Pressure-Induced Densification of Ice Ih under Triaxial Mechanical

Aug 26, 2018 - Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin Key Laboratory of Applied Catalysis Science and ...
0 downloads 0 Views 5MB Size
Download PDF
Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 5267−5274

pubs.acs.org/JPCL

Pressure-Induced Densification of Ice Ih under Triaxial Mechanical Compression: Dissociation versus Retention of Crystallinity for Intermediate States in Atomistic and Coarse-Grained Water Models Qiang Guo,†,‡ Mohammad Reza Ghaani,*,‡ Prithwish K. Nandi,‡,§ and Niall J. English*,‡ †

Downloaded via DURHAM UNIV on September 1, 2018 at 20:48:57 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin Key Laboratory of Applied Catalysis Science and Technology, College of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P.R. China ‡ School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland § Irish Centre for High-End Computing, Grand Canal Quay, Dublin 2, Ireland S Supporting Information *

ABSTRACT: Molecular-dynamics (MD) simulation of triaxially pressurized ice Ih up to 30 kbar at 240 K (with sudden mechanical pressurization from its ambient-pressure structure) has been carried out with both the single-particle mW and atomistic TIP4P-Ice water potentials on systems of up to ∼1 million molecules, for times of the order of 100 ns. It was found that the TIP4P-Ice systems adopted a high-density liquid state above ∼7 kbar, while densification of the mW systems retained essentially crystalline order, owing to a failure for the tetrahedral network to break down appreciably from its ice Ih lattice structure. Both are intermediate states adopted along the path toward respective thermodynamically stable states (and with pressure removal show reversion to Ih for mW and to supercooled liquid for TIP4P-Ice), similar to recent ice electro-freezing simulations in “No Man’s Land”. Densification kinetics showed faster mW-system adaptation.

release elastic energy of ∼4.5 kJ/mol.10 The unusual thermal conductivities of amorphous ices have been investigated by equilibrium molecular-dynamics calculations.2 The structure change from the LDA to HDA ice was gauged by Hoshino et al., using TIP4P-Ice at 77 K, concluding that a 4-fold coordinated tetrahedral structure in LDA is replaced by 5-fold one in HDA with increasing pressure.3 Furthermore, the electronic structure of ice Ih, LDA and HDA due to pressurizing ice Ih to 1.2 GPa at 77 K was investigated by He et al.,11 with Futera and English carrying out similar studies recently for ice VII.13 Phonon properties of HDA ice have been studied by Koza et al. using high-resolution inelastic X-ray spectroscopy, with a focus on the first pseudo-Brillouin zone.12 In the past couple of decades or so, molecular simulation has proven of great use in elucidating microscopic behavior of water−ice nucleation, crystallization, as well as on amorphization.14−17 Until the advent of massively parallel supercomputing platforms, most molecular simulations on ice transitions have had relatively small molecular system sizes, with usually no more than a few thousand atoms or molecules which can limit the realism of the simulations in some cases.14 For instance, periodic “replicae” of nuclei or crystallites for each other under periodic boundary conditions structure may not be investigated clearly in clathrate methane hydrate or liquid water of crystal-

T

he study of the high-pressure stability of ice polymorphs, and amorphous structures, is an intriguing field.1 Indeed, amorphous and structurally disordered ices, often encountered during ice-compaction experiments, display a rich variety of different physical properties, which vary with pressure.2,3 On one hand, understanding how a material’s characteristic changes with increasing pressure can provide us valuable information to modify or create the novel function material with special characteristic feature. On the other, mastering the changing behavior of materials under pressurization can help us to explore or assess for industrial exploitation, e.g., methane− hydrate extraction from marine sediments,4 or CO2 sequestration in clathrate hydrates.5 Indeed, in recent years, a large number of the investigation regarding how high pressure influences liquid water and ice has been published,6−12 where amorphous ices, or at least disordered structures of ice, are important in terms of governing mechanical properties, in particular, which sometimes display anomalous behavior. Katayama et al. studied microstructural change in liquid water with increasing pressure up to 17.1 GPa and 850 K along the melting curve, with 4 GPa acting as a turning point vis-à-vis structural change.7 French et al. used ab initio molecular-dynamics (AIMD) simulations to probe water’s electrical conductivity pressures up to 80 Mbar and temperatures up to 130 000 K.8 Indeed, most solid water in the universe is in the form of high-density amorphous (HDA) ice, which does not occur naturally on Earth.9 In earlier work by English and Tse, compression of hexagonal ice (ice-Ih) to HDA was shown to be a reversible first-order phase transition, with a large hysteresis which can © XXXX American Chemical Society

Received: July 23, 2018 Accepted: August 26, 2018 Published: August 26, 2018 5267

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274

Letter

The Journal of Physical Chemistry Letters lization without the massive molecular system size.15−17 Even some inevitable defects in, say, cubic or hexagonal ice may impact the underlying crystal structure if the simulation system size is too small. It is reported that finite system size (few hundred molecules) could indeed cause the problem in studying density fluctuations in small systems, due to the nature of the phonon wavelengths permitted by the artificially small box size, compared to the bigger systems of million(s) of water molecules.17 Therefore, bearing in mind the salutary lessons of ref 17 (as well as of refs 15 and 16), it may well be the case that systems composed of up to a million water molecules are needed to capture rigorously the ice-transition processes (whether solid-sold or solid−liquid), particularly if there is any hint of polycrystalline behavior.18 In any event, given that pressure-induced amorphization (PIA) of crystalline ice occurs typically below the glass transition temperature (∼136 K),19 an unanswered question in water−ice physics relates to whether such processes could occur transiently as an intermediate pathway, prior to taking up thermodynamically stable phases in the mildly supercooled region (but marginally above the spontaneous nucleation temperature of ∼232 K, i.e., outside the “No Man’s Land (NML)” region). Equally succinctly, if not them, which? Certainly, in molecular simulation of gas−hydrate nucleation at supercooled temperatures of ∼30−50 K, the formation of amorphous hydrates is often seen as a precursor prior to adoption of (kinetically accessible) crystal polymorphs.4,20 Indeed, MD is a leading technique with the necessary time and spatial resolution to detect such intermediate states, which may be difficult to observe with state-of-the-art experimental methods. Moreover, for quenched nanodroplets under NML conditions, low-density amorphous (LDA) ice has been gauged as an intermediate to ice Ih via MD,21 as well as during electro-freezing along the way to ice Ic via NEMD (with external-electric-field forces rivalling in intensity those of massive external pressures applied in the present work).22 Conversely, electromagnetic fields led to retention of nanodroplets in the supercooled-liquid state via NEMD probing of entropic trapping.23 Bearing in mind this NML behavior of nanoscale liquid/solid water,21−23 particularly in strong extraneous-force regimes,22,23 as well as non-NML amorphous states, it is interesting to investigate the possibility of whatever high-density phase may emerge as a potential intermediate state upon sudden and intense mechanical compaction just outside NML, e.g., PIA to HDA or VHDA,3,10,19,24 or the possibility of high-density liquid (HDL) despite no clear-cut evidence of its observation experimentally and presently studied temperatures being outside its hypothesized stability envelope,19,24−26or indeed, something else unanticipated. Bearing this essential question in mind, as well as lessons learned on system-size limits,15−17 we apply sudden triaxial compression here to both popular atomistic and coarse-grained representations of water (TIP4P-Ice27 and tetrahedrally biased mW,28 respectively) for large systems from bulk ice Ih, in the spirit of ref 15. Both potential are proven in terms of reasonable thermodynamics for ice, e.g., with accurate melting points of ∼270 K.28,29 Naturally, TIP4P-Ice is expected to be more accurate (at the very least kinetically),15,30 due to explicit long-range dipolar and Coulombic electrostatic interactions, particularly at solid−liquid interfaces.16 Indeed, one interesting matter concerns a detailed comparison of mW versus TIP4P-Ice in terms of sudden pressurization-response behavior, as regards characterization of (probably metastable

intermediates’) structural, energetic and dynamical properties, as well as their likelihood of reversibility within nanoseconds to ice Ih, given that refs10,31 found that for both pressureamorphised ice and methane hydrate, removal of pressure led to recovery of a defective, near-crystalline state, i.e., the transformations were near-reversible. We performed MD for ∼70−130 ns at 240 K (owing to be a near-optimal temperature for potential interesting propagation of ice-stacking faults, if present),32 under pressures of up 30 kbar, on systems ranging in size from ∼40,000 to 1 million molecules for TIP4P-Ice and at the latter size for mW (given greater computational speed). We discuss simulation and structure/disordered-recognition (e.g., CHILL)33 techniques under Methodology. We note that the thermodynamically stable phases for TIP4P-Ice and mW at 240 K and these elevated pressure ranges are ice VI27 and SC16,34 respectively, so study of suddenly pressurized intermediate structures adopted, as well as kinetics of adoption and reversibility, is the key focus of the present study. Experimentally,1 one would expect Ih compaction to yield II above ∼ 2 kbar and VI above ∼6 kbar and VIII above ∼16 kbar. Details of simulation and analysis techniques are discussed in Methodology. During compression over ∼70−130 ns, the new density and configurational energy was achieved within a few nanoseconds. After 10 kbar compaction, pressure was also removed instantaneously (back to atmopsheric pressure). For 10 kbar-compressed systems, sudden decompression to 1 bar was also undertaken under NPT conditions. For comparison with ice, supercooled liquid water (SCW) was also pressurized to 10 kbar to observe structural and energetic response, while this was then removed. We found that mW exhibited a simple “squashing”, or elastic compression, of the underlying hexagonal structure (cf. Figure 1, upper). For instance, at 10 kbar, the inter-ring spacing declined from 4.15 to 3.79 Å upon compaction from atmospheric to 10 kbar; this ring strain is reflected by an averaged-per-water configurational-energy increase of ∼2.7 kcal/mol (primarily composed of additional elastic energy in the squashed hexagonal lattice). TIP4P-Ice (Figure 1, lower) is dramatically different: above ∼7 kbar, ice Ih ruptures to produce, in time, (high-density) liquid. This is redolent of PIA,3,10 except, of course, this is occurring at 240 K rather than below the glasstransition temperature. In Figure 2, we depict typical systemdensity time-evolution examples at 5 and 10 kbar, with dramatic phase change evident for TIP4P-Ice between 5 and 10 kbar cases. At 5 kbar, the TIP4P-ice density reaches about 940 kg/m3 - lower by around 100 kg/m3 than the mW-case density. Conversely, at 10 kbar, the dramatic increase by nearly 300 kg/m3 in TIP4P-ice density model exceeds the ∼60 kg/m3 increase in mW-case density in going between 5 and 10 kbar. Further details of potential-energy and density evolution are provided in the Supporting Information (Figures S1−S7). The plateaux-times (defined here as those needed to reach within 1% of the final density and configurational-energy values at each pressure) shed light on compaction kinetics, with mW generally and unsurprisingly a good deal faster than TIP4P-Ice (cf. Figures S3 and S6−S8), although the phase change of dissociation for TIP4P-Ice just above 7 kbar is a nanosecondlong “special case” (Figure S8). In any event, regardless of potential model, the ultimate density is generally realized slightly more quickly, with the configurational energy relaxing quickly thereafter (cf. Figures S3, S6, and S7). In Figure 3, the pressure dependence of density and configurational energy (i.e., the mean values at their plateaux, cf. Figure 2) is shown. The TIP4P-Ice 5268

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274

Letter

The Journal of Physical Chemistry Letters

Figure 1. Variation of both gross morphological and local molecular structure during compression at 240 K and 10 kbar. For mW (upper section), parts A and B, before and after million-molecule compaction, respectively, show simply a “squashing” (elastic compaction) of the hexagonal structure with concomitant increase in configurational energy by ∼2.7 kcal/mol. For TIP4P-Ice (lower panel), for the ∼40 k and million- molecule (“small” and “large”) systems, the energy increase upon compaction from part A to part E is ∼1.15 kcal/mol, albeit with the large system exhibiting slower kinetics and more interesting (i.e., less uniform) morphological characteristics during compression: CHILL-designation33 coloring for subpanels B−E shows the expansion of high-density liquid (yellow) at the expense of hexagonal ice (Ih) in blue. All is fully HDL (i.e., yellow) within a further half-nanosecond of part E. For the “small” system, the transition of Ih to HDL is faster and more homogeneous.

Ih → “HDL” transition is evident at ∼7 kbar. In Figure 4, typical CHILL33 analysis is shown vis-à-vis the change of cubic, hexagonal, interfacial and liquid -type percentage with rising pressure: this confirms beyond any doubt that the TIP4P-Ice system experiences pressure-driven dissociation to supercooled, pressurized liquid slightly above 7 kbar. Incidentally, the rough one-third/two-thirds CHILL-classification split between interfacial and hexagonal ice, respectively, arises from an artifact in the CHILL algorithm, in that it was not parametrized specifically for higher-pressure, elastically compressed hexagonalice states. Visualization confirms that this régime corresponds to squashed hexagonal ice (cf. Figure 1). In Figure 5, radial distribution functions (RDFs) during 0.5 ns compaction from ambient pressure (1 bar) to 10 kbar, and 0.8 ns depressurisation back to ambient (see also Figure S9 and Table S1), allow for further structural characterization, and insights into potential reversibility for the heavily compacted

states (i.e., mW’s squashed ice and TIP4P-Ice’s defacto HDL, albeit outside of the predicted thermal stability envelope for the latter).19,24−26 Using both supercooled liquid water (SCW) and ice Ih as starting points in this cycle, it is interesting to note that residual shorter-range ordering appears to persist in mW SCW after depressurisation, but this “compaction memory” is due to the very long relaxation times in supercooled water vis-à-vis the 0.8 ns decompression time.23 In any event, the TIP4P-Ice equivalence between SCW and ice Ih as starting points both yielding the same pressurized SCW (or, loosely, HDL) in Figure 5 (and Figure S9), as well as depressurisation of both 10 kbar SCW phases leading to the same ambient-pressure liquid state. In closing, we have performed MD simulations of suddenly pressurized ice Ih up to 30 kbar at 240 K with both the mW and TIP4P-Ice potentials on systems of up to ∼1 million molecules, for times of the order of 100 ns. TIP4P-Ice systems 5269

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274

Letter

The Journal of Physical Chemistry Letters

Figure 2. Time evolution of density for mW and TIP4P-Ice upon sudden compression (on left) at 240 K for (a) 5 kbar and (c) 10 kbar. Evolution for potential energy (on right) at (b) 5 kbar and (d) 10 kbar.

Figure 3. Pressure dependence of (a) density and (b) configurational energy (at plateaux, cf. Figure 2) at 240 K with increasing pressure, for both mW and TIP4P-Ice. The TIP4P-Ice Ih → “HDL” transition is evident at ∼7 kbar.

adopted a defacto “HDL” state above ∼7 kbar, while mW-systems densification was elastic (i.e., with retention of hexagonal crystalline order, albeit with VHDA-like density10,19 of over 1,200 kg/m3 in the 25−30 kbar range). This retention of residual crystallinity for mW in the face of such high-pressure compaction stems from a failure for the tetrahedral network to break down appreciably from its hexagonal lattice structure. In the case of TIP4P-Ice, it is important to note that the observed high-density liquid phase is not reflective or indicative of the putative−and controversial - hypothesized HDL phase, in that this is outside its predicted (thermal-) stability envelope;19,24−26 as such, this study offers no comment on the general, heavily contested “two-liquid” picture of water. However, both of these high-pressure states are judged to be intermediate ones adopted along the path toward respective thermodynamically stable

states for mW and TIP4P-Ice, i.e., toward SC1634 and ice VI, respectively.27 This is similar to observations of amorphous phases of ice during recent supercooled-water nanodroplet freezing21 and electro-freezing22 simulations in “No Man’s Land” along the path toward their ultimate thermodynamically stable states (with strong external electric fields in electrofreezing mimicking intense applied pressures).22 Finally, in an indictment of poorer performance of popular, and very useful, atomistic and coarse-grained water models, such as TIP4P-Ice and more especially mW (with its strong tetrahedral biasing, so appropriate for lower-pressure conditions), farther from their “comfort zone” of parametrization and generally good performance for lower-pressure ice and water, it is clear that much developmental work needs to be made in more popular, fixedcharge water potentials, especially for higher-pressure work. 5270

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274

Letter

The Journal of Physical Chemistry Letters

Figure 4. Typical CHILL33 analysis with regard to the change of cubic, hexagonal, interfacial and liquid ice-crystal-type percentage with rising pressure, using (a) mW and (b) TIP4P-Ice.

water.40 All of this points to TIP4P/Ice being superior in the present study to mW (in that it handles the gross situation of Bernal-Fowler hydrogen-bond and ice-lattice collapse), but also serves to highlight that more sophisticated treatments are needed for more quantitatively accurate high-pressure ice and water simulation, e.g., path-integral dynamics with accurate polarizable water models.

Indeed, one may speculate, perhaps not unfruitfully, as to why mW and TIP4P/Ice offer such radically different behavior under high pressure. Certainly, the strong tetrahedral biasing in mW appears to be reinforced by the smaller interplanar spacing (e.g., 3.79 versus 4.15 Å at 10 kbar, cf. Figure 1) under higherpressure conditions, with the three-body nature of the Stillinger−Weber potential not capturing the atomistic realism of explicit Bernal−Fowler (ice-rule) hydrogen bonds35 under severe compaction, and the tendency for these to collapse into the amorphous10,31 or liquid state. Indeed, at elevated pressures, nuclear quantal effects become all the more important in high-pressure ices (whether crystalline or amorphous), or condensed aqueous phases in general; French and Redmer have taken great care in developing a thermodynamic potential for high-pressure ices,36 while Sugimura et al. have highlighted the delicate intricacies of hydrogen-bond symmetrization in highpressure ice polymorphs37 and Ikeda has very recently shown that path-integral simulation is needed to define pressure more accurately for high-pressure-ice dynamics.38 All of these stateof-the-art experimental and molecular-simulation studies (albeit, admittedly, typically going to more extreme pressures than in the present study)36−38 do highlight in clear detail that quantum effects become important at high pressures, especially in its treatment of the hydrogen bond under severe pressure compaction. Although classical propagation is used in the present work, thereby, strictly, neglecting nuclear quantum effects, the empirical nature of TIP4P/Ice takes into account implicitly quantal effects to some extent in its parametrization (albeit this is more for lower-pressure ice); a further complication is that TIP4P/Ice is a rigid, fixed charge model, ideal for ambient-to-lower pressure ice simulation, and does not take into account intramolecular flexibility and polarizability changes that are evident for higher-pressure ice simulation, and on how this affects the definition of pressure and other thermodynamic and physical properties.38 Aside from atomistic resolution needed to probe realistically the subtleties of hydrogen bonding in water and ice at high pressure, there is the further matter of how mW and TIP4P/Ice, and other popular potentials, handle more collective system (vibrational) properties, such as phonon propagation. Reference 15 compares mW and TIP4P/ Ice for massive (million-molecule) simulation of water/ice, and shows that TIP4P/Ice is needed for more quantitatively realistic ice-crystallization kinetics, due to the explicit hydrogenbond rearrangements that are necessary, while refs 39 and 40 show that the TIP4P-type family is suitable for handling thermal-conduction processes in ice Ih39 and supercooled

■

METHODOLOGY

Sudden triaxial compression was applied via an NPT ensemble,41,42 at 240 K with pressures from 1 kbar up to 30 kbar, to large systems of bulk ice Ih, following NVT relaxation at 240 K using a Nosé−Hoover thermostat and 9 Å cutoff.42,43 For TIP4P-Ice, the smooth particle-mesh Ewald (SPME) method was used to handle long-range electrostatic interactions.44 As mentioned previously, compression time was ∼70−130 ns, and the new density and overall configurational energy was generally achieved within a few nanoseconds. Almost cubic simulation boxes were fashioned from supercells of Hayward−Reimers ice Ih coordinates45 for 1 064 448 molecules for mW and 43 200 molecules for TIP4P-Ice, with one TIP4P-Ice simulation for this larger million-molecule cell at 10 kbar. Supercooled liquid water (SCW), consisting of 43,200 molecules, was also relaxed under NPT conditions at 240 K and 1 bar until the density reached a plateau of ∼940 kg/m3 for TIP4P-Ice (in agreement with ref 46) and ∼1010 kg/m3 for mW and changed no further. The LAMMPS simulation software was used.47 To observe structural response on foot of compaction, in terms of phase/polymorph identification, CHILL33 (cubic hexagonal interfacial liquid) analysis was applied, in addition to computing site−site radial distribution functions (RDFs). In addition, for evolution of (rising) density and energetic properties, we detect the “plateaux time” to reach the ultimate values (or plateaux) of the system density and averaged configurational energy per water molecule. Here, the density and potential energy are binned for every 10 consecutive sampled values, obtaining an underlying average per bin; the first bin time whose average is found to equal or surpass 99% of the final result for density and averaged-per-water potential energy yields the plateau time. Based on the above-described binning procedure, a transition rate can be defined for the first average binning time whose corresponding data is found to equal or surpass 1079 kg/m3 and −14.07 kcal/mol (TIP4P-Ice) and 1039 kg/m 3 and −11.58 kcal/mol (mW) for the respective density and 5271

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274

Letter

The Journal of Physical Chemistry Letters

Figure 5. O−O radial distribution functions (RDFs) during compaction from 0.001 to 10 kbar, and depressurisation back to 0.001 kbar. For mW in the upper panel (A), the phase transition is reversiblethe postdepressurisation phase is to the original ice Ih. The postcompaction is squashed ice Ih (cf. Figure 1, upper right), and not SC16,32 but, in any event, this is probably a high-pressure intermediate phase. In part B, for supercooled water (SCW) as the starting point “MS1” (cf. Figure S9), shorter-range ordering appears upon compression, detected via peak splitting and shifting to shorter distances. After pressure removal, the potential and density of the phase ‘MS3′ (cf. Figure S9) is almost the same as MS1, but with different molecular order. In the lower section for TIP4P-Ice (C), ice Ih transitions to HDL, and after pressure removal back to 0.001 kbar yields supercooled liquid (SCW). In (D), compaction of initially ambient-pressure supercooled liquid leads to 10 kbar-pressurized liquid (defacto HDL), in excellent agreement with subpanel C, which shows pressure-driven Ih dissociation to HDL. Upon pressure release, the identical ambient-pressure liquid is retrieved, as in the beginning (and also as in subpanel C on the left after depressurisation of HDL).

averaged configurational potential energy. Then this can be normalized in terms of time, producing the transition rate.

■

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b02270.

system potential energies and densities during compaction-and-depressurization cycle with both supercooled water and ice Ih as starting points. (PDF)

AUTHOR INFORMATION

Corresponding Authors

*(M.R.G.) E-mail: [email protected]. *(N.J.E.) E-mail: [email protected].

(i) Evolution of the potential energy and density for both models over the full pressure range studied, (ii) plateaux times for both models, in terms of potential energy and system density, (iii) dependence of plateaux times upon pressure, (iv) evolution and tabulation of

ORCID

Mohammad Reza Ghaani: 0000-0002-5511-5775 Prithwish K. Nandi: 0000-0003-3458-8853 Niall J. English: 0000-0002-8460-3540 5272

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274

Letter

The Journal of Physical Chemistry Letters Notes

Incipient-Nucleation Behaviour and Role of System Size. Phys. Rev. E 2015, 92, 032132. (18) Wu, J.; Ning, F.; Trinh, T. T.; Kjelstrup, S.; Vlugt, T. J. H.; He, J.; Skallerud, K B.H.; Zhang, Z. Mechanical Instability of Monocrystalline and Polycrystalline Methane Hydrates. Nat. Commun. 2015, 6, 8743. (19) Johari, G. P.; Teixeira, J. Thermodynamic Analysis of the TwoLiquid Model for Anomalies of Water, HDL−LDL Fluctuations, and Liquid−Liquid Transition. J. Phys. Chem. B 2015, 119, 14210−14220. (20) Lauricella, M.; Meloni, S.; Liang, S.; English, N. J.; Kusalik, P. G.; Ciccotti, G. Clathrate Structure-Type Recognition: Application to Hydrate Nucleation and Crystallisation. J. Chem. Phys. 2015, 142, 244503. (21) Nandi, P. K.; Burnham, C. J.; Futera, Z.; English, N. J. IceAmorphization of Supercooled Water Nanodroplets in No Man’s Land. ACS Earth Space Chem. 2017, 1, 187−196. (22) Nandi, P. K.; Burnham, C. J.; English, N. J. Electro-Nucleation of Water Nano-droplets in No Man’s Land to Fault-Free Ice Ic. Phys. Chem. Chem. Phys. 2018, 20, 8042−8053. (23) Nandi, P. K.; Burnham, C. J.; English, N. J. Electro-Suppression of Water Nano-droplets’ Solidification in No Man’s Land: Electromagnetic Fields’ Entropic Trapping of Supercooled Water. J. Chem. Phys. 2018, 148, 044503. (24) Soper, A. K. Recent Water Myths. Pure Appl. Chem. 2010, 82, 1855−1867. (25) Nilsson, A.; Pettersson, L. G. M. The Structural Origin of Anomalous Properties of Liquid Water. Nat. Commun. 2015, 6, 8998. (26) Perakis, F.; et al.et al. Diffusive Dynamics During the High-toLow Density Transition in Amorphous Ice. Proc. Natl. Acad. Sci. U. S. A. 2017, 114, 8193−8198. (27) Abascal, L. F.; Sanz, E.; García Fernández, R.; Vega, C. A Potential Model for the Study of Ices and Amorphous Water: TIP4P/ Ice. J. Chem. Phys. 2005, 122, 234511. (28) Molinero, V.; Moore, E. B. Water Modeled as an Intermediate Element Between Carbon and Silicon. J. Phys. Chem. B 2009, 113, 4008−4016. (29) Conde, M. M.; Rovere, M.; Gallo, P. High-Precision Determination of the Melting Points of Water TIP4P/2005 and Water TIP4P/Ice Models by the Direct Coexistence Technique. J. Chem. Phys. 2017, 147, 244506. (30) Moore, E. B.; Molinero, V. Ice Crystallisation in Water’s ″NoMan’s Land″. J. Chem. Phys. 2010, 132, 244504. (31) English, N. J.; Tse, T. S. Pressure-Induced Amorphisation of Methane Hydrate. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 104109. (32) Lupi, L.; Hudait, A.; Peters, B.; Grunwald, M.; Mullen, R. G.; Nguyen, A. H.; Molinero, V. Role of Stacking Disorder in Ice Nucleation. Nature 2017, 551, 218−222. (33) Moore, E. B.; de la Llave, E.; Welke, K.; Scherlis, D. A.; Molinero, V. Freezing, Melting and Structure of Ice in a Hydrophilic Nanopore. Phys. Chem. Chem. Phys. 2010, 12, 4124−4134. (34) Romano, F.; Russo, J.; Tanaka, H. Novel Stable Crystalline Phase for the Stillinger-Weber Potential. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 014204. (35) Bernal, J. D.; Fowler, R. H. A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions. J. Chem. Phys. 1933, 1, 515−548. (36) French, M.; Redmer, D. Construction of a Thermodynamic Potential for the Water Ices VII and X. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 014308. (37) Sugimura, E.; Iitaka, T.; Hirose, K.; Kawamura, K.; Sata, N.; Ohishi, Y. Compression of H2O Ice to 126 GPa and Implications for Hydrogen-Bond Symmetrization: Synchrotron X-Ray Diffraction Measurements and Density-Functional Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 214103. (38) Ikeda, T. First principles centroid molecular dynamics simulation of high pressure ices. J. Chem. Phys. 2018, 148, 102332.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank Christian Burnham for technical assistance and Peter Kusalik for interesting conversations, as well as provision of computing resources from the Irish Centre for High-End Computing. N.J.E. and P.K.N. thank Science Foundation Ireland for funding under Grant SFI 15/ERCI3142, including additional computing. M.R.G. thanks the Irish Research Council for his Government-of-Ireland postdoctoral fellowship, under Grant No. GOIPD/2016/365.

■

REFERENCES

(1) Eisenberg, D.; Kauzmann, W. The Structure and Properties of Water; Oxford University Press: Oxford, U.K., 1969. (2) English, N. J.; Tse, J. S.; Gallagher, R. Thermal Conductivity in Amorphous Ices from Molecular Dynamics. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 092201. (3) Hoshino, K.; Yoshikawa, T.; Munejiri, S. Pressure-Induced Structural Change from Low-Density to High-Density Amorphous Ice by Molecular-Dynamics Simulations. Comput. Phys. Commun. 2011, 182, 49−51. (4) English, N. J.; MacElroy, J. M. D. Perspectives on Molecular Simulation of Clathrate Hydrates: Progress, Prospects and Challenges. Chem. Eng. Sci. 2015, 121, 133−156. (5) English, N. J.; El-Hendawy, M. M.; Mooney, D. A.; MacElroy, J. M. D. Perspectives on Atmospheric CO2 Fixation in Inorganic and Biomimetic Structures. Coord. Chem. Rev. 2014, 269, 85−95. (6) Chiu, J.; Starr, F. W.; Giovambattista, N. Pressure-Induced Transformations in Computer Simulations of Glassy Water. J. Chem. Phys. 2013, 139, 184504. (7) Katayama, Y.; Hattori, T.; Saitoh, H.; Ikeda, T.; Aoki, K.; Fukui, H.; Funakoshi, K. Structure of Liquid Water under High Pressure up to 17 GPa. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 014109. (8) French, M.; Mattsson, T. R.; Redmer, R. Diffusion and Electrical Conductivity in Water at Ultrahigh Pressures. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 174108. (9) Jenniskens, P. B.; Blake, D. F.; Wilson, M. A.; Pohorille, A. HighDensity Amorphous Ice: The Frost on Interstellar Grains. Astrophys. J. 1995, 455, 389−401. (10) English, N. J.; Tse, J. S. Reversible Pressure-Induced CrystalAmorphous Structural Transformation in Ice Ih. Chem. Phys. Lett. 2014, 609, 54−58. (11) He, C.; Lian, J. S.; Jiang, Q. Electronic Structures and Hydrogen Bond Network of High-Density and Very High-Density Amorphous Ices. J. Phys. Chem. B 2005, 109, 19893−19896. (12) Koza, M. M.; Geil, B.; Scheuermann, M.; Schober, H.; Monaco, G.; Requardt, H. Vibrational Dynamics of Very High Density Amorphous Ice Studied by High-Resolution X-ray Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 224301. (13) Futera, Z.; English, N. J. Pressure Dependence of Structural Properties of Ice VII: an Ab-Initio Molecular-Dynamics Study. J. Chem. Phys. 2018, 148, 204505. (14) Matsumoto, M.; Saito, S.; Ohmine, I. Molecular Dynamics Simulation of the Ice Nucleation and Growth Process Leading to Water. Nature 2002, 416, 409−413. (15) English, N. J. Massively Parallel Molecular-Dynamics Simulation of Ice Crystallisation and Melting: the Roles of System Size, Ensemble, and Electrostatics. J. Chem. Phys. 2014, 141, 234501. (16) English, N. J.; Lauricella, M.; Meloni, S. Massively-Parallel Molecular Dynamics Simulation of Clathrate Hydrate Precursors at Planar Water-Methane Interfaces: Insights into Heterogeneous Nucleation. J. Chem. Phys. 2014, 140, 204714. (17) English, N. J.; Tse, J. S. Massively-Parallel Molecular Dynamics Simulation of Ice-Crystallite Pre-cursors in Supercooled Water: 5273

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274

Letter

The Journal of Physical Chemistry Letters (39) English, N. J.; Tse, J. S.; Carey, D. J. Mechanisms for Thermal Conduction in Various Polymorphs of Methane Hydrate. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 134306. (40) English, N. J.; Tse, J. S. Thermal conductivity of supercooled water: an equilibrium molecular-dynamics exploration. J. Phys. Chem. Lett. 2014, 5, 3819−3824. (41) Andersen, H. C. Molecular Dynamics Simulations at Constant Pressure and/or Temperature. J. Chem. Phys. 1980, 72, 2384. (42) Hoover, W. G. Canonical dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695−1697. (43) Nosé, S. A Unified Formulation of the Constant-Temperature Molecular-Dynamics Methods. J. Chem. Phys. 1984, 81, 511. (44) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A. A Smooth Particle Mesh Ewald method. J. Chem. Phys. 1995, 103, 8577−8593. (45) Hayward, J. A.; Reimers, J. R. Unit Cells for the Simulation of Hexagonal Ice. J. Chem. Phys. 1997, 106, 1518. (46) Espinosa, J. R.; Sanz, E.; Valeriani, C.; Vega, C. Homogeneous Ice Nucleation Evaluated for Several Water Models. J. Chem. Phys. 2014, 141, 18C529. (47) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19.

5274

DOI: 10.1021/acs.jpclett.8b02270 J. Phys. Chem. Lett. 2018, 9, 5267−5274