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New Concepts at the Interface: Novel Viewpoints and Interpretations, Theory and Computations
Phase Transition in Monolayer Water Confined in Janus Nanopore Hemant Kumar, Chandan Dasgupta, and Prabal K. Maiti Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02147 • Publication Date (Web): 14 Sep 2018 Downloaded from http://pubs.acs.org on September 14, 2018
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Phase Transition in Monolayer Water Confined in Janus Nanopore Hemant Kumar,1, ∗ Chandan Dasgupta,2, † and Prabal K. Maiti2, ‡ 1
Department of Material Sciences and Engineering,
University of Pennsylvania, Philadelphia, USA, 19104 2
Centre for Condensed Matter Theory,
Indian Institute of Science, Bangalore, India-560012
Abstract The ubiquitous nature of water invariably leads to a variety of physical scenarios that can result in many intriguing properties. We investigate the thermodynamics and associated phase transitions for a water monolayer confined within a quasi-two-dimensional nanopore. An asymmetric nanopore constructed by combining a hydrophilic (hexagonal Boron Nitride) sheet and a hydrophobic (Graphene) sheet leads to an ordered water structure at much higher temperatures compared to a symmetric hydrophobic nanopore consisting of two graphene sheets. The discontinuous change in the thermodynamic quantities, potential energy (U) and entropy (S) of confined water molecules computed from the all-atom molecular dynamics simulation trajectories, uncovers a first-order phase transition in the temperature range of T = 320 K to T = 330 K. Structural analysis reveals that water molecules undergo a disorder-to-order phase transformation in this temperature range with a 4-fold symmetric phase persisting at lower temperatures. Our findings predict a novel confinement system which has the melting transition for monolayer water above the room temperature, and provide a microscopic understanding which will have important implications for other nanofludic systems as well.
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INTRODUCTION
Confinement is known to bring out many extraordinary physical properties which are not observed in the bulk systems. In particular, water molecules have been shown to exhibit intriguing dynamical and structural behavior when subjected to nanoscale confinement. A major interest in the subject stems from the prospect of observing two-dimensional (2D) ice at ambient temperature/pressure conditions. Formation of the 2D ordered structure is important not only from the fundamental point of view to understand physical properties of water but also have technological applications such as designing a network of water molecules for efficient proton transport. Several simulations and experimental studies including a recent TEM study by Algara-Siller et al. have demonstrated the formation of various two-dimensional ice polymorphs for water molecules subjected to confinement between two hydrophobic sheets at high pressure and low temperature conditions. [1–6] However, observation of two-dimensional ordered water at ambient temperature and pressure conditions remains a challenge. The degree of confinement and interaction with the confining surfaces are the two main factors that can be fine-tuned to govern the properties of confined water. Emergence of ordered structure of water is well known near hydrophobic surfaces while glassy behavior is often associated with hydrophilic confining surfaces. [7, 8] In this article, we explore an interesting prospect- can the tendency of water molecules to order near hydrophobic surfaces be combined with the slower dynamics near hydrophilic surfaces to maintain the ordered phase of water molecules at higher temperatures?
Formation of monolayer and bilayer ice structures under high pressure was first reported for water molecules confined between graphene sheets by Zangi et al.. [9] Findings from other simulation studies conducted at very high densities suggest water freezing between graphene layers even at ambient temperature. [10] Later, Choudhury et al. systematically investigated structural and dynamical properties of water molecules confined between graphene sheets in an open system and showed that both translational and reorientational mobilities of water molecules confined between graphene sheets are significantly decreased for separations below 13 ˚ A . [11, 12] However, no freezing was observed. Similar behavior was observed for other hydrophobic confiments. [13–15] Iiyama et al. performed X-ray diffraction experiments to ACS Paragon 2Plus Environment
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determine the structure of water molecules in a hydrophobic nano-space between 148 K and 303 K. [16] X-ray diffraction patterns were shown to possess sharp peaks suggesting that the water molecules have an ordered structure. Recent studies also provide a set of consistent and important results on the nature of confined water in hydrophilic confinement, in particular, on the glassy state of confined water. Funnel et al. conducted inelastic neutron scattering experiments to characterize the structure of water molecules in contact with Vycor glass and showed that water structure at room temperature (298 K) is similar to that of bulk supercooled water at 273 K. [17] MD study performed by Gallo et al. provide evidence that the water molecules close to the hydrophilic surface shows slow dynamics at room temperature . [18, 19] Experiments have also observed the slow dynamics near the silica nanopores. [20] Another study conducted by Lombardo et al. found long-range spatial correlations for the water molecules near a hydrophilic surface. [21, 22] Recently Youssef et al. concluded, based on the analysis of data obtained from MD simulation, that water confined between Calcium-Silicate-hydride (CSH) surfaces exhibit glassy behavior. [8] It is evident from the discussion that water molecules show very different characteristics depending on the hydrophobic or hydrophilic confinement. In this article, we systematically investigate the structure, dynamics and thermodynamics of water molecules confined between an asymmetrical channel of graphene and hBN (GR-BN)(Figure 1 a), and demonstrate that the water molecules remain in an ordered phase up to 320 K in atmospheric pressure conditions. A first-order solid-liquid transition occurs between T = 320 K and T = 330 K as evident from the discontinuous change in entropy and energy of confined water molecules. A direct comparison with the results for the water molecules confined between symmetrical graphene-graphene (GR-GR) sheets suggests that the presence of a hydrophilic surface elevates the transition temperature by 30 K. We further establish that below the phase transition temperature, the ordered phases have strikingly similar structural arrangement of water molecules for both the pores.
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a)
b)
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FIG. 1. Simulated bilayer system. a) Bilayer consists of one graphene sheet and other Boron Nitride sheet (GR-BN). For clarity, solvating water molecules in all three directions are not shown. b) Instantaneous snapshots of the water molecules between GR-BN sheets below (T = 320K) and above (T = 330K) the transition temperatures. Blue dotted lines represent hydrogen bonds.
RESULTS
Free Energy of Water Molecules Between Bilayers
We begin by examining the thermodynamic stability of confined water molecules by means of the Helmholtz free energy (A = U − T S). The components of the entropy, namely translational (Strans ) and rotational (Srot ) entropy per water molecule, were obtained from the power spectrum of the respective velocity autocorrelation functions using the two-phase thermodynamics (2PT) method. [23, 24] Potential energy (U ) was obtained by decomposing the total energy of the system in per atom energy using the potential function. Figure 2 shows the U and S(= Strans + Srot ) as functions of temperature for the water molecules confined in GR-BN pore. Water molecules confined in the GR-BN channel have lower potential energy compared to the bulk water molecules due to the altered hydrogen bond network and favorable interactions with the hydrophilic confining surface [25]. U value per water molecule in bulk system at T = 300 K is −10.97 kcal/mol while that of the water molecule confined between GR-BN sheets has value of −12.63 kcal/mol. This decrease of the potential energy is accompanied by a reduction of rotational entropy (SI, Table S1). ACS Paragon 4Plus Environment
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FIG. 2. Temperature dependence of the potential energy (U ) and entropy (S) per confined water molecule. Water molecules confined between graphene sheets have less favorable energy compared to those confined inside GR-BN pore which is partly compensated by the entropy gain. A sudden jump in the energy and entropy can be seen for both GR-GR and GR-BN.
Due to the attractive interaction between the water molecules and polar Boron and Nitrogen atoms, both transnational and rotational motions of the water molecules are retarded which leads to the reduced transnational and rotational entropies. These entropy values are lower as compared to the bulk water (see SI, Table S1). Nonetheless, the average free energy (A) per confined water molecules remains favorable compared to bulk water molecules, and we observe that the slit pore remains occupied by the water molecules during the whole simulation time. Next, we conduct a series of NVT simulations in the temperature range of 260 K to 340 K at an interval of 20 K. Before production run for all the temperatures, each system was equilibrated in NPT ensemble with pressure controlled at atmospheric value. U and S as functions of temperature are shown in the Figure 2. The potential energy per water molecule confined in GR-BN pore increases ( becomes less negative ) gradually with increasing temperature but a large jump of energy (1.13 kcal/mol ) was observed between T = 320 K and T = 330 K. Such a sudden change in thermodynamic quantities suggests a first-order phase transition. However, more data with finer temperature resolution would be required for determining the true nature of the transition. Similar changes are also observed for the entropy of water molecules; clearly demonstrating a phase transition between T = 320 K ACS Paragon 5Plus Environment
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and T = 330 K. Transition from the ordered hydrogen-bonded network phase to disordered liquid phase at higher temperatures leads to significant increase of intermolecular interaction energy due to broken hydrogen bond network (Figure 1b). The loss of hydrogen bonds also leads to increased entropy above transition temperatures. It is worth mentioning that such first order transitions have been reported for the smooth hydrophobic nanochannel as well as for the channels consisting of two graphene (GR-GR) layers. However, different studies consider different types of the confining system and the phase transition has been reported at varying thermodynamic state points e.g. high pressure ( 2 GPa), high densities (ρc = 1.3 g/cm3 ) or combination of low temperature and high pressure conditions. [1, 3] Hence, to make a direct comparison and to elucidate the specific role of hydrophilic-hydrophobic confinement on the phase transition, we compare this GRBN pore with an identical GR-GR pore simulated under same thermodynamic conditions. A contrasting behavior as compared to GR-BN slit-pore emerges for the water molecules confined between graphene sheets. In the absence of any favorable interactions from the confining surfaces, both the average energy and entropy per confined water molecule are higher compared to the bulk water molecules (as opposed to the lower energy and entropy for GR-BN pore). The quasi-2D network of hydrogen bonds of confined water molecules and interactions with graphene sheets are not able to compensate the energy decrease from altered bulk tetrahedral structure. While this energy decrease is partially compensated by the rotational entropy gain, the total free energy of the confined water molecules remains slightly unfavorable compared to bulk water molecules (SI, Table S1).
It is clear from the discussion above that energy and entropy exhibit very different behavior for the two systems but water molecules confined in both the pores are thermodynamically stable at room temperature. The observed variation of energy and entropy with temperature shows that the first order liquid-solid transition also occurs for the GR-GR pore; consistent with previous reports. [3] However the transition temperature T = 290 K is much lower as compare to T = 320 K for GR-BN pore. This clearly demonstrate that the presence of hydrophilic confining layer helps to maintain the ordered state of water molecules at much higher temperatures compared to purely hydrophobic confinement. This behavior is highly beneficial for the applications where ordered state of water molecules is desired at ambient conditions. Next, we investigate the structure of water molecules before and after phase ACS Paragon 6Plus Environment
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0.4
0.8 0.2
0.4 0 -1
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d)
-90
0
90
0.8
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260K 280K
320K 330K
0.4
300K
340K
gOOxy
Order Parameters
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0.4
0.2
0.2 0 260
180
0 280
300
320
340
2
3
4
5
6
7
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9
Temperature (K)
FIG. 3. Characterization of the molecular arrangement of water molecules confined between two sheets and its variation with temperature. Structural transition from ordered phase to disordered phase can be seen at T = 330 K for water molecules confined in GR-BN pore, a) Oxygen probability distribution function b) distribution of dipole angles c) structural order parameters d) pair-correlation function. Transition is very evident from the clear change in distribution functions and order parameters.
transition temperature to understand the nature of the transition.
Structure
To investigate the structural difference between two phases of confined water molecules, we examine the probability distribution of oxygen atoms along the normal to the plane of ACS Paragon 7Plus Environment
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the confining sheets. The probability distribution is defined as: P (z) =
1 X h δ(z − zi )i δz i
(1)
Here zi is the distance of ith oxygen atom from the center of the pore, δz is the bin size, and hi represent an average over configurations generated from the MD simulation trajectories. Figure 3(a) show the probability distribution of oxygen inside GR-BN nanopore. We have also plotted the probability distribution for hydrogen for both the systems in Figure S1. Oxygen atoms lie symmetrically with respect to the center of the bilayer with an unimodal distributions for GR-GR system. Similar symmetric oscillatory density distributions have been observed also by Gordillo et al. for water molecules between graphene bilayers. [26] Asymmetric nature of the confining space is reflected in the density profile of the water molecules confined between graphene and Boron Nitride sheet in the GR-BN system. Due to the hydrophilic nature of the Boron Nitride sheet, water molecules are attracted to it and the probability distributions have larger weight towards the Boron Nitride surface (higher value of z). This distribution suggests that the water molecules form a monolayer such that the oxygen atoms are arranged in a plane geometry to maximize the hydrogen bonding with neighboring water molecules. Secondary peaks in the distribution of hydrogen atoms close to the surfaces are due to the hydrogen atoms of dangling OH bonds from reorienting water molecules (Figure S1). These observations are further confirmed by the instantaneous snapshot from the simulation shown in Figure 1. Figure 3(a) also shows the probability distribution of oxygen atoms at various temperatures for both the systems. As the system temperature is increased, thermal fluctuations increase and more hydrogen bonds are broken. This is reflected in the slight broadening of the peaks with increasing temperature for both the systems. No other drastic changes is observed in the distribution functions indicating that the monolayer structure of water molecules persists above the transition temperature for both the systems.
Based on the above analysis, it is evident that the water molecules are arranged approximately in a plane parallel to the two confining layers, with a few hydrogen atoms lying out of the plane. Further insight into the structural arrangement of water can be obtained by analyzing the orientation of dipole vectors. Figure 3 (b) shows the distribution of angles which water dipoles make with a fixed axis (X-axis) in a plane parallel to the confining surfaces ACS Paragon 8Plus Environment
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(XY plane) just above and below the transition temperature. Above the transition temperature (T = 320 K ) all dipole orientation are equally probable indicating disordered phase of water molecule. However, below the transition temperature four distinct peaks separated by approximately 90◦ appear, further demonstrating the existence of an ordered phase of water molecules with 4-fold symmetry. To characterize this 4-fold symmetric structural order, we compute the four-fold bond orientational (Φ4 ) and translational order parameter (ΨT ) for two-dimensional confined water molecules. For a 4-fold symmetric lattice, these are given as: + * Nb N 1 X 1 X e4ιθmn Φ4 = N m=1 Nb n=1 + * N 1 X ΨT = eιG.rm N m=1
(2)
(3)
Where N is the total number of confined water molecules, Nb is the number of nearest neighbors within a cutoff (the number of nearest neighbors is different for different water molecules. So, Nb is different for different m), and θmn is the angle between O − O bonds of neighboring molecules, and G is the first shell reciprocal lattice vector. For a liquid phase, Φ4 → 0 while Φ4 → 1 for perfectly ordered phase. The bond order parameter Φ4 is plotted in the Figure 3 (c) at different temperatures. At low temperatures, average value of Φ4 is close to 0.65 and does not decay significantly till T = 320 K implying an orientationally ordered phase. Above 320 K, bond order parameter Φ4 decays rapidly to zero. It provides a strong evidence of disordered-ordered phase transition above T = 320 K. The same transition occurs between T = 290 K and T = 300 K for the GR-GR pore consistent with transition predicted from the change in energy and entropy discussed above. Further confirmation of the phase transition comes from the change in long range order exhibited by the radial distribution functions gxy (r). Effect of increasing temperature on gxy (r) for oxygen-oxygen correlation is shown in Figure 3 (d). Above T = 320 K, gxy (r) is characterized by a dominant single peak at 2.8 ˚ A, followed by a low intensity peak at 5.6 ˚ A; resembling bulk water in liquid state. The characteristics features of the gxy (r) change abruptly when the temperature crosses the transition temperature between T = 320 K and T = 330 K, a signature of first order transition. Below 320 K a significant long-range order is observed as reflected by the presence of three distinct peaks. Similar transition was observed for GR-GR (Figure S1) pore at T = 290 K consistent with the transition observed earlier. While the above ACS Paragon 9Plus Environment
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MSD(Å2)
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260K 280K 300K 320K 330K 340K
10-2 10-3 10-3
10-2
10-1
100
101
102
103
time (ps)
FIG. 4. Characterization of the translational dynamics of confined water molecules. a) MSD of the confined water molecules has been plotted from T = 260 K to T= 340 K. Above the transition temperature, liquid-like diffusive behavior is evident with the M SD ∝ t above the transition temperature ( 330 K). Below the transition temperature dynamics is sub-diffusive at long times.
discussion clearly establishes the structural phase transition between 320 K and 330 K for the GR-BN pore and between 290 K and 300 K for GR-GR pore, a closer look at dynamical properties of confined water molecules during phase transition provides further insight.
Dynamics
Dynamical properties of water molecules in confinement can be understood by analyzing the mean square displacement (MSD) as a function of time. The diffusion constant of water ACS Paragon10 Plus Environment
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molecules between bilayer graphene sheets is known to be much lower than that of bulk water [10]. Hirunsit et al. [10] have shown that the diffusion behavior of water molecules confined between bilayer graphene sheets separated by 8 ˚ A at T = 298 K is very similar to that of bulk water at 213 K. Water molecules confined in GR-BN bilayer interact with one hydrophobic and one hydrophilic surface, and hence their diffusion is even slower. However, we find liquid-like behavior with reduced mobility of water molecules for temperatures above the transition point, consistent with the study conducted by Pettitt et al. [11] where they find similar values for the diffusion constants of water molecules confined between graphene sheets. We have plotted the MSD as a function of time on a log-log scale for different temperatures, as shown in Figure 4. It is evident that for the initial time up to 0.1 ps, the diffusion behavior remains the same for all the temperatures, which signifies ballistic behavior at very short times. At longer time scales, diffusive behavior emerges and normal diffusion is observed above the transition temperature. However, at lower temperatures, such as 320 K (as shown in the Figure 4), the MSD is sub diffusive over fairly long time, signifying the occurrence of slower dynamics at these time scales. To get further insight into the phase transition, the diffusion constants have been plotted for various temperatures in Figure 5. We obtained the diffusion constant from the integration of velocity-velocity autocorrelation function. Due to sub-linear dependence of MSD with time below the transition temperature, diffusion constant computed is not true diffusion constant. The logarithm of the diffusion constant is plotted versus 1000/T , so that Arrhenius behavior would correspond to a straight line in this plot. It is clear from the plots that the dependence of the diffusion constant on the temperature is not well-described by the Arrhenius form with a fixed activation energy. Similar behavior was also observed for the water molecules interfacial to lipid bilayer. [27] The effective activation energy obtained from the local slope of the curve increases as T is decreased. As shown in the Figure 5, the activation energy obtained by fitting the data in the temperature range of 340 K-330 K (340 K -300 K for GR-GR) is clearly different than that obtained from the data at lower temperatures. The data show evidence for a crossover in the temperature dependence of the diffusion constant near 330 K (290 K for GR-GR). This crossover may be related to structural changes near 330 K, as indicated by the sudden jump in the energy (see Figure 2) and the emergence of signatures of ordering in the pair correlation function shown in Figure 3). Recently Fogarty et al. also explained ACS Paragon11 Plus Environment
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10-4 Diffusion Constant
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10-5 10-6 10-7 10-8 2.8
GR-GR GR-BN 3
3.2
3.4
3.6
3.8
4
1000/T (K-1)
FIG. 5. Variation of the diffusion constant of confined water molecules as a function of temperature. The translation motion reflects Arrhenius behavior at high temperatures but a sudden jump in the diffusion constant near the transition temperature indicates a change in the activation energy barrier which arises due to structural transformation.
non-Arrhenius behavior of the diffusion constant of bulk water on the basis of continuous structural changes occurring at low temperatures. [28] The results discussed above imply that confined water molecules located between the surfaces exhibit similar effects, but with considerably slower dynamics.
CONCLUSION AND DISCUSSION
Various properties of the water molecules confined between Janus bilayer composed of hydrophobic and hydrophilic sheets were investigated. To our knowledge, it is the first attempt to characterize the structure, dynamics and thermodynamics of water molecules ACS Paragon12 Plus Environment
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confined between the combination of graphene and Boron Nitride sheets. We have shown that water molecules have favorable free energy inside GR-BN bilayer slit pore as compared to bulk and graphene bilayer. This thermodynamic stability was shown to be present for all the temperatures studied. Water molecules arranges their positions to stay closer to the Boron Nitride surface in the GR-BN bilayer system, leading to an asymmetric density profile along the confinement axis. Symmetric confinement space of graphene bilayer has symmetric density profiles with respect to the mid plane. However, the peak density is higher for the GR-BN bilayer as compared to the graphene bilayer system. The onset of the order-disorder transition is 30 K higher in the presence of hydrophilic confining wall but the structure of the ordered phase is the same for hydrophobic-hydrophobic and hydrophilichydrophobic slit pores. It has been established that by combining the hydrophobic and hydrophilic confining walls the ordered phase of two-dimensional water can be maintained at much higher temperatures. These results can be applied to obtain the ordered water monolayer above room temperature.
Method
Atomistic MD simulations were carried out using the LAMMPS [29] simulation package to explore the properties of a monolayer of water molecules confined between two extended surfaces. Two different confining geometries are considered: ; I) one graphene layer and one Boron Nitride layer; II) two graphene layers. We call these systems as GR-GR, and GR-BN, respectively. Graphene surfaces exhibit hydrophobic character while Boron Nitride sheets have hydrophilic character. These bilayer systems were solvated such that at least 15 ˚ A of SPC/E [30] water layer is present in all three directions. The sheets were 54.2 ˚ A in length along the x-direction and 52.2 ˚ A along the y-direction and were kept at 7 ˚ A separation along the z-direction, the separation being defined as the distance between the centers of mass of the two plates. Figure 1 shows the simulated system, for visual clarity solvating water molecules are not shown. Force field parameters to model graphene sheet were taken from the AMBER ff16 force field [31]. Hilder et al. [32] have optimized charges and LJ parameters for Boron and Nitrogen to accurately reproduce energetics of water molecules in contact with Boron Nitride nanotube. We have used the same parameters to model Boron Nitride sheets in this study. Charge and LJ-potential parameters for Boron Nitride sheets ACS Paragon13 Plus Environment
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TABLE I. Charge and LJ parameters of Boron (B) and Nitrogen (N) used for the Boron Nitride simulation in this study. Parameters were taken from Ref. [32] (kJ/mol) σ(˚ A)
Atom
q
B
0.975
0.4530
3.380
N
−0.975
0.2030
3.215
used in this study are given in Table I.
Acknowledgments
We thank DST, India for financial support.
Supporting Information
Translational and rotational entropy values along with the energy per water molecule, comparison of the structure of water molecules confined in GR-BN and GR-GR slit pores at different temperatures.
∗
[email protected] †
[email protected] ‡
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-10
Hydrophillic
Hydrophobic
Energy (Kcal/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
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TOC
280
300
320
Temperature (K)
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a)
1 2 b)34 5 6 7 8 9 10 11 12 13 14
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320K
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330K
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a) 320K
260K 280K 300K
1.2 PO
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0.6
1.6
330K 340K
320K 330K
0.4
0.8 0.2
0.4 0 -1
-0.5
0
0.5
0 -180
1
c)
d)
-90
0
90
0.8
0.8
0.6
0.6
260K 280K
320K 330K
0.4
300K
340K
gOOxy
Order Parameters
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
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0.4 0.2
0.2
0
0
260
280
300
320
340
2
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3
4
5
6
7
180
8
9
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102
MSD(Å2)
1 2 1 10 3 4 0 10 5 6 -1 7 10 8 9 10-2 10 11 10-3 12 10-3 13 14 15
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-2 0 ACS Paragon Environment 10 10-1 Plus10 101
time (ps)
102
103
Langmuir
10-4 Di usion Constant
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
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10-5 10-6 10-7 10-8 2.8
GR-GR GR-BN 3
3.2
3.4
3.6
1000/T (K-1)
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3.8
4
Hydrophillic
1 2 3 4
Hydrophobic
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Langmuir Energy (Kcal/mol)
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280
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320
Temperature (K)
340
