Thomas Loerting

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

Water’s second glass transition

Significance Water is not only the most important liquid for life on Earth, but also one of the most anomalous liquids. These anomalies become most evident in the supercooled state at subzero temperatures. We show from dielectric and calorimetric studies that water in the deeply supercooled regime, below –120 °C, can even exist as two distinct, ultraviscous liquids at ambient pressure, a low- (LDL, 0.92 g/cm3) and high-density liquid (HDL, 1.15 g/cm3), which can both remain in the metastable, equilibrium liquid state for many hours above their calorimetric glass transition temperatures of –137 °C (136 K) and –157 °C (116 K). LDL is identified as the strongest of all liquids, and also HDL is a strong liquid at record low temperature. The glassy states of water are of common interest as the majority of H2O in space is in the glassy state and especially because a proper description of this phenomenon is considered to be the key to our understanding why liquid water shows exceptional properties, different from all other liquids. The occurrence of water’s calorimetric glass transition of low-density amorphous ice at 136 K has been discussed controversially for many years because its calorimetric signature is very feeble. Here, we report that high-density amorphous ice at ambient pressure shows a distinct calorimetric glass transitions at 116 K and present evidence that this second glass transition involves liquid-like translational mobility of water molecules. This “double Tg scenario” is related to the coexistence of two liquid phases. The calorimetric signature of the second glass transition is much less feeble, with a heat capacity increase at Tg,2 about five times as large as at Tg,1. By using broadband-dielectric spectroscopy we resolve loss peaks yielding relaxation times near 100 s at 126 K for low-density amorphous ice and at 110 K for high-density amorphous ice as signatures of these two distinct glass transitions. Temperature-dependent dielectric data and heating-rate–dependent calorimetric data allow us to construct the relaxation map for the two distinct phases of water and to extract fragility indices m = 14 for the low-density and m = 20–25 for the high-density liquid. Thus, low-density liquid is classified as the strongest of all liquids known (“superstrong”), and also high-density liquid is classified as a strong liquid.

Amorphous ices : experiments and numerical simulations

Polyamorphism, i.e. the presence of more than one amorphous state, was observed for the first time in amorphous ice or glassy water. In addition to LDA (low-density amorphous ice), a second amorphous state, HDA (high-density amorphous ice), was discovered ∼20 years ago. Since then, polyamorphism has been observed in many other substances, such as SiO2 ,G eO 2, Si, and Ge. Five years ago, experimental results suggesting the existence of a third amorphous state, VHDA (very high-density amorphous ice), were reported, opening the possibility that more than two amorphous states could also be observed in other substances. A consistent phase diagram of glassy water does not yet exist. Such a phase diagram is necessary if one also wants to understand the anomalous behaviour of supercooled liquid water. Since the discovery of HDA, a large amount of work based on experiments and computer simulations has appeared. It is the purpose of this work to review such studies with special emphasis in comparing the experimental and simulation results. In particular, we review the recent studies concerning VHDA and its nature, and discuss the main open questions relating to the phase diagram of glassy water. (Some figures in this article are in colour only in the electronic version)

A second distinct structural “state” of high-density amorphous ice at 77 K and 1 bar

High-density amorphous ice (HDA), further densified on isobaric heating from 77 K to 165 (177) K at 1.1 (1.9) GPa, relaxes at 77 K and 1 bar to the same structural “state” with a density of 1.25 ± 0.01 g cm−3. Its density is higher by ≈9% than that of HDA, and thus it is called very-high-density amorphous ice (VHDA). X-ray diffractogram and Raman spectrum of VHDA clearly differs from that of HDA, and the hydrogen-bonded O–O distance increases from 2.82 A in HDA to 2.85 A in VHDA. Implications for the polyamorphism of the amorphous forms of water are discussed.

Water polyamorphism: Reversibility and (dis)continuity

An understanding of waters anomalies is closely linked to an understanding of the phase diagram of waters metastable noncrystalline states. Despite the considerable effort, such an understanding has remained elusive and many puzzles regarding phase transitions in supercooled liquid water and their possible amorphous proxies at low temperatures remain. Here, decompression of very high density amorphous ice (VHDA) from 1.1 to 0.02 GPa at 140 K is studied by means of dilatometry and powder x-ray diffraction of quench-recovered states. It is shown that the three amorphous states of ice are reversibly connected to each other, i.e., LDA<-->e-HDA<-->VHDA. However, while the downstroke VHDA-->e-HDA transition takes place in the pressure range of 0.06 GPaLDA transition takes place quasi-discontinuously at p approximately 0.06 GPa. That is, two amorphous-amorphous transitions of a distinct nature are observed for the first time in a one-component system-a first-order-like transition (e-HDA-->LDA) and a transition which is not first-order like but possibly of higher order (VHDA-->e-HDA). VHDA and e-HDA are established as the most stable and limiting states in the course of the transition. We interpret this as evidence disfavoring the hypothesis of multiple first-order liquid-liquid transitions (and the option of a third critical point), but favoring a single first-order liquid-liquid transition (and the option of a second critical point).

The local and intermediate range structures of the five amorphous ices at 80 K and ambient pressure: A Faber-Ziman and Bhatia-Thornton analysis

Using isotope substitution neutron scattering data, we present a detailed structural analysis of the short and intermediate range structures of the five known forms of amorphous ice. Two of the lower density forms--amorphous solid water and hyperquenched glassy water--have a structure very similar to each other and to low density amorphous ice, a structure which closely resembles a disordered, tetrahedrally coordinated, fully hydrogen bonded network. High density and very high density amorphous ices retain this tetrahedral organization at short range, but show significant differences beyond about 3.1 A from a typical water oxygen. The first diffraction peak in all structures is seen to be solely a function of the intermolecular organization. The short range connectivity in the two higher density forms is more homogeneous, while the hydrogen site disorder in these forms is greater. The low Q behavior of the structure factors indicates no significant density or concentration fluctuations over the length scale probed. We conclude that these three latter forms of ice are structurally distinct. Finally, the x-ray structure factors for all five amorphous systems are calculated for comparison with other studies.

Equilibrated High-Density Amorphous Ice and Its First-Order Transition to the Low-Density Form

We investigate the downstroke transition from high- (HDA) to low-density amorphous ice (LDA) at 140 (H(2)O) and 143 K (D(2)O). The visual observation of sudden phase separation at 0.07 GPa is evidence of the first-order character of the transition. Powder X-ray diffractograms recorded on chips recovered from the propagating front show a double halo peak indicative of the simultaneous presence of LDA and HDA. By contrast, chips picked from different parts of the sample cylinder show either HDA or LDA. Growth of the low-density form takes place randomly somewhere inside of the high-density matrix. The thermal stability of HDA against transformation to LDA at ambient pressure significantly increases with decreasing recovery pressure and reaches its maximum at 0.07 GPa. A sample decompressed to 0.07 GPa is by ~17 K more stable than an unannealed HDA sample. An increasingly relaxed nature of the sample is also evident from the progressive disappearance of the broad calorimetric relaxation exotherm, preceding the sharp transition to LDA. Finally, we show that two independent thermodynamic paths lead to a very similar state of (relaxed) HDA at 140 K and 0.2 GPa. We argue that these observations imply an equilibrated nature of the amorphous sample in the pressure range of p ≲ 0.2 GPa and speculate that the observation of macroscopic phase separation involves two ultraviscous liquid phases at 140 K. This supports the scenario of a first-order liquid-liquid transition in bulk water.

Towards the Experimental Decomposition Rate of Carbonic Acid (H2CO3) in Aqueous Solution

Dry carbonic acid has recently been shown to be kinetically stable even at room temperature. Addition of water molecules reduces this stability significantly, and the decomposition (H2CO3 + nH2O --> (n+1)H2O + CO2) is extremely accelerated for n = 1, 2, 3. By including two water molecules, a reaction rate that is a factor of 3000 below the experimental one (10 s(-1)) at room temperature was found. In order to further remove the gap between experiment and theory, we increased the number of water molecules involved to 3 and took into consideration different mechanisms for thorough elucidation of the reaction. A mechanism whereby the reaction proceedes via a six-membered transition state turns out to be the most efficient one over the whole examined temperature range. The determined reaction rates approach experimental values in aqueous solution reasonably well; most especially, a significant increase in the rates in comparison to the decomposition reaction with fewer water molecules is found. Further agreement with experiment is found in the kinetic isotope effects (KIE) for the deuterated species. For water-free carbonic acid, the KIE (i.e., kH2CO3/kD2CO3) for the decomposition reaction is predicted to be 220 at 300 K, whereas it amounts to 2.2-3.0 for the investigated mechanisms including three water molecules. This result is therefore reasonably close to the experimental value of 2 (at 300 K). These KIEs are in much better accordance with the experiment than the KIE for decomposition with fewer water entities.

The optimal tunneling path for the proton transfer in malonaldehyde

The proton tunneling reaction in malonaldehyde at low temperatures is investigated. The principal aim of this study is to find the optimal tunneling path at 0 K in the framework of the semiclassical theory with a global optimization method. An amount of 11366 ab inito points was determined in the reaction swath (i.e., the conformational space enclosed by the minima and the transition state) of malonaldehyde. With a simulated annealing approach, the path with the smallest integral of the imaginary action through the swath from minimum to minimum was determined. Surprisingly the optimal tunneling path was found to be quite far off the large curvature tunneling path [i.e., the straight connection of the two minima large-current tunneling (LCT path)]. At the beginning, it is following the minimum energy path (MEP) (i.e. the path with the lowest energy connecting the two minima and passing through the transition state), and then it is describing a curved path through the reaction swath. This curve was determin...

Anomalous Behavior of the Homogeneous Ice Nucleation Rate in “No-Man’s Land”

We present an analysis of ice nucleation kinetics from near-ambient pressure water as temperature decreases below the homogeneous limit TH by cooling micrometer-sized droplets (microdroplets) evaporatively at 103–104 K/s and probing the structure ultrafast using femtosecond pulses from the Linac Coherent Light Source (LCLS) free-electron X-ray laser. Below 232 K, we observed a slower nucleation rate increase with decreasing temperature than anticipated from previous measurements, which we suggest is due to the rapid decrease in water’s diffusivity. This is consistent with earlier findings that microdroplets do not crystallize at <227 K, but vitrify at cooling rates of 106–107 K/s. We also hypothesize that the slower increase in the nucleation rate is connected with the proposed “fragile-to-strong” transition anomaly in water.