Two-dimensional Ice Research Articles

Superheating of monolayer ice in graphene nanocapillaries.

The freezing and melting of low-dimensional materials, either via a first-order phase transition or without any discontinuity in thermodynamic, still remain a matter of debate. Melting (superheating) in two-dimensional (2D) ice is fundamentally different from that in bulk counterpart. Here, we perform comprehensive molecular dynamics simulations of the superheating of monolayer ice in graphene nanocapillaries to understand the nature of melting transition in 2D water/ice. We find four different superheating (melting) scenarios can happen in the superheating of monolayer square-like ice, which are closely related to the lateral pressure and the channel width. The anomalous two-stage melting transition with arisen coexistence phase is found, which reveals the unknown extraordinary characteristics of melting in 2D water/ice. Under ultrahigh lateral pressure, the intermediate monolayer triangular amorphous ice will be formed during the superheating of monolayer square-like ice with both continuous-like and first-order phase transitions. Whereas, under low lateral pressure, the melting in monolayer square-like ice manifests typical discontinuity with notable hysteresis-loop in potential energy during the heating/cooling process. Moreover, we also find that highly puckered monolayer square-like ice can transform into bilayer AB-stacked amorphous ice with square pattern in the superheating process. The superheating behavior under high lateral pressure can be partly regarded as the compression limit of superheated monolayer water. The intrinsic phenomena in our simulated superheating of monolayer ice may be significant for understanding the melting behavior in 2D water/ice.

Double-layer ice from first principles

The formation of monolayer and multilayer ice with a square lattice structure has recently been reported on the basis of transmission electron microscopy experiments, renewing interest in confined two-dimensional ice. Here we report a systematic density functional theory study of double-layer ice in nanoconfinement. A phase diagram as a function of confinement width and lateral pressure is presented. Included in the phase diagram are honeycomb hexagonal, square-tube, hexagonal-close-packed, and buckled-rhombic structures. However, contrary to experimental observations, square structures do not feature: our most stable double-layer square structure is predicted to be metastable. This study provides general insight into the phase transitions of double-layer confined ice and a fresh theoretical perspective on the stability of square ice in graphene nanocapillary experiments.

Two-dimensional ice mapping of molecular cores

We present maps of the column densities of H$_2$O, CO$_2$, and CO ices towards the molecular cores B~35A, DC~274.2-00.4, BHR~59, and DC~300.7-01.0. These ice maps, probing spatial distances in molecular cores as low as 2200~AU, challenge the traditional hypothesis that the denser the region observed, the more ice is present, providing evidence that the relationships between solid molecular species are more varied than the generic picture we often adopt to model gas-grain chemical processes and explain feedback between solid phase processes and gas phase abundances. We present the first combined solid-gas maps of a single molecular species, based upon observations of both CO ice and gas phase C$^{18}$O towards B~35A, a star-forming dense core in Orion. We conclude that molecular species in the solid phase are powerful tracers of "small scale" chemical diversity, prior to the onset of star formation. With a component analysis approach, we can probe the solid phase chemistry of a region at a level of detail greater than that provided by statistical analyses or generic conclusions drawn from single pointing line-of-sight observations alone.

Integer quantum magnon Hall plateau-plateau transition in a spin-ice model

Low-energy magnon bands in a two-dimensional spin ice model become integer quantum magnon Hall bands. By calculating the localization length and the two-terminal conductance of magnon transport, we show that the magnon bands with disorders undergo a quantum phase transition from an integer quantum magnon Hall regime to a conventional magnon localized regime. Finite size scaling analysis as well as a critical conductance distribution shows that the quantum critical point belongs to the same universality class as that in the quantum Hall transition. We characterize thermal magnon Hall conductivity in disordered quantum magnon Hall system in terms of robust chiral edge magnon transport.

Hydrophobic Ice Confined between Graphene and MoS2

The structure and nature of water confined between hydrophobic molybdenum disulfide (MoS2) and graphene (Gr) are investigated at room temperature by means of atomic force microscopy. We find the formation of two-dimensional (2D) crystalline ice layers. In contrast to the hexagonal ice 'bilayers' of bulk ice, these 2D crystalline ice phases consist of two planar hexagonal layers. Additional water condensation leads to either lateral expansion of the ice layers or to the formation of three-dimensional water droplets on top or at the edges of the two-layer ice, indicating that water does not wet these planar ice films. The results presented here are in line with a recent theory suggesting that water confined between hydrophobic walls forms 2D crystalline two-layer ice with a nontetrahedral geometry and intrahydrogen bonding. The lack of dangling bonds on either surface of the ice film gives rise to a hydrophobic character. The unusual geometry of these ice films is of great potential importance in biological systems with water in direct contact with hydrophobic surfaces.

Thermodynamics of emergent magnetic charge screening in artificial spin ice.

Electric charge screening is a fundamental principle governing the behaviour in a variety of systems in nature. Through reconfiguration of the local environment, the Coulomb attraction between electric charges is decreased, leading, for example, to the creation of polaron states in solids or hydration shells around proteins in water. Here, we directly visualize the real-time creation and decay of screened magnetic charge configurations in a two-dimensional artificial spin ice system, the dipolar dice lattice. By comparing the temperature dependent occurrence of screened and unscreened emergent magnetic charge defects, we determine that screened magnetic charges are indeed a result of local energy reduction and appear as a transient minimum energy state before the system relaxes towards the predicted ground state. These results highlight the important role of emergent magnetic charges in artificial spin ice, giving rise to screened charge excitations and the emergence of exotic low-temperature configurations.

HIGH SPEED COMPUTING OF ICE THICKNESS EQUATION FOR ICE SHEET MODEL

Two-dimensional (2-D) ice flow thermodynamics coupled model acts as a vital role for visualizing the ice sheet behaviours of the Antarctica region and the climate system. One of the parameters used in this model is ice thickness. Explicit method of finite difference method (FDM) is used to discretize the ice thickness equation. After that, the equation will be performed on Compute Unified Device Architecture (CUDA) programming by using Graphics Processing Unit (GPU) platform. Nowadays, the demand of GPU for solving the computational problem has been increasing due to the low price and high performance computation properties. This paper investigates the performance of GPU hardware supported by the CUDA parallel programming and capable to compute a large sparse complex system of the ice thickness equation of 2D ice flow thermodynamics model using multiple cores simultaneously and efficiently. The parallel performance evaluation (PPE) is evaluated in terms of execution time, speedup, efficiency, effectiveness and temporal performance.

Experimental investigation of flowfield over an iced aerofoil

ABSTRACTWind-tunnel measurements were used to study the characteristics of the unsteady separation bubbles on a NACA 0015 aerofoil with simulated two-dimensional leading-edge glaze ice accretions. The unsteadiness present in the iced-aerofoil flowfield was determined using measurements of the time-dependent aerofoil surface pressure distribution at Reynolds number of 1.0 × 106. Additionally, the unsteady flow features were investigated through the power spectrum of the stream-wise velocity fluctuations using a hot-wire anemometry. The results showed that the highest value of root-mean-square fluctuation of the surface pressure consistently occurred upstream of the mean shear-layer reattachment location. Spectral analysis of stream-wise velocity fluctuations near reattachment location revealed evidence of the regular frequency at Strouhal numbers of 0.5-0.63. Moreover, the low-frequency oscillations associated with shear-layer flapping was also identified in the wake velocity spectra on the order of 10 Hz that resulted in Strouhal numbers of 0.0186-021.

Discrete-Element bonded-particle Sea Ice model DESIgn, version 1.3a – model description and implementation

Abstract. This paper presents theoretical foundations, numerical implementation and examples of application of the two-dimensional Discrete-Element bonded-particle Sea Ice model – DESIgn. In the model, sea ice is represented as an assemblage of objects of two types: disk-shaped "grains" and semi-elastic bonds connecting them. Grains move on the sea surface under the influence of forces from the atmosphere and the ocean, as well as interactions with surrounding grains through direct contact (Hertzian contact mechanics) and/or through bonds. The model has an experimental option of taking into account quasi-three-dimensional effects related to the space- and time-varying curvature of the sea surface, thus enabling simulation of ice breaking due to stresses resulting from bending moments associated with surface waves. Examples of the model's application to simple sea ice deformation and breaking problems are presented, with an analysis of the influence of the basic model parameters ("microscopic" properties of grains and bonds) on the large-scale response of the modeled material. The model is written as a toolbox suitable for usage with the open-source numerical library LIGGGHTS. The code, together with full technical documentation and example input files, is freely available with this paper and on the Internet.

Numerical simulation of the flow velocity and temperature of the Dongkemadi Glacier

The flow velocity and ice temperature of a glacier reflect the response of the glacier to climate change. However, because of the restrictions of observation conditions, it is often difficult to acquire the ice velocity and temperature field for the entire glacier profile. In this study, we use a two-dimensional ice flow model and energy balance model to simulate the ice velocity and temperature using field measurements made with ground penetrating radar for the profile of the small Dongkemadi Glacier, and verify the simulated surface velocity with interferometric synthetic aperture radar data. The simulation for the flow velocity shows that the velocity depends on the surface and bedrock slopes, glacier profile shape and mass supply way, and the surface velocity increases with an increase in the surface slope. Sensitivity analysis shows that the terrain and slope affect the profile velocity. Simulation results for temperature show that the ice-body temperature is highest in the lower ice body at a subglacial position altitude of 5520 m a.s.l. This location not only gathers melt water most easily but also undergoes the strongest effect of geothermal heat flow. The distributions of the ice velocity and ice-body temperature provide a good reference for research on glacier vulnerability assessment and the response of glaciers to climate change.

Dynamics of Bound Monopoles in Artificial Spin Ice: How to Store Energy in Dirac Strings.

Dirac strings in spin ices are lines of reversed dipoles joining two quasiparticle excitations. These excitations behave as unbound emergent monopoles if the tension of Dirac strings vanishes. In this Letter, analytical and numerical analysis are used to study the dynamics of two-dimensional dipolar spin ices, artificially created analogs of bulk spin ice, in the regime of bound monopoles. It is shown that, in this regime, strings, rather than monopoles, are effective degrees of freedom explaining the finite-width band of Pauling states. A measurable prediction of path-time dependence of endpoints of a stretched and, then, released Dirac string is made and verified via simulations. It is shown that string dynamics is defined by the characteristic tension-to-mass ratio, which is determined by the fine structure constant and lattice dependent parameter. It is proposed to use string tension to achieve spontaneous magnetic currents. A concept of an energy storing device on the basis of this principle is proposed and illustrated by an experimental demonstration. A scheme of independent measurement at the nanoscale is proposed.

AA-stacked bilayer square ice between graphene layers

Water confined between two graphene layers with a separation of a few $\AA{}$ forms a layered two-dimensional ice structure. Using large scale molecular dynamics simulations with the adoptable ReaxFF interatomic potential we found that flat monolayer ice with a rhombic-square structure nucleates between the graphene layers which is nonpolar and nonferroelectric. We provide different energetic considerations and H-bonding results that explain the interlayer and intralayer properties of two-dimensional ice. The controversial AA stacking found experimentally [Algara-Siller et al., Nature (London) 519, 443 (2015)] is consistent with our minimum-energy crystal structure of bilayer ice. Furthermore, we predict that an odd number of layers of ice has the same lattice structure as monolayer ice, while an even number of ice layers exhibits the square ice AA stacking of bilayer ice.

Water in Inhomogeneous Nanoconfinement: Coexistence of Multilayered Liquid and Transition to Ice Nanoribbons.

Phase behavior and the associated phase transition of water within inhomogeneous nanoconfinement are investigated using molecular dynamics simulations. The nanoconfinement is constructed by a flat bottom plate and a convex top plate. At 300 K, the confined water can be viewed as a coexistence of monolayer, bilayer, and trilayer liquid domains to accommodate the inhomogeneous confinement. With increasing liquid density, the confined water with uneven layers transforms separately into two-dimensional ice crystals with unchanged layer number and rhombic in-plane symmetry for oxygen atoms. The monolayer water undergoes the transition first into a puckered ice nanoribbon, and the bilayer water transforms into a rhombic ice nanoribbon next, followed by the transition of trilayer water into a trilayer ice nanoribbon. The sequential localized liquid-to-solid transition within the inhomogeneous confinement can also be achieved by gradually decreasing the temperature at low liquid densities. These findings of phase behaviors of water under the inhomogeneous nanoconfinement not only extend the phase diagram of confined water but also have implications for realistic nanofluidic systems and microporous materials.

Offshore drilling rig ice accretion modeling including a surficial brine film

This article presents an extension of the two-dimensional icing model ICEMOD2. In contrast to this model the new model (called ICEMOD2.1) considers the inertia terms in the momentum equation. The derivation of the model is presented and the model is applied to two typical structures of an offshore drilling rig which may be exposed to spray icing: a corner column and a truss. A mean impact-generated spray mass flux formula (called the “normal” value) based on droplet kinematics and spray measurements on the Norwegian semi-submersible rig “Treasure Scout” has been implemented in the model. The model results showed satisfactory agreement with some actual icing registration data from the drilling rigs “SEDCO 708” and “SEDCO 709”. Additionally sensitivity tests are presented for a selected section of a rig column of diameter 5.0m varying air temperatures, wind speeds and spray frequencies as expected ice accretion increases with decreasing air temperature. With the chosen formula for the spray mass flux and wind speed (17–25ms−1) ice accretion also increases with increasing wind speed. The available field results of Treasure Scout enable us only to construct a time-average spray mass flux formula independent of spray frequency. The single spray mass flux is then in the model a derived quantity obtained by dividing the time-average value by the product of spray frequency and spray duration. Based on these presumptions the sensitivity tests show that spray frequency variations have only a minor effect upon accreted ice load when normal spray mass flux is assumed (corresponding here to 5–10gm−2s−1). If however the spray mass flux is put 25 times as large as the normal value a substantial increase in model ice load with increasing spray frequency is obtained. Probably this is due to a large increase in brine film thickness (a factor of about 10). A possible theoretical explanation is given in the text. Finally the significance of brine film motion in icing modeling has been discussed. It turns out that for cylinder icing ICEMOD2.1 and ICEMOD2 give the same ice load and thickness distribution. The only noticeable difference in the two model results is the brine film horizontal velocity, but only for an increased spray mass flux (of order 102‐103gm−2s−1). For normal spray mass flux a simplified time-dependent model version with brine film velocity put equal to zero (Model01) gives similar ice accretion results as ICEMOD2.1. Even a stationary version of the latter model (Model02) gives adequate results for normal spray conditions. For the increased spray mass flux some brine may however be pushed over to the lee side by wind stress, especially if the cylinder is slim such as a truss, and only the complete versions of ICEMOD2.1 or ICEMOD2 can handle this situation. Model01 will still give correct ice thickness results on the major part of the upwind side of the cylinder while Model02 only will give some icing close to the cylinder shoulders (which means that this model cannot approximate periodic icing in this case).

Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method

River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.

The description of grounding line migration in a two-dimensional mathematical model of an ice sheet

Contemporary thinning of the marine-based areas of ice sheets is believed to be the consequence of the grounding line retreat caused mainly by ocean gradual warming beneath the ice shelves. In order to estimate potential contribution of ice sheets into the future sea-level rise grounding line migration must be accurately described in the mathematical models. We incorporated an algorithm based on application of the boundary condition on the mass flux across the grounding line into a two-dimensional ice flow model. In the numerical experiments, externally forced ice sheet returns to its initial equilibrium state after termination of the external forcing (either accumulation rate or sea-level change anomalies). In future, the model will be modified to incorporate buttressing effect.

Scaling ansatz for the ac magnetic response in two-dimensional spin ice

Scaling ansatz for the ac magnetic response in two-dimensional spin ice

Highly confined water: two-dimensional ice, amorphous ice, and clathrate hydrates.

Understanding phase behavior of highly confined water, ice, amorphous ice, and clathrate hydrates (or gas hydrates), not only enriches our view of phase transitions and structures of quasi-two-dimensional (Q2D) solids not seen in the bulk phases but also has important implications for diverse phenomena at the intersection between physical chemistry, cell biology, chemical engineering, and nanoscience. Relevant examples include, among others, boundary lubrication in nanofluidic and lab-on-a-chip devices, synthesis of antifreeze proteins for ice-growth inhibition, rapid cooling of biological suspensions or quenching emulsified water under high pressure, and storage of H2 and CO2 in gas hydrates. Classical molecular simulation (MD) is an indispensable tool to explore states and properties of highly confined water and ice. It also has the advantage of precisely monitoring the time and spatial domains in the sub-picosecond and sub-nanometer scales, which are difficult to control in laboratory experiments, and yet allows relatively long simulation at the 10(2) ns time scale that is impractical with ab initio molecular dynamics simulations. In this Account, we present an overview of our MD simulation studies of the structures and phase behaviors of highly confined water, ice, amorphous ice, and clathrate, in slit graphene nanopores. We survey six crystalline phases of monolayer (ML) ice revealed from MD simulations, including one low-density, one mid-density, and four high-density ML ices. We show additional supporting evidence on the structural stabilities of the four high-density ML ices in the vacuum (without the graphene confinement), for the first time, through quantum density-functional theory optimization of their free-standing structures at zero temperature. In addition, we summarize various low-density, high-density, and very-high-density Q2D bilayer (BL) ice and amorphous ice structures revealed from MD simulations. These simulations reinforce the notion that the nanoscale confinement not only can disrupt the hydrogen bonding network in bulk water but also can allow satisfaction of the ice rule for low-density and high-density Q2D crystalline structures. Highly confined water can serve as a generic model system for understanding a variety of Q2D materials science phenomena, for example, liquid-solid, solid-solid, solid-amorphous, and amorphous-amorphous transitions in real time, as well as the Ostwald staging during these transitions. Our simulations also bring new molecular insights into the formation of gas hydrate from a gas and water mixture at low temperature.

An unconventional bilayer ice structure on a NaCl(001) film.

Water-solid interactions are of broad importance both in nature and technology. The hexagonal bilayer model based on the Bernal-Fowler-Pauling ice rules has been widely adopted to describe water structuring at interfaces. Using a cryogenic scanning tunnelling microscope, here we report a new type of two-dimensional ice-like bilayer structure built from cyclic water tetramers on an insulating NaCl(001) film, which is completely beyond this conventional bilayer picture. A novel bridging mechanism allows the interconnection of water tetramers to form chains, flakes and eventually a two-dimensional extended ice bilayer containing a regular array of Bjerrum D-type defects. Ab initio density functional theory calculations substantiate this bridging growth mode and reveal a striking proton-disordered ice structure. The formation of the periodic Bjerrum defects with unusually high density may have a crucial role as H donor sites in directing multilayer ice growth and in catalysing heterogeneous chemical reactions on water-coated salt surfaces.

Residual entropy of ices and clathrates from Monte Carlo simulation.

We calculated the residual entropy of ices (Ih, Ic, III, V, VI) and clathrates (I, II, H), assuming the same energy of all configurations satisfying the Bernal-Fowler ice rules. The Metropolis Monte Carlo simulations in the range of temperatures from infinity to a size-dependent threshold were followed by the thermodynamic integration. Convergence of the simulation and the finite-size effects were analyzed using the quasichemical approximation and the Debye-Hückel theory applied to the Bjerrum defects. The leading finite-size error terms, ln N/N, 1/N, and for the two-dimensional square ice model also 1/N(3/2), were used for an extrapolation to the thermodynamic limit. Finally, we discuss the influence of unequal energies of proton configurations.