Confined Water as Model of Supercooled Water - ACS Publications

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Confined Water as Model of Supercooled Water Silvina Cerveny,†,‡ Francesco Mallamace,§ Jan Swenson,*,∥ Michael Vogel,⊥ and Limei Xu#,▽ †

Centro de Física de Materiales (CFM CSIC/EHU) - Material Physics Centre (MPC), Paseo Manuel de Lardizabal 5, 20018 San Sebastian, Spain ‡ Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018 San Sebastián, Spain § Dipartimento di Fisica, Università di Messina, Vill. S. Agata, CP 55, I-98166 Messina, Italy ∥ Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden ⊥ Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstraße 6, 64289 Darmstadt, Germany # International Centre for Quantum Materials and School of Physics, Peking University, , Beijing 100871, China ▽ Collaborative Innovation Center of Quantum Matter, Beijing 100871, China ABSTRACT: Water in confined geometries has obvious relevance in biology, geology, and other areas where the material properties are strongly dependent on the amount and behavior of water in these types of materials. Another reason to restrict the size of water domains by different types of geometrical confinements has been the possibility to study the structural and dynamical behavior of water in the deeply supercooled regime (e.g., 150−230 K at ambient pressure), where bulk water immediately crystallizes to ice. In this paper we give a short review of studies with this particular goal. However, from these studies it is also clear that the interpretations of the experimental data are far from evident. Therefore, we present three main interpretations to explain the experimental data, and we discuss their advantages and disadvantages. Unfortunately, none of the proposed scenarios is able to predict all the observations for supercooled and glassy bulk water, indicating that either the structural and dynamical alterations of confined water are too severe to make predictions for bulk water or the differences in how the studied water has been prepared (applied cooling rate, resulting density of the water, etc.) are too large for direct and quantitative comparisons.

CONTENTS 1. Introduction 2. Experimental Techniques 3. Differerent Types of Confinements 3.1. Hard Confinement Systems 3.2. Soft Confinement Systems 3.3. Microemulsions 3.4. Comparison of Water Dynamics in Hard and Soft Confinement Systems 4. Dynamic Crossover under Confinements 5. Possible Implications for Supercooled Bulk Water 6. Conclusion Author Information Corresponding Author Notes Biographies Acknowledgments Glossary References

a substantial fraction of these water molecules are located in the vicinity (within approximately 5 Å) of different kinds of biomolecules.1 Since the presence of such water is necessary for life,2 it is obvious that it is important to understand the structural and dynamical properties of confined water. The properties of confined water are also of central importance for many geological problems and applications. However, in this review we will not focus on these life science- or geologyrelated applications of confined water. Instead we use confined water as a means to enter into the “no man’s land” region (about 150−230 K at ambient pressure)3,4 without facing the problem of immediate crystallization, either when liquid water is cooled from high temperatures or when amorphous solid water (ASW) is heated from lower temperatures. It has been established that confined water can avoid crystallization at any temperature, provided that the geometrical restriction is sufficiently severe to prevent water molecules from arranging in a tetrahedral ice structure. The main methods to achieve this are (a) confining water in different types of porous solid materials, (b) mixing water with a salt or another liquid, or (c) hydrating surfaces or larger molecules, such as biomolecules. Exact requirements for avoiding crystallization are

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1. INTRODUCTION It is well-known that many biological processes take place in crowded aqueous surroundings, and therefore water in our bodies can be considered as confined water. The size of this confinement can vary in the range from about 1 to 100 nm and © 2016 American Chemical Society

Special Issue: Water - The Most Anomalous Liquid Received: October 13, 2015 Published: March 4, 2016 7608

DOI: 10.1021/acs.chemrev.5b00609 Chem. Rev. 2016, 116, 7608−7625

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This is the reason why it has been proposed that supercooled water undergoes a FS transition around 228 K and that this should be caused by an end point in the formation of a hydrogen-bonded tetrahedral network structure.10 Whether such a FS transition can be directly related to the similar dynamic crossover for confined supercooled water is therefore an important issue in this review.

difficult to provide, since it depends on many parameters, such as the nature of interaction with the surface, geometry of waterfilled cavities, or dispersion of the water molecules in a solution. However, to get a rough idea of the maximum size to which a water cluster can grow without crystallizing at any temperature, it can be mentioned that water intercalated in cylindrical pores of MCM-41 will not form an undistorted crystal structure if the pore diameter is about 20 Å or less.5−9 Hence, there are various approaches to confine water and avoid regular crystallization in the no man’s land region. The question is whether the structural and dynamical properties of such supercooled water are of relevance for supercooled bulk water. There is no clear answer to this question, but in this review we will discuss the issue in some details. We will also discuss differences and similarities in the relaxation properties of water that has been confined by the three approaches given to avoid crystallization. However, to somewhat restrict this broad topic, our main focus will be on approach (a) and to discuss how the so-obtained relaxation data for confined supercooled water may be related to supercooled bulk water. The most likely relaxation scenarios for bulk water will, however, depend on how the relaxation data for confined water are interpreted. As will be evident in this review, this is still debated. Therefore, we will present different possible relaxation scenarios for the most common interpretations of the experimental data for confined water. Since we are mainly interested in experimental relaxation data of relevance for the viscosity and glass transition of water, we have to focus on experimental techniques where the viscosity and glass-transition-related structural relaxation process (α-relaxation) can be probed. This is possible with broadband dielectric spectroscopy (BDS) and nuclear magnetic resonance (NMR) techniques, as well as quasielastic neutron scattering (QENS). Furthermore, these techniques have the advantage that they can also probe faster and more local secondary relaxation processes (β-relaxation) and partly distinguish these from α-relaxation. Differences and similarities of these techniques will also be briefly discussed in this review to better understand the physical nature of the experimental data. Common for all these techniques is that their measured relaxation data for confined supercooled water exhibit a dynamic crossover in their temperature dependence. This dynamic crossover is of central importance for understanding the dynamic properties of confined supercooled water, as well as for determining the most probable relaxation scenario for supercooled bulk water, which is currently heavily debated due to its possible fragile-to-strong (FS) crossover10−13 and its not fully established glass-transition temperature.13−22 With fragility23 we refer to the temperature dependence of the viscosity (η) or related α-relaxation time (τα) of a supercooled liquid. A fragile glass-forming liquid exhibits a highly nonArrhenius temperature dependence, typical for ionic and van der Waals systems, whereas a strong supercooled liquid shows a temperature dependence close to the Arrhenius law, which is typical for materials with strong (commonly covalent) bonds forming a network structure. Since it is well-established that water above approximately 233 K is one of the most fragile liquids that has ever been studied11 and that the temperature dependence of its viscosity (or τα) seems to follow a power law diverging at about 228 K,24 a glass-transition temperature Tg (which is usually assigned to the temperature for which τα ≈ 100 s) substantially lower than 228 K can be obtained only if the fragile behavior above 233 K changes to a stronger Arrhenius-like temperature dependence slightly below 233 K.

2. EXPERIMENTAL TECHNIQUES The results from experimental studies on confined water are often sensitive to the confinement constraints, which can be of different natures, and also sensitive to the coupling between the studied system and the probe. It is well-known that the coupling between the probe and the system can be of different nature and strength depending on the physical nature of the probe−system interaction. In some cases the exchanged energy during the probe−system interaction is local, on the scale of single molecules (e.g., Raman scattering); in other cases it is of collective nature and involves the whole system and its thermodynamics (e.g., calorimetry). These differences also imply that very different information about the samples can be gained from the wide range of available experimental techniques. However, it is not our purpose to review all possible experimental techniques but to briefly discuss the three main techniques that have been used to study the translational and reorientational dynamics of water in confined geometries: BDS, NMR, and QENS. BDS is a broadband technique (10−6 to 1012 Hz) based on the interaction between an external electric field and the electric dipoles of the sample.25,26 In this huge frequency range, dielectric dispersion and absorption phenomena occur due to the dipole relaxation arising from the reorientational motions of molecular dipoles and electrical conduction arising from translational motions of electric charges (ions, electrons). The measured quantity is the frequency-dependent complex dielectric permittivity, ε(ω)* = ε′(ω) − iε′′(ω), which can also be expressed as the Laplace transformation of a time domain relaxation function φ(t). The molecular relaxation processes are observed as multiple dielectric loss peaks in plots of ε′′ versus log (f/[Hz]). It is well-established that at least two different types of relaxation processes are present in glass-forming systems: primary or structural α-relaxation, which is directly related to the macroscopic viscosity of a glass-forming liquid, and secondary β-relaxation, also known as the Johari−Goldstein process (βJG). BDS provides information about the temperature dependence of characteristic times and spectral shapes of these relaxations. This implies that BDS does not provide space−time information about the processes involved in the dynamics. To obtain such information, QENS can be used since it probes all types of self-particle motions in the case of incoherent scattering and all types of correlated particle motions in the case of coherent scattering. For hydrogen-rich materials, such as H2O, the total scattering is strongly dominated by the selfmotions of hydrogen atoms, due to the high incoherent scattering cross-section of hydrogen. The great advantage with QENS is that information about the physical nature of the dynamical processes can be gained from the length-scale dependences of their relaxation times, which are probed by varying the momentum transfer (Q) at the scattering event. Hence, by studying the Q dependence of a relaxation process, it is possible to determine whether it is due to long-range translational diffusion, localized diffusion, or rotational motion. 7609


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systems, it is important to consider that cross-relaxation effects can interfere with a straightforward interpretation of the experimental results in terms of molecular diffusion.39,40 In view of the different properties of the BDS, NMR, and QENS methods, a combination of all three techniques is desirable to understand the mechanisms behind the dynamics of α- and β-relaxations observed in glass-forming materials. However, it should here be noted that even if there is a wide spectrum of opportunities to explore the physical and chemical properties of condensed matter in all their aggregation states, it happens that the different experimental techniques give different results for parameters related to molecular motions. As an example, it can be mentioned that optical Kerr effect,41 BDS,42 QENS,43,44 and depolarized light scattering45 measure the molecular relaxation time in bulk water in the stable and supercooled regime with a spread of about 1 order of magnitude. Another effect that needs to be considered when results are compared from different experimental techniques is the wellknown rototranslation paradox proposed by Frank Stillinger, that is, the decoupling of rotational and translation motions that takes place upon approaching the dynamical arrest at a certain temperature well above the calorimetric glass-transition temperature Tg.46 As a consequence, violation of the Stokes− Einstein law is observed in many glass-forming liquids.47−59 Generally, the Stokes−Einstein relationship (SER) is valid at high temperatures; that is, the rotational and translational diffusions exhibit the same temperature dependence. However, in the case of fragile supercooled liquids approaching Tg, it is common that the inverse rotational diffusion constant 1/Dr (or the corresponding relaxation time τr) has the same temperature behavior as viscosity (η), whereas translational diffusion Ds declines more slowly than Dr with decreasing temperature. Such a breakdown of the SER at low temperatures has also been observed for confined water.49,60

On the other hand, the QENS technique is limited by its rather narrow frequency range. A single QENS spectrometer can only cover a frequency range of about 2 orders of magnitude on a picosecond to nanosecond time scale, but if several spectrometers are combined (e.g., backscattering and time-offlight instruments), and also the so-called spin−echo technique is used, the dynamical time window can be extended to 10−14− 10−7 s. When experimental data obtained by QENS and BDS are compared, the normalized intermediate scattering function I(Q,t) is often compared with the dielectric relaxation function φ(t). Several experiments on different materials have shown that φ(t) and I(Q,t) show a similar nonexponential shape (in the high-frequency range where both techniques overlap) and the measured relaxation times become generally similar27,28 in the region of Q = 1 Å−1. Therefore, the results obtained through both techniques are comparable, despite the fact that the two techniques probe different physical quantities. NMR techniques were intensively used to study the phase behavior as well as structural and dynamical properties of water in confinement.29−33 In these approaches, 1H, 2H, and 17O are suitable probe nuclei. With regard to dynamics, NMR experiments can be performed in homogeneous fields and gradient fields to investigate rotational water motion on local scales and translational diffusion on mesoscopic scales, respectively. Relating to water reorientation, it is possible to analyze the spin−lattice relaxation (SLR) time T1 to obtain information about the spectral density of this dynamical process in a fast dynamical regime, in particular, in the vicinity of a T1 minimum, occurring in temperature-dependent measurements for rotational correlation times on the order of the inverse Larmor frequency (∼10−9 s). Straightforward insights into the shape of the spectral density are available from 1H and 2H field-cycling relaxometry, yielding SLR dispersions.29,34 Direct measurement of rotational correlation functions of water in a slow dynamical regime (∼10−6−100 s) is possible in 2H stimulated echo (STE) experiments.33,35 Thus, combining 2H SLR and STE measurements provides access to a broad dynamic range of about 10−11−100 s. While all these NMR approaches provide rotational correlation functions of rank l = 2, BDS probes that of rank l = 1. Thus, NMR and BDS correlation times can differ by up to a factor of 3, as found in the case of isotropic rotational diffusion. Usually, NMR experiments yield insights into not only the rates but also the geometry for molecular reorientation. In this regard, 2H STE NMR is a particularly useful tool. In these experiments, variation of the evolution time tp, an alterable interpulse delay, allows one to adjust the angular resolution of the experiment; that is, this parameter has a meaning analogous to that of the momentum transfer Q in QENS experiments.36 Specifically, the evolution-time dependence of the correlation functions yields valuable information about the overall amplitude and jump angles of a reorientation process and hence enables discrimination between α- and β-relaxations.36,37 By application of pulsed field gradients (PFG) or static field gradients (SFG) in NMR experiments, the molecular selfdiffusion coefficient Ds of water can be measured.29,31,38 Hereby, the translational motion is probed on length scales of about 100 nm, depending on the experimental parameters, for example, gradient strength. Usually, self-diffusion coefficients in the range 10−9−10−12 m2/s are available. In studies of slow diffusion in heterogeneous systems such as liquid−matrix

3. DIFFERERENT TYPES OF CONFINEMENTS 3.1. Hard Confinement Systems

As mentioned, water can be confined to porous materials (hard confinements) to study its liquid behavior below the homogeneous nucleation temperature, as discussed in more detail in several reviews.61−64 Rigid porous materials can be classified according to the topology of the network (order/ disorder) and the pore diameter d (micro, d < 20 Å; meso, 20 Å < d < 500 Å; macro, d > 500 Å) as well as the degree of hydrophilicity or hydrophobicity. Water has been confined in disordered porous materials such as silica hydrogels,65 Vycor glasses,66,67 molecular sieves,68 mineral clays,69 graphite oxide,70 and cement-like materials.71,72 All these materials are hydrophilic (generally with hydroxyl groups on the surface) and exhibit an interconnected pore structure with a broad pore size distribution. These characteristics give rise to an incomplete filling of the pores, and water−surface interactions are therefore promoted. These interactions cause system-dependent alterations in the dynamical behavior of the confined water, as shown in Figure 1a. However, when water is confined in more regular systems, such as SBA-1573 and MCM-41,7,74−76 the water dynamics seems to be less influenced by surface interactions, and a more “universal” relaxation behavior is obtained. Furthermore, since MCM-41 consists of cylindrical silica mesoporous material packed into a hexagonal array,64 with a porosity much simpler 7610


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interactions with solute molecules tend to slow down the water dynamics (see Figure 1b). Thus, the problem in studying the dynamics of water in solutions is the unavoidable interaction between solutes and water molecules as well as the ill-defined size and geometry of the confinement.77 However, despite these problems it is evident from Figure 1b that a general trend can be observed when liquid water pools are present in the solutions. First, there is a crossover in the water dynamics to a low-temperature Arrhenius dependence at the glass transition of the solution, and second, the low-temperature water relaxation becomes faster (up to 4 orders of magnitude), and its activation energy lower, with increasing water content. 3.3. Microemulsions

Between the two extremes of soft and hard confinement systems, microemulsions can be regarded as a class of systems that combines both properties of confinement. Microemulsions are stable solutions of two liquids (for instance, water and any water-insoluble liquid such as oil) stabilized with a surfactant that forms a monolayer separating the two liquids into two phases. In these mixtures of polar and nonpolar liquids, the radius of the water droplets can be varied in the range from about 1 to 100 nm by changing the water to surfactant molar ratio. In particular, surfactants dissolved in organic solvents form spheroidal aggregates called reverse micelles (RM). In the presence of water, the polar head groups of the surfactant molecules organize themselves around small water droplets.78 One of the most studied microemulsions is based on the surfactant sodium di(2-ethylhexyl) sulfosuccinate, commonly called aerosol OT (AOT).79−81 In this system the size of the encapsulated water core can be varied from a few angstroms up to several nanometers by decreasing the surfactant concentration. Molecular dynamics (MD) simulations82,83 showed that two types of water are present inside the RM: water interacting with the interface and water in the bulk-like core. For small RM, the properties of the water differ significantly from those of bulk water since in this case a major fraction of the water interacts directly with the micellar interface.84,85 However, for large RM, the water in the core exhibits properties similar to bulk water.86,87 Water in RM has been analyzed by different experimental methods, such as neutron scattering,84,88 X-ray Raman spectroscopy,85 femtosecond solvation dynamics,89−91 dielectric relaxation in the gigahertz92 and terahertz region,93,94 and ultrafast IR techniques.95 However, as in the case of aqueous solutions and hard confinement systems, it is extremely difficult to distinguish the structure of interfacial water from core water and to estimate the ratio of the two species. Nevertheless, femtosecond transient vibrational spectroscopy,86 which accesses vibrational lifetimes, has shown that water molecules in the core have similar orientational dynamics as that of bulk water, whereas the water layer solvating the interface is highly immobile.86 In spite of the fact that these types of systems are used as model systems to study water trapped in semispherical nanometric cavities, we have to mention that there is no available data for relaxation times at temperatures lower than 220 K.

Figure 1. Temperature dependence of relaxation time in (a) hard and (b) soft confinement systems. Colored area indicates the temperature range where crossovers are produced. In the case of water solutions, this area coincides with the glass-transition (Tg) of the solutions. Techniques and solutes are indicated, and the water content by weight is given in parentheses. (a) Hard confinement systems: BDSvermiculite clays,69 BDS-molecular sieves,68 BDS-MCM-41,7 NMRMCM-41,75,76 QENS-MCM-41,74 BDS-silica hydrogel,65 QENSGO,110 BDS-GO,70 QENS-white cement,71 BDS-CSH,72 and QENSRM88 (rc = 10.25 or 12.5 Å). The arrow indicates the direction of increasing regularity of porosity. (b) Soft confinement systems: BDSdeoxyribose and BDS-ribose,97 BDS-sucrose,98 NMR-elastin,35,99 BDS-myoglobin,100 BDS-4EG, BDS-5EG, and BDS-PEG600,101 BDS-PPG425,102 BDS-BSA,103 NMR-collagen,104 BDS-nPG,105 BDSPVME,106 BDS-PVP,107 QENS-PVP and NMR-PVP, 108 BDSPGME,109 QENS-RM84 (rc = 10.25, 12.5, or 15.4 Å), and QENSRM88(rc = 12 or 7 Å). cw represents the water concentration in weight. The arrow indicates the direction of increasing water content. BDS relaxation times for liquid bulk water42 and LDL96 are also included for comparison.

than that in SBA-15, we base the general scenario of confined water mainly on results for water in MCM-41 (20 Å). Thus, we made the assumption that water in MCM-41 can be regarded as an ideal model system of confined water. 3.2. Soft Confinement Systems

An alternative to avoid crystallization of supercooled water is mixing water with different types of solutes (sugars, salts, polymers, liquids crystals, ionic liquids, colloids, etc.) or biomaterials (proteins, DNA, or peptides). All these systems have huge importance in different areas of knowledge from biology to technological problems. In solutions, water molecules are confined by the freezing-in of the solution itself (soft confinement) below the glass-transition temperature (which is due to the relaxation of solute molecules plasticized by water). The properties of water in solutions can be affected by the structure, interactions, or even local motions of the solutes. For example, the dynamics of bulk water at room temperature is typically faster than that of water in solutions, as

3.4. Comparison of Water Dynamics in Hard and Soft Confinement Systems

Let us now make a comparison between the different systems of hard and soft confinements and microemulsions, even if the nature of these confinements is different. In Figure 1a it can be seen that in hard confinements the dynamics of water shows a 7611


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center. The variation of correlation times in these confinements can span several orders of magnitude, and hence it needs to be considered when experimental results are interpreted. In Figure 2, we see that the slowdown at solid walls is not restricted to

crossover between two different behaviors at a certain temperature. The origin and implications of these crossovers will be discussed in section 4, so here we focus on the differences and similarities of the water dynamics in the three types of systems. At temperatures higher than the crossover, the dynamics of water in all types of confinements is strongly dependent on the host material or the solute (see Figure 1), but at lower temperatures the similarities between the different systems are more pronounced. In fact, when the most regular hard confinement systems and the highest water concentrations for solutions (when water−water interactions are dominant and just before crystallization occurs) are considered, the water relaxation is similar in both types of systems with activation energy of roughly 0.5 eV (see dashed-dotted lines in Figures 1). For the rest of the solutions the water dynamics is systematically slower than this “universal” water relaxation (probably because of the interaction with the solute), whereas water dynamics in disordered hard confinement systems is systematically faster. These results show that there are a very restricted number of confinement systems that exhibit this “universal” water relaxation at low temperatures (for RM there are not available data in this low-temperature range, and therefore we do not include RM in this discussion). Furthermore, if one aims to make predictions for supercooled bulk water in the no man’s land region, one would expect that this “universal” water relaxation reflects the most relevant scenario for bulk water at low temperatures. It is therefore somewhat surprising that the relaxation times and particularly the activation energy of bulk low-density liquid (LDL) water is so different from that observed for water under confinement96 (×, Figure 1). This suggests that another type of relaxation process is probed in the case of LDL. The authors of ref 96 have assigned it to the αrelaxation of deeply supercooled LDL, but its exceptionally low activation energy may suggest another origin. Thus, although the “universal” water relaxation in confinements is expected to be similar to that in bulk water, it is still an open question whether this is really the case. As evident from Figure 1a, finite size effects and surface chemistry of nanoscopic hard confinements may play a role in the properties of the embedded water. Therefore, it is an important question to what extent the behavior of confined water can be equivalent to that of bulk water. Xu and Molinero111 studied the anomalous properties of mW water in strongly hydrophilic nanopores. They found that the temperature of maximum density (TMD) line in confined water follows a similar trend as that of bulk water, indicating that hydrophilic confinement itself may not significantly affect the density anomaly. However, no direct evidence of a first-order liquid−liquid phase transition (LLPT) in confined water was found in strongly confined water, mainly due to the absence of accessible LLPT in the bulk mW water. Nevertheless, a LLPT was observed for confined ST2 water, but the transition temperature differed in hydrophilic and hydrophobic pores.112 Further aspects, related to thermodynamics and structure of water models in various confinements, have been discussed in recent review articles.113,114 A number of MD simulation studies ascertained the dynamical behavior of water near different types of surfaces, ranging from molecular surfaces117,118 to solid walls. The latter surfaces include idealistic plain walls119 as well as chemically realistic silica pores.120,121 For silica pores, it was found that structural relaxation is slower at the pore walls than in the pore

Figure 2. Correlation times of water dynamics in various regions of cylindrical confinements, as obtained from MD simulations of incoherent intermediate scattering functions for water oxygen at 230 K. Strong slowdowns are observed near both silica walls115 and neutral walls composed of fixed water molecules.116

silica pores but also occurs in “water” pores, that is, when fixed water molecules form the confinement so as to remove different interactions at the liquid−solid interface.

4. DYNAMIC CROSSOVER UNDER CONFINEMENTS When experimental relaxation data of supercooled water in hard confinements are analyzed, it is evident that a dynamic crossover occurs, as discussed. However, since it has been widely debated exactly how experimental data should be analyzed and interpreted (particularly in the case of QENS), it is difficult to present an established relaxation scenario for confined supercooled water. Therefore, we are here presenting three different relaxation scenarios, which are the main scenarios presented in the literature. These three different relaxation scenarios for confined water also suggest different relaxation scenarios for supercooled bulk water, which are discussed in section 5. The first scenario for dynamical crossover, as illustrated in Figure 3a, is based on the liquid−liquid critical point (LLCP) hypothesis, which predicts the existence of two different liquid water phases, low-density liquid (LDL) and high-density liquid (HDL).122,123 The polymorphism hypothesis of liquid water is further supported by the observation of three different amorphous solid phases at different pressures below the noman’s land region;124−127 low-density amorphous (LDA), highdensity amorphous (HDA), and very high density amorphous (VHDA) ices. Depending on the sample preparation method, glassy water is also called hyperquenched glassy water (HGW) or amorphous solid water (ASW). ASW is formed by the deposition of water vapor at low pressure onto a cold solid surface,128 and HGW is formed by quickly spraying micrometer-sized droplets on substrates cooled at 77 K.129 In both cases a cooling rate exceeding 106 K/s is obtained, which is needed to avoid crystallization in the no man’s land. LDA, ASW, and HGW have very similar structure and density and therefore LDA is used as a common acronym for LDA, HGW, and ASW. The distinction between LDA and HDA is made at 1 g/cm3, implying that amorphous ices with densities lower than that are denoted LDA, whereas those with higher densities are classified as HDA or even VHDA. According to the first relaxation scenario presented above, critical fluctuation in the vicinity of the LLCP is the origin of water anomalies. According to theoretical studies,127,130 beyond 7612


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Figure 3. Schematic diagram at ambient pressure of different scenarios for the dynamical behavior of supercooled confined water. αconf indicate confined α-relaxation, and βJG means Johari−Goldstein β-relaxation.

Figure 4. Neutron scattering correlation times (right)133 and inverse of NMR self-diffusion (left)38 data for water in silica (MCM-41) nanotubes. The neutron data have been measured in the wave-vector range 0.25 < Q < 1.93 Å−1 and in the temperature range 200−240 K; the main value used was 1.32 Å−1. In addition, the inverse of NMR self-diffusion in bulk is reported for comparison.153 (Inset) Fractional SE representation: measured Ds and ⟨τr⟩ in a log−log scaling plot.48,49

the LLCP in the one-phase region, there exists a locus of response function extrema, which is regarded as the extension of the HDL−LDL coexistence line into the one-phase region and is also called the Widom line.130 At the high-temperature side of the Widom line the liquid resembles the HDL structure, while it resembles the LDL structure at low temperature. In this frame it has been proposed that water shows a dynamic crossover when the local structure changes from LDL-like to HDL-like.47,130−132 The data presented in Figure 3a, obtained at ambient pressure, were therefore interpreted as due to the crossing of the Widom line, a continuous evolution of the water structure from HDL-like to LDL-like liquid state. The cusplike dynamic crossover from non-Arrhenius behavior at high temperature to Arrhenius behavior at low temperature was first observed in water confined in MCM4138,133,134 via QENS and NMR.38,133,134 This transition was then linked to the FS transition upon crossing the Widom line in the vicinity of the LLCP,74 though other authors135−137 argued against a true FS transition for confined water, in consistency with the two other relaxation scenarios proposed below. Fourier transform infrared (FTIR) experiments on confined water at ambient pressure also indicated that a LDL-

like to HDL-like continuous structural transition occurs upon crossing the Widom line49,131 at T ≈ 225 K. As mentioned, liquid water polymorphism arises from the existence of two amorphous phases, LDA and HDA, that can be transformed one into the other by tuning the pressure. In these terms the dynamical crossover temperature or the temperature upon crossing the Widom line depends on the pressure. In other words, if the hypothesized LLCP exists, according to the convergence of supercritical phenomena127,130,132 in the vicinity of the critical point, one should be able to trace the LLCP as the terminal point of the dynamic crossover, located in the supercooled region at PC = 1600 ± 400 bar and TC = 200 ± 10 K. The dynamical crossover has been studied in the frame of the liquid−liquid critical point scenario in many different aqueous systems, such as water in aerogels,138 alcohol,139 salts,140 or confined in ice,141 and in proteins.142,143 Here, we report in Figure 4 some results for water confined in MCM-41 nanotubes. Figure 4 highlights the distinct roles of the confined water translational dynamics (self-diffusion, Ds) and the relaxation time ⟨τr⟩ measured by QENS in a wide temperature range above and below the dynamical crossover. Here it should 7613


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coexistence line of LDL and HDL is still debated.50−54 The controversial results by simulations are particularly focused on whether there exists a LLPT in the ST2 water.50−54 Recently, Xu et al.163 investigated how confinement and surface chemistry affect the LLCP164 by confining liquid in slits with different separations based on the Jagla model164 with an accessible LLCP and water-like anomalies. They found that as the separation decreases, the LLCP shifts to lower temperature and higher pressure. More importantly, under severe confinement the LLCP becomes inaccessible. This indicates that severe confinement smears first-order transitions; thus direct evidence of a first-order LLPT in confined water may not be found in strongly confined water, even though it does not mean that there is no LLPT without well-defined first-order structural transformation. A LLPT was observed for confined ST2 water, but the transition temperature differed in hydrophilic and hydrophobic pores.112 Further aspects, related to thermodynamics and structure of water models in various confinements, have been discussed in recent review articles.113,114 Nevertheless, if confined water is studied as a function of pressure, the ensemble of all obtained findings may be considered useful to understand at least some aspects of water complexity, although the findings cannot be considered as proof of the existence of a LLCP. The second scenario on the dynamics of water under confinement (Figure 3b) is mainly based on BDS data, and therefore it extends to longer time scales (up to seconds) and lower temperatures compared to the QENS and NMR data behind Figure 3a. This is possible by the use of broadband techniques such as BDS. We first focus on the results of the model system for studying water under confinement, MCM-41 (C10) with a pore diameter of 21 Å. Figure 5 shows the

be noticed that this latter quantity obtained by the QENS spectra, in terms of the so-called relaxing cage model,144 is the intermediate scattering function I(Q,t), which at low Q values (0.25 < Q < 1.93 Å−1) measures a density−density correlation time that is assumed to be coupled to the viscosity.144 Whereas the NMR data correspond to a translational motion, it is possible to determine the rotational motion by applying the relaxing cage model to the neutron data (at least in the Q range used). The obtained results show the following for supercooled water: (i) decoupling between translational and rotational transport coefficients and (ii) crossover from fragile to strong glass-former. In addition, the data analysis131 in terms of proper scaling concepts145 show the violation of SER and the onset of the fractional SER (reported in the inset as Ds vs ⟨τr⟩ on a log− log scale).48 Note that the same processes characterize the complex thermodynamic behavior of supercooled glass-forming materials146,147 accompanied by the onset of dynamical heterogeneities and subsequent violation of the SER.47 Bulk supercooled systems (o-terphenyl, salol, etc.) also seem to show, in their transport parameters, universal behavior when the temperature of the FS dynamical crossover is considered.148,149 In terms of the proper statistical physics, inherent structures or basin energy landscapes,150,151 the crossover has been related to a decoupling between translational and rotational motions.152 In the frame of the LLCP, the dynamic crossover has been linked to the Widom line, which is the continuation of the liquid−liquid coexistence line into the one-phase region beyond the hypothesized LLCP of water (supercritical region). According to this scenario, the FS crossover temperature is correlated with the Widom temperature defined as the loci of the response function maxima117 in the vicinity of the LLCP. The maxima in configurational specific heat cP have been observed by using the NMR proton chemical shift in confined154 and hydration protein water.155 This finding was obtained by simply considering that the proton chemical shift δ is directly related to the local order, therefore its temperature derivative, ∂δ/∂T, must be proportional to the configurational specific heat. The Widom line is also reflected in the structural relaxation of water, and recently it has been proposed to be responsible for the density hysteresis of water.156,157 It was also proposed that sound propagation identifies the Widom line as the locus of crossovers in the sound velocity along some isochores158 in the region of negative pressures. Upon changing the pressure for water confined in MCM-4174 and protein (lysozyme hydration water),142 the neutron scattering findings of Figure 4 suggest an evolution that shows the pressure− temperature behavior of the Widom line,130,131 as supported also by simulation studies.117 Another relevant and new situation, proposed in the frame of this HDL-like to LDL-like crossover by neutron scattering studies on MCM-41,159 cement,160 and proteins161 and by simulations,162 is the observation of the onset of the Boson peak, characteristic of supercooled glass-forming materials. From these studies it appears that when water is cooled below the Widom temperature, the extra “rigidity” of molecules with LDL-like local structure supports a new vibration. It should be noted that the properties of confined water in the supercooled region, proposed in the frame of this first scenario, may be affected by the constraints imposed by the confinement. Therefore, besides the large amount of experiments supporting the presence of a LLCP nowadays, the

Figure 5. Temperature dependence of relaxation times of the main relaxation process of water confined in approximately 21 Å pores of MCM-41 (C10), obtained by dielectric spectroscopy7 (triangles). (Inset) Temperature dependences of relaxation times of water in aqueous solutions107,172 and hard confinement systems.68,69 Note that the water relaxation in all types of systems approaches a universal βrelaxation of water.

relaxation time of water confined in MCM-41 (C10) obtained through BDS.7 In the temperature region of 180 K, we observe a change in the dynamics from liquidlike behavior [Vogel− Fulcher−Tammann (VFT)] toward localized (Arrhenius activated) motions with decreasing temperature. Note that the change of dynamics is produced at lower temperatures and longer time scales than that observed in the scenario of Figure 7614


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can be elucidated by direct comparison with the corresponding bulk liquids. This has been done, for example, for ethylene glycol137 and poly(ethylene oxide),170 where the liquid has been trapped in cages of sufficiently small sizes to allow only a few liquid molecules. The results from such studies clearly show that severe confinement causes the α-relaxation to vanish. In the case of confined supercooled water, this finding suggests that the observed dynamic crossover can be explained by finite size effects.171 In fact, it is well-established that when a liquid is confined within a pore, its structural and dynamical properties can be strongly modified. The crossover would be associated with the fact that any presumed characteristic length of the dynamics in a supercooled liquid cannot extend further than the typical pore size. This implies that at a certain temperature (i.e., the crossover temperature), the characteristic length of the dynamics becomes equal to the size of the confinement, which prevents the characteristic length from growing further, and as a result the high-temperature VFT dependence transforms to a low-temperature Arrhenius behavior. A third scenario for the dynamical behavior of deeply supercooled confined water is schematically depicted in Figure 3c. It is mainly based on recent 2H NMR results for heavy water in mesoporous silica,75,76,173 which are compared with other experimental findings for water dynamics in nanoscopic confinements in Figure 6.

3a. Moreover, the low-temperature activation energy in BDS (Figure 5) is substantially higher than that in QENS (Figure 4). The characteristics of high-temperature water relaxation are quite similar to those exhibited by the well-known α-relaxation, which is observed in supercooled systems above the glasstransition temperature (Tg). In addition, low-temperature water relaxation exhibits all the characteristics typical for βrelaxations, as discussed in some detail in ref 137. Therefore, this low-temperature process is not related to the viscosity of the water molecules, which further implies that the dynamic crossover is likely due to a crossover from a α-like relaxation above the crossover temperature to a β-like process below the crossover. The question is whether this behavior is general for water under confinement or it is a feature of this particular system. The answer can be found in studies of water dynamics in other types of confinements such as water solutions77 or even imperfect porous solids (for instance, molecular sieves).165 In such cases, the comparison should be established with some care, since the water concentration considered should be the maximum water concentration before crystallization occurs. At such high water concentrations, most of the water molecules are expected to be surrounded by other water molecules (the response is dominated by water−water interactions), and its relaxation should be less influenced by the presence of the solute.166 When temperature dependence of the relaxation time of water in these diverse materials is considered (see inset of Figure 5), the same scenario as that proposed in Figure 3b is found, even if the nature of the confinement is different. For solutions at temperatures above Tg, we can assume that the reorientation of water molecules is coupled to cooperative motions related to α-relaxation of the whole system (solute− water). When the temperature approaches Tg, upon decreasing temperature, the global dynamics becomes frozen but water molecules still have enough mobility to be detected by dielectric spectroscopy. Below Tg, water molecules are trapped in the frozen matrix and their motions are restricted and similar to those corresponding to a secondary β-relaxation in a simple glass. As a consequence, temperature dependence of relaxation times is Arrhenius-like. This restricted dynamics is called αconfined in Figure 3b. The following common features of water dynamics under confinements can be identified: (1) lowtemperature relaxation is symmetrically broadened and Arrhenius-like, (2) activation energy is 0.50 ± 0.03 eV, (3) the time scale of this Arrhenius relaxation differs by less than 1 order of magnitude for all systems, and (4) high-temperature relaxation depends on the host system since surface or solute interactions dominate. Therefore, the change of temperature dependence for water in MCM-41 is not an exceptional result, since it shares the most common features for supercooled water in other types of confinement. As a conclusion, the lowtemperature relaxation can be regarded as the universal βrelaxation of water. Moreover,167 recent experiments show that this universal β-relaxation is pressure-dependent,107,168 which indicates that this process is of Johari−Goldstein type169 (βJG) and therefore a universal property of glasses. This type of relaxation involves all atoms in the water molecule in a local (noncooperative) and anisotropic motion, and it is coupled to translational motions. These last characteristics of water under confinement were probed75,76 by means of NMR studies of water in MCM-41. To rationalize the change in water dynamics at 180 K, it is valuable to compare with other liquids, where finite size effects

Figure 6. Correlation times of (heavy) water in silica (MCM-41) and myoglobin (MYO, hydration levels h = 0.35−0.45 g/g) matrices. (a) Results from 2H NMR spin−lattice relaxation (SLR) and stimulatedecho experiments (STE) for heavy water in MCM-41 C1075and MYO,104 from BDS studies on water in MCM-41 C10172 and MYO, and from QENS work on water in MCM-41-S.74 In addition, correlation times from mechanical relaxation and thermally stimulated current investigations on hydrated collagen (h = 0.5 g/g, △)188 and hydrated elastin (h = 0.25 g/g, ▽),189 are shown. The arrow marks the glass-transition temperature of interfacial water obtained from positron annihilation lifetime spectroscopy.186 (b) 2H NMR SLR and STE data for heavy water in MCM-41 C12 and C14.75

Above ∼225 K, an isotropic reorientation associated with αrelaxation of confined water was observed by 2H NMR studies.75,76,173 In this high-temperature range, the absolute value and temperature dependence of τα substantially depend on the type of confinement. In particular, fragility decreases when the size of the confinement is reduced. This effect is evident when the diameter of the silica pores is diminished from 2.9 to 2.1 nm, that is, when the water is confined in MCM-41 (C10) (see Figure 6a) rather than in MCM-41 (C14) (see Figure 6b). The phenomenon can also be seen when confinement is further downsized to very few molecular diameters and, hence, the majority of water molecules reside in the immediate vicinity of an interface. Then, only minor deviations from Arrhenius behavior remain, a situation found in 7615


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narrow slits of clays69 or for weakly hydrated proteins.35,104 This ”FS crossover” in response to a reduction of confinement size and, hence, of the average distance of a water molecule to a solid surface is in harmony with results from neutron scattering studies8,174,175 and molecular dynamics simulations.116 In the range 220−230 K, 2H NMR results revealed a change in the temperature dependence of water dynamics in the studied silica matrices. This change is more pronounced when the temperature dependence of α-relaxation is more nonArrhenius above the crossover temperature, as in wider pores, but it is less prominent than the sharp kink, which was reported in QENS work and taken as evidence for a FS crossover of water.74 The 2H NMR correlation times for water in MCM-41 C10 are consistent with the QENS data at high temperatures, while they follow BDS results7 at low temperatures; see Figure 6. In 2H NMR,75,76,173 it was observed that, near the crossover temperature, a solid fraction of confined water forms and, hence, the liquid fraction becomes most probably sandwiched between this solid water and the silica wall. Then, the liquid dynamics can be expected to become interface-dominated, resembling the situation in clay slits or at protein surfaces, where deviations from Arrhenius behavior are weak. Thus, within this scenario, the dynamic crossover near 225 K results from a reduction of fragility due to a restriction of accessible volume. Therefore, the crossover temperature should change when a solid fraction of confined water emerges at other temperatures in different types of confinements. A dynamic crossover in response to a freezing transition was recently also proposed on the basis of theoretical arguments.176 For MCM-41 (C12 and C14), this picture is consistent with differential scanning calorimetry (DSC) studies, which reported melting points of water in the range 220−230 K in these pores.6,177,178 For MCM-41 (C10), the situation is less clear. While scanning calorimetry does not show indications of a crystallization of water in such 2.1 nm pores, adiabatic calorimetry does reveal specific heat signals in the relevant temperature range,179,180 which were attributed to a formation of highly distorted ice.181 Another thermodynamic study on water in this confinement argued in favor of a homogeneous nucleation-like structuring without crystallization to ice.180 Upon decreasing the temperature below 225 K, 2H NMR results related to liquid interfacial water become dominated by β-relaxation. Mainly two observations supported this conclusion. First, water dynamics no longer results in a complete decay of 2H NMR correlation functions,35,76,173 and second, 2H NMR line shapes are indicative of anisotropic rather than isotropic motional averaging.104,182 Such change from α-like to β-like dynamics upon cooling is consistent with the already discussed conclusion of BDS work.137 β-relaxation exhibits several universal properties, for example, a low-temperature activation energy of ∼0.5 eV,77,183 but its molecular mechanism is still elusive. It was not only regarded as a typical relaxation of a glass-forming liquid but also related to water-specific motions, for example, to local rotations in a plastic ice phase.184 The conclusion that β-relaxation dominates BDS and NMR single-particle rotational correlation functions at sufficiently low temperatures does not exclude that α-relaxation still exists at longer time scales. In fact, it was argued that structural rearrangements of interfacial water continue down to a glasstransition-like dynamic arrest near ∼180 K.75,76,173 At this temperature, there is a crossover from exponential to nonexponential 2H spin−lattice relaxation, indicating that the water molecules cease to explore different local environments;

that is, the system becomes nonergodic. Findings obtained with various other experimental methods corroborate this conclusion. In BDS, a kink in temperature-dependent proton relaxation times was reported for protein hydration water at 181 K due to an onset of cooperative reordering of the hydrogen-bond network,185 positron annihilation lifetime spectroscopy found a glass transition of interfacial water at Tg = 190 K,186 and neutron scattering work reported a somewhat lower glass-transition temperature of Tg = 165 K for water at silica surfaces.187 Furthermore, indications for coexistence of two relaxation processes of interfacial water at sufficiently low temperatures were reported. Examples include results from BDS,68,183 mechanical relaxation,188 and thermally stimulated current studies.189,190 Water in bread shows, in addition to a βrelaxation, a slower α-relaxation with correlation times consistent with a DSC glass transition at Tg = 173 K.183 However, it should here be noted that the reason α-relaxation of water could be observed in bread is most likely that the water is not “clean”, that is, it contains ions and smaller carbohydrates that act as probe additives for observing the α-relaxation of deeply supercooled confined water by BDS. This role of additives to make dielectric α-relaxation (as well as calorimetric Tg) of confined water clearly visible was demonstrated in ref 191, where a dielectric α-relaxation and a related calorimetric Tg at 187 K were observed for water confined in MCM-41 only if 10 wt % glycerol was added as probe molecules. Thus, although dielectric α-relaxation and calorimetric Tg of confined water seem difficult to observe, these dielectric studies of diluted confined solutions indicate a Tg of confined water in the range 170−190 K. In Figure 6 we also show correlation times of two relaxation processes observed in mechanical relaxation and thermally stimulated current studies.188,189 We see that these results support the conclusion that interfacial water exhibits a slower α process, undergoing a glass transition somewhat below 200 K, and a faster β-relaxation, reaching a correlation time τβ = 100 s near 130 K. Thus, within this scenario, the mild bending observed for temperature-dependent NMR and BDS correlation times at 180−190 K (see Figure 6) receives a straightforward interpretation as the commonly observed change in τβ(T) at Tg.21 Altogether, the scenario sketched in Figure 3c attributes the crossover at ∼225 K to a solidification of inner water, which will be further discussed in section 5, and the crossover at ∼185 K to a glass transition of interfacial water.

5. POSSIBLE IMPLICATIONS FOR SUPERCOOLED BULK WATER The first relaxation scenario presented in Figure 3a for confined water is close to the FS crossover that has been proposed to occur for supercooled bulk water.11 It is therefore generally believed that if the scenario shown in Figure 3a is correct, it is highly relevant (at least on a qualitative level) for supercooled bulk water, which should exhibit a similar crossover in its relaxation behavior. Thus, the crossover is believed to be caused by the presence of a LLCP beyond which, in the one-phase region, a continuous LDL-like to HDL-like transition occurs at the dynamic crossover temperature of about 225 K. Thus, if the experimental data shown in Figure 4 are correct and correctly interpreted, they are most likely reflecting the relaxation scenario also of supercooled bulk water, since no experimental results for bulk water strongly contradict such an analogy. 7616


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the believed Tg of bulk water at 136 K14 is rather due to the freezing-in of the βJG-relaxation than the viscosity-related αrelaxation. However, this possibility is also in conflict with other types of experimental studies of LDA, which have shown that 136 K is also associated with an onset of viscous flow.12,195,196 This observation strongly suggests that LDA crosses its Tg when the temperature is raised above 136 K. The question is then whether a Tg of bulk water above 190 K must be completely ruled out, despite its indication from confinement studies. A possible answer to this apparent conflict between the most likely Tg of bulk water and the indicated Tg of bulk water from confinement studies may be found in the extremely rapid cooling rate required to produce LDA by cooling of water. It is well-known that bulk water crystallizes so rapidly in the “no man’s land” that LDA has to be produced with a cooling rate no lower than 105 K/s. However, such a fast cooling rate also implies that supercooled water may fall out of equilibrium already at about 220 K, as recently suggested by Limmer197 in a theoretical paper. Thus, Tg is reached already at that temperature during such rapid cooling. This also prevents the length scale of the cooperative α-relaxation from growing further, and this gives rise to a dynamic crossover of the αrelaxation at 220 K to a low-temperature Arrhenius dependence. Hence, the extremely rapid cooling rate is causing a FS crossover to occur at 220 K, and therefore the relaxation time of the α-process does not reach a time scale of about 100 s until a temperature of 136 K is reached.197 Limmer’s suggestion further implies that the α-relaxation during such fast cooling must be very similar to the behavior of the βJG-relaxation proposed above. Then 136 K will also be the measured Tg of LDA when it is heated from low temperatures. However, for a slow cooling rate of less than 0.1 K/s, the supercooled water would not fall out of equilibrium (if one would had been able to avoid crystallization) at 220 K, but rather a pronounced nonArrhenius temperature dependence of τα would continue, because such behavior is expected when the cooperativity length of the α-relaxation increases with decreasing temperature, until a true glass-transition temperature is reached.197 This glass-transition temperature was estimated to be at about 180 K by Limmer,197 but for more fragile behavior of supercooled water than estimated by Limmer, Tg would be even higher, and in good agreement with the indications from the confinement studies. However, it should here be noted that LDA can also be produced from HDA, which has been formed by pressure amorphization of ice. Such LDA does not fall out of equilibrium during preparation but nevertheless shows a Tg at 136 K.20 On the other hand, as for the hyperquenched glassy water, it is not obvious that this method should produce the same type of glassy water that it was possible to produce from liquid water by a slow cooling rate. Thus, maybe neither of the two mentioned methods to produce amorphous solid water is able to produce a glassy material with the same cooperativity length of the α-relaxation when it is heated up as a glassy material produced from liquid water by a slow cooling rate. The third relaxation scenario, as depicted in Figure 3c, implies that it is not straightforward to draw definite conclusions about bulk water based on findings for confined water. In the weakly supercooled regime, the properties of the confinement crucially determine the correlation times of the αrelaxation, and hence, one may expect that there are also implications for a change from HDL-like to LDL-like water structure. In order to still be able to obtain useful information about bulk behavior, it is necessary to further improve our

In the case of the second relaxation scenario shown in Figure 3b, it is also possible to suggest likely implications for supercooled bulk water, because if the almost universal lowtemperature Arrhenius-dependent relaxation is a βJG-relaxation, it should be very similar in glassy bulk water. Hence, if the experimental data shown in Figure 5 are correctly interpreted, the low-temperature Arrhenius process should be close to the intrinsic βJG-relaxation of bulk water. This interpretation suggests also that the confined supercooled water must reach its glassy state at a temperature close to the crossover temperature of approximately 180 K. The question is, however, if a similar relaxation behavior occurs for bulk water, at which temperature should the βJG-relaxation decouple from the αrelaxation and where should Tg be located? To answer this question, we have to discuss the expected structural and dynamical changes of deeply supercooled water in confinements. Almost all structural studies of water in confined geometries have shown that the number of hydrogen bonds between the water molecules is reduced compared to bulk water. Moreover, for confined hydrogen-bonded liquids in general, it is commonly observed that the dynamics is slower than in the corresponding bulk liquids at high temperatures, due to a dominating effect from surface interactions, whereas the dynamics is faster at low temperatures close to Tg, due to a dominating contribution from geometrical confinement effects.9,192,193 Since also a reduced number of hydrogen bonds in the network structure of water is expected to speed up the dynamics, Tg of confined water should be located at a lower temperature than for bulk water, as typically observed for hydrogen-bonded confined liquids.9,193,194 This assumption is further supported by the fact that surface ice melts at a lower temperature than bulk ice, due to the speeding up of dynamics caused by a reduced number of hydrogen bonds at the surface. Thus the dynamics of confined water is generally slower than for bulk water around room temperature, but at a low temperature where a tetrahedral network structure is completed in bulk water, the situation is often the reverse. The exact temperature where this occurs depends on how fragile supercooled water is when it enters into the “no man’s land”, that is, how rapidly the time scale of the structural α-relaxation increases with decreasing temperature. Above 235 K, measurements of different dynamical properties indicate that the αrelaxation time should increase exceptionally rapidly below this temperature and follow a power-law behavior diverging already at 228 K,11 implying that Tg of bulk water must be located at about the same temperature. Whether the increase in relaxation time of the α-process is really that fast cannot be established, but from the indicated Tg of confined water75,186,191 and the rapid change of dynamical properties of bulk water close to 235 K, it seems likely that Tg of bulk water is located above 190 K, provided that the relaxation scenario presented for confined water in Figure 3b is correct. This further implies that the βJGrelaxation decouples from the α-relaxation at about the same temperature, since this decoupling should occur just above Tg. The possible relaxation scenario outlined above for supercooled bulk water is the scenario most consistent with the interpretations resulting in Figure 3b for confined water. However, this relaxation scenario, with a Tg of bulk water above 190 K, is not consistent with many studies of LDA, which indicate that Tg is located as low as 136 K.14 Since this is the temperature where the more local βJG-relaxation is expected to reach a time scale of 100 s, that is, to give rise to a small step in the heat capacity measured by calorimetry, we may suggest that 7617


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6. CONCLUSION From the discussions in this review, it is clear that there are both advantages and disadvantages to the three different relaxation scenarios presented in Figure 3 and their possible relationships to supercooled bulk water. The first relaxation scenario for confined water (Figure 3a) is in best agreement with the most commonly believed behavior of supercooled bulk water, but for confined water it is the most questionable interpretation of the experimental data, since there is no clear evidence that the relaxation process below the crossover temperature at 225 K is related to a structural α-relaxation. The second relaxation scenario (Figure 3b) seems to have the strongest experimental support from studies of confined water, but nevertheless this scenario is questionable since it predicts a Tg of bulk water above 190 K, which is in conflict with experimental studies of LDA.12,14,195,196 The third relaxation scenario suggests that small crystalline regions may appear in many of the confinement systems, making a relationship to bulk water even more uncertain, provided that similar nanocrystalline regions are not formed also in the supercooled bulk liquid. However, if such crystalline regions are also formed when ultraviscous bulk water is produced in hyperquenching or pressurizing approaches, then these may be responsible for the slow dielectric relaxation process observed for LDL and HDL96 and explain its low activation energy. Thus, none of the proposed scenarios for confined water is fully satisfactory for explaining the glass-transition and relaxation behavior of LDL and HDL. Possibly, the structural layering effects at surfaces and the restricted length scale of cooperative molecular motions in confined water make direct comparisons to supercooled bulk water impossible. It is also possible that the apparent conflict between the findings for confined water and bulk water can be explained by the extremely rapid cooling rate required to produce glassy bulk water,197 as discussed in section 5. Another problem is to understand and interpret the experimental data correctly. For instance, with QENS a pronounced dynamic crossover is obtained at about 225 K, but whether this is a true fragile-to strong crossover in the sense that the viscosity-related dynamics changes is highly unlikely, since no such crossover is observed in BDS data. More likely, QENS data detects the splitting of more local water dynamics from the viscosity-related dynamics at this crossover temperature. However, with BDS it is even more difficult to determine the physical nature of an observed relaxation process, due to the impossibility of studying Q dependence of the dynamics with this technique. Although the temperature dependence of both amplitude and relaxation time, as well as the shape of the dielectric loss peak, are generally different for the viscosityrelated α-relaxation and more local β-relaxations, it is still difficult to safely distinguish such relaxation processes, particularly for supercooled liquids in confined geometries where the temperature dependences can be altered compared to bulk. Usually, α- and β-relaxations can also be distinguished on the basis of the mechanism for the underlying molecular reorientation, which is isotropic and anisotropic, respectively. However, for confined water, 2H NMR studies found that the anisotropy of β-related reorientations is unusually weak, rendering a clear discrimination from α-related reorientations difficult even by NMR.35,75,76 To conclude, we still believe that studies of confined water can be a useful approach to understand the relaxation behavior

understanding of confinement effects, in particular, to answer the following questions arising from observations for the MCM-41 C10 model confinement. What is the nature of a solid fraction of confined water, which was found to emerge at 220−230 K in 2H NMR studies? Existence of an amorphous phase would support the conjecture of a glass transition of bulk water in this temperature range. However, the correlation times of the α-process amount to ∼100 ns at the relevant temperatures, and hence, despite the fact that this value is an average of a broad distribution of time constants across the confinement, it is unlikely that there are water molecules with τα ≈ 100 s. Rather, it is likely that crystal nuclei form,181,198 which are highly limited in size and order due to the confinement but stable on a time scale of seconds. As discussed in theoretical work,176 the latter conjecture can be reconciled with the absence of a freezing peak in DSC measurements. Anyway, the dynamic crossover observed for the liquid fraction of confined water is accompanied by the formation of a solid fraction, and hence it may not be taken as evidence for a FS transition of bulk water. Is there a dynamical-arrest phenomenon resembling a liquid−glass transition at 180−190 K? 2H SLR studies75,76 concluded that water molecules of the liquid fraction cease to explore different regions of the confinement on a time scale of about 1 s during a glass-transition-like arrest at these temperatures. This conjecture received support from positron annihilation lifetime spectroscopy work, reporting a glass transition of interfacial water in this range.186,199 When we assume a glass transition of interfacial water at 180−190 K, the implications for the Tg value of bulk water still remain unclear. As discussed, interfacial water exhibits slower dynamics than bulk water in the weakly supercooled regime, suggesting that the former species has a higher Tg than the latter, while a recent fast scanning calorimetry study observed just the opposite.200 Therefore, it is necessary to gain fundamental knowledge about the effects of various types of interfaces on the temperaturedependent correlation times of water dynamics before unambiguous conclusions can be drawn. What is the nature of the low-temperature process of confined water? In harmony with the conclusions based on BDS data, NMR results for confined water provide evidence for a crossover from high-temperature isotropic and diffusive (αlike) water motion to low-temperature anisotropic and localized (β-like) water dynamics. If it is assumed that the lowtemperature relaxation observed in BDS and NMR can be identified with a β-relaxation, the correlation times of this dynamical process may not be used to conclude the existence of a FS transition. Despite a lack of straightforward relationships, studies of confined water may be of higher relevance for an understanding of bulk water in the deeply supercooled regime than usually assumed. The conjecture that small nuclei exist even in narrow confinement underlines the high propensity for crystallization. Hence, one may wonder whether tiny nuclei are also formed and frozen when bulk water is quenched. Then the structural relaxation of the reheated water would correspond to the relaxation of the liquid between these nuclei and, hence, of interfacial water, bearing some resemblance to the situation in aqueous mixtures, where water dynamics is affected by surfaces of solute molecules. In such a scenario, it would be questionable whether the true behavior of the bulk liquid is observed when reheating hyperquenched amorphous water. 7618


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of bulk water in the no man’s land region. However, this requires that we first reach a better understanding of the observed water dynamics in confinements. This goal can likely be reached by more accurate and detailed experimental studies of confined water, such as neutron spin−echo studies, reaching experimental time scales of several hundred nanoseconds, of the Q-dependent dynamics, in combination with improved MD simulations. Only when the structural and dynamical behavior of supercooled confined water has been understood will it be possible to make clear evaluation of its relevance for supercooled bulk water.

physics at the Technische Universität Darmstadt. He uses both experimental and computational approaches to investigate complex molecular dynamics in disordered materials. The spectrum of studied systems comprises organic and inorganic glasses, crystalline and glassy ion conductors, and polymer-based systemswhich include pure polymer melts, polymer−plasticizer systems, polymer electrolytes, and polymer nanocompositesas well as biological materials, in particular, hydrated proteins. Limei Xu received her Ph.D. from the Department of Physics at Boston University in 2007. After that she was a postdoctoral fellow in the University of Utah Chemistry Department. In 2008 she joined the Advanced Institute of Materials Research (WPI-AIMR) at Tohoku University as an assistant professor. In 2011, she took a tenure-track associate professor position in the International Center for Quantum Materials (ICQM) at Peking University and was promoted to tenured professor in 2015. She was selected for the Junior 1000 Talents by the Chinese Recruitment Program of Global Experts in 2011 and was awarded the National Science Fund for Distinguished Young Scholars in 2015. Her current research interests include critical and supercritical phenomena, properties of water in confinement and on surfaces, and nonequilibrium statistical physics.

AUTHOR INFORMATION Corresponding Author

*E-mail [email protected]; phone +46-31-772 5680. Notes

The authors declare no competing financial interest. Biographies Silvina Cerveny studied physics at the University of Buenos Aires, Argentina, and obtained her Ph.D. at the same university in 2001. After postdoctoral stays in Chalmers University of Technology (Sweden) and at the Donostia International Physics Center in San Sebastian (Spain), she is currently a scientist at the Spanish Research Council [Consejo Superior de Investigaciones Cientificas (CSIC), Spain]. She uses a combination of experimental techniques to study the relationship between the dynamics and structure of disordered materials. Her research interests include problems associated with the dynamic of water in polymers and biopolymers and under soft and hard confinements. In addition, she studies elastomeric materials and nanocomposites.

ACKNOWLEDGMENTS This review was initiated during the Nordita (Nordic Institute for Theoretical Physics) scientific program “Water - the Most Anomalous Liquid”. Additional financial support for this program was provided by the Royal Swedish Academy of Sciences through its Nobel Institutes for Physics and Chemistry, by the Swedish Research Council, and by the Department of Physics at Stockholm University. Furthermore, M.V. thanks the Deutsche Forschungsgemeinschaft for funding through Grants Vo-905/8-2 and Vo-905/9-2. S.C. thanks the Basque government for support through the Nanoiker Project (Grant IE14-393) under the ETORTEK Program and the Spanish Ministry of Education, (MAT2015-63704-P). J.S. acknowledges the Swedish Research Council (Grant 6212012-4013) for further financial support. L.X. acknowledges support from the NSFC (11174006, 11290162, and 11525520) and National Basic Research Program of China (973 program) (2012CB921404 and 2015CB856801).

Francesco Mallamace received his B.E. from the Department of Physics at Messina University in 1973. In 1979 he became professor of physics. He started his scientific career at Rome La Sapienza by working on laser experiments related with the theory of coherence of light. After that, he worked on the physics of complex liquids and systems by studying their thermodynamic properties from the stable to the supercooled regime by using several different experimental approaches, such as scattering (light and neutron), viscoelasticity, sound propagation, and nuclear magnetic resonance. In all of these studies, his approach is based on the use of the proper model of statistical physics. His current research interests include dynamical properties of glass forming materials (molecular or polymeric) on approaching the arrested-glassy state.

GLOSSARY ASW BDS FS HDL HDA HGW LDL LDA LLCP LLPT MCM-41

amorphous solid water broadband dielectric spectroscopy fragile-to-strong high-density liquid high-density amorphous ice hyperquenched glassy water low-density liquid low-density amorphous ice liquid−liquid critical point Liquid−liquid phase transition Mobil Composition of Matter Number 41; cylindrical silica mesoporous packed into a hexagonal array with a tunable pore diameter MCM-41 (C10) cylindrical silica mesoporous packed into a hexagonal array with a pore diameter of 21 Å MCM-41 (C14) cylindrical silica mesoporous packed into a hexagonal array with a pore diameter of 28 Å MD molecular dynamics

Jan Swenson earned his Ph.D. in physics from Chalmers University of Technology, Sweden, in 1996. After that he was a postdoctoral fellow at University College London, before he returned to Chalmers in 1998 as an assistant professor. In 2001 he earned a research position at the Royal Swedish Academy of Sciences, and in 2005 he became a professor in condensed matter physics at the Norwegian University of Science and Technology, Trondheim, Norway. The year after, he returned to his current position as professor in physics at Chalmers University of Technology. His current research interests are broad and range from understanding the role of water and other solvents for biomolecular dynamics and functions to how the properties of polymer-based solid electrolytes for batteries and other electrochemical devices can be improved. Michael Vogel received his Ph.D. in physics from the University of Bayreuth, Germany, in 2000. Afterward, he worked as a postdoctoral fellow at the University of Michigan and at the University of Münster, Germany. In 2008, he started his current position as a professor in 7619


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PFG QENS RM SBA-15

SER SFG SLR ST2 water

STE TMD VFT

VHDA

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coarse-grained model of water (mW) that is essentially an atom with a tetrahedrality intermediate between carbon and silicon nuclear magnetic resonance phase region where crystallization is unavoidable, either when liquid water is cooled from high temperatures or when amorphous solid water is heated from lower temperatures pulsed field gradients (in NMR) quasielastic neutron scattering reverse micelles Santa Barbara Amorphous type material; ordered mesoporous material having hexagonal pores with pore diameter between 5 and 15 nm Stokes−Einstein relationship static field gradients (in NMR) Spin−lattice relaxation (in NMR) water model proposed by Stillinger and Rahman in 1974 that has five sites with negative charge placed on dummy atoms representing the lone pairs of the oxygen atom, with a tetrahedral-like geometry stimulated echo (in NMR) temperature of maximum density Vogel−Fulcher−Tammann equation, used for analysis of temperature dependences of relaxation times, viscosities, and diffusion coefficients very high density amorphous ice

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