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The Old Problems of Glass and the Glass Transition, and the Many New Twists C

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The Old Problems of Glass and the Glass Transition, and the Many New Twists C Proc. Natl. Acad. Sci. USA Vol. 92, pp. 6675-6682, July 1995 Colloquium Paper This paper was presented at a colloquium entitled "Physics: The Opening to Complexity, " organized by Philip W. Anderson, held June 26 and 27, 1994, at the National Academy of Sciences, in Irvine, CA. The old problems of glass and the glass transition, and the many new twists C. A. ANGELL Department of Chemistry, Arizona State University, Tempe, AZ 85287-1604 ABSTRACT In this paper I review the ways in which the mediate range order (4), has been found (5-7) to correlate with glassy state is obtained both in nature and in materials science the temperature dependence of the viscosity (i.e., with the and highlight a "new twist"-the recent recognition of poly- so-called "fragility" of the liquid or polymer). At the same morphism within the glassy state. The formation of glass by time, the notion that a given liquid on slow cooling at constant continuous cooling (viscous slowdown) is then examined, the pressure always tends toward the same conformational ground strong/fragile liquids classification is reviewed, and a new state has recently been overturned by the recognition of the twist-the possibility that the slowdown is a result of an existence of polymorphism in the glassy state (8-11) [called avoided critical point-is noted. The three canonical charac- "polyamorphism" (12)]. Thus the field is in a state of flux. It teristics of relaxing liquids are correlated through the fragil- is an exciting period, as Anderson has opined (13), that a ity. As a further new twist, the conversion of strong liquids to theory of the nature of glass and the glass transition is the fragile liquids by pressure-induced coordination number in- "deepest and most interesting unsolved problem in solid state creases is demonstrated. It is then shown that, for comparable theory." systems, it is possible to have the same conversion accom- Many of the problems in this field are encountered at such plished via a first-order transition within the liquid state long relaxation times as to be "safe" from resolution by the during quenching. This occurs in the systems in which "poly- method of molecular dynamics computer simulation (14), amorphism" (polymorphism in the glassy state) is observed, though the behavior of real systems near the critical temper- and the whole phenomenology is accounted for by Poole's ature (ideal dynamical glass transition temperature) of MCT is bond-modified van der Waals model. The sudden loss of some within range. This is certainly also true of the boson peak, liquid degrees of freedom through such weak first-order which is a short time scale phenomenon; hence, elucidation of transitions is then related to the polyamorphic transition the short time dynamics may be expected in the near future. between native and denatured hydrated proteins, since the Indeed some progress in this domain is being reported cur- latter are also glass-forming systems-water-plasticized, hy- rently (15-17) and will be briefly described herein. In this drogen bond-cross-linked chain polymers (and single mole- article, both old and new aspects of the problem are reviewed. cule glass formers). The circle is closed with a final new twist The transition between the configurationally labile liquid, or by noting that a short time scale phenomenon much studied rubbery, state and the configurationally rigid glassy state is a by protein physicists-namely, the onset of a sharp change in phenomenon of very broad importance in the physical and d<r2>/dT (<r2> is the Debye-Waller factor)-is general for materials sciences and in biology. It is, of course, the manner glass-forming liquids, including computer-simulated strong in which the optically isotropic materials of ubiquitous impor- and fragile ionic liquids, and is closely correlated with the tance in optics are prepared, but it is also, rather less obviously, experimental glass transition temperature. The latter thus the strategy by which nature protects vital organisms against originates in strong anharmonicity in certain components of harsh environmental conditions (seeds and desert insects the vibrational density of states, which permits the system to against drought, Arctic insects against deep freezing). It is also access the multiple minima of its configuration space. The the strategy mankind uses in the preservation of foodstuffs by connection between the anharmonicity in these modes, vibra- desiccation or freezing processes. tional localization, the Kauzmann temperature, and the fra- This article is condensed from a more detailed paper (16) for gility of the liquid is proposed as the key problem in glass the proceedings of the recent Conference on Scaling Concepts science. in Complex Systems.* As in that case, I will mention the various routes to the glassy state of matter, highlighting the The study of viscous liquids and the glassy state has become evidence for polyamorphism. Then we will explore in more increasingly popular since Anderson's review of the field in detail the "normal" route to the glassy state (namely, the 1978 (1) and particularly since the mode-coupling theory cooling of an initially liquid state) and consider the variations (MCT) for viscosity divergence was presented in 1984 (2). It is in the way liquids slow down as the temperature decreases. In now recognized as one of the most significant unsolved the cases of substances where more than one major amorphous problems in condensed matter physics and consequently has form can be identified, it will be seen that, on cooling, the provoked increasingly sophisticated experimental study and transformation from one form to another may be observed as the involvement of an increasing number of theorists. In a liquid-state transition phenomenon. Since the origin of such addition to the existence of new theoretical predictions (3), an astonishing event is not obvious, its explanation by means new aspects of the phenomenology have recently come into of a recent simple thermodynamic model obtained by modi- focus. For instance the damping of the little understood fying the van der Waals equation, recently developed by Poole "boson peak", believed by many to originate in some inter- et al. (18), will be summarized. The publication costs of this article were defrayed in part by page charge Abbreviation: MCT, mode-coupling theory. payment. This article must therefore be hereby marked "advertisement" in *Conference on Scaling Concepts in Complex Systems, June 28-July accordance with 18 U.S.C. §1734 solely to indicate this fact. 6, 1994, Catanzano, Calabria, Italy. 6675 Downloaded by guest on September 26, 2021 6676 Colloquium Paper: Angell Proc. Natl. Acad. Sci. USA 92 (1995) I will refer briefly to the relation of this phenomenology to ered and are the subject of much interest in the recent the dynamics of hydrated proteins, and particularly the un- literature. folding transition, before closing with some notes relating the Later I will relate this phenomenon to the equally important very short-time dynamic features of proteins to similar features matter of liquid-liquid transformations, after first discussing in simple systems and identifying these as a basis for recon- the basic phenomenology of glass formation by viscous slow- sideration of the basic nature of the glass transition. down. Diverse Routes to the Glassy State and Polyamorphism Glass Formation by Viscous Slowdown: Strong and Fragile Liquids and Systems That Can Be Both While the glassy state is conventionally obtained by the cooling of a liquid, it is well known that many alternative routes, such Glasses are normally prepared by the steady cooling of an as vapor-phase deposition, desolvation, and in situ chemical initially liquid state, often followed by an annealing stage in reaction, are available and in most cases were practiced by which stresses induced during the vitrification are removed. It nature before materials science took over. The most recently is the viscous slowdown process that has been most intensively recognized method of amorphization is the least obvious- studied among the various routes to the glassy state and to amorphization by steady compression of open-structured crys- which I also give most attention. tals (8-12); a related method is by decompression of extremely The glassy state is entered when the cooling liquid passes compact high-pressure stable crystals (19, 20). The many through the "glass transition," which is actually a range of alternative processes are summarized in Fig. 1. temperatures over which the system "falls out of equilibrium." After a suitable annealing procedure, it is found that the It is manifested most directlyby the systematic decrease ofheat glassy state realized for a given substance by any one of a capacity from liquid-like to crystal-like values. This abrupt selection of these methods is remarkably close to that pro- change in the heat capacity, usually amounting to 40-100% of duced by any other, implying that the glassy state exists in a the vibrational heat capacity (i.e., the heat capacity below Tg), rather well-defined "pocket" in configurational space. How- is regarded by most workers as the primary signature of the ever, in certain cases, the glassy state may, in fact, occupy more transition between ergodic and nonergodic states. It is illus- than one distinct pocket, constituting an important "new trated in Fig. 2 for various representative systems. One ob- twist." It now seetns that polyamorphism (12) is a reality. serves in Fig. 2 that the relative change in heat capacity differs Mishima et al. (8-11), who first recognized the process of greatly among different systems. Interestingly enough, of the compression vitrification, also showed that the vitreous form primeval examples of the glassy state (16, 17), three key obtained in the initial is of members (glassy water, vitreous silica, and amber) lack any compression very high density pronounced thermal signature of the passage from glass to compared to the normal vitreous ice.
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