Relation between the Widom line and the breakdown of the Stokes–Einstein relation in supercooled water

Proc. Natl. Acad. Sci. U.S.A.

2013

The anomalous behavior of thermodynamic response functions is an unsolved problem in the physics of water. The mechanism that gives rise to the dramatic indefinite increase at low temperature in the heat capacity, the compressibility, and the coefficient of thermal expansion, is unknown. We explore this problem by analyzing both new and existing experimental data on the power spectrum S(Q, ω) of bulk and confined water at ambient pressure. When decreasing the temperature, we find that the liquid undergoes a structural transformation coinciding with the onset of an extended hydrogen bond network. This network onset seems to give rise to the marked viscoelastic behavior, consistent with the interesting possibility that the sound velocity and response functions of water depend upon both the frequency and wave vector.A lthough water is one of the simplest molecules, it is in reality a very complex liquid displaying more than 64 counterintuitive anomalies, most of which have not been adequately explained (1, 2). The best known of these is its density behavior: unlike most liquids, water displays a maximum at 4°C, and becomes less dense rather than more dense when it freezes. Other unexplained anomalies occur for response functions such as the isothermal compressibility K T , the isobaric heat capacity C P , and the thermal expansion coefficient α P . Moreover, if one extrapolates these functions into the metastable supercooled phase of water below the melting temperature (T M = 273 K at atmospheric pressure), and above the homogeneous nucleation temperature (T H ∼ 231 K), they behave as if they might diverge at a singular temperature T S ∼ 228 K (1). Water is a glassy liquid below the glass transition temperature T g ∼ 130 K (2). Immediately above T g it transforms into a highly viscous fluid and ultimately crystallizes at T X ∼ 150 K. The region between T X and T H is a "no-man's land" within which bulk liquid water cannot be studied (1). For these and other reasons, liquid water is one of the most exciting research topics, and an enormous number of studies have sought to elucidate the physical reasons for water's unusual properties.There are four current hypotheses (1), two of which have gained considerable attention: the singularity-free hypothesis (3, 4) and the liquid-liquid critical point (LLCP) hypothesis (5). The LLCP hypothesis is based on two assumptions: (i) that water displays the phenomenon of "liquid polymorphism" (6) and (ii) as T decreases, the hydrogen bonds (HBs) begin to form an open tetrahedrally coordinated HB network. If we begin with the stable liquid phase and decrease T, the HB lifetime and the cluster stability increase, and this altered local structure continues through the no-man's land down to the amorphous phase region. Amorphous solid water is widely believed to display polymorphism: below T g , low-density amorphous (LDA) and high-density amorphous (HDA) structures (7) can be transformed from one to the other by tuning the pressure. Hence liquid water may have local structural features...

mentioning

confidence: 87%

mentioning

confidence: 99%

Possible relation of water structural relaxation to water anomalies

Mallamace

Corsaro

Proc. Natl. Acad. Sci. U.S.A.

2013

“…In this work we concentrated on reviewing the evidence for changes in dynamic transport properties, such as diffusion constant and relaxation time. Additional examples include: (1) a breakdown of the Stokes-Einstein relation for ToT W ðPÞ [74][75][76][77][78][79], (2) systematic changes in the static structure factor SðqÞ and the corresponding pair correlation function gðrÞ revealing that for ToT W ðPÞ the system more resembles the structure of LDL than HDL, (3) appearance for ToT W ðPÞ of a shoulder in the dynamic structure factor Sðq; oÞ at a frequency o % 60 cm À1 % 2 THz [51], (4) rapid increase in hydrogen bonding degree for ToT W ðPÞ [80,81], (5) a minimum in the density at low temperature [82], and (6) a scaled equation of state near the critical point [83]. It is important to know how general a given phenomenon is, such as crossing the Widom line which by definition is present whenever there is a critical point.…”

Section: Discussionmentioning

confidence: 99%

The puzzling unsolved mysteries of liquid water: Some recent progress

Physica A: Statistical Mechanics and its Applications

Kumar

et al. 2007

Water is perhaps the most ubiquitous, and the most essential, of any molecule on earth. Indeed, it defies the imagination of even the most creative science fiction writer to picture what life would be like without water. Despite decades of research, however, water's puzzling properties are not understood and 63 anomalies that distinguish water from other liquids remain unsolved. We introduce some of these unsolved mysteries, and demonstrate recent progress in solving them. We present evidence from experiments and computer simulations supporting the hypothesis that water displays a special transition point (which is not unlike the ''tipping point'' immortalized by Malcolm Gladwell). The general idea is that when the liquid is near this ''tipping point,'' it suddenly separates into two distinct liquid phases. This concept of a new critical point is finding application to other liquids as well as water, such as silicon and silica. We also discuss related puzzles, such as the mysterious behavior of water near a protein. r

“…The average value Q ≡ (1/N) k Q k increases with decreasing T and saturates at lower T, whereas |d Q /dT| has a maximum at the Widom line T W ≈ 250 K (31)(32)(33).…”

Section: Space-and Time-dependent Correlations Of the Tetrahedral Ordermentioning

confidence: 99%

“…4B shows the temperature dependence of C Q P and total specific heat C Total P for P = 1 atm. C Q P shows a maximum at T ≈ 250 ± 10 K ≈ T W , where the total specific heat C Total P also has a maximum (19,(31)(32)(33), suggesting that the fluctuations in tetrahedral order reach a maximum at T W (P). Moreover, comparing the tetrahedral specific heat in Fig.…”

Section: [8]mentioning

confidence: 99%

A tetrahedral entropy for water

Kumar

Buldyrev

Proc. Natl. Acad. Sci. U.S.A.

2009

Self Cite

104

124

We introduce the space-dependent correlation function C Q (r) and time-dependent autocorrelation function C Q (t) of the local tetrahedral order parameter Q ≡ Q(r, t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C Q (r) in a broad region of the phase diagram. We find that at low temperatures C Q (t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time τ Q displays a dynamic cross-over from non-Arrhenius behavior for T > T W to Arrhenius behavior for T < T W , where T W denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S Q associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that τ Q can be extracted from S Q by using an analog of the Adam-Gibbs relation.specific heat of water | orientational entropy of tetrahedral liquids | anomalies of liquid water | Widom line I t has long been appreciated that the local structure around a molecule of liquid water arising from the vertices formed by four nearest neighbors is approximately tetrahedral at ambient pressure and that the degree of tetrahedrality increases when water is cooled (1-5). An important advance occurred in the past 10 years when computer simulations allowed the quantification of the degree of tetrahedrality (6-10) by assigning to each molecule a local tetrahedral order parameter Q (11-16). At high temperatures, the probability distribution P(Q, T) is bimodal, with one peak corresponding to a high degree of tetrahedrality and the other to a less tetrahedral environment (Fig. 1). Upon decreasing temperature, the peak associated with a high degree of tetrahedrality grows, suggesting that the local structure of water becomes much more tetrahedral at lower temperatures (13,14,17). IntroductionWater has been hypothesized to belong to the class of polymorphic liquids, phase separating-at sufficiently low temperatures and high pressures-into two distinct liquid phases: a high density liquid (HDL) with smaller Q and a low density liquid (LDL) with larger Q (18). The coexistence line separating these two phases may terminate at a liquid-liquid (LL) critical point, above which (in the LL supercritical region) appears a line of correlation length maximum in the pressure-temperature plane. The locus of maximum correlation length in the one-phase region is called the Widom line T W ≡ T W (P) (19), near which different response functions, such as isobaric specific heat C P and isothermal compressibility K T , display maxima. Recent neutron-scattering experiments (20) and computer simulations (19) show that the dynamics of water gradually cross over from being non-Arrhenius for T > T W to Arrhenius for T < T W .Although dynamic heterogeneities h...