sI Hydrate Research Articles

Heat of dissociation from Statistical Thermodynamics: Using calorimetric data to estimate gas hydrate parameters

Statistical Thermodynamics was used to derive an expression for hydrate enthalpy of dissociation. From this expression, a parameter regression methodology was proposed in which calorimetric experiments were included along with cage occupancies, guest mole fraction and equilibrium condition experiments.Since not all the experiments depend on the whole set of hydrate parameters, we developed a stepwise methodology that reduces hydrate estimation problem to three simple sub problems, being two of them analytically solvable. The solution of the stepwise methodology is then the initial guess of the hydrate global parameter estimation that can be solved using a deterministic algorithm.From the parameter estimation, we observed that the hard-core sphere parameter of the Kihara potential was not statistically significant in the case studied here. It was rejected with a significance degree of 5%, which lead to the use of the Lennard-Jones potential.After estimating hydrate parameters for carbon dioxide and methane sI hydrates, we could relate hydrate enthalpy of dissociation to equilibrium conditions for this binary mixture. We found that the empirical law that states that enthalpy of dissociation of mixed hydrates increases with the increase of occupancy of the largest guest in the large cavity was verified only when the water-poor fluid phase is a vapor. This means that fluid phases also have an important role in hydrate enthalpy of dissociation.

Secondary gaseous guest-dependent structures of binary neopentyl alcohol hydrates and their tuning behavior for potential application to CO2 capture

Clathrate hydrates, commonly called gas hydrates, are non-stoichiometric inclusion compounds with tunable gas storage and separation capabilities. Various efforts have been made to apply these hydrates to energy and environmental fields including energy storage and greenhouse gas capture and separation technologies. Although the unary use of gaseous guest molecules such as methane, carbon dioxide, and nitrogen is generally expected to achieve maximal storage capacity by filling the guest in both small and large cages of each structure, introducing additional liquid guest molecules into the clathrate hydrates could be a more feasible option from an engineering perspective, since such liquid guest molecules often play a critical role in stabilization of the clathrate hydrate by shifting the thermodynamic phase equilibria to practically implementable milder pressure and temperature conditions. Here, we focus on the binary neopentyl alcohol clathrate hydrates with gaseous guest molecules, including carbon dioxide, methane, and nitrogen, to provide a better understanding of the complex nature of the host–guest interactions occurring in the clathrate hydrates. Thermodynamic P – T phase equilibria were measured, and spectroscopic analyses were performed employing HRPD, Raman, and NMR spectrometers. The results revealed that the NPA guest molecule forms sI or sII hydrate depending on the binary gaseous guest molecules. This paper also reports for the first time that the composition of CO2 guest molecules may be ‘tuned’ within the cages of sI hydrate of NPA.

Effect of guest gas on the mixed tetrahydrofuran hydrate kinetics in a quiescent system

Clathrate hydrates are ‘inclusion compounds’ that have the ability to encompass multifold volumes of guest gas molecules, thus being advantageous for gas storage and gas separation applications. CO2 capture in the form of hydrates is an environmentally benign and cost-effective approach. In this work, we examine the kinetics of CO2 hydrate formation at different operating conditions that result in the formation of pure sI hydrate, pure sII hydrates and/or a mixture of sI and sII hydrates. Morphology observations of different hydrates formed are presented with the associated CO2 uptake achieved under different experimental conditions. We report strikingly contrasting morphology of mixed CO2 and mixed CH4 hydrates observed in presence of stoichiometric THF (5.6mol%) under similar pressure diving force and operating conditions. Interesting results observed during mixed CO2 hydrates using Differential Scanning Calorimetry (DSC) are documented. Based on DSC thermograms, we report interesting observations on the effect of guest gas in the mixed THF hydrate formation and dissociation. Moreover, mixed CH4/THF hydrates were found to be more stable in comparison to mixed CO2/THF hydrates. This work highlights that the choice of guest gas plays a significant role in the associated hydrate formation kinetics in presence of THF.

Greenhouse Gas (CHF3) Separation by Gas Hydrate Formation

In this study, the feasibility of gas hydrate-based greenhouse gas (CHF3) separation was investigated with a primary focus on thermodynamic, structural, and cage-filling characteristics of CHF3 + N2 hydrates. The three-phase (hydrate (H)–liquid water (LW)–vapor (V)) equilibria of CHF3 (10%, 20%, 40%, 60%, and 80%) + N2 + water systems provided the thermodynamic stability conditions of CHF3 + N2 hydrates. Powder X-ray diffraction revealed that the structure of the CHF3 + N2 hydrates was identified as sI (Pm3n) for all the CHF3 concentration ranges considered in this study. A pressure–composition diagram obtained at two different temperature conditions (279.15 and 283.15 K) demonstrated that 40% CHF3 could be enriched to 88% CHF3 by only one step of hydrate formation and that separation efficiency was higher at the lower temperature. Furthermore, Raman spectroscopy revealed that CHF3 molecules preferentially occupy large (51262) cages of the structure I (sI) hydrate during CHF3 + N2 hydrate formation. The o...

CO2 Hydrates – Effect of Additives and Operating Conditions on the Morphology and Hydrate Growth

In this paper, we present the kinetics of CO2 hydrate formation in presence of additives at different operating conditions that result in the formation of pure sI hydrate, pure sII hydrates and a mixture of sI and sII hydrates. Visual observations of different hydrates formed are presented with the associated CO2 uptake achieved under different experimental conditions. We observe a striking contrast in hydrate formation behavior observed for CH4 hydrate and CO2 hydrate in presence of tetrahydrofuran (THF) under similar diving force and operating conditions. Based on our experiments, it can be inferred that hydrate formation kinetics in presence of the THF is highly influenced by the type of guest gas.

Ab Initio Studies on the Clathrate Hydrates of Some Nitrogen- and Sulfur-Containing Gases.

Ab initio calculations are performed to investigate the host-guest interactions and multiple occupancies of some sulfur- (H2S, CS2) and nitrogen-containing (N2, NO, and NH3) molecules in dodecahedral, tetrakaidecahedral, and hexakaidecahedral water cages in this work. Five functionals in the framework of density functional theory are compared, and the M06-2X method appears to be the best to predict the binding energies as well as the geometries. Results show that N2 and NO molecules are more stable in the 51264 cage, while NH3 and H2S prefer to stabilize in the 51262 cage. This suggests that the sI hydrates of NH3 and H2S exhibit higher stability than the sII structures and that sII NO hydrate is more stable than sI NO hydrate. N2 is found to be more stable in type II structure with single occupancy and to form type I hydrate with multiple occupancy, which is consistent with the experimental observations. As to the guest molecule CS2, it may undergo severe structural deformation in the 512 and 51262 cage. For multiple occupancies, the 512, 51262, and 51264 water cages can trap up to two N2 molecules, and the 51264 water cage can accommodate two H2S molecules. This work is expected to provide new insight into the formation mechanism of clathrate hydrates for atmospherically important molecules.

Selective Encaging of N2O in N2O-N2 Binary Gas Hydrates via Hydrate-Based Gas Separation.

The crystal structure and guest inclusion behaviors of nitrous oxide-nitrogen (N2O-N2) binary gas hydrates formed from N2O/N2 gas mixtures are determined through spectroscopic analysis. Powder X-ray diffraction results indicate that the crystal structure of all the N2O-N2 binary gas hydrates is identified as the structure I (sI) hydrate. Raman spectra for the N2O-N2 binary gas hydrate formed from N2O/N2 (80/20, 60/40, 40/60 mol %) gas mixtures reveal that N2O molecules occupy both large and small cages of the sI hydrate. In contrast, there is a single Raman band of N2O molecules for the N2O-N2 binary gas hydrate formed from the N2O/N2 (20/80 mol %) gas mixture, indicating that N2O molecules are trapped in only large cages of the sI hydrate. From temperature-dependent Raman spectra and the Predictive Soave-Redlich-Kwong (PSRK) model calculation, we confirm the self-preservation of N2O-N2 binary gas hydrates in the temperature range of 210-270 K. Both the experimental measurements and the PSRK model calculations demonstrate the preferential occupation of N2O molecules rather than N2 molecules in the hydrate cages, leading to a possible process for separating N2O from gas mixtures via hydrate formation. The phase equilibrium conditions, pseudo-pressure-composition (P-x) diagram, and gas storage capacity of N2O-N2 binary gas hydrates are discussed in detail.

Flash crystallization kinetics of methane (sI) hydrate in a thermoelectrically-cooled microreactor.

The crystallization kinetics of methane (sI) hydrate were investigated in a thermoelectrically-cooled microreactor with in situ Raman spectroscopy. Step-wise and precise control of the temperature allowed acquisition of reproducible data within minutes, while the nucleation of methane hydrates can take up to 24 h in traditional batch reactors. The propagation rates of methane hydrate (from 3.1-196.3 μm s-1) at the gas-liquid interface were measured for different Reynolds' numbers (0.7-68.9), pressures (30.0-80.9 bar), and sub-cooling temperatures (1.0-4.0 K). The precise measurement of the propagation rates and their subsequent analyses revealed a transition from mixed heat-transfer-crystallization-rate-limited to mixed heat-transfer-mass-transfer-crystallization-rate-limited kinetics. A theoretical model, based on heat transfer, mass transfer, and intrinsic crystallization kinetics, was derived for the first time to understand the non-linear relationship between the propagation rate and sub-cooling temperature. The molecular diffusivity of methane within a stagnant film (ahead of the propagation front) was discovered to follow Stokes-Einstein, while calculated Hatta (0.50-0.68), Lewis (128-207), and beta (0.79-116) numbers also confirmed that the diffusive flux influences crystal growth. Understanding methane hydrate crystal growth is important to the atmospheric, oceanic, and planetary sciences and to energy production, storage, and transportation. Our discoveries could someday advance the science of other multiphase, high-pressure, and sub-cooled crystallizations.

Temperature and pressure correlation for volume of gas hydrates with crystal structures sI and sII

The temperature and pressure correlations for the volume of gas hydrates forming crystal structures sI and sII developed in previous study [Fluid Phase Equilib. 427 (2016) 268-281], focused on the modeling of pure gas hydrates relevant in CCS (carbon capture and storage), were revised and modified for the modeling of mixed hydrates in this study. A universal reference state at temperature of 273.15 K and pressure of 1 Pa is used in the new correlation. Coefficients for the thermal expansion together with the reference lattice parameter were simultaneously correlated to both the temperature data and the pressure data for the lattice parameter. A two-stage Levenberg Marquardt algorithm was employed for the parameter optimization. The pressure dependence described in terms of the bulk modulus remained unchanged compared to the original study. A constant value for the bulk modulus B 0 = 10 GPa was employed for all selected hydrate formers. The new correlation is in good agreement with the experimental data over wide temperature and pressure ranges from 0 K to 293 K and from 0 to 2000 MPa, respectively. Compared to the original correlation used for the modeling of pure gas hydrates the new correlation provides significantly better agreement with the experimental data for sI hydrates. The results of the new correlation are comparable to the results of the old correlation in case of sII hydrates. In addition, the new correlation is suitable for modeling of mixed hydrates.

High Pressure Structural Transitions in Kr Clathrate-Like Clusters

Classical thermodynamic properties of a size-specific Kr clathrate-like cluster, modeled by an ab initio and a semiempirical Kr–water potential, were computed from parallel-tempering Monte Carlo simulations. The temperature and pressure dependence of the cluster’s heat capacity was studied, and phase diagrams were constructed using a multiple-histogram method. By associating the heat capacity (maxima) and the Pearson correlation coefficient (minima/maxima) values with the phase transitions, attempts were made to identify such changes to particular cluster structures. Various isomers were computed by local optimizations of the interaction enthalpy at a set of randomly selected configurations at each temperature–pressure grid point. Their energy distributions and relative abundances were then employed to assign the observed phase transitions of the cluster. It was found that the structural changes at high pressures are related to Kr clathrate-like cages, such as those of the sI, sII, and sH hydrates, as wel...

Understanding decomposition and encapsulation energies of structure I and II clathrate hydrates.

When compressed with water or ice under high pressure and low temperature conditions, some gases form solid gas hydrate inclusion compounds which have higher melting points than ice under those pressures. In this work, we study the balance of the guest-water and water-water interaction energies that lead to the formation of the clathrate hydrate phases. In particular, molecular dynamics simulations with accurate water potentials are used to study the energetics of the formation of structure I (sI) and II (sII) clathrate hydrates of methane, ethane, and propane. The dissociation enthalpy of the clathrate hydrate phases, the encapsulation enthalpy of methane, ethane, and propane guests in the corresponding phases, and the average bonding enthalpy of water molecules are calculated and compared with accurate calorimetric measurements and previous classical and quantum mechanical calculations, when available. The encapsulation energies of methane, ethane, and propane guests stabilize the small and large sI and sII hydrate cages, with the larger molecules giving larger encapsulation energies. The average water-water interactions are weakened in the sI and sII phases compared to ice. The relative magnitudes of the van der Waals potential energy in ice and the hydrate phases are similar, but in the ice phase, the electrostatic interactions are stronger. The stabilizing guest-water "hydrophobic" interactions compensate for the weaker water-water interactions and stabilize the hydrate phases. A number of common assumptions regarding the guest-cage water interactions are used in the van der Waals-Platteeuw statistical mechanical theory to predict the clathrate hydrate phase stability under different pressure-temperature conditions. The present calculations show that some of these assumptions may not accurately reflect the physical nature of the interactions between guest molecules and the lattice waters.

Cage Occupancy and Stability of N2O-Encaged Structure I and II Clathrate Hydrates

The crystal structure and guest inclusion behaviors of nitrous oxide (N2O) hydrates with/without tetrahydrofuran (THF) were investigated through spectroscopic observations. The X-ray diffraction results showed that pure N2O hydrate has the formation of structure I (sI) hydrate and N2O–THF hydrate has the formation of structure II (sII) hydrate. For pure N2O hydrate, the Raman spectra revealed the occupation of N2O molecules in both the small 512 and large 51262 cages of the sI hydrate. There was a single Raman band in the ν1 and ν3 spectral regions for the N2O–THF (5.56 mol %) sII hydrate, indicating that the N2O molecules occupied only the small 512 cages of the sII hydrate. However, both sI and sII hydrate phases were monitored from the N2O–THF (2 mol %) hydrate sample. From a combination of Raman results and the thermodynamic model, the occupancies of N2O molecules in the small 512 and large 51262 cages of sI hydrate were estimated to be 0.746 and 0.978, respectively. The phase equilibrium conditions o...

Storage of Methane in Clathrate Hydrates: Monte Carlo Simulations of sI Hydrates and Comparison with Experimental Measurements

Extensive grand canonical Monte Carlo simulations are performed for the calculation of the amount of methane gas that can be stored inside the hydrate structure sI focusing on temperature and pressure conditions that are of interest to practical applications (e.g., methane storage/transportation, methane hydrates in nature). Langmuir-type “absorption isotherms” are used in order to present the results for methane in the cages of the hydrate structure. In particular, the methane content inside the different type of hydrate cages is given as a function of pressure, where the parameters of this function are temperature-dependent. A comparison between available experimental data for cage occupancies and calculated values resulted in good agreement. The correlation between chemical potential and pressure is determined through NVT Monte Carlo simulations. Simulations are performed for the TIP4P/Ice water model and two methane models (United–Atom and All–Atom). The calculations of the current study can be utiliz...

Model for gas hydrates applied to CCS systems part I. Parameter study of the van der Waals and Platteeuw model

In this study, divided in a series of three articles, the model for pure CO2 hydrate by Jäger et al. [Fluid Phase Equilib. 338 (2013) 100–113] has been improved and extended to other gases relevant in Carbon Capture and Storage (CCS) applications. The new gas hydrate model is inspired by the currently most accurate model available for natural gas hydrates by Ballard and Sloan [Fluid Phase Equilib. 194 (2002) 371–383], which belongs to the family of van der Waals and Platteeuw (vdWP) models [Adv. Chem. Phys. 2 (1959) 1]. The new model is combined with highly accurate equations of state (EoS) in form of the Helmholtz energy for fluid phases and with Gibbs energy models for pure solid phases. Part I describes a critical analysis of the main parameters of the vdWP-based hydrate model. The influences of the specific hydrate volume, of the Langmuir constant, and of the EoSs used for other phases than hydrate on the predicted hydrate composition and on phase equilibria with gas hydrates were investigated. A new correlation for the pressure dependency of the volume of gas hydrates forming structures sI and sII has been developed. The correlation based on the Murnaghan EoS [Proc. Natl. Acad. Sci. U. S. A. 30 (1944) 244] has good extrapolating behavior and behaves in a physically reasonable manner. It is shown that all experimental data for hydrate formers including mixed hydrates can be represented reasonably well by a universal bulk modulus around 10 GPa. Furthermore, it was found that the bulk modulus affects phase equilibria at high pressures while its impact on phase equilibria at moderate and low pressures below about 30 MPa is negligible. A strong influence of the Langmuir constant on the hydrate composition was observed, especially in case of small cavities of both sI and sII hydrate structures. Additionally, the influence of EoSs used for other phases than hydrate on the accuracy of quadruple point predictions is discussed. A multi-property fitting algorithm developed for optimization of parameters of the new hydrate model is introduced in part II. Results of the model including phase equilibria with hydrates, composition of hydrates, and enthalpy of formation of hydrates are provided in part III. The model has been implemented in the software package TREND 2.0 by Span et al. [Thermodynamic Reference and Engineering Data 2.0. (2015) Lehrstuhl fuer Thermodynamik, Ruhr-Universitaet Bochum].

Enclathration of CHF3 and C2F6 molecules in gas hydrates for potential application in fluorinated gas (F-gas) separation

In this study, gas hydrate-based fluorinated gas (F-gas) separation is proposed as a novel method to capture F-gases. This study investigates the thermodynamic, structural, and cage filling characteristics of the gas hydrates formed by two representative F-gases (CHF3 and C2F6) in order to verify the feasibility of the F-gas separation using gas hydrate formation. The three-phase (gas hydrate (H) – liquid water (LW) – vapor (V)) equilibria of the pure CHF3 and C2F6 hydrates are measured in order to examine the hydrate formation conditions. The PXRD patterns reveal the structure of the CHF3 hydrate and the C2F6 hydrate as a cubic structure I (sI) and structure II (sII), respectively. The enclathration of CHF3 and C2F6 molecules in each pure CHF3 and C2F6 hydrate is confirmed through 13C and 19F NMR analyses. In-situ Raman measurements are used to monitor the growth process of pure CHF3 hydrates, and they reveal the CHF3 molecules trapped in the sI large (51262) cages as well as in the sI small (512) cages. The computational study also demonstrates that CHF3 is encaged in both small (512) and large (51262) cages of the sI hydrate, whereas C2F6 only occupies the large (51264) cages of the sII hydrate.

Isostructural and cage-specific replacement occurring in sII hydrate with external CO2/N2 gas and its implications for natural gas production and CO2 storage

A replacement technique has been regarded as a promising strategy for both CH4 exploitation from gas hydrates and CO2 sequestration into deep-ocean reservoirs. Most research has been focused on replacement reactions that occur in sI hydrates due to their prevalence in natural gas hydrates. However, sII hydrates in nature have been also discovered in some regions, and the replacement mechanism in sII hydrates significantly differs from that in sI hydrates. In this study, we have intensively investigated the replacement reaction of sII (C3H8+CH4) hydrate by externally injecting CO2/N2 (50:50) gas mixture with a primary focus on powder X-ray diffraction, Raman spectroscopy, NMR spectroscopy, and gas chromatography analyses. In particular, it was firstly confirmed that there was no structural transformation during the replacement of C3H8+CH4 hydrate with CO2/N2 gas injection, indicating that sII hydrate decomposition followed by sI hydrate formation did not occur. Furthermore, the cage-specific replacement pattern of the C3H8+CH4 hydrate revealed that CH4 replacement with N2 in the small cages of sII was more significant than C3H8 replacement with CO2 in the large cages of sII. The total extent of the replacement for the C3H8+CH4 hydrate was cross-checked by NMR and GC analyses and found to be approximately 54%. Compared to the replacement for CH4 hydrate with CO2/N2 gas, the lower extent of the replacement for the C3H8+CH4 hydrate with CO2/N2 gas was attributable to the persistent presence of C3H8 in the large cages and the lower content of N2 in the feed gas. The structural sustainability and cage-specific replacement observed in the C3H8+CH4 hydrate with external CO2/N2 gas will have significant implications for suggesting target gas hydrate reservoirs and understanding the precise nature of guest exchange in gas hydrates for both safe natural gas production and long-term CO2 sequestration.

A Theoretical Study of the Hydration of Methane, from the Aqueous Solution to the sI Hydrate-Liquid Water-Gas Coexistence.

Monte Carlo and molecular dynamics simulations were done with three recent water models TIP4P/2005 (Transferable Intermolecular Potential with 4 Points/2005), TIP4P/Ice (Transferable Intermolecular Potential with 4 Points/ Ice) and TIP4Q (Transferable Intermolecular Potential with 4 charges) combined with two models for methane: an all-atom one OPLS-AA (Optimal Parametrization for the Liquid State) and a united-atom one (UA); a correction for the C–O interaction was applied to the latter and used in a third set of simulations. The models were validated by comparison to experimental values of the free energy of hydration at 280, 300, 330 and 370 K, all under a pressure of 1 bar, and to the experimental radial distribution functions at 277, 283 and 291 K, under a pressure of 145 bar. Regardless of the combination rules used for σC,O, good agreement was found, except when the correction to the UA model was applied. Thus, further simulations of the sI hydrate were performed with the united-atom model to compare the thermal expansivity to the experiment. A final set of simulations was done with the UA methane model and the three water models, to study the sI hydrate-liquid water-gas coexistence at 80, 230 and 400 bar. The melting temperatures were compared to the experimental values. The results show the need to perform simulations with various different models to attain a reliable and robust molecular image of the systems of interest.

13C NMR analysis of C2H6+C2H4+THF mixed hydrate for an application to separation of C2H4 and C2H6

Mixed hydrates (C2H4+5.56mol% THF, and C2H4+C2H6+5.56mol% THF) were analyzed using 13C MAS NMR spectroscopy. The hydrates were formed using a variety of feed gas compositions (100% C2H4; 20% C2H4+80% C2H6; 40% C2H4+60% C2H6; 60% C2H4+40% C2H6; and 80% C2H4+20% C2H6). According to the peak identification results, C2H4 molecules can occupy both the small and large cavities in the sI and sII hydrate structures, while C2H6 molecules can occupy only the large cavities of sI. Moreover, the mole fraction of C2H4 in the hydrate matrix was found to increase with increasing feed ratio of C2H4. On the basis of the NMR analysis, a hydrate-based process for separating C2H4 and C2H6 by repeated hydrate formation and dissociation was proposed. For cases with a feed-gas mixture with 20% C2H4 and 80% C2H6, a recovery of more than 88% C2H4 in the gas mixture could be achieved after five cycles of hydrate-based separation.

Hydrates of Cyclobutylamine: Modifications of Gas Clathrate Types sI and sH

Cyclobutylamine (cBA) and its four new hydrates were crystallized using an in situ crystallization technique with a focused infrared laser beam procedure on a single crystal diffractometer. Two groups of hydrates, separated by a gap, can be identified: the “lower hydrates” (the known hemi- and new monohydrate) plus the “higher hydrates”: (6 3/7, approximately 7 1/2 and 9 1/2). The “lower hydrates” are fully ordered structures with well-defined stoichiometries; in contrast the “higher hydrates” are severely disordered with water molecules organized into three-dimensional networks, similar to clathrate hydrate type sI (hydrate 7 1/2) and sH (hydrates 6 3/7 and 9 1/2). The latter two structures can be considered as extensions of the hexagonal clathrate hydrate sH with addition of water segments in a manner which preserves the hexagonal/trigonal symmetry of the lattice, changing only the c axis of the unit cell. Such a variation is commonly used in engineering for modifying standard structures to “extended” v...

Communication: Librational dynamics in water, sI and sII clathrate hydrates, and ice Ih: Molecular-dynamics insights.

Equilibrium molecular-dynamics simulations have been performed for liquid water, and on metastable sI and sII polymorphs of empty hydrate lattices, in addition to ice Ih, in order to study the dynamical properties of librational motion (rotation oscillation) depicted by protons in water molecules. In particular, hydrate lattices were found to display prominent "bifurcated" features, or peaks, at circa 70 and 80-95 meV (or ∼560 and 640-760 cm(-1), respectively), also displayed by ice, in essentially quantitative agreement with experimental neutron-scattering data. However, observed differences in dispersion between these librational modes between these two structures (both hydrate polymorphs vis-à-vis ice), owing primarily to density effects, have been decomposed into contributions arising from angular-velocity dynamics about axes in the local molecular frame of water molecules, with in-plane "wagging" and "twisting" rationalising one mode at ∼70 meV, and out-of-plane motion for the higher-frequency band. This was confirmed explicitly by a type of de facto normal-mode analysis, in which only immediate layers of water molecules about the one under consideration were allowed to move. In contrast, liquid water displayed no marked preference for such local in- or out-of-plane modes characterising librational motion, owing to the marked absence of rigid, pentamers or hexamers therein.