represor, in the T -P plane. The AWSEM is a coarse-grained force field that has been optimized using energy landscape algorithms based on a database of solved protein structures obtained from experiments. 42 However, the interactions in the AWSEM force field are valid near physiological conditions. In Ref., 41 it is shown that by adding explicit contributions to the AMSEM force field that take into consideration the effects of T and P on the WMI between the

3



protein residues, one obtains parabolic phase diagrams for ubiquitin and λ-represor that are consistent with experiments (and with Fig. 1). In this work, partially motivated by the phenomena of cooling-, heating-, compression-, and decompression-induced protein denaturation (Fig. 1), we perform molecular dynamics simulations to study the effects of T and P on the WMI interactions between two apolar nanoscale solutes. Specifically, we study the mean forces and potential of mean force between two graphene plates immersed in water (Fig. 2), over a wide range of T and P . Our aim is to compare quantitatively the changes in the WMI between apolar surfaces along (i) isothermal compression/decompression, and (ii) isobaric cooling/heating thermodynamic paths. By using simple model surfaces, we avoid the complexity of biological surfaces. Numerous computational studies (see, e.g. Refs. 5,18,43–51 ) have employed simple model surfaces to study different aspects of WMI as well as water hydration in confined geometries, providing very insightful results that helped in our understanding of more complex aqueous systems. However, to our knowledge, a systematic study of WMI that compares the effects of T and P over a wide range of working conditions is not available. In this regard, we note that employing the same model system is necessary if one wants to compare quantitatively how T and P affect WMI since the behavior of nanoconfined water can be largely affected by surface details. 52 The present study is built upon our previous work 53 that addresses the effects of T , at P = 0.1 MPa, on the WMI between the same graphene plates considered in this work. Briefly, we observed that, at normal pressure, cooling and heating tend to suppress 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 while 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 . This picture is not inconsistent with computational studies of cold-induced protein

4


Page 4 of 44

Page 5 of 44 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


denaturation 34,35,41 that find an intrusion of water molecules within the protein interior upon cooling. This work is organized as follows. In Sec. 2, we describe the computer simulation details. The temperature effects on the WMI between graphene plates under pressure (P > 0) and tension (P < 0) are discussed in Sec. 3.1. The effects of pressure on the WMI between graphene plates at constant temperature are presented in Sec. 3.2. In Sec. 3.3 we compare the effects of T and P on the WMI between the graphene plates. A brief description of the role of crystallization of nanoconfined water on the WMI between the graphene plates is included in Sec. 3.4. We summarize the results presented in this work in Sec. 3.5.

2

Computational Details

We perform molecular dynamics (MD) simulations of two graphene plates immersed in water at constant pressure and temperature. We follow the same methodology as in our previous work and we refer the reader to Ref. 53 for MD simulations details. Briefly, we consider two graphene plates composed by 135 carbon atoms and with surface area A = dx × dy = 1.709 × 1.762 nm2 ; see Fig. 2a. The graphene plates are immobile and are located symmetrically with respect to the center of the box, parallel to the xy-plane; see Fig. 2b. The system contains N = 6541 water molecules, and periodic boundary conditions are applied along the three dimensions. 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 and, from the MD simulations, we obtain the mean force between the plates, F (r) (at the given T and P ). The PMF between the graphene plates is calculated as a function of the plates separation r by integration,

G(r) − G(r0 ) = −

Z

r

F (r)dr,

(1)

r0

where r0 is a reference separation and G(r0 ) is an arbitrary constant; we set r0 = 1.5 nm 5



and G(r0 ) = 0.0. From a mechanistic point of view, 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 and P in the presence of the solvent. From a thermodynamic point of view, the PMF for a given r is the Gibbs free energy of the system at (T, P, r). Following Ref., 53 we perform MD simulations using the SPC/E 54 and TIP4P/2005 55 water models. Both models reproduce relatively well the thermodynamic and dynamical properties of liquid water. However, the TIP4P/2005 model is remarkably superior to the SPC/E model in reproducing the phase diagram of ice. 56,57 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 Ref. 53 While the specific LJ parameters associated to water O-graphene C interactions vary slightly with the water model considered, we find that the contact angles of SPC/E and TIP4P/2005 water on graphene T IP 4P/2005

are θcSP CE ≈ 970 and θC

≈ 960 at T = 300 K and P = 0.1 MPa, suggesting that the

hydrophobicity/hydrophilicity of the graphene model surface considered is not affected by the water model employed. 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 (i.e., θc > 900 ). All MD simulations are performed using the GROMACS computer simulations package. 58 MD simulations at a given temperature (T, P ) 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 nonequilibrium artifacts in our measurements at all temperatures; see Ref. 53 We also confirm that our results are reliable by performing a second independent simulation at T = 240 K for 4 ns at P = 0.1 MPa and confirm that our results remain unchanged. Computer simulations are performed at −100 MPa ≤ P ≤ 1200 MPa and 240 ≤ T ≤ 400 K. The specific state points simulated for each water model are summarized in Fig. 3.

6


Page 6 of 44

Page 7 of 44 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


3

Results

3.1

Temperature Effects on the Water-Mediated Interactions between Graphene Plates at Constant Pressure

In this section, we discuss the effects of isobaric cooling/heating on the PMF and mean force between the graphene plates. We discuss separately the cases where P > 0 and P < 0 (water under tension). 3.1.1

Positive Pressures

In our previous work, 53 we studied the effects of T on the WMI between the same graphene plates considered in this work at P = 0.1 MPa. Briefly, it was found that (a) the PMF between the graphene plates is an oscillatory function of r and decays to zero for approximately r > 1 − 1.3 nm. (b) The effect of heating is to reduce such oscillation in the PMF as well as the range of WMI between the plates from r ≈ 1.3 nm at T = 240 K to r ≈ 1.0 nm at T = 400 K, while (c) the effects of cooling is to increase the maxima and minima of the total PMF between the graphene plates. As explained in Ref., 53 both (b) and (c) imply that heating and cooling tend to suppress the attraction and ultimate collapse of the graphene plates. Specifically, upon cooling, the free energy barriers separating the stable/metastable plates separations grow and the plates become increasingly kinetically trapped in the metastable states where one or more water layers occupy the confined space. Instead, upon heating, the graphene plates PMF flattens and the WMI between the plates weaken. Next, we show that results (a)-(c) hold qualitatively at 0.1 < P ≤ 1200 MPa. Since the discussion below (at P > 0) follows closely Ref. 53 (at P = 0.1 MPa), we refer the reader to Ref. 53 for a more detailed discussion. The total PMF between the graphene plates, G(r), at P = 400 MPa and in the presence of SPC/E water is shown in the inset of Fig. 4a. 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 7



Page 8 of 44

between the graphene plates in vacuum separated by a distance r; Gw (r) is shown in Fig. 4b. Fig. 4c shows the mean force on the plates obtained from the MD simulations. It follows from Fig. 4a that, at all temperatures studied, G(r) exhibits oscillations that become negligible at approximately r > 1.5 nm. The local minima at r1 ≈ 0.32 nm, r2 ≈ 0.65 nm, r3 ≈ 0.92 nm, and r4 ≈ 1.25 nm correspond to plates separations where there are, respectively, 0, 1, 2, and 3 water layers between the plates. The deepest local minimum of the PMF occurs at r1 and corresponds to the stable state of the system where the plates are in contact with each other (collapsed-plates state). The minima at ri with i > 1 represent metastable states of the system. It follows that the energy barriers separating these stable/metastable local 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). Such a ‘layering effect’ is also evident in the water contribution to the PMF (Fig. 4b). In addition, since F (r) = − (∂G/∂r)T,P,N (see Eq. 1), the oscillatory behavior of the plates PMF leads to attractive and repulsive forces (Fig. 4c) between the plates for ri < r < ri+1 . As found in Ref. 53 at P = 0.1 MPa, Fig. 4 shows that isobaric heating at P = 400 MPa leads to a reduction of the maxima/minima of the total PMF between the plates and to a reduction of the range of the WMI between the plates. This implies that the WMI between the graphene plates weaken upon heating at T ≥ 400 K. Alternatively, cooling to T = 240 K leads to more pronounced maxima/minima of the total PMF between the plates. This leads to stronger repulsive forces upon cooling (for ri < r < ri+1 ) that the plates need to overcome in order to expel water layers from the confined space and finally collapse. The effects of cooling/heating on the WMI between the graphene plates is better quantified by calculating the energy barriers separating the stable/metastable states corresponding to r = r1 , r2 , r3 , r4 . Figure 5a shows the corresponding activation free energies, ∆Gij act (T )/kB T , that the plates need to overcome in order to move from ri to rj (i, j = 1, 2, 3, 4, j = i±1). For given consecutive PMF minimum and maximum, with free energies Gmin and Gmax , the corresponding activation free energy is defined as (Gmax (T ) − Gmin (T )) /kB T .

8


Page 9 of 44 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


It follows from Fig. 5a that all activation energies increase linearly with 1/T . As we will show, all ∆Gij act (T )/kB T increase linearly with 1/T for all values of (i, j) and at all pressures studied (P = 0.1, 400, 800, 1200 MPa). The total PMF between the graphene plates immersed in TIP4P/2005 water is shown in Fig. 6a. The contribution to the total PMF due solely to water and the mean force between graphene plates are included in Figs. 6b and 6c. At high temperatures, Figs. 4 and 6 are qualitatively similar, with the total PMF exhibiting minima/maxima at roughly the same plates separations. However, a closer look shows that the role of the water model in the WMI between the graphene plates is indeed relevant at low temperatures. For example, at P = 0.1 MPa, SPC/E water confined between the plates remains in the liquid state at all temperatures studied. Instead, TIP4P/2005 water crystallizes into a defective bilayer hexagonal ice 53 at r ≈ 0.92 nm; the thermodynamic states at which crystallization occurs are shown in Figs. 3a and 3b. At P = 400 MPa, SPC/E water crystallizes into a defective monolayer, square, flat ice at T ≤ 260 K and for r ≈ 0.64 nm, while TIP4P/2005 water crystallizes into a defective monolayer, square, buckled ice only at T = 240 K and for r ≈ 0.78 nm. Crystallization of SPC/E and TIP4P/2005 water confined by the graphene plates is discussed in Sec. 3.4. Interestingly, regardless of the different role of crystallization in SPC/E and TIP4P/2005 water, our MD simulations show that, for the case of TIP4P/2005 water, the activation free energies also increase linearly with 1/T ; see Fig. 5b. We also calculate the WMI between the plates at P = 800 and 1200 MPa for both SPC/E and TIP4P/2005 water. As an example, we include in Fig. 7a-c the total PMF, water contribution to the total PMF, and mean force between the plates immersed in TIP4P/2005 water, at P = 1200 MPa. The corresponding data for the case of SPC/E water are included in Fig. S1 of the Supplementary Information (SI). The effects of cooling at different pressures can be determined by comparing the total PMFs and mean forces of Fig. 7 at P = 1200 MPa, Fig. 6 at P = 400 MPa, and Fig. 4 of Ref. 53 at P = 0.1 MPa. It follows from these figures that cooling/heating have the same qualitative effects on the mean force and total PMF

9



Page 10 of 44

between the plates at all pressures studied. However, the changes in the WMI between the plates induced by cooling become more pronounced with increasing pressure. To demonstrate this point, we compare the changes in the PMF activation energy barriers upon cooling, at different pressures. At all pressures studied, we find that the activation free energies are linear functions of 1/T ; see, e.g., Figs. 8 and 5b of this work, and Fig. 3b of Ref. 53 for the case of TIP4P/2005 (see Figs. S2 of the SI, 5a, and Fig. 3a of Ref. 53 for the case of SPC/E water). It follows that, the effect of temperature (at constant pressure) on the activation free energies is approximately given by ∆Gij act /kB T = Cij (P ) + Dij (P )/T, i, j = 1, 2, 3, 4; j = i ± 1

(2)

where Cij (P ) and Dij (P ) are coefficients that depend solely on the pressure considered. These coefficients are summarized in Table 1. The behavior of Cij (P ) and Dij (P ) as function of pressure is shown in Fig. 9. In particular, Fig. 9b shows that all coefficients Dij (P ) increase with increasing pressure, implying that the effect of changing 1/T in Eq. 2 becomes more important as pressure increases. 3.1.2

Negative Pressures

In this section, we show that WMI between the graphene plates at negative pressure are drastically different from the WMI reported at P ≥ 0.1 MPa. This strongly suggest that self-assembly processes in aqueous solutions, e.g., protein folding, can be largely affected under tension. Indeed, protein denaturation induced by decompression to negative pressures has been observed in NMR experiments and computer simulations of the protein ubiquitin. 33 Computer simulations of the miniprotein trp-cage also show denaturation at negative pressures. 59 Decompression-induced protein denaturation is predicted by Hawley’s theory 29 that proposes the elliptical protein phase diagram of Fig. 1 (see also Ref. 40 ). We note that experiments in water under tension indicate that cavitation in bulk water can be avoided down to

10


Page 11 of 44 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


P ≈ −100 MPa at T ≈ 300 K, 60 which is consistent with the liquid-to-vapor spinodal line shown in Figs. 3a and 3b. Accordingly, we limit our discussion to the case P = −100 MPa. The total PMF, water contribution to the total PMF, and mean force between the plates at P = −100 MPa are shown in Figs. 10a-c for the case of TIP4P/2005 water. The main differences with the case P ≥ 0.1 MPa are as follows. (i) The second minimum in the total PMF at r = r2 ≈ 0.60 − 0.65 nm found at P ≥ 0.1 MPa [Figs. 6a and 7a of this work, and Fig. 3a of Ref. 53 ] is absent at P = −100 MPa (Fig. 10a). Accordingly, the first maximum in F (r) at r ≈ 0.55 nm found at P ≥ 0.1 MPa (Figs. 6c and 7c of this work, and Fig. 2c of Ref. 53 ) is absent at P = −100 MPa (Fig. 10c). This is because under tension, dewetting (of TIP4P/2005 water) in the confined space occurs at dc = 0.86 nm while dc ≈ 0.60 nm at P ≥ 0.1 MPa. Physically, tension removes the metastable state where the graphene plates are separated by one layer of water (r = r2 ). It follows that the weak free energy barrier at r = 0.86 nm in Fig. 10c separates the state where two water layers fit within the confined space (r3 ≈ 0.92 nm) from the collapse plates state (r1 = 0.32 nm). Our results are consistent with previous studies showing that hydrophobic confinement tends to induce evaporation of nanoconfined water at conditions where bulk water remains in the liquid state (see, e.g., Ref. 44,52 ). We also note that the PMF at P = −100 MPa is rather flat at r > 1.0 nm. In other words, this only means that there are no free energy barriers (or penalty) separating the states where there are n ≥ 3 water layers between the plates. In particular, this means that the states where 3 or 4 water layers separate the plates are no longer metastable at P = −100 MPa. Regarding the temperature effects on the WMI under tension, (ii) cooling enhances the energy barrier that the plates need to overcome in order to move between r = r1 and r = r3 . Indeed, we find that ∆Gij act /kB T for (i = 1, j = 3) and (i = 3, j = 1) are linear functions of 1/T . (iii) At T = 240 K, this is due to the presence of crystallization at r = r3 ; as for the case of P ≥ 0.1 MPa, water confined between the graphene plates at P = −100 MPa also crystallizes into a defective bilayer hexagonal ice at r = r3 ; see Ref. 53

11



We note that, as found at P ≥ 0.1 MPa, cooling under tension deepens the first minimum of the total PMF, i.e., it makes the collapsed-plates (stable) state more stable relative to the state where the plates are dissociated, r > 1.5 nm. However, cooling also increases the energy barrier between the (r = r3 )-state and the collapsed-plates state at r = r1 (Fig. 10a). Equivalently, cooling increases the repulsive force at r ≈ 0.86 nm that the plates need to overcome in order to collapse (Fig. 10c). Accordingly, as for the case P ≥ 0.1 MPa, this repulsive force implies that, from a kinetic point of view, cooling under tension may frustrate the collapse of the graphene plates at low temperature.

3.2

Pressure Effects on the Water-Mediated Interactions between Graphene Plates at Constant Temperature

Next, we study the effects of isothermal compression/decompression on the WMI between the graphene plates. As indicated in Fig. 3, we study the effects of pressure at T = 240, 260, 300, 360, and 400 K for both water models considered. Crystallization becomes unavoidable at Tx = 240 K for the case of TIP4P/2005 water, and at Tx ≤ 240 − 300 K (at high pressures) for the case of SPC/E water. At T > Tx , the effect of pressure on the WMI is qualitatively similar for both water models considered. Hence, we focus on the case where the graphene plates are immersed in TIP4P/2005 water at T = 300 K; see Fig. 11 (results for SPC/E water are included in Figs. S3 and S4 of the SI). The main conclusion of this section is that isothermal compression/decompression (i.e, increase/decrease in P ) and isobaric cooling/heating (i.e., decreasing/increasing 1/T ) lead to similar effects on the WMI between the plates. This is evident from a comparison of Fig. 6 (isobaric cooling/heating at P = 400 MPa) and Fig. 11 (isothermal compression/decompression at T = 300 K). It follows from these figures that: (a) along both kinds of thermodynamic paths, the total PMF between the graphene plates is an oscillatory function of r that decays to zero for approximately r > 1 − 1.3 nm; (b) the effects of isobaric heating (isothermal decompression) are to reduce such oscillations in the PMF as well as 12


Page 12 of 44

Page 13 of 44 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


the range of WMI between the plates, while (c) the effects of isobaric cooling (isothermal compression) is to increase the maxima and minima of the total PMF between the graphene plates. Hence, in analogy with the discussion in Sec. 3.1.1, both compression to P > 400 MPa and decompression to P < 0.1 MPa tend to weaken the WMI between the graphene plates. Specifically, (i) compression enhances the activation free energy barriers separating the stable/metastable states where an integer number of water layers accommodate in between the graphene plates, (kinetically) trapping the plates at separations r = ri (i = 2, 3, 4). Instead, (ii) decompression flattens the total PMF between the plates, weakening the interactions between the graphene plates. The effect of pressure at constant temperature are exposed in Fig. 12 that shows the activation free energy barriers that the plates need to overcome to move from ri to rj (i, j = 0, 1, 2, 3; j = i ± 1). Remarkable, Fig. 12 shows that upon isothermal compression, all ∆Gij act (P )/kB T are, approximately, linear functions of P , ∆Gij act (P )/kB T = Aij (T ) + Bij (T ) P, i, j = 1, 2, 3, 4; j = i ± 1

(3)

Interestingly, the coefficients Aif (T ) and Bij (T ) are approximately linear functions of T ; see Table 2 and Fig. 13. We note that Eq. 3 is consistent with computer simulations and theoretical studies of water-methane mixtures. 17,31 Specifically, in Ref., 31 it was found that the PMF between methane molecules (i.e., small hydrophobic molecules) also exhibits an oscillatory dependence on the methane-methane separations r, as we find for the graphene plates, and in particular, that the activation free energy barrier for dissociation of the methane-methane PMF increase linearly with increasing P .

13



3.3

Water-Mediated Interactions between the Graphene Plates in the P-T plane

The free energy barriers ∆Gij act are key quantities that define the WMI between the graphene plates. In this section, we compare the effects of T and P on ∆Gij act /kB T . The similarities between Figs. 5b and 12 imply that the roles played by P and 1/T on the WMI along, respectively, isothermal compression/decompression and isobaric cooling/heating, are indeed analogous. In particular, our MD simulations show that the changes in the total PMFs along both processes are comparable at the quantitative level if one considers ranges of P and T that are relevant to protein denaturation. To clarify this point, we compare the activation free energy barriers at states (i) (T = 240 K, P = 0.1 MPa) [Fig. 3b of Ref. 53 ] and (ii) (T = 300 K, P = 400 MPa) [Fig. 12]. State (i) corresponds to thermodynamic conditions at which Staphylococcal nuclease 36 denatures upon isobaric cooling at P = 0.1 MPa; state (ii) corresponds to conditions at which Staphylococcal nuclease denatures upon isothermal compression at T = 300 K. The activation energy barriers at state (i) are ∆Gij act /kB T = 207.4, 14.2, 31.8, 58.9, 38.4, 6.6 for the cases (i, j) = (1, 2); (2, 1); (2, 3); (3, 2); (3, 4); (4, 3) while the corresponding values at state (ii) are ∆Gij act /kB T = 235.8, 61.7, 53.6, 58.6, 32.5, 3.9. It follows that the corresponding free energy barriers at states (i) and (ii) are indeed very close to each other, although differences are relevant for the cases (i, j) = (2, 1) and (2.3) [associated to the state where the plates are separated by a single water layer (r = r2 )]. To visualize the effects of T and P on the WMI between the plates, we present in Fig. 14 lines of constant ∆Gij act /kB T in the (T, P ) plane for selected values of i and j (the qualitative behavior of the constant-∆Gij act /kB T lines is common to all values of i and j since, for all ij (i, j), ∆Gij act /kB T follows Eqs. 2 and 3). Strictly speaking, constant-∆Gact /kB T lines indicate

(T, P ) states where the free energy barrier that the plates need to overcome in order to move from ri to rj remains constant (relative to the available thermal energy). Roughly speaking, one may interpret the constant-∆Gij act /kB T lines to indicate (T, P ) thermodynamic states 14


Page 14 of 44

Page 15 of 44 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


along which the WMI between the plates remain constant. Fig. 14a shows the constant-∆Gij act /kB T lines when the plates are initially in the collapseplates state (r1 ) and one water layer is allowed to form within the plates (r2 ). Fig. 14b shows the constant-∆Gij act /kB T lines for the opposite process. In both cases, the constant∆Gij act /kB T lines have positive slopes in the (T, P ) plane. This is because as previously shown, the activation free energies decrease upon heating (e.g., Fig. 5) while they increase upon compression (e.g., Fig. 12). In other words, in order to maintain invariant the WMI between the plates during heating, one needs to increase the pressure. Similarly, in order to maintain invariant the WMI between the plates during compression, one needs to increase the temperature. We conclude this section by noticing that it is not possible to obtain an analytical expression for ∆Gij act /kB T that depends (only) on T, P and that is consistent with Eqs. 2 and 3. Specifically, Eqs. 2 and 3 imply that

Bij (T ) =

∂[∆Gij act /kB T ] ∂P

!

Dij (P ) = T

∂[∆Gij act /kB T ] ∂[1/T ]

!

(4) P

However, an analytical expression for ∆Gij act /kB T requires that ∂ 2 [∆Gij act /kB T ] ∂P ∂[1/T ]

!

=

∂ 2 [∆Gij act /kB T ] ∂[1/T ]∂P

!

(5)

or, equivalently, that dBij (T ) dDij (P ) = d[1/T ] dP

(6)

It follows from Figs. 9b and 13b that Eq. 6 does not hold. It is possible that an analytical expression for ∆Gij act /kB T depends on additional variables, such as ri and rj , or that Eqs. 2 and 3 need to be replaced by other mathematical expressions.

15



3.4

Page 16 of 44

Role of Crystallization on the Water-Mediated Interactions between Graphene Plates

Water confined between the graphene plates rapidly crystallizes at low temperatures. As discussed in detail in our previous work, 53 crystallization in the confined space can be detected by calculating the number N (t) and mean-square displacement M SD(t) of water molecules found between the plates as function of time. Specifically, when ice forms between the plates, the M SD(t) saturates at long times while N (t) reaches a constant value. Instead, in the liquid state, the MSD increases with increasing time until N (t) ≈ 0 (i.e., all molecules leave the confined space); see Ref. 53 for details. In this work, we follow the same procedure of Ref. 53 to detect crystallization. The thermodynamic states (T, P ) and plates separation r at which crystallization occurs vary considerably with the water model studied. In the case of SPC/E water, crystallization occurs at T = 240 − 300 K and high pressures, P ≥ 400 MPa; see Fig. 3a. As shown in the SI, SPC/E water crystallizes into a defective monolayer square ice at r ≈ 0.54−0.76 nm and, depending on the pressure and specific value of r, this ice can be buckled or flat. Instead, crystallization of TIP4P/2005 water occurs only at T = 240 K and for all pressures studied; see Fig. 3b. Next, we focus on TIP4P/2005 water and summarize briefly the different ice forms observed. We note that both water models crystallize into a square ice-like structure at very high pressure which is consistent with the square ices observed in experiments

61

and

computer simulations 62–65 of water confined by graphene sheets. Crystallization of TIP4P/2005 water at P = 0.1 MPa (and T = 240 K) is discussed in detail in our previous work. 53 Briefly, at these conditions and for r ≈ 0.92 nm, TIP4P/2005 water forms a defective bilayer ice composed of hexagons, pentagons, and heptagons. We observe the same bilayer ice at P = −100 MPa and for r ≈ 0.92 nm. As shown in Fig. 15a, molecules in one ice layer are in registry with molecules in the opposite ice layer (AA stacking). As for the case P = 0.1 MPa, the presence of this defective bilayer ice is responsible of the deep minimum in the plates PMF shown in Fig. 10a at r ≈ r3 ≈ 0.92 nm and for 16


Page 17 of 44 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


T → 240 K. We note that at both P = −100 and 0.1 MPa, the bilayer ice is very sensitive to r and it vanishes rapidly for r > 0.92 nm, i.e., as confined water evolves into a trilayer liquid. Similarly, the bilayer ice vanishes rapidly for r < 0.92 nm. In the case of P = 0.1 MPa, the crystal evolves into a monolayer liquid as r → r2 ≈ 0.65 nm. However, at P = −100 MPa, the vapor forms already at dc ≈ 0.86 nm and hence, the bilayer ice transforms into the vapor phase (i.e., it sublimates) as r → dc . At P = 400 MPa, the defective bilayer ice at r ≈ 0.92 nm is not found. Instead, TIP4P/2005 water crystallizes only at r = 0.76−0.80 nm into a defective monolayer, buckled, square ice. Snapshots of this ice form are shown in Fig. 15b. Interestingly, it follows from Fig. 6a that, at r = 0.80 nm, the plates PMF exhibits a maximum. This implies that the observed buckled monolayer ice is indeed unstable, i.e., if the plates were allowed to move, and r to change, the system would evolve into a monolayer liquid (r → r2 ≈ 0.65 nm) or a bilayer liquid (r → r3 ). We note that signatures of crystallization are not evident in the total PMF between the plates (Fig. 6a) but are found in the mean force between the plates. Specifically, F (r) develops a small shoulder at r = 0.78 − 0.80 nm as T → 240 K; see Fig. 6c. We confirmed that this feature in F (r), and the observed monolayer ice, remain if we extend our simulation for additional 4 ns. At P = 800 MPa, we observe two kinds of crystal-like structures. At r ≈ 0.62 nm, confined water forms a monolayer ice. The structure of this monolayer ice is not very clear but it seems to contain squares and rhomboidal features; see, e.g., Fig. 15c. The total PMF at P = 800 MPa (T = 240 K) exhibits a minimum at r ≈ 0.62 nm and hence, this ice structure is stable relative to small variations in r. The second ice structure at P = 800 MPa forms at r = 0.76 − 0.80 nm and is identical to the defective monolayer, buckled, square ice that is found at P = 400 MPa for same plates separations (Fig. 15b). As for the case P = 400 MPa, this buckled square ice is unstable since the total PMF between the plates shows a maximum at r = 0.76 − 0.80 nm. Signatures of the buckled ice are evident in the mean force between the plates; F (r) exhibits a small shoulder at r ≈ 0.80 nm as shown in Fig. 6c for the case

17



P = 400 MPa. At P = 1200 MPa, crystallization occurs at approximately r ≤ 0.78 nm. For 0.70 ≤ r ≤ 0.78 nm, the ice is identical to the monolayer, buckled, square ice found at P = 400, 800 MPa, at same plates separations. Again, as in the previous cases, this ice is unstable; see Fig. 7a. As r decreases towards r = r1 = 0.62 nm, the buckled square ice evolves into a flat monolayer ice characterized by rhomboidal structures oriented along perpendicular directions; see Fig. 15c. This ice structure is particularly clear at approximately r = 0.64 − 0.68 nm. Interestingly, at r ≈ 0.64, one can observe both rhomboidal and square structures; see Fig. 15d. At dc ≤ r < 0.64 nm, it is less evident what the ice structure is but we can identify signatures of square ice (as r → dc , defects in the ice increase, as the ice and liquid become unstable relative to the vapor).

3.5

Discussion and Conclusions

We presented MD simulations of two nanoscale, weakly-hydrophobic and apolar, graphene plates immersed in water at −100 ≤ P ≤ 1200 MPa and T = 240 − 400 K. The aim of this work was to compare the effects of T and P on the WMI between the graphene plates. Our MD simulations show that, at all (T, P ) studied, the total PMF between graphene plates exhibits an oscillatory behavior that vanishes for plates separations r > 1 − 1.5 nm. The local minima in the total PMF occurs at plates separations that accommodate zero (collapsed-plates state), one, two, and three water layers. It follows that the free energy barriers separating consecutive local minima of the plates PMF correspond to the addition and removal of one water layer between the plates. These results are consistent with previous studies at limited T and P conditions (see, e.g., Refs. 46,47,66 ) and are independent of the water model employed (SPC/E and TIP4P/2005 water model). We observe remarkable similarities in the effects of P and T on the WMI between the graphene plates. Specifically, (i) isobaric cooling and (ii) isothermal compression both enhance the free energy barriers separating the plates PMF, with ∆ij act /kB T ∝ 1/T along 18


Page 18 of 44

Page 19 of 44 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


isobaric cooling and ∆ij act /kB T ∝ P along isothermal compression. This implies that both thermodynamic processes can kinetically frustrate the attraction and ultimate collapse of the graphene plates. Specifically, the increase of ∆ij act /kB T upon cooling and compression tend to trap the graphene plates at the metastable states where there is an integer number of water layers between the plates. Our results may be relevant in the understanding of (i’) cooling-induced and (ii’) compression-induced protein denaturation. Extension of the present results to the case of WMI between hydrophobic protein residues, suggest that cooling and compression may weaken the attraction and ultimate collapse between apolar residues by forcing water molecules to move in between the apolar residues. This picture is consistent with computational and theoretical studies of small hydrophobic solutes and small proteins. 31,34,35 Remarkably, we observed that the values of ∆ij act /kB T are quantitatively similar at pressures and temperatures where, roughly, proteins denature. Interesting, the effects of (iii) isobaric heating and (iv) isothermal decompression are also similar. Specifically, both thermodynamic process tend to reduce the range and strength of the WMI between the plates. These results suggest that weakening of the attraction between apolar residues contribute to the well-known phenomena of (iii’) heating-induced protein denaturation, as expected. In addition, the similarities in the WMI between the graphene plates along the thermodynamic paths (iii) and (iv) suggests that, proteins may be denatured by isothermal decompression (if the liquid-to-vapor spinodal in bulk water does not interefere). Indeed, (iv’) decompression-induced protein denaturation is consistent with Hawley’s theory 29 that propose an ellipsoidal protein phase diagram when P is extended to negative pressures (Fig. 1); decompression-induced protein denaturation has been observed in experiments 33 and simulations. 40,59 The role of crystallization on the WMI between the graphene plates is already relevant at T = 240 K and P = 0.1 MPa (and at T = 300 K at P = 1200 MPa). Our MD simulations show that crystallization occurs rapidly at these temperatures. In the case of TIP4P/2005 water, we find defective bilayer hexagonal ice as well as monolayer square (buckled) and

19



rhomboidal ices, depending on (T, P, r). In the case of SPC/E, we only observed a monolayer square, flat or buckled, ice, depending on (T, P, r). While the resulting ice form may depend on the confining surface and geometry, our simulations clearly indicate the possibility that defective ices or perhaps, vitrification, can frustrate self-assembly processes in aqueous solutions at low temperature and/or high pressure. WMI between model apolar nanoscale surfaces have been studied in the past. In some of these studies, the role of T and P has been explored to some extent. In many of these works, the surfaces have been modeled with atomic-like sites that interact with water via Lennard-Jones interactions. As we showed in Ref., 53 if the water-plates LJ parameters are not realistic (e.g, the interacting sites in the walls represent coarse-grained interactions), it is possible to loose the layering effect that we describe at r < 0.8 − 1 nm (see, e.g., Refs. 23,67 ). It follows that coarse-grain model surfaces may overshadow the effects of T and P on WMI between solutes. We conclude by noticing that the plates PMF and F (r) reported in this work may vary with changes in the properties of the surfaces considered, such as the surfaces curvature. 50 For example, the PMF and F (r) must increase as the plates surface area increases (the effect of varying the surface area of the graphene plates on the plates PMF is studied in detail in Ref. 68 ). Nonetheless, we expect the observed effects of T and P on the WMI between the graphene plates to be rather general, common to other interacting (apolar and hydrophobic) solutes. In this regard, we note that our results that ∆Gij act /kB T ∝ P (at contant pressure) and ∆Gij act /kB T ∝ P (at constant temperature) are fully consistent with the work of Sirovetz et al. 41 that finds parabolic phase diagrams (at P > 0) for the proteins ubiquitin and λrepresor (consistent with experiments and Fig.1). In their work, an implicit water model is used to describe the interactions between the protein residues. This model (AWSEM) incorporates explicitly the effects of temperature and pressure on the WMI by including two terms in the Hamiltonian of the system. Specifically, the effects of T on the WMI is represented in the Hamiltonian by a term ∆Vtemp ≈ mT +b and applies only to WMI between

20


Page 20 of 44

Page 21 of 44 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


hydrophobic residues. The effects of P on the WMI is more complex but involves terms that vary as ∆Vpress ≈ m′ P + b′ (m, m′ , b and b′ are constants). Since our total PMF can be thought of as the effective potential energy of the plates in the presence of water (Sec. 2), it follows that our expressions for ∆Gij act /kB T (Eqns. 2 and 3) are qualitatively identical to those used in Ref. 41

4

Supporting Information

Additional material is included showing MD simulations results (PMF, F (r), and crystallization) for the case where the graphene plates are immersed in SPC/E water.

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.

References (1) Dill, K. A.; Bromberg, S. Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology; Garland Science: New York, USA, 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.

21



(4) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley: New York, USA, 1980. (5) 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. (6) Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly. Nature 2005, 437, 640-647. (7) Dobson, C. M. Protein Aggregation and its Consequences for Human Disease. Protein Pept Lett. 2006, 13, 219-27. (8) Dobson, C. M. Protein Folding and Misfolding. Nature 2003, 426, 884-890. (9) Everts, S. Protein Folding: Much More Intricate Than We Thought. Chem. & Eng. 2017, 95, 32-38. (10) Kauzmann, W. Some Factors in the Interpretation of Protein Denaturation. Adv. Protein Chem. 1959, 14, 1-63. (11) Rabani, E.; Reichman, D. R.; Geissler, P. L.; Brus, L. E. Drying-Mediated SelfAssembly of Nanoparticles. Nature 2003, 436, 271-274. (12) Percec, V.; Wilson, D. A.; Leowanawat, P.; Wilson, C. J.; Hughes, A. D.; Kaucher, M. S.; Hammer, D. A.; Levine, D. H.; Kim, A. J.; Bates, F. S., et al. Self-assembly of Janus Dendrimers into Uniform Dendrimersomes and Other Complex Architectures. Science 2010, 328, 1009-1014. (13) Chen, Q; Yan, J.; Zhang, J.; Bae, S. C.; Granick, S. Janus and Multiblock Colloidal Particles. Langmuir 2012, 28, 13555-13561. (14) 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. 22


Page 22 of 44

Page 23 of 44 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


(15) Lund, M.; Jungwirth, P.; Woodward, C. E. Ion Specific Protein Assembly and Hydrophobic Surface Forces. Phys. Rev. Lett. 2008, 100, 258105. (16) 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. (17) 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. (18) 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. (19) 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. (20) Ghosh, T.; Garc´ıa, A. E.; Garde, S. Water-Mediated Three-Particle Interactions between Hydrophobic Solutes: Size, Pressure, and Salt Effects. J. Phys. Chem. B 2003, 107, 612-617. (21) 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. (22) 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. (23) 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.

23



(24) Ravindra, R; Winter, R. On the Temperature-Pressure Free-Energy Landscape of Proteins. ChemPhysChem 2003, 4, 359-365. (25) Meersman, F.; Dobson, C. M.; Heremans, K. Protein Unfolding, Amyloid Fibril Formation and Configurational Energy Landscapes under High Pressure Conditions. Chem. Soc. Rev. 2006, 35, 908-917. (26) Privalov, P. L. Cold Denaturation of Proteins. Crit. Rev. Biochem. Mol. Biol. 1990, 281-305. (27) Scharnagl, C.; Reif, M.; Friedrich, F. Stability of Proteins: Temperature, Pressure and the role of the Solvent. Biochimica et Biophysica Acta 2005, 1749, 187-213. (28) Smeller, L. Pressure-Temperature Phase Diagrams of Biomolecules. Biochimica et. Biophysica Acta 2002, 1595, 11-29. (29) Hawley, S. A. Reversible Pressure-Temperature Denaturation of Chymotrypsinogen. Biochem. 1971, 10, 2436-2442. (30) Vidugiris, G. J. A.; Markley, J. L.; Royer, C. A. Evidence for a Molten GlobuleLike Transition State in Protein Folding from Determination of Activation Volumes. Biochemistry 1995, 34, 4909-4912. (31) Hillson, N.; Onuchic, J. N.; Garc´ıa, A. E. Pressure-Induced Protein-Folding/Unfolding Kinetics. Proc. Natl. Acad. Sci. USA 1999, 96, 14848-14853. (32) Pastore, A.; Martin, S. R.; Politou, A.; Kondapalli, K. C; Stemmler, T.; Temussi, P. A. Unbiased Cold Denaturation: Low- and High-Temperature Unfolding of Yeast Frataxin under Physiological Conditions. J. Am. Chem. Soc. 2007, 129, 5374-5375. (33) Larios, E.; Gruebele, M. Protein Stability at Negative Pressure. Methods 2010, 52, 51-56.

24


Page 24 of 44

Page 25 of 44 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


(34) Lopez, C. L.; Darst, R. K., Rossky, P. J. Mechanistic Elements of Protein Cold Denaturation. J. Phys. Chem. B 2008, 112, 5961-5967. (35) 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. (36) 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. (37) Marqu´ez, M. L.; Borreguero, J. M.; Stanley, H. E.; Dokholyan, N. V. Possible Mechanism for Cold Denaturation of Proteins at High-Pressures. Phys. Rev. Lett. 2003, 91, 138103. (38) Patel, B. A.; Debenedetti,P. G.; Stillinger, F. H.; Rossky, P. J. A Water-Explicit Lattice Model of Heat-, Cold-, and Pressure-Induced Protein Unfolding. Biophys. J. 2007, 93, 4116-4127. (39) Matysiak, S.; Debenedetti, P. G.; Rossky, P. J. Role of Hydrophobic Hydration in Protein Stability: A 3D Water-Explicit Protein Model Exhibiting Cold and Heat Denaturation. J Phys Chem B. 2012, 116, 8095-8104. (40) Bianco, V.; Franzese, G. Phys. Rev. Lett. 2015, 115, 108101. (41) Sirovetz, B. J; Schafer, N. P.; Wolynes, P. G. Water Mediated Interactions and the Protein Folding Phase Diagram in the Temperature-Pressure Plane. J. Phys. Chem. B 2015, 119, 11416-11427. (42) Davtyan, A.; Schafer, N. P.; Zheng, W.; Clementi, C.; Wolynes, P. G.; Papoian, G. A. AWSEM-MD: Protein Structure Prediction Using Coarse-Grained Physical Potentials

25



and Bioinformatically Based Local Structure Biasing. J. Phys. Chem. B 2012, 116, 8494-8503. (43) 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. (44) 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. (45) Giovambattista, N.; Rossky, P. J.; Debenedetti, P. G. Phase Transitions Induced by Nanoconfinement in Liquid Water. Phys. Rev. Lett. 2009, 102, 050603. (46) Choudhury, N.; Pettitt, M. On the Mechanism of Hydrophobic Association of Nanoscopic Solutes. J. Am. Chem. Soc. 2005, 127, 3556-3567. (47) Lu, L.; Berkowitz, M. L. Hydration Force between Model Hydrophilic Surfaces: Computer Simulations. J. Chem. Phys. 2006, 124, 101101. (48) Sharma, S.; Debenedetti, P. G. Evaporation Rate of Water in Hydrophobic Confinement. Proc. Natl. Acad. Sci. USA 2012, 109, 4365-4370. (49) Eun, C.; Berkowitz. M. L. Fluctuations in Number of Water Molecules Confined between Nanoparticles. J. Phys. Chem. B 2010, 114, 13410-13414. (50) Jabes, B. S.; Bratko, D.; Luzar, A. Curvature Dependence of the Effect of Ionic Functionalization on the Attraction among Nanoparticles in Dispersion. J. Chem. Phys. 2018, 148, 222815. (51) Choudhury, N.; Pettitt, M. The Dewetting Transition and the Hydrophobic Effect. J. Am. Chem. Soc. 2007, 129, 4847-4852.

26


Page 26 of 44

Page 27 of 44 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


(52) 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. (53) Engstler, J.; Giovambattista, N. Temperature Effects on Water-Mediated Interactions at the Nanoscale. J. Phys. Chem. B 2018, 122, 8908-8920. (54) Berendsen, H. J. C.; Grigera, J. R.; Stroatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269-6271. (55) Abascal, J. L. F.; Vega, C. A General Purpose Model for the Condensed Phases of Water: TIP4P/2005. J. Chem. Phys. 2005, 123, 234505. (56) 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. (57) Sanz, E.; Vega, C.; Abascal, J. L. F.; MacDowell, L. G. Phase Diagram of Water from Computer Simulation. Phys. Rev. Lett. 2004, 92, 255701. (58) 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. (59) Hatch, H. W.; Stillinger, F. H.; Debenedetti, P. G. Computational Study of the Stability of the Miniprotein Trp-Cage, the GB1 β-Hairpin, and the AK16 Peptide, under Negative Pressure. J. Phys. Chem. B 2014, 118, 7761-7769. (60) Pallares, G.; Gonzalez, M. A.; Abascal, J. L. F.; Valeriani, C.; Caupin, F. Equation of State for Water and its Line of Density Maxima Down to −120 MPa. Phys. Chem. Chem. Phys. 2016, 18, 5896.

27



(61) Algara-Siller, G.; O. Lehtinen, O.; Wang, F. C.; Nair, R. R.; Kaiser, U.; Wu, H. A.; Geim, A. K; Grigorieva, I. V. Square Ice in Graphene Nanocapillaries. Nature 2015, 519, 443-445. (62) Chen, J.; Schusteritsch, G.; Pickard, C. J.; Salzmann, C. G.; Michaelides, A. Two Dimensional Ice from First Principles: Structures and Phase Transitions. Phys. Rev. Lett. 2016, 116, 025501. (63) Zangi, R.; Mark, A. E. Monolayer Ice. Phys. Rev. Lett. 2003, 91, 025502. (64) Zhu, Y.; Wang, F.; Bai, J.; Zeng, X. C.; Wu, H. AB-Stacked Square-Like Bilayer Ice in Graphene Nanocapillaries. Phys. Chem. Chem. Phys. 2016, 18, 22039-22046. (65) Gao, Z.; Giovambattista, N.; Sahin, O. Phase Diagram of Water Confined by Graphene. Sci. Rep. 2018, 8, 6228. (66) Walqvist, A.; Berne, B. J. Computer Simulation of Hydrophobic Hydration Forces on Stacked Plates at Short Range. J. Phys. Chem. 1995, 99, 2893-2899. (67) Bauer, B. A.; Patel, S. Role of Electrostatics in Modulating Hydrophobic Interactions and Barriers to Hydrophobic Assembly. J. Phys. Chem. B 2010, 114, 8107-8117. (68) Zangi, R. Driving Force for Hydrophobic Interaction at Different Length Scales. J. Phys. Chem. B 2011, 115, 2303-2311. (69) Netz, P. A.; Starr, F. W.; Stanley, H. E.; Barbosa, M. C. J. Chem. Phys. 2001, 115, 344-348. (70) Biddle, J. W.; Singh, R. S.; Sparano, E. M.; Ricci, F.; Gonz´alez, M. A.; Valeriani, C.; Abascal, J. L. 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.

28


Page 28 of 44

Page 29 of 44 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


Table 1: Parameters Cij (P ) and Dij (P ) defined in Eq. 2 for the case of TIP4P/2005 watera . P [MPa] C12 (P ) D12 (P ) C21 (P ) D21 (P ) C23 (P ) D23 (P ) C32 (P ) D32 (P ) C34 (P ) D34 (P ) C43 (P ) D43 (P )

a

0.1 -5.56 51.49 -19.101 8.90 -18.53 12.40 -76.08 32.44 -53.31 21.30 -8.17 3.58

400 17.74 65.10 7.45 15.95 -14.98 19.97 -65.32 36.83 -40.41 21.78 -16.27 9.09

800 26.98 78.98 28.18 24.49 22.83 17.53 -26.68 32.91 -37.58 25.88 -23.73 14.98

1200 40.68 88.47 12.88 52.24 31.20 21.50 -24.20 38.71 -32.49 29.02 -24.56 19.30

These parameters quantify the temperature-dependence of the energy barriers separat-

ing the total PMF minima i and j at constant pressure, ∆Gij act /kB T = Cij (P ) + Dij (P )/T (i, j = 1, 2, 3, 4, i 6= j); see, e.g., Figs. 6a and 7a. Parameters Cij (P ) are adimensional; parameters Dij (P ) are given in units of 103 K. Data at T = 240 K includes states at which TIP4P/2005 water crystallizes into defective ices for some values of r.

29



Page 30 of 44

Table 2: Parameters Aij (T ) and Bij (T ) defined in Eq. 3 for the case of TIP4P/2005 watera . T [K] A12 (T ) B12 (T ) A21 (T ) B21 (T ) A23 (T ) B23 (T ) A32 (T ) B32 (T ) A34 (T ) B34 (T ) A43 (T ) B43 (T )

a

240 214.74 167.74 7.21 174.08 34.89 73.08 59.12 65.77 36.83 41.40 5.34 41.44

260 199.03 157.00 7.76 164.31 31.69 71.11 53.36 57.97 27.40 43.82 4.87 37.52

300 173.72 139.33 8.50 140.58 25.38 66.23 31.35 63.14 15.75 40.44 3.15 29.57

360 134.94 161.14 3.58 121.23 16.62 59.89 12.96 59.13 6.10 34.04 1.31 18.79

400 124.90 135.99 2.26 110.36 11.39 56.16 7.86 46.08 2.52 28.82 0.73 14.38

These parameters quantify the pressure-dependence of the energy barriers separating

the total PMF minima i and j at constant temperature, ∆Gij /kB T = Aij (T ) + Dij (T ) P (i, j = 1, 2, 3, 4, i 6= j); see, e.g., Fig. 11a. Parameters Aij (P ) are adimensional; parameters Bij (P ) are given in MPa−1 . Data at T = 240 K includes states at which TIP4P/2005 water crystallizes into defective a ice for some values of r.

30


Page 31 of 44 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


Figure 1: Schematic phase diagram for proteins. The interior of the ellipse represents the states (T, P ) at which the protein is in its folded (nature) state; states (T, P ) falling outside the ellipse represent thermodynamic states at which the protein is in its denatured (unfolded) state. The red, blue, green, and magenta arrows indicate, respectively, thermodynamic paths followed in the processes of heating-, cooling-, compression-, and decompression-induced protein denaturation.

31



Figure 2: (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. Panels (a) and (b) are reproduced from Ref. 53

32


Page 32 of 44

Page 33 of 44

400

400

Liquid Defective Crystal Liquid-to-vapor spinodal line

Liquid Defective Crystal Liquid-to-vapor spinodal line

350 T [K]

350 T [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


300 250

300 250

(a) SPC/E 200

-500

0

500 P [MPa]

1000

(b) TIP4P/2005 1500

200

-500

0

500 P [MPa]

1000

1500

Figure 3: Thermodynamic states simulated for the case of the graphene plates immersed in (a) SPC/E and (b) TIP4P/2005 water. Blue circles indicate states where water confined by the graphene plates remains in the liquid state for plates separation r < 1.5 nm and no crytallization occurs; crosses indicate states where water is found in the liquid state for some plates separations and crystallizes for others (r < 1.5 nm). Confined TIP4P/2005 water crystallizes at T = 240 K into diverse ices: (i) defective bilayer hexagonal ice at P = −100, 0.1 MPa and r ≈ 0.92 nm, (ii) defective buckled, monolayer square ice at P ≈ 400 MPa and r ≈ 0.78 nm, (iii) defective monolayer rhomboidal and square ices (r ≈ 0.64 nm) at P = 800 and 1200 MPa, respectively, and (iv) defective buckled, monolayer square ice (r ≈ 0.78 nm) at P = 800, 1200 MPa. Instead, confined SPC/E water crystallizes into a monolayer (flat or buckled) square ice at all T and P indicated (at r ≈ 0.54 − 0.76 nm in all cases; see SI). Data points for the liquid-to-vapor spinodal lines are from Refs. 69,70

33



(a) SPC/E

50

P=400 MPa

PMFTOTAL [kJ/mol]

PMFTOTAL/kBT

0 -50 -100 -150 -200 0.2

100 0 -100 -200 -300 -400 -500 0.2 0.4 0.6 0.8

0.4

0.6

0.8 1 r [nm]

1.2

1.4

P=400 MPa

0 PMFWATER [kJ/mol]

PMFWATER/kBT

1.2 1.4

(b) SPC/E

-50 -100 -150 0.2

2

1

r [nm]

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

Page 34 of 44

0.4

100 0 -100 -200 -300 0.2 0.4 0.6 0.8 1 1.2 1.4 r [nm]

0.6

0.8 1 r [nm]

60 50 40 30 20 10 0 -10 -20 -30 -40 0.2

1.2

1.4

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

(c) SPC/E P=400 MPa 0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 4: (a) Total PMF between the graphene plates immersed in SPC/E water at P = 400 MPa and for different temperatures. The total PMF is divided by the thermal energy, kB T , in the main panel. Inset: total PMF without the factor 1/kB T . (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 (without the factor 1/kB T ) and mean force between the graphene plates in vacuum.

34


Page 35 of 44

ij

∆Gact /kBT

250

(a) SPC/E P=400 MPa

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

200 150 100 50 0 2.5

250

ij

∆Gact /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


3

3.5 -1 1000/T [K ]

4

(b) TIP4P/2005 P=400 MPa

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

200 150 100 50 0 2.5

3

3.5

4

-1

1000/T [K ]

Figure 5: (a) Temperature-dependence of the activation free energies obtained from the total PMFs shown in Fig. 4a for the case where the graphene plates are immersed in SPC/E water. (b) Activation free energies for the plates immersed in TIP4P/2005 water obtained from Fig. 6a. 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.

35



(a) TIP4P/2005

50

P=400 MPa

PMFTOTAL [kJ/mol]

PMFTOTAL/kBT

0 -50 -100 -150 -200 0.2

100 0 -100 -200 -300 -400 -500 0.2 0.4 0.6 0.8

0.4

0.6

0.8 1 r [nm]

1.2

1.4

P=400 MPa

0 PMFWATER [kJ/mol]

PMFWATER/kBT

1.2 1.4

(b) TIP4P/2005

-50 -100 -150 0.2

2

1

r [nm]

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

Page 36 of 44

0.4

200 100 0 -100 -200 -300 0.2 0.4 0.6 0.8 1 1.2 1.4 r [nm]

0.6

0.8 1 r [nm]

60 50 40 30 20 10 0 -10 -20 -30 -40 0.2

1.2

1.4

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

(c) TIP4P/2005 P=400 MPa 0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 6: Same as Fig. 4 for the case where the graphene plates are immersed in TIP4P/2005 water.

36


Page 37 of 44

200

(a) TIP4P/2005 P=1200 MPa

0 PMFTOTAL [kJ/mol]

PMFTOTAL/kBT

100

-100 -200 -300 -400

400 200 0 -200 -400 0.2 0.4 0.6 0.8

1

1.2 1.4

r [nm]

0.2

0.4

0.6

0.8 1 r [nm]

200

0 PMFWATER [kJ/mol]

PMFWATER/kBT

1.4

P=1200 MPa

-100 -200 -300 -400 0.2

2

1.2

(b) TIP4P/2005

100

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

400 200 0 -200 -400 0.2 0.4 0.6 0.8 1 1.2 1.4 r [nm]

0.6

0.8 1 r [nm]

140 120 100 80 60 40 20 0 -20 -40 -60 -80 0.2

1.2

1.4

(c) TIP4P/2005 P=1200 MPa

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

0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 7: Same as Fig. 6 for the case P = 1200 MPa.

37


ij

450 400 350 300 250 200 150 100 50 0

TIP4P/2005 P=1200 MPa

3

Page 38 of 44

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

3.5

4 -1

1000/T [K ]

Figure 8: Same as Fig. 5b for the case P = 1200 MPa.

40

(b) TIP4P/2005

(a) TIP4P/2005 80 Dij(P) [1000 K]

20 0 Cij(P)

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

∆Gact /kBT


-20 -40

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

-60 -80 0

200

400

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

60 40 20

600 800 1000 1200 P [GPa]

0

0

200

400

600 800 1000 1200 P [MPa]

Figure 9: Parameters (a) Cij (P ) and (b) Dij (P ) defined in Eq. 2 (see Table 1). Lines are guides to the eye.

38


Page 39 of 44

(a) TIP4P/2005

50

P=-100 MPa

PMFTOTAL [kJ/mol]

PMFTOTAL/kBT

0 -50 -100 -150 -200 0.2

100 0 -100 -200 -300 -400 -500 0.2 0.4 0.6 0.8

0.4

0.6

1.2 1.4

0.8 1 r [nm]

1.2

1.4

(b) TIP4P/2005 P=-100 MPa

0 PMFWATER [kJ/mol]

PMFWATER/kBT

1

r [nm]

50

-50 -100 -150 -200 0.2

0.4

200 100 0 -100 -200 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=300 K No Water

20 10 0

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


-10

(c) TIP4P/2005

-20 0.2

P=-100 MPa 0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 10: Same as Fig. 6 for the case P = −100 MPa.

39


Page 40 of 44

200

(a) TIP4P/2005

150

T=300 K

100 50 0 -50 -100 -150 -200

PMFWATER/kBT

0.2

0.4

0.6

0.8 1 r [nm]

1.2

1.4

200

(b) TIP4P/2005

150

T=300 K

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

0.4

0.6

0.8 1 r [nm]

1.2

1.4

P=-100 MPa P=0.1 MPa P=400 MPa P=800 MPa P=1200 MPa No Water

100

50

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

PMFTOTAL/kBT


0

(c) TIP4P/2005 -50 0.2

T=300 MPa 0.4

0.6

0.8 1 r [nm]

1.2

1.4

Figure 11: (a) Total PMF between the graphene plates immersed in TIP4P/2005 water at T = 300 K and for different pressures. The total PMF is divided by the thermal energy, kB T . (b) Contribution to the total PMF due solely to water. (c) Mean force acting on the plates. Dashed-line in (c) is the mean force between the graphene plates in vacuum.

40


Page 41 of 44

350 300

TIP4P/2005 T=300 K

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

200

ij

∆Gact /kBT

250

150 100 50 0 0

0.2

0.4

0.6

0.8

1

1.2

P [MPa]

Figure 12: Activation free energies for the plates immersed in TIP4P/2005 water at T = 300 K obtained from Fig. 11a. 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 compression, disfavoring (i.e., making kinetically more difficult) the collapse of the graphene plates.

(a) TIP4P/2005

200

100

(b) TIP4P/2005 150

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

1 to 2 2 to 1 2 to 3 3 to 2 3 to 4 4 to 3

-1

Bij(T) [MPa ]

150 Aij(T)

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


50

100

50

0 250

300

350

0

400

250

T [K]

300

350 T [K]

Figure 13: Parameters (a) Aij (T ) and (b) Bij (T ) defined in Eq. 3.

41


400


1500

(a) TIP4P/2005

12

∆G /kT=200

(b) TIP4P/2005

21

∆G /kT=200 21

∆G /kT=150

1500 12

∆G /kT=150

21

∆G /kT=100

P [MPa]

1000 P [MPa]

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 44

500 12

∆G /kT=100

1000 21

∆G /kT=50

500

0 12

∆G /kT=50

0

-500 200 300 400 500 600 700 800 900 T [K]

-500 0

100

200

300

400

500

T [K]

Figure 14: (a) Constant-∆Gij act /kB T lines in the P-T plane for the free energy barriers that the plates need to overcome in order to move from the collapsed-plates (stable) state (r = r1 ; i = 1) to the metastable state where a water monolayer separates the graphene plates (r = r2 ; j = 2). (b) Constant-∆Gij act /kB T lines in the P-T plane corresponding to the transition from r2 to r1 . Up-triangles (right-triangles) are obtained from the evaluation of ∆Gij act /kB T at constant temperature (pressure). Lines are guides to the eye. Squares indicate the liquid-tovapor spinodal line, Plv (T ), for bulk TIP4P/2005 water. Accordingly, data at P < Plv (T ) is unphysical (see text).

42


Page 43 of 44 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


Figure 15: Top and side views of TIP4P/2005 ices found between the confined plates at −100 ≤ P ≤ 1200 MPa and T = 240 K. (a) Defective bilayer ice at r ≈ 0.92 nm and P = −100 MPa; molecules in different layers are shown with oxygens in red and green. (b) Defective monolayer, buckled, square ice at r ≈ 0.78 nm and P = 400 MPa; molecules closer to the left and right graphene plates are shown with oxygens in red and green, respectively. (c) Defective monolayer ice found at r = 0.68 nm and P = 1200 MPa. This ice is composed of rhomboids oriented perpendicular to one another. (d) As r decreases, this structure evolves, including molecules arranged in squares. Side views only show the water molecules confined between the graphene plates and the C atoms of the graphene plates (in gray).

43



Figure 16: TOC graphic.

44


Page 44 of 44

Comparative Study of the Effects of Temperature ... - ACS Publications

Recommend Documents