Chapter 1
A Brief IntroductiontoSupercooled Liquids 1
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John T. Fourkas , Daniel Kivelson , Udayan Mohanty , and Keith A. Nelson 1
Eugene F. Merkert Chemistry Center, Boston College, Chestnut Hill, M A 02167 Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139
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In nature, supercooled liquids play an important role in areas as diverse as volcanoes and hibernating animals. From a technological standpoint, supercooled liquids are linked intimately to processes ranging from the development of new materials to the storage of nuclear waste. It is also becoming increasingly evident that the dynamics of supercooled liquids can shed light on numerous problems that, upon a superficial ex amination, appear unrelated. As a result of this broad importance, the study of super cooled liquids has received considerable scientific attention over die past century. Su percooled liquids have yet to yield their deepest secrets to our scrutiny, however. This introduction is devoted to the newcomer in the field, for whom we outline the current hot topics in the field and provide the background necessary to understand the contemporary experiments and theory on supercooled liquids contained within this volume and in the literature in general. In the following chapter Austen Angell pres ents a detailed overview of the field and of this book. Current Issues We begin with a description of the phenomenology that characterizes the field of su percooled liquids, which we define as metastable liquids that have been cooled below the melting point (Tm) but not below the temperature at which a dynamic arrest occurs (i.e., the glass-transition temperature, Tg). Although it is presumably only the crystal line phase that is stable below T , the first-order crystallization process may be blocked dynamically by a high free energy of activation, so that the crystalline phase need not be considered except when it makes an unwanted heterogeneous entry. The supercooled liquid may therefore be considered "equilibrated," and the feature that should concern us first and foremost is the drastic increase of its viscosity (r\) and structural-relaxation (generally denoted a-relaxation) time with decreasing tempera ture. The more drastic this temperature dependence, the more "fragile" the super cooled liquid is said to be. Fragile liquids are typified by van der Waals organic liqm
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© 1997 American Chemical Society
1. FOURKAS ET AL.
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A Brief Introduction to Supercooled Liquids
uids with weak intermolecular interactions and widely varying intermolecular geome tries with similar energies. At the opposite extreme are "strong" liquids, which are typified by silicate and other network materials with a smaller number of strongly fa vored local interionic geometries. Below Tg the relaxation time becomes so long that the liquid can no longer structurally equilibrate. The glass-transition temperature can be specified in numerous ways, since itrepresentsa crossover between relaxation and experimental times. Un like the melting point, which is well defined thermodynamically, the glass transition temperature is generally defined on the basis of an empirical standard such as the vis cosity reaching a value of 10*3 Poise. The time scale on which "dynamic arrest" oc curs is defined by essentially the same limits of human patience, not by any fundamen tal parameter. In this sense, we should not expect Tg to provide meaningful theoretical insights. Characteristic Temperatures. This is not to say that characteristic temperatures are not important to the understanding of supercooled liquids; indeed, the question of die characteristic temperature about which to scale or expand functional forms describing the properties of viscous liquids is fundamental to the field. Thus we look with some degree of envy at the description of phase transitions and critical phenomena, in which a critical temperature T can generally be defined such that many static and dynamics quantities (including the heat capacity and the cooperative relaxation time) follow the form IT-TcrK , where a is a critical exponent. Although some approaches focus on the melting point, we would suggest that crystallization is a distinct and separate phe nomenon from supercooling. There is an inherent dynamic insulation from crystalli zation in the supercooled state, and T consequently has little connection with the theory of supercooled liquids. There are currently three schools of thought on the subject of choosing a char acteristic temperature. One school focuses on a possible critical point (T ) that lies below the glass transition temperature. Extrapolation of the rapidly increasing viscos ity and a-relaxation time to temperatures below Tg suggests that there may indeed be a divergence at T . Furthermore, extrapolation of the rapidly decreasing entropy to temperatures below Tg suggests that the entropy of the liquid is equal to that of the crystal at a temperature (Tfc) that lies in the vicinity of T ; this is known as the Kauzmann paradox. At some temperature above 0 K but below Tk the extrapolated entropy of the liquid becomes negative. This apparent violation of the third law of thermody namics is merely a consequence of die extrapolation, and might be avoided through a phase transition in the vicinity of T «Tk, where both die dynamic relaxation time and the thermodynamic entropy appear to exhibit anomalies. Another school has focused on the opposite end of the temperature scale, pos tulating a cross-over temperature T* above which the liquid is molecular in character and below which it exhibits enhanced collective behavior. T* lies near or above the melting point, so this picture is vastly different from the one above. A third school considers the possibility of a critical or characteristic tempera ture T that lies between Tg and T . In this region, many properties of supercooled liquids exhibit what might be call cross-over behavior; for instance, a plot of log(T|) vs. T " l exhibits a considerable elbow and the time scales of various relaxations become distinct in this temperature region. One must keep in mind that all of these temperaC T
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SUPERCOOLED LIQUIDS
turcs (Tg, T , Tk, T* and T ) arc floating about in this volume and in the literature of supercooled liquids in general. If the newcomer begins to feel a sense of confusion upon seeing such a wide range of descriptions for what is ostensibly die same phe nomenon, then it is probable that we have provided a realistic introduction to the field! 0
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Phenomenology. We should now identify those properties that are generally consid ered to define supercooled liquids, insofar as these properties cannot be derived from a simple extrapolation of the properties of liquids at temperatures well above T . We have already mentioned the dramatic increase in the a-relaxation time and the rapid decrease in entropy with decreasing T. The temporal behavior of the relaxation func tion describing the response of a supercooled liquid to a perturbation (and the subse quent return of the liquid to its non-crystalline "equilibrium" state) is also of interest. At long times this relaxation appears to be described by a stretched exponential func tion exp[-(t/x)P], where x is a characteristic relaxation time and the stretching exponent P lies between zero and one. The relaxation becomes slower (i.e., % increases) and of ten increasingly stretched (i.e., P becomes smaller) as the temperature is lowered. At shorter times, the a-relaxation appears to be described by a power law of die general form a-b(t/x) , where % is a characteristic relaxation time and 0
