Nature of the Volume Isotope Effect in Ice

New Insights into the Volume Isotope Effect of Ice Ih from Polarizable Many-Body Potentials

The anomalous volume isotope effect (VIE) of ice Ih is calculated and analyzed based on the quasi-harmonic approximation to account for nuclear quantum effects in the Helmholtz free energy. While a lot of recently developed polarizable many-body potential functions give a normal VIE contrary to experimental results, we find that one of them, MB-pol, yields the anomalous VIE in good agreement with the most recent high-resolution neutron diffraction measurements─better than DFT calculations. The short-range three-body terms in the MB-pol function, which are fitted to CCSD(T) calculations, are found to have a surprisingly large influence. A vibrational mode group decomposition of the zero-point pressure together with a hitherto unconsidered benchmark value for the intramolecular stretching modes of H₂O ice Ih obtained from Raman spectroscopy data unveils the reason for the VIE: a delicate competition between the latter and the librations.

On the role of intermolecular vibrational motions for ice polymorphs. III. Mode characteristics associated with negative thermal expansion

Low-pressure ice forms, such as hexagonal and cubic ice, expand on cooling below temperature 60 K. This negative thermal expansivity has been explored in terms of phonon frequency modulation with varying volume and attributed to the negative Grüneisen parameters unique mostly to tetrahedrally coordinated substances. However, an underlying mechanism for the negative Grüneisen parameters has not been known except some schematic analyses. We investigate in this study the characteristics of the intermolecular vibrational modes whose Grüneisen parameters are negative by examining the individual vibrational modes rigorously. It is found that the low frequency modes below 100 cm^-1, which we explicitly show are mostly bending motions of three hydrogen-bonded molecules, necessarily accompany elongation of the hydrogen bond length at peak amplitudes compared with that at the equilibrium position in executing the vibrational motions. The elongation gives rise to a decrease in the repulsive interaction while an increase in the Coulombic one. The decrease in the repulsive interaction is relaxed substantially by expansion due to its steep slope against molecular separation compared with the sluggish increase in the Coulombic one, and therefore, the negative Grüneisen parameters are obtainable. This scenario is tested against some variants of cubic ice with various water potential models. It is demonstrated that four interaction-site models are suitable to describe the intermolecular vibrations and the thermal expansivity because of the moderate tendency to favor the tetrahedral coordination.

The microscopic origin of the anomalous isotopic properties of ice relies on the strong quantum anharmonic regime of atomic vibration

Water ice is a unique material presenting intriguing physical properties, such as negative thermal expansion and anomalous volume isotope effect (VIE). They arise from the interplay between weak hydrogen bonds and nuclear quantum fluctuations, making theoretical calculations challenging. Here, we employ the stochastic self-consistent harmonic approximation to investigate how thermal and quantum fluctuations affect the physical properties of ice XI with ab initio accuracy. Regarding the anomalous VIE, our work reveals that quantum effects on hydrogen are so strong to be in a nonlinear regime: When progressively increasing the mass of hydrogen from protium to infinity (classical limit), the volume first expands and then contracts, with a maximum slightly above the mass of tritium. We observe an anharmonic renormalization of about 10% in the bending and stretching phonon frequencies probed in IR and Raman experiments. For the first time, we report an accurate comparison of the low-energy phonon dispersion with the experimental data, possible only thanks to high-level accuracy in the electronic correlation and nuclear quantum and thermal fluctuations, paving the way for the study of thermal transport in ice from first-principles and the simulation of ice under pressure.

Calorimetric Signature of Deuterated Ice II: Turning an Endotherm to an Exotherm

Calorimetric studies on ice II reveal a surprising H₂O/D₂O isotope effect. While the ice II to ice Ic transition is endothermic for H₂O, it is exothermic for D₂O samples. The transition enthalpies are +40 and -140 J/mol, respectively, where such a sign change upon isotope substitution is unprecedented in ice research. To understand the observations we employ force field calculations using two water models known to perform well for H₂O ice phases and their vibrational properties. These simulations reveal that the isotope effect can be traced back to zero-point energy. q-TIP4P/F fares better and is able to account for approximately three-fourths of the isotope effect, while MB-pol only catches approximately one-third. Phonon and configurational entropy contributions are necessary to predict reasonable transition enthalpies, but they do not have an impact on the isotope effect. We suggest to use these calorimetric isotope data as a benchmark for water models.

On the role of intermolecular vibrational motions for ice polymorphs I: Volumetric properties of crystalline and amorphous ices

Intermolecular vibrations and volumetric properties are investigated using the quasiharmonic approximation with the TIP4P/2005, TIP4P/Ice, and SPC/E potential models for most of the known crystalline and amorphous ice forms that have hydrogen-disordering. The ice forms examined here cover low pressure ices (hexagonal and cubic ice I, XVI, and hypothetical dtc ice), medium pressure ices (III, IV, V, VI, XII, hydrogen-disordered variant of ice II), and high pressure ice (VII) as well as the low density and the high density amorphous forms. We focus on the thermal expansivities and the isothermal compressibilities in the low temperature regime over a wide range of pressures calculated via the intermolecular vibrational free energies. Negative thermal expansivity appears only in the low pressure ice forms. The sign of the thermal expansivity is elucidated in terms of the mode Grüneisen parameters of the low frequency intermolecular vibrational motions. Although the band structure for the low frequency region of the vibrational density of state in the medium pressure ice has a close resemblance to that in the low pressure ice, its response against volume variation is opposite. We reveal that the mixing of translational and rotational motions in the low frequency modes plays a crucial role in the appearance of the negative thermal expansivity in the low pressure ice forms. The medium pressure ices can be further divided into two groups in terms of the hydrogen-bond network flexibility, which is manifested in the properties on the molecular rearrangement against volume variation, notably the isothermal compressibility.

Origin of the low-temperature endotherm of acid-doped ice VI: new hydrogen-ordered phase of ice or deep glassy states?

The discovery of deep glassy states of ice reveals a fascinating new facet of ice research.

On the basis of a low-temperature endotherm, it has recently been argued that cooling acid-doped ice VI at high pressures leads to a new hydrogen-ordered phase. We show that the endotherms are in fact caused by the glass transitions of deep glassy states related to ice VI. As expected for such endothermic overshoot effects, they display a characteristic dependence on pressure and cooling rate, they can be produced by sub-T_g annealing at ambient pressure, and they can be made to appear or disappear depending on the heating rate and the initial extent of relaxation. It is stressed that the existence of a new crystalline phase, as it has been suggested, cannot depend on the heating rate at which it is heated. X-ray diffraction shows that samples for which the low-temperature endotherm is present, weak or absent, as observed at a heating rate of 5 K min^–1, are structurally very similar. Furthermore, we show that the reported shifts of the (102) Bragg peak upon heating are fully consistent with our scenario and also with our earlier neutron diffraction study. Deuterated acid-doped ice VI cooled at high pressure also displays a low-temperature endotherm and its neutron diffraction pattern is consistent with deep glassy ice VI. Accessing deep glassy states of ice with the help of acid doping opens up a fascinating new chapter in ice research. Compared to pure ice VI, the glass transition temperature is lowered by more than 30 K by the acid dopant. Future work should focus on the deep glassy states related to all the other hydrogen-disordered ices including the ‘ordinary’ ice Ih.

Accurate and precise lattice parameters of H2O and D2O ice Ihbetween 1.6 and 270 K from high-resolution time-of-flight neutron powder diffraction data

Accurate and precise lattice parameters for D2O and H2O varieties of hexagonal ice (ice Ih, space groupP63/mmc) have been obtained in the range 1.6 to 270 K. Precision of the lattice parameters (∼0.0002% inaand 0.0004% incfor D2O, 0.0008% inaand 0.0015% incfor H2O) is ensured by use of the time-of-flight method on one of the longest primary neutron flight-path instruments in the world, the High-Resolution Powder Diffractometer at the ISIS neutron source. These data provide a more precise description of the negative thermal expansion of the material at low temperatures than the previous synchrotron `gold standard' [Röttgeret al.(1994).Acta Cryst.B50, 644–648], including the region below 10 K where the lattice parameters saturate. The volume expansivity of both isotopologues turns negative below 59–60 K, in excellent agreement with a recent dilatometry study. The axial expansivities are highly isotropic (differing by < 1% in D2O ice Ih). Furthermore, thec/aratio of different D2O ice samples exhibit a statistically significant dispersion of ∼0.015% below 150 K that appears to depend on the thermal history of the sample, which disappears on warming above 150 K. Similarly, H2O ice exhibits a `kink' in thec/aratio at ∼115 K. The most plausible explanation is a freezing-in of the molecular reorientation process on cooling and subsequent relaxation on warming.

H/D isotope effect on the molar volume and thermal expansion of benzene

Time-of-flight neutron powder diffraction data have been collected from C₆H₆ and C₆D₆ between 10 and 276 K, revealing no cross-over in their molar volumes and an almost temperature invariant volume-isotope-effect, in contrast with previously published work.