Liquid Polymorphism

By H. Eugene Stanley and Pablo Debenedetti

The Advances in Chemical Physics series—the cutting edge of research in chemical physics

The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series presents contributions from internationally renowned chemists and serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

This volume explores:

• Electron Spin Resonance Studies of Supercooled Water
• Water-like Anomalies of Core-Softened Fluids: Dependence on the Trajectories in (P, ϱ, T) Space
• Water Proton Environment: A New Water Anomaly at Atomic Scale?
• Polymorphism and Anomalous Melting in Isotropic Fluids
• Computer Simulations of Liquid Silica: Water-Like Thermodynamic and Dynamic Anomalies, and the Evidence for Polyamorphism

• Language: English
• Publisher: Wiley
• Release date: Apr 22, 2013
• ISBN: 9781118540374

Book preview

Contributors to Volume 152

Katrin Amann-Winkel, Institute of Physical Chemistry, University of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria

Debamalya Banerjee, Department of Physics, Indian Institute of Science, Bangalore 560 012, India

Marcia C. Barbosa, Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS, Brazil

Subray V. Bhat, Department of Physics, Indian Institute of Science, Bangalore 560 012, India

Vadim V. Brazhkin, Institute for High Pressure Physics RAS, 142190 Troitsk Moscow Region, Russia

F. Bruni, Dipartimento di Fisica E. Amaldi, Università degli Studi di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

Frédéric Caupin, Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Institut Universitaire de France, Université de Lyon 69622 Villeurbanne cedex, France

Sow-Hsin Chen, Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Carmelo Corsaro, Dipartimento di Fisica and CNISM, Università di Messina, I-98166 Messina, Italy

Dominik Daisenberger, 1-185 (Zone 12), Diamond Light Source Ltd., Diamond House, Harwell Science Campus, Didcot, Oxfordshire, OX11 0DE, UK

Jack F. Douglas, Materials Science and Engineering Division, NIST, Gaithersburg, MD 20899, USA

Carlos E. Fiore, Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531 Curitiba, PR, Brazil

Yu. D. Fomin, Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia

Valentina Maria Giordano, Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon 69622 Villeurbanne cedex, France; European Synchrotron Radiation Facility, 6 rue Jules Horowitz, BP220, 38043 Grenoble Cedex, France

Nicolas Giovambattista, Department of Physics, Brooklyn College of the City University of New York, Brooklyn, NY 11210-2889, USA

Mauricio Girardi, Universidade Federal de Santa Catarina, 88900-000, Araranguá, SC, Brazil

A. Giuliani, Dipartimento di Fisica E. Amaldi, Università degli Studi di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

G. Neville Greaves, Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK; Centre for Advanced Functional Materials and Devices, Institute of Mathematics and Physical Sciences, University of Wales at Aberystwyth, Ceredigion SY23 3BZ, UK

Vera B. Henriques, Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315970, São Paulo, SP, Brazil

Masami Kanzaki, Institute for Study of the Earth Interior, Okayama University, Yamada 827, Misasa, Tottori 682-0193, Japan

Yoshinori Katayama, Japan Atomic Energy Agency (JAEA), SPring-8, 1-1-1 Kuoto, Sayo-cho, Sayo-gun, Hyogo 679-5143, Japan

Dino Leporini, Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy; IPCF-CNR, UoS Pisa, Italy

Thomas Loerting, Institute of Physical Chemistry, University of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria

Alexander G. Lyapin, Institute for High Pressure Physics RAS, 142190 Troitsk Moscow Region, Russia

Gianpietro Malescio, Dipartimento di Fisica, Università degli Studi di Messina, Contrada Papardo, 98166 Messina, Italy

Domenico Mallamace, Dipartimento di Scienze degli Alimenti e dell’ Ambiente, Università di Messina, I-98166 Messina, Italy

Francesco Mallamace, Dipartimento di Fisica and CNISM, Università di Messina, I-98166 Messina, Italy; Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Masakazu Matsumoto, Department of Chemistry, Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kitaku, Okayama 700-8530, Japan

Paul F. McMillan, Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK

Osamu Mishima, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

Giulio Monaco, European Synchrotron Radiation Facility, 6 rue Jules Horowitz, BP220, 38043 Grenoble Cedex, France

Peter H. Poole, Department of Physics, St. Francis Xavier University, Antigonish, NS, B2G 2W5, Canada

M. A. Ricci, Dipartimento di Fisica E. Amaldi, Università degli Studi di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

V. N. Ryzhov, Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia

Ivan Saika-Voivod, Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, NL, A1B 3X7, Canada

Srikanth Sastry, Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bangalore 560 064, India; TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500 075, India

H. Eugene Stanley, Center for Polymer Studies, Department of Physics, Boston University, Boston, MA 02215, USA

Abraham D. Stroock, School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA

Marcia M. Szortyka, Departamento de Física, Universidade Federal de Santa Catarina, Caixa Postal 476, 88010-970, Florianópolis, SC, Brazil

Hajime Tanaka, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

Hideki Tanaka, Department of Chemistry, Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kitaku, Okayama 700-8530, Japan

Vishwas V. Vasisht, Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bangalore 560 064, India

Mark Wilson, Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK

Martin C. Wilding, Centre for Advanced Functional Materials and Devices, Institute of Mathematics and Physical Sciences, University of Wales at Aberystwyth, Ceredigion SY23 3BZ, UK

Hao Zhang, Department of Chemical and Materials Engineering, University of Alberta, AB T6G 2V4, Canada

Foreword

Conventional wisdom, that perennial adversary of novelty, asserts that a pure substance can have only one liquid phase. This volume of Advances in Chemical Physics contains a representative cross section of research that questions established thinking by scrutinizing the evidence for and against, and inquiring into the possibility and consequences of, the existence of more than one liquid phase in a pure substance.

Liquid polymorphism is a term used to describe coexistence of two distinct liquid phases of the same substance, both lacking long-range order, differing in density and enthalpy, and having the same chemical potential (hence coexistence). The concept dates back likely to the 1960s (C. A. Angell, private communication, 2012), when theoretical calculations suggested the possibility of a first-order phase transition between two liquids of the same substance [1]. Years later, experiments showing an abrupt transformation between two forms of glassy water [2,3], and computer simulations [4] suggesting the tantalizing possibility that supercooled water may exhibit liquid polymorphism (of which the glassy observations would be the structurally arrested manifestation) brought the attention of the scientific community to what had hitherto been a mere curiosity. These laboratory [2,3] and computational studies [4] also provided a potent nexus linking the phenomenologies of liquid and glassy polymorphism (the latter often referred to nowadays as polyamorphism) and offered one possible explanation for the striking anomalies in supercooled water's response functions [5]; alternative interpretations do not invoke polymorphism [6]. Further enrichment of the topic came from the possible occurrence of a phase transition between two binary supercooled liquids of identical composition but different density [7].

A transition between two liquid phases of the same substance necessarily involves modest changes in density and enthalpy compared to, say, the familiar liquid–vapor transition. Accordingly, the critical temperature for such a transition should be much lower than the vapor–liquid critical temperature [8]. It is, therefore, not surprising that most investigations of liquid polymorphism involve deeply supercooled liquids. While this is not a problem for pencil and paper theory [9], the combination of low temperature (intended here to mean lower than the equilibrium freezing point) and a high degree of metastability poses significant challenges to experimental and computational investigations. Examples of the ingenuity deployed in trying to measure the properties of cold, metastable matter in search of liquid polymorphism include ultrafast spectroscopic probes of electronic structure [10] and confinement-induced suppression of crystallization [11].

In this field, as in so many other areas of science, water occupies pride of place. Supercooled water is not just a laboratory curiosity. It occurs in large quantities in high-altitude clouds, influencing their radiative properties, and hence climate [12]. Glassy water is, by some estimates, the most common form of water in the universe, constituting the bulk of matter in comets and occurring as a frost in interstellar dust [13,14]. Both supercooled and glassy forms of water are important players in industrial processes designed to prolong the shelf life and stability of labile biochemicals [15]. Thus, the possible existence of a liquid–liquid critical point in deeply supercooled water has implications that go well beyond liquid-state theory. Not surprisingly, this is a very active area of research, whose present state of affairs is one of ferment and debate. Much has been learned about ways of avoiding crystallization by confining water in nanoscale hydrophilic pores [11], but it is not yet well understood how the properties of confined water relate to those in the bulk [16]. Excellent studies have been conducted to explore the volumetric properties of glassy water over broad ranges of pressure and temperature [17], but the kinetic or thermodynamic connections between the apparently different forms of amorphous water thereby identified are still a matter of ongoing investigation [18]. And, the ever-increasing power of modern high-performance computing infrastructure notwithstanding, proving the existence of polymorphism in well-established water models is still a challenging problem and a frontier area of research [19–23]. But this unsettled state of affairs casts a reassuring light on the vitality of this particular research area. From today's debates will emerge not only the resolution of a fascinating question (does water have a second critical point?) but also a deeper understanding of the relationship between this most peculiar and important of substances [24] and the liquid state of matter in general. The relationship between vitreous polyamorphism [25] and the recently discovered method for making ultrastable glasses by vapor deposition [26] is especially intriguing, because of the deep insights it appears to offer on apparently unrelated topics, with the energy landscape [27] as an underlying and unifying perspective.

The chapters included in this volume encompass experiment, theory, and computation; water as well as its tetrahedral analogues; liquid metals as well as inorganic melts; positive and negative pressures; transport properties as well as phase behavior. There can be no better testament to the vitality of the research enterprise that these scientists and many others across the globe are engaged in, driven by the quest to understand liquid and vitreous poly(a)morphism.

Pablo G. Debenedetti

Department of Chemical and Biological Engineering

Princeton University

Princeton, NJ 08544, USA

References

1. E. Rapoport, J. Chem. Phys. 46, 2891 (1967).

2. O. Mishima, L. D. Calvert, and E. Whalley, Nature 314, 76 (1985).

3. O. Mishima, J. Chem. Phys. 100, 5910 (1994).

4. P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Nature 360, 324 (1992).

5. R. J. Speedy and C. A. Angell, J. Chem. Phys. 65, 851 (1976).

6. S. Sastry, P. G. Debenedetti, F. Sciortino, and H. E. Stanley, Phys. Rev. E 53, 6144 (1966).

7. S. Aasland and P. F. McMillan, Nature 369, 633 (1994).

8. P. H. Poole, T. Grande, C. A. Angell, and P. F. McMillan, Science 275, 322 (1997).

9. P. H. Poole, F. Sciortino, T. Grande, H. E. Stanley, and C. A. Angell, Phys. Rev. Lett. 73, 1632 (1994).

10. M. Beye, F. Sorgenfrei, W. F. Schlotter, W. Wurth, and A. Föhlisch, PNAS 107, 16772 (2010).

11. F. Mallamace, M. Broccio, C. Corsaro, A. Faraone, D. Majolino, V. Venuti, L. Liu, C.-Y. Mou and S.-H. Chen, PNAS 104, 424 (2007).

12. K. Sassen, Science 257, 516 (1992).

13. P. Jenniskens and D. F. Blake, Science 265, 753 (1994).

14. P. G. Debenedetti, J. Phys.: Condens. Matter 15, R1669 (2003).

15. C. J. Roberts and P. G. Debenedetti, AIChE J. 48, 1140 (2002).

16. J. Swenson, Phys. Rev. Lett. 97, Art. No. 189801 (2006).

17. J. L. Finney, D. T. Bowron, A. K. Soper, T. Loerting, E. Mayer, and A. Hallbrucker, Phys. Rev. Lett. 89, Art. No. 205503 (2002).

18. K. Winkel, E. Mayer, and T. Loerting, J. Phys. Chem. B 115, 14141 (2011).

19. Y. Liu, A. Z. Panagiotopoulos, and P. G. Debenedetti, J. Chem. Phys. 131, Art. No. 104508 (2009).

20. F. Sciortino, I. Saika-Voivod, and P. H. Poole, Phys. Chem. Chem. Phys. 13, 19759 (2011).

21. D. Limmer and D. Chandler, J. Chem. Phys. 135, Art. No. 134503 (2011).

22. Y. Liu, J. C. Palmer, A. Z. Panagiotopoulos, and P. G. Debenedetti, J. Chem. Phys. 137, Art. No. 214505 (2012).

23. T. A. Kesselring, G. Franzese, S. V. Buldyrev, H. J. Herrmann, and H. E. Stanley, Sci. Rep. 2, 474 (2012).

24. C. A. Angell, Science 319, 582 (2008).

25. A. Sepúlveda, E. Leon-Guterrez, M. Gonzalez-Silveira, and M. T. Clavaguera-Mora, J. Phys. Chem. Lett. 3, 919 (2012).

26. S. F. Swallen, K. L. Kearns, M. K. Mapes, Y. S. Kim, R. J. McMahon, M. D. Ediger, T. Wu, L. Yu, and S. Satija, Science 315, 353 (2007).

27. F. H. Stillinger, Science 267, 1935 (1995).

Preface

We teach our students that solids can exist in more than one form. A striking example is solid water. The many polymorphs of ice have been intensely studied ever since the classic work of Bridgeman 100 years ago [1]. While solid polymorphism is by now a well-established scientific fact, the possibility of liquid polymorphism is much more controversial. The first evidence for water polymorphism was put forth over 20 years ago by a very young graduate student at Boston University and two young postdocs [2]. Their computer simulations were consistent with the novel idea of a line of first-order phase transitions in deeply supercooled water. Further, they found that this first-order transition line extends into the solid amorphous region of the phase diagram. Since the predicted line of first-order transitions traverses the liquid phase below the liquid's line of homogeneous nucleation transitions, it is difficult to probe it experimentally. However, the prediction that this line extends into the amorphous solid water region of the phase diagram was tested 2 years later by Osamu Mishima [3] who succeeded in demonstrating that the same first-order phase transition between two liquid phases also occurs in amorphous solid water. Soper and Ricci then demonstrated that above the critical point predicted by simulations, water indeed occurs in two local structural forms, differing not only in density but also in structure [4].

Making experimental measurements is challenged by the fact that water's hypothesized liquid–liquid phase transition line and associated critical point lie below the homogeneous nucleation temperature. Hence on timescales longer than the nucleation temperature, water is solid. Other materials with two length scales in their interaction potential do not suffer from this fact, so a great deal of experimental and computational work has been carried out on materials other than water for which the hypothesized liquid–liquid phase transition line can be probed directly. It seems that while the water case is still being debated, liquid polymorphism exists in a number of other materials. Hence this volume is far more general than water alone, even though it was the initial work on water that stimulated much of the subsequent work on liquid–liquid phase transitions.

Any edited volume requires an unexpectedly staggering time investment of many people. Three deserve special mention. I have been extremely fortunate that Mr. Jerry D. Morrow has been willing to work tirelessly to manage the collection of the 19 different chapters, and that the staff of Wiley—particularly Ms. Cecilia Tsai, Ms. Anita Lekhwani, and Ms. Kris Parrish—and Mr. Faraz Sharique Ali from Thomson Digital have with good cheer managed the transformation of complex source files and artwork into a coherent book form.

H. Eugene Stanley

References

1. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 47, 441–558 (1912).

2. P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Nature 360, 324–328 (1992).

3. O. Mishima, J. Chem. Phys. 100, 5910–5912 (1994).

4. A. K. Soper and M. A. Ricci, Phys. Rev. Lett. 84, 2881–2884 (2000).

Preface to the Series

Advances in science often involve initial development of individual specialized fields of study within traditional disciplines followed by broadening and overlap, or even merging, of those specialized fields, leading to a blurring of the lines between traditional disciplines. The pace of that blurring has accelerated in the last few decades, and much of the important and exciting research carried out today seeks to synthesize elements from different fields of knowledge. Examples of such research areas include biophysics and studies of nanostructured materials. As the study of the forces that govern the structure and dynamics of molecular systems, chemical physics encompasses these and many other emerging research directions. Unfortunately, the flood of scientific literature has been accompanied by losses in the shared vocabulary and approaches of the traditional disciplines, and there is much pressure from scientific journals to be ever more concise in the descriptions of studies, to the point that much valuable experience, if recorded at all, is hidden in supplements and dissipated with time. These trends in science and publishing make this series, Advances in Chemical Physics, a much needed resource.

The Advances in Chemical Physics is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, a field that we interpret very broadly. Our intent is to have experts' present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field.

Stuart A. Rice

Aaron R. Dinner

Electron Spin Resonance Studies of Supercooled Water

Debamalya Banerjee,¹ Subray V. Bhat,¹ and Dino Leporini²,³

¹Department of Physics, Indian Institute of Science, Bangalore 560 012, India

²Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy

³IPCF-CNR, UoS Pisa, Italy

I. Introduction

Electron spin resonance (ESR) spectroscopy, also known as electron paramagnetic resonance (EPR), was discovered by Yevgeny Zavoisky in 1944 in Kazan [1,2]. Zavoisky was likely also the first one to observe nuclear magnetic resonance (NMR) in 1941, but he never published his attempts. ESR is an important spectroscopic technique to study paramagnets, that is, atoms and molecules containing unpaired electrons. Diamagnetic systems in which all the electrons are paired do not provide ESR signal. Commonly encountered paramagnetic species include organic free radicals (of major interest in this review), metal complexes, transition metal ions, intrinsic and doping-related defect centers, triplet excited states of diamagnetic molecules, as well as molecules such as molecular oxygen (O2) or nitric oxide (NO) that are examples of stable free radicals. Principles, theoretical aspects, and applications of the ESR spectroscopy are covered in a number of books [3–9]. The basic physical concepts of ESR are analogous to those of NMR. Both techniques involve the interaction between magnetic moments and electromagnetic radiation; in the case of ESR it is electron spins that are excited instead of spins of atomic nuclei.

The ESR technique has been used to study many types of systems, including biological systems (e.g., hemoglobin, nucleic acids, enzymes, irradiated chloroplasts, riboflavin, and carcinogens), synthetic systems (polymers, catalysts, rubber, charred carbon, and chemical complexes with transition metals), conduction electrons, and free radicals in gaseous, liquid, and solid systems both stable and short-lived intermediates in chemical reactions or created by irradiation with implications in many areas, including physics, chemistry, biology, mineralogy, and geophysics [3].

In this review, we are interested in the ESR signal of stable free radicals (spin probes) dissolved in liquid environments with particular reference to water. The key question to be addressed is the effectiveness of the spin probe as transmitter to supply information on the host. First studies of paramagnetic solutes in liquids involved copper chelates in organic solvents [10] and transition ions in solution [11] with attempts to describe the ESR lineshape as being influenced by the Brownian tumbling motion of the paramagnet in the liquid state [12]. Subsequent theoretical refinements in the case of fast reorientation [13,14] (see also Refs [4,15]) with clear experimental confirmation [16] and further extension and experimental validation of the theory of the ESR lineshape to arbitrary reorientation rates [17–21] paved the way to the quantitative use of ESR to characterize the liquid state of matter.

The review is organized as follows. In Section II, the ESR spectroscopy is outlined in an intuitive, introductory way. In Section III more interpretative details are given. Uninterested readers may skip this section and proceed to Section IV where ESR investigations on water and aqueous solutions are briefly reviewed. In Section V, the ESR studies on supercooled water confined in polycrystalline ice are presented in detail. Finally, conclusions of this review are summarized in Section VI.

II. Outline of ESR Spectroscopy

ESR spectroscopy detects the dynamics of the magnetization M of an ensemble of electrons in the presence of a static magnetic field B0 and under driving by (ideally) a rotating magnetic field B1(t) ⊥ B0 with angular frequency ω. Two primary classes of ESR spectrometers exist, allowing for either continuous or pulsed irradiation by the magnetic field B1(t) [8,9,22]. This section will only consider continuous-wave ESR. The standard frequency of the ESR spectroscopy is ω/2π ~ 9.4 GHz (X band) [3,7], where samples are most conveniently sized and spectrometers most available. However, the ESR signal may be detected also at other frequencies, especially higher ones [23,24] such as Q band (35 GHz) and W band (95 GHz), which are extremely useful to discriminate more strongly between different motional models [22,25]. These recent developments are beyond the purposes of the present review.

The electron has a magnetic dipole moment m that stems from its intrinsic angular moment (spin) S with = h/2π, h being the Planck constant. For a free electron m = − geβeS, where ge = 2.0023 and βe are the electron Lande’ g-factor and the Bohr magneton, respectively. If B1(t) = 0 and the spins are isolated, M, if misaligned with respect to B0, performs a precession around B0 with angular Larmor frequency ω0 = γB0, where γ = geβe/ is the magnetogyric ratio (Fig. 1a). The ESR spectroscopy usually investigates condensed-matter systems, where the electrons exchange energy with the surroundings. When the rotating field B1(t) acts on the magnetization M, the latter undergoes a precession around B0 with angular frequency ω in the stationary state (Fig. 1b). For ω ω0, a resonance is observed corresponding to a marked power absorption by the spin system.

Figure 1. Classical interpretation of ESR spectroscopy. (a) Free precession of the magnetization M of an ensemble of isolated electrons around the static magnetic field B0 with Larmor angular frequency ω0 = γB0, γ being the magnetogyric ratio. The transverse magnetization oscillates at the same frequency. (b) In condensed matter, the electrons exchange energy with the surroundings. A rotating microwave field B1(t) ⊥ B0 with angular frequency ω forces the precession of the magnetization around B0 with the same angular frequency. When ω ω0, an absorption resonance occurs. Adapted from Ref. [26].

A. Spin Probes

Liquids are usually diamagnetic and therefore provide no ESR signal. The issue is circumvented by dissolving paramagnetic guest molecules (spin probes), usually nitroxide free radicals with one unpaired electron, at an extremely low concentration to make their influence on the host and their mutual interactions vanishingly small [27,28]. In nitroxide spin probes, the unpaired electron is localized in a highly directional, that is, anisotropic, molecular bond (see Fig. 2a). On this basis, a quantum-mechanical analysis shows that the Larmor frequency of the dipole moment of the spin probe depends on the orientation of the latter with respect to B0 (see Section III).

Figure 2. (a) The structure of the spin probe free-radical TEMPOL. The unpaired electron is located in the NO bond. The magnetic principal axes are drawn. The principal values of the Zeeman g and the hyperfine A tensors of TEMPOL in water are gxx = 2.0093, gyy = 2.0064, gzz = 2.00215; Axx = 18.76 MHz, Ayy = 19.88 MHz, Azz = 104.4 MHz, respectively. (b) The energy levels of an electron with spin S = 1/2 in the static magnetic field B0 (g ≠ 0, A = 0). (c) Same as in (b) including the hyperfine interaction with a nucleus with spin I = 1 (g ≠ 0, A ≠ 0). ms and M are the projections of the electron and the nuclear spin along the direction of the static magnetic field, respectively. The dashed arrows denote the transitions induced by the oscillating microwave field during the ESR spectroscopy.

B. Rigid-Limit and Motional Narrowing of the Lineshape

We now illustrate how the ESR lineshape conveys information on the rotational dynamics of the spin probe [3,4,14,15,21]. Additional details are found in Section III. We first consider an ensemble of immobile spin probes, for example, like in a frozen host, with different fixed orientations. The different resonances of their magnetic dipole moments are detected by sweeping the ω frequency of B1(t) and their superposition gives rise to a broad absorption with width Δω0, usually referred to as rigid-limit or powder lineshape (Fig. 3a). If the spin probe undergoes a rotational motion, the Larmor frequency of the associated dipole changes randomly in time. Figure 3b pictures the case of a reorientation occurring by sudden jumps separated by random waiting times with average value τ (τ denotes the rotational correlation time, i.e., the area under the normalized correlation function of the spherical harmonic Y2,0 [3,15]). The fluctuation gives rise to frequency averaging. For example, let us consider two Larmor frequencies differing by δω0. If the accumulated phase difference in a time τ, δω0 τ, is less than one, the two frequencies cannot be distinguished and are replaced by their average. This process affects the rigid-limit lineshape to an extent that is controlled by the product τΔω0. Illustrative cases are shown in Fig. 3b. If τΔω0 > 1, the rigid-limit lineshape is rounded off on the frequency scale 1/τ. If τΔω0 ~ 1, the average process manifests as a coalescence of the lineshape (motional narrowing [4,14]) that becomes extreme for τΔω0 < 1. In the latter case the width of a single line is roughly given by [4,14,15].

Figure 3. ESR lineshapes of spin probes in frozen (a) and mobile (b) hosts. (a) The magnetic dipoles m of immobile spin probes in a frozen liquid have different ω0 values due to their different orientations with respect to B0, thus resulting in a broad line with width Δω0 (black line), usually referred to as rigid-limit or powder lineshape. (b) If the spin probe undergoes rotation (sketched as instantaneous clockwise jumps at random times), ω0 fluctuates. When the rotational rate 1/τ is larger than the width of the ω0 distribution Δω0, the different precession frequencies become indistinguishable and an average value is seen, that is, the ESR lineshape coalesces (motional narrowing) [4,14]. Adapted from Ref. [26].

The motional narrowing is nothing but a frequency-modulation (FM) effect. This is appreciated by noting in Fig. 3b that, due to the spin probe reorientation, the associated magnetic dipole moment m has a precession frequency that changes randomly in time. To see that the random character of the frequency fluctuations is irrelevant in order to observe the linewidth decrease, let us assume that mx(t) changes due to deterministic FM (e.g., by modulating the static magnetic field B0):

(1) equation

(2) equation

ω0 is the base angular frequency that is modulated with angular frequency ωm and maximum positive deviation from ω0 equal to Δω0. Jn is a Bessel function of the first kind. Replacing the integer index n with the continuous variable (ω − ω0)/ωm, one may interpret the series of the amplitudes of the different harmonics of Eq. (2) as a continuous spectrum with lineshape

(3) equation

Figure 4 shows a plot of the lineshape . If one identifies 1/ωm with the deterministic equivalent of τ, it is seen that the linewidth narrowing of Figs. 3b and 4 and is quite the same effect.

Figure 4. Deterministic motional narrowing. Plot of [Eq. (3)].

C. Accessible Range of the Rotational Dynamics

The longest detectable τ value of a nitroxide spin probe by ESR, τmax, is set by the changes of the Larmor frequency, occurring each on average, due to the magnetic field produced by the rotating methyl groups close to the unpaired electron [3]. If , the spin probe does not rotate within appreciably, the lineshape is independent of the reorientation rate 1/τ and virtually coincident with the rigid-limit lineshape. On the other hand, in the extreme narrowing regime the line coalescence cannot lead to linewidth less than in that is the upper limit of the lifetime of the coherent oscillation of the magnetization [3]. Then, the shortest detectable τ value, τmin, is found when the linewidth . For nitroxide spin probes τmin ~ 10 ps.

III. ESR Spectroscopy of Spin Probes: Basic Theoretical Introduction

ESR is a spectroscopy observing a paramagnetic system situated in a static magnetic field B0 and forced by an oscillating magnetic field B1(t) ⊥ B0. Our system of interest is a single unpaired electron located in a free radical (spin probe) dissolved as a guest molecule in a diamagnetic liquid. The mutual interactions between the spin probes are negligible owing to their low concentration and one has to consider the intramolecular interactions only. ESR spectroscopy provides information on both the statics and the dynamics of the orientational degrees of freedom of the spin probe. To get to that information, the quantitative description of the coupling between the magnetic properties and the orientation of the spin probe must be carried out in terms of quantum mechanics.

A. Spin Hamiltonian

The electron has a magnetic dipole moment m that stems from its intrinsic angular moment (spin) S with = h/2π, h being the Planck constant. For a free electron m = − geβeS, where ge = 2.0023 and βe are the electron Lande’ g-factor and the Bohr magneton, respectively. The coupling of the magnetic moment m with B0 (Zeeman coupling) is expressed by the hamiltonian . In the nitroxide spin probes there is also a magnetic coupling (hyperfine coupling) between the unpaired electron and the close nitrogen nucleus with magnetic dipole moment mn = + gnβnI, where gn, βn, and I are the nuclear g-factor, magneton, and spin (I = 1), respectively (Fig. 2a).

In addition to the spin, the magnetic properties of the unpaired electron are also set by the orbital angular momentum L. Even if L does not affect the electron dipole moment at first order, second-order effects are possible via the spin–orbit interaction (due to the magnetic field in the rest frame of the electron originating in its motion through the molecular electric field). Usually, one does not consider the complete hamiltonian including both the orbital and the spin degrees of freedom but, rather, an effective hamiltonian derived by averaging over all the spatial variables. The resulting quantity, consisting of parameters and spin operators, is called a spin hamiltonian[3,4,6]. In nitroxide free radicals, the orbital part of the unpaired electron wave function exhibits the local symmetry of the highly directional NO bond where it is localized (Fig. 2a) [27,28]. As a consequence, the orbital average leads to express the Zeeman and the hyperfine interactions in terms of the tensors g and A, respectively, and the spin hamiltonian takes the form

(4) equation

g and A assumed to be having coinciding principal axes (Fig. 2a). We define g = Tr[g]/3 and A = Tr[A]/3, where Tr denotes the trace operation. It is also convenient to consider the largest differences between the principal values of the g and A tensors, ΔA and Δg, respectively.

B. Lineshape Analysis

1. No Tumbling: Powder Lineshape

We first consider the spin probes as immobile in a frozen host with isotropic distribution of their orientations. In that case the energy levels of the spin hamiltonian, Eq. (4), are (Fig. 2b and c) [6]

(5)

equation

with ms = ± 1/2, M = ± 1, 0 and B0 = nB0, where n ≡ (nx, ny, nz) denotes the direction cosines of B0 with respect to the principal axes of the magnetic tensors g and A. Equation (5) assumes that the g tensor is almost spherical, that is, Δg g.

Let us consider the simple case of no hyperfine interaction, A = 0 (Fig. 2b). A transition is induced by the microwave field when its angular frequency ω equals the Larmor frequency ω0(n) = (E1/2− E−1/2)/ :

(6) equation

Owing to the orientation distribution of the spin probes, and then of n, ω0(n) exhibits a distribution resulting in a broad absorption line when ω is swept (Fig. 5, top left). In the actual ESR experiment one sweeps B0 while keeping the frequency ω constant and the absorption is observed in derivative mode, due to the phase-sensitive signal detection. The field-swept derivative pattern of the ESR lineshape in the absence of spin probe motion (powder lineshape) shows sharp details that allow one to measure the principal values of the Zeeman g tensor (Fig. 5, top right).

Figure 5. ESR lineshapes of a spin probe (gx = 2.0093, gy = 2.0064, gz = 2.00215, A = 0) undergoing reorientation with jump angle θ = 80° and rotational correlation times τ = 900 (top), 45 (middle), and 9 ns (bottom). The lineshapes are convoluted by a Lorentzian with width to account for the changes of the Larmor frequency, occurring each on average, due to the magnetic field produced by the rotating methyl groups close to the unpaired electron. Left: Absorption versus frequency of the microwave field for constant magnetic field G. Right: Absorption in derivative mode versus static magnetic field for constant microwave frequency ω = 58.05 rad · GHz. The lineshapes with τ = 900 ns are virtually coincident with the powder lineshapes corresponding to immobile spin probes in a frozen host. Dots locate the frequencies (left) and magnetic fields Bi = ω /giβe (right) values with i = x, y, z. Note that the ESR lineshapes in Fig. 3 correspond to gx = gy = 2.0064, gz = 2.00215, A = 0.

If the hyperfine tensor is present as in the nitroxides spin probes, three transitions are seen when the angular frequency of the microwave field ω equals the transition frequencies ωM(n) = (E1/2,M− E−1/2,M)/ , M = ± 1, 0 (see Fig. 2c):

(7)

equation

The powder lineshape is given by the sum of three components, corresponding to the three possible transitions (see Fig. 2, bottom) and each labeled by one value of the nuclear quantum number M (Fig. 6, top). Also in the presence of the hyperfine interaction, the principal values of both the g and A tensors may be measured from the powder lineshape [29].

Figure 6. ESR lineshapes of a nitroxide spin probe (g tensor as in Fig. 5, Ax = 18.76 MHz, Ay = 19.88 MHz, Az = 104.4 MHz, ) undergoing reorientation with jump angle θ = 80° and rotational correlation times τ = 860 (top), 9.04 (middle), 1.81 ns (bottom). Left: Absorption versus frequency of the microwave field for constant magnetic field G. Right: Absorption in derivative mode versus static magnetic field for constant microwave frequency ω = 58.05 rad · GHz. The lineshapes with τ = 860 ns (top panel) are virtually coincident with the powder lineshapes corresponding to immobile spin probes in a frozen host. In that case the three hyperfine components with M = ± 1, 0, corresponding to the three possible transitions (see Fig. 2, bottom), are explicitly shown. The motional narrowing [4,14,15] reduces the three components to three distinct lines when the spin probe rotates fast (bottom panel).

2. Tumbling: Motional Narrowing of the ESR Lineshape

To deal with the reorientation of the spin probes, it is convenient to consider the spin hamiltonian , Eq. (4), as a sum of two contributions: an isotropic orientationally invariant part and an orientation-dependent part . The explicit form of is

(8) equation

(9) equation

Equation (9) well approximates Eq. (8) since B0, which defines the laboratory Z-axis, is strong, namely gβeB0 > A. The energy levels of , as given by Eq. (9), are

(10)

equation

They are still represented by the pattern in Fig. 2 c. The explicit form of the orientation-dependent part is

(11) equation

where g ' and A ' are traceless tensors. When the spin probe reorients, is a random function of time. This is made explicit by considering the time-dependent rotation matrix :

(12) equation

transforming the electron and nuclear spins from the fixed laboratory frame {X, Y, Z}, where they are quantized, to the rotating principal axes of the magnetic tensors {x, y, z} (Fig. 2a). The unit vector ni, with nZ ≡ n, encloses the direction cosines of the ith laboratory axes with respect to the magnetic principal axis. Then, Eq. (11) is rewritten in the explicit time-dependent form [13,15,16,17,20,21,27]

(13)

equation

where is the transpose of and

(14)

equation

a. Fast Tumbling: Redfield Limit

Xredfield If the rotation is very fast, that is, the rotational correlation time τ fullfills the inequalities ΔA, ΔgβeB0 < τ−1 (in practice τ 1 ns), is almost averaged out and the ESR lineshape, which is quite broad if no motion is present (see Figs. 5 and 6, top), experiences a strong motional narrowing [4,14]. The lineshape reduces to one peak if the hyperfine tensor A = 0 (Fig. 5, bottom), or, if A ≠ 0 as in nitroxides, to three peaks (Fig. 6, bottom), corresponding to the possible transitions induced by the microwave field (Fig. 2). The peak positions are set by Eq. (10) and the resonance conditions , M = ± 1, 0 that read

(15) equation

If A = 0, the position of the single peak is set by the condition ω = −1gβeB0. In the limit of fast tumbling the lineshape was expressed analytically without relying on any specific rotational model (Redfield theory) [4,14]. It is found that each peak is Lorentzian in shape with width given by [15]

(16)

equation

The analytic expressions of the coefficients α, β, γ for A ≠ 0 were derived elsewhere (if A = 0, β = γ = 0) [15]. They are given in terms of the principal values of both the g and A tensors and the rotational correlation time that for a spherical molecule like TEMPOL is defined as

(17) equation

where ζ(t) is the angle spanned by one molecular axis in a time t.

b. Slow Tumbling

Xslowtumbling If τ exceeds a few nanoseconds, the widths of the narrow lines increase and in the limit τ→ ∞ the lineshape recovers the powder lineshape. In the slow tumbling regime of long, but finite, τ values the analytic lineshape theory presented in Section III.B.2 fails and one must resort to sophisticated approaches, for example, see Refs [17,18,19,20,21]. In general the lineshape L(B0) recorded by sweeping the static magnetic field B0 is evaluated by a stochastic memory-function approach [21] that will now be briefly outlined. The starting point is writing L(B0) as the Laplace transform of the correlation function of the perpendicular component of the magnetic dipole moment of the spin probe m = − geβeS perpendicular to B0[3,30]:

(18)

equation

(19) equation

The brackets indicate a proper thermal average, C is a constant, is the real part of z, and i² = − 1. The derivative takes into account that the lineshape is usually displayed in derivative mode. The correlation function is evaluated by the quantum time evolution of the electron spin under the influence of the reorientation of the spin probe according to the equation of motion [31]:

(20) equation

where [A, B] = AB − BA and the spin hamiltonian , with and given by Eqs. (9) and (13), respectively. The Γ operator describes the rotational motion of the spin probe by considering its orientation as a classical, stochastic variable. Equation (20) is an example of the so-called Stochastic Liouville equation (SLE) and its relation with the case of fast tumbling (Redfield limit [4,14]) has been recently reviewed [31].

For a nearly spherical molecule rotating by instantaneous random jumps of fixed size θ after a mean residence time τ0, according to the irreducible representation of the rotation group of rank , Γ is a multiple of the identity operator , which is given by [30]

(21)

equation

and the related correlation time τ [Eq. (17)] takes the form

(22) equation

By using a suitable memory–function approach, it is possible to derive an exact expression of the Laplace transform as a continued-fraction expansion [21]:

(23) equation

where λi and are (complex) constants depending on the principal values of the and tensors [Eq. (14)] and the parameters θ and τ0. The middle panels of Figs. 5 and 6 show typical patterns in the slow tumbling regime if A = 0 and A ≠ 0 as in nitroxides, respectively. Note that in the latter case the resulting three lines, corresponding to the three possible transitions induced by the microwave field (see Fig. 2, bottom), overlap resulting in a complex pattern.

IV. ESR Studies of Liquid Water and Aqueous Solutions: A Review

Historically, Jolicoeur and Friedman were the first to suggest using a stable free radical as a noninteracting probe to study aqueous solutions with hydrophobic solutes or solutes with substantial hydrophobic groups [32].

Freed and coworkers investigated the anisotropic rotational reorientation and slow tumbling of peroxylamine disulfonate (PADS) radical (Frémy's salt) in 85% glycerol aqueous solution and frozen water and D2O [18]. PADS has geometric radius rPADS ~ 0.22 nm [19] to be compared with nm. For frozen water solvent one obtains 14.7 ± 0.2 kcal mol−1 as the activation energy for the reorientation process and about 11 kcal mol−1 in glycerol aqueous solution. Owing to the fast rotational dynamics, it was concluded that PADS must be contained in clathrate-type cage in both liquid and frozen water and, perhaps, in the glycerol–H2O solution. Freed and coworkers also noted that, unlike PADS, the perdeuterated spin probe PD-Tempone (2,2,6,6-tetramethyl-4-piperidone N-oxide) in perdeuterated 85% glycerol-d3 D2O solution undergoes isotropic reorientation simplifying the interpretation of the ESR spectra. It was concluded that the reorientation of PD-Tempone is best described as occurring by jumps of moderate size (~50°). Moderate jumps of vanadyl ions (VO(H2O) ) in aqueous sucrose solution was also reported [33].

Ahn [34] investigated the reorientation of di-tert-butylnitroxide (DTBN) in supercooled water at temperatures ranging from 15 to −33°C. The apparent Stokes hydrodynamic radius of DTBN in water was estimated to be about 0.35 nm. Good linear dependence of the reorientation time of the spin probe with the water viscosity is found according to the Debye–Stokes–Einstein (DSE) law. It is found that the ESR signal of DTBN is due to the supercooled liquid state, and not due to the signal from the rapid rotational motion of a spin probe in frozen water. Notice that the smaller spin probes PADS form clathrate cages in ice [18].

Roozen and Hemminga [35] used conventional and saturation transfer ESR spectroscopies to study the rotational behavior of two different nitroxide spin probes—4-hydroxy-2,2,6,6-tetramethylpiperidinyloxyl (TEMPOL) and 3-maleimido-2,2,5,5-tetramethyl-1-pyrrolodinyloxy—in sucrose—water and glycerol—water mixtures as a function of temperature. Due to the relative basic character of the probes, they form hydrogen bonds with water rather than with sucrose molecules. Furthermore, it is found that both probes interact stronger with water than with glycerol molecules. The authors found that the mobility of the spin probes starts to increase strongly close to the glass transition of the sucrose—water mixtures and interpret their results in terms of the coupling of the reorientation with the viscosity (DSE law) that depend on the strength of the hydrogen bonds between the probe and the solvent.

Ramachandran and Balasubramanian used the method to monitor structural alterations caused in water by added solutes. They used the spin probe 2,2,6,6-tetramethyl piperid-4-one N-oxide (TEMPO) to study structural alterations caused in water by the addition of urea and sodium butyrate. They studied the variation of hydrogen hyperfine linewidth as a function of the solute concentration and extracted information on the reorientation time [36]. They conclude that urea disrupts water structure continuously and this effect is significant at low molarities. With sodium butyrate they see evidence for two different environments, one attached to the solute and the other far away from it.

Okazaki and Toriyama studied the dynamics of liquid molecules 2-propanol and water confined to nanochannels (pore size ~3–4 nm) of the mesoporous material MCM-41 as a function of temperature using spin probe ESR [37]. They used DTBN and TEMPOL as the spin probes (concentration: 0.2 mM). Both the spin probes were freely soluble in the two liquid hosts and did not have any strong interaction with the channel walls of MCM-41. It was seen that in both the liquids, the ESR spectra were characteristic of immobilized spin probes at temperatures even as high as 40° above their respective melting points. In addition, the 2-propanol spectra showed evidence of phase separation, they being a mixture of both mobile and immobile spin probes. However, quite significantly, no phase separation was observed in water and all the spin probes were seen to be immobilized. Of course, the immobilization of the spin probes is on the ESR timescale and therefore does not imply solidification of the solvent. The rotational diffusion of the spin probes is seen to be highly anisotropic even at high temperatures. This is concluded to be a consequence of collective behavior of the solvent molecules in the nanochannels because of the reinforced intermolecular network. In contrast, Santangelo et al., working with a slightly smaller spin probe (TEMPO) and at comparatively lower temperatures observe isotropic diffusion of the probes in water confined in silica hydrogel [38]. In a comprehensive study that combines spin probe ESR with differential calorimetry (DSC), they show very clearly that supercooled liquid water exists down to 198K, much below 235K, the homogenous nucleation temperature of water. They also studied bulk water and a sample of 80% glycerol/20% water, v/v for comparison. It was observed that when the water confined to the pores of the silica gel was cooled, only a small fraction of the water in the matrix freezes and the rest (between 75% and 90%) is supercooled. When looked at qualitatively, the results with TEMPO [38] and TEMPOL [37] are expected to be different because their differing H-bonding properties with water: TEMPOL is expected to form stronger hydrogen bonds than TEMPO. However, as recently shown by Houriez et al. [39], there is not as yet a satisfactory definition of hydrogen bond itself and therefore it is difficult to quantitatively estimate the influence of hydrogen bond in determining the spectromagnetic properties of nitroxide radicals in water. Integrated computational efforts provide also insights in the solvation networks surrounding nitroxide spin probes in aqueous solutions [40].

Finally, Banerjee and Bhat have shown that the spin probe dynamics in a glycerol–water system can sense the mesoscopic inhomogeneities of the host matrix by demonstrating a discontinuity in the glycerol concentration dependence of the spin probe-free volume [41].

V. ESR Studies of Confined Water in Polycrystalline Ice

In a recent paper, Bhat et al. demonstrated the possibility of vitrifying bulk water by rapid quenching [42]. The glass transition of this vitrified water occurring on subsequent heating, and the supposed impossibility of obtaining supercooled water between 150 and 233K, the so-called No-man's Land (NML) of its phase diagram [43], were investigated by the ESR study of the rotational dynamics of the spin probe TEMPOL. The results suggest that water undergoes a glass transition at 135K, that is, close to the commonly accepted value of the glass transition temperature Tg = 136K [44], and the TEMPOL reorientation between 165 and 233K closely follows the predictions of the Adam–Gibbs model. Further, the spectra for T > 165K were characteristic of motionally averaged g and A tensors indicating the presence of supercooled liquid water in the temperature corresponding to NML. More light was thrown on this unexpected result in the following paper by Banerjee et al. where evidence was provided that devitrification of amorphous bulk water results in polycrystalline ice where interstitial liquid water is present and hosts the spin probes expelled by the ice grains [26]. Below, the main features of polycrystalline ice and the localization of spin probes in this medium are briefly outlined in Sections V.A and V.B, respectively. After these introductory sections, the findings by Banerjee et al. are discussed in Section V.C.

A. Water Confinement in Polycrystalline Ice

The coexistence of crystals and deeply supercooled liquids was suspected already one century ago for bulk systems [45]. More recently, the ice–water coexistence was reported by experiments, especially in the temperature range 140–210K [46,47,48,49], and by simulations in NML [50,51], evidencing the presence of 15–20% of liquid water between nanometer-sized ice crystals [50]. Notably, recent simulations concluded that in polycrystalline materials grain boundaries exhibit the dynamics of glass-forming liquids [52].

In polycrystalline ice liquid water is localized, like in a sponge, in the intergranular junctions (pockets) connected by vein systems [48,51,53,54,55] that serve as interstitial reservoirs for impurities [56,48]. The average volume of the pockets and volume per unit length of the veins are controlled by temperature and pressure, and independent of the average grain size [48,49]. The vein system has been impressively visualized by colloidal nanoparticles that are excluded from ice grains and form chains in the ice veins [55].

B. Location of Paramagnetic Solutes in Water–Ice Mixtures

The segregation of paramagnetic solutes in frozen aqueous solutions attracted attention of ESR spectroscopists since long time ago. By studying frozen solutions of Mn²+ and Gd³+ in water, Ross was the first to point out that in aqueous solutions, where strong hydrogen bonding makes the ice very reluctant to include a foreign ion, ice formation will greatly segregate ionic solute species in the interstices of crystallites [56]. As a result, a broad structureless line is observed that he ascribed to dipolar coupling between close paramagnetic ions. Later, Leigh and Reed used a number of paramagnetic solutes, including TEMPOL, to show that they segregate in slowly frozen water samples and the ESR spectra exhibit strong dipolar and magnetic exchange interactions between the solutes [57]. These intermolecular effects are only partially removed by rapid freezing techniques. Instead, they are suppressed by imbedding aqueous solutions in polydextran gels prior to freezing. Segregation of PADS in H2O and D2O was observed for concentrated samples but not in very dilute samples frozen either slowly or more rapidly [18]. Ahn noted that the ESR line of DTBN in water disappears at −34°C due to the segregation and the subsequent huge broadening by strong dipolar and magnetic exchange interactions [34]. Interestingly, the ESR signal is detected again only when the frozen sample is heated above 0°C. Santangelo et al. observed a remarkable broadening of the ESR line of TEMPO in bulk water at about −33°C and concluded that TEMPO molecules tend to precipitate out of the crystalline lattice formed by water molecules [38]. Roozen and Hemminga studied sucrose–water mixtures at subzero temperatures. They found that at temperatures where a part of the water is frozen, the spin probes are not present in the ice lattice but in the concentrated amorphous solution [35]. In conclusion, there is wide evidence that spin probes in ice–water mixtures are confined in the interstitial region between ice grains.

C. Rotational Dynamics of TEMPOL in Interstitial Water of Polycrystalline Ice

Banerjee et al. [26] detected the ESR signal of TEMPOL (Fig. 2a) dissolved in interstitial supercooled water of polycrystalline ice and performed a detailed lineshape analysis. Samples were prepared by doping a small amount of triple distilled water with about 0.1% by weight of TEMPOL. The ESR signal of TEMPOL is recorded during the slow reheating of the quenched sample following the thermal protocol of Ref. [42]. In most runs the crystallization occurring during the thermal cycle did not affect the ESR signal of the spin probes, that is, none of the well-known artifacts discussed in Section V.B became apparent. This led to the conclusion that the ice loosely confines TEMPOL in liquid pockets.

1. Spin Probe Mobility Above 130K

Figure 7 presents the temperature dependence of the ESR signal of the spin probe. As usual, the lineshape, due to phase-detection, is displayed in derivative mode by sweeping the static magnetic field B0 with constant microwave frequency ω (see Section III.B). The lineshapes in Fig. 7 are strikingly similar to the usual ones of spin probes dissolved in viscous liquids [3,30,38,42,57,58]. At low temperatures (≤90K) the ESR lineshape exhibits the rigid-limit pattern, namely the reorientation of TEMPOL is very slow (rotational correlation time τ τmax ~ 0.1 μs). Above 120K the ESR lineshape changes and its motional narrowing becomes apparent signaling the increased mobility of the spin probe (see Sections III.B and III.B.2 for introductory remarks and detailed discussion about motional narrowing, respectively). For T 220K narrowing is extreme and the lineshape collapses to three lines. The three-line pattern connects smoothly to the one detected in equilibrium condition at 300K. Note that the observed narrowing of the lineshape is opposite to the crystallization-driven broadening discussed above.

Figure 7. Selected ESR lineshapes of the spin probe TEMPOL (see Fig. 2a) in quenched bulk water and subsequent reheating at the indicated temperature. Note that (i) for technical convenience the static magnetic field B0, and not the microwave frequency ω as in Fig. 1b, is swept; (ii) the phase-sensitive detection displays the lineshape in derivative mode. Adapted from Ref. [26].

The temperature dependence of the ESR lineshape shown in Fig. 7 excludes the possibility that the spin probes are trapped into the solid crystalline matrix developed during the initial quench-cooling or the subsequent slow reheating (when the ESR data are collected). In fact, if trapping occurs during the quench, the rigid-limit ESR lineshape at 90K should be observed on heating up to Tm, where a sudden collapse to a three-line pattern much similar to the one observed at 300K should occur due to the large increase in mobility. Instead, one notes the continuous narrowing of the lineshape, that is, the progressively increasing mobility of TEMPOL, across the supercooled region from, 120 up to 300K. Moreover, the motionally narrowed lineshape at 220K, pointing to fast reorientation, is almost identical to the one at 300K indicating that TEMPOL has similar mobility at those temperatures. Since fast reorientation is also seen between 220K and Tm (see below), the trapping of the spin probes into the ice fraction can be safely ruled out. Instead, it has to be concluded that, when ice freezes, TEMPOL, as most impurities (see Section V.B), is expelled from the ice and accumulate in liquid pockets (see Section V.A). The volume fraction of the liquid water ϕw is estimated to be ϕw 0.04 − 0.07 [26].

2. Dynamical Heterogeneities

In-depth numerical analysis of the ESR lineshape was first carried out by modeling the jump reorientation of TEMPOL in terms of the jump angle θ and the mean residence time τ0 in each angular position (see Section III.B.2) that are related to the rotational correlation time τ [Eq. (17)] by Eq. (22). Having defined the reorientation model, the ESR lineshape is evaluated according to the approach outlined in Section III.B.2. When fitted to the experiment, the model, relying on a homogeneous mobility scenario, worked nicely except in the temperature region 140–180K and typical results are shown in Fig. 7. In the temperature region 140–180K dynamical heterogeneity (DH) is apparent. In fact, entering the DH regime, on heating, a second component, to be ascribed to a TEMPOL fraction with greater rotational mobility, appears (Fig. 8). In the DH regime, the lineshape was evaluated as a weighted sum of two components, that is, the fast (F) component with weight and the slow (S) component with weight . Results are shown in Fig. 9. In DH regime fitting, the theory to the ESR lineshape requires three adjustable parameters, the jump angle θ, one of the weights, and the mean residence time τ0. The temperature dependence of the first two parameters are shown in Fig. 10. On increasing the temperature, increases and above 180K, still well inside NML, (see Fig. 10b). The missing evidence of heterogeneous dynamics above 180K is due to the limited ability of the ESR spectroscopy to discriminate between different TEMPOL rotational mobilities if the correlation times are too short (τ 1 ns) and cannot be taken as evidence of no actual DH.

Figure 8. ESR lineshapes of TEMPOL in DH regime. Note the growth of the two narrow lines at ~3340 and ~3360 G that superimpose to the overall lineshape with increasing temperature. Further analysis is presented in Fig. 9. Adapted from Ref. [26].

Figure 9. Fast (dashed curve) and slow (dotted-dashed curve) components of the overall lineshape (solid curve) of TEMPOL at two temperatures in DH regime. Adapted from Ref. [26].

Figure 10. (a) Average jump angle of the S fraction. (b) Weights of the F and S fractions. Adapted from Ref. [26].

3. Temperature Dependence of the Spin Probe Reorientation

Figure 11 presents the temperature dependence of the reorientation time of the two TEMPOL fractions evaluated via Eq. (22). It is seen that at the lowest temperatures the dominant S fraction of TEMPOL undergoes small-size diffusive rotational jumps (see Fig. 9a) with nearly constant τs correlation times. Crossing over 127K, τs starts to drop and the jump size to increase that is consistent with a more mobile and open structure of the surroundings of TEMPOL consequent to the glass transition. At 140K, the F component becomes apparent in the ESR lineshape and its weight increases with the temperature. The presence of the F fraction leads to no anomaly in the rotational dynamics of TEMPOL molecules belonging to the S fraction. In particular, θs levels off to 60° (see Fig. 10a) in agreement with simulations on water [59]. The DH region ends at about 180K above which only the F component is seen. The correlation time τf decreases with the temperature and shows an inflection point at about 225K. At higher temperatures τf connects smoothly to the equilibrium value at 300K.

Figure 11. Temperature dependence of the rotational correlation times τf and τs of the fast (F) and the slow (S) fractions of TEMPOL in deeply supercooled bulk water, respectively. Note (i) the knee at ~127K close to Tg = 136K, (ii) the DH regime (140–180K), where the two coexisting TEMPOL fractions with different mobilities are evidenced, (iii) the inflection close to TFSC~228K. Adapted from Ref. [26].

We note that the temperature dependence of the TEMPOL correlation times in Fig. 11 shows a crossover at 225K from a high-temperature fragile behavior (non-Arrhenius) to a low-temperature strong one (Arrhenius) that strongly resembles the FSC crossover that has been hypothesized for water at TFSC ~ 228K [60]. The FSC crossover has obtained recent support from simulation [61] and experiments in confined environments [62]. The observation of fragile behavior in weakly supercooled water is fully consistent with the views that the water glass transition is kinetic in nature [63,64].

4. Breakdown of the Debye–Stokes–Einstein Law

Both the FSC and DH in