Pablo G. Debenedetti - Professor in Engineering and Applied Science - Princeton University
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Reviews of Metastable Liquids

Since Skripov's 'Metastable Liquids' appeared in 1974, there has been an enormous growth of literature in this area during the past twenty odd years. A monograph on the subject incorporating modern developments fills a real need. In particular, density functional theory of nucleation, glassy matter, computer simulation of liquids, etc. are some of the novel topics, which have advanced our microscopic understanding to a great extent. Against this background Debenedetti's book has appeared at an appropriate time.

While thermodynamics determines absolute stability limits, it is the kinetics that determine the practical stability limits. The relationship between the two kinds of limits, and the extent to which kinetics and thermodynamics determine the behaviour of metastable liquids, is the basic theme that this book addresses. It contains five chapters beginning with an introduction of metastable liquids in nature as well as in the technological world. The next two chapters contain detailed discussions on thermodynamics and kinetics. Chapter four deals with supercooled liquids followed by a brief chapter on the outlook. Each chapter has an extensive reference list.

In my view this book is an excellent reference for those interested in advanced chemical science and engineering. It is also a book on practical statistical mechanics. One will find a number of experimental details and results on the physical and chemical properties of metastable liquids. The book provides a clear exposition of an advanced topic and is also provocative at times. For example, "The statistical mechanics of metastable (constrained) systems is still in its infancy. Much has been learned about the limitations of the phenomenological approach to metastability, but very little progress has been made on the more difficult task of translating this criticism into useful results for realistic systems."

More discussion on glassy and polymeric liquids would have been useful; but in his own admission Debenedetti has been selective in the choice of topics considering the volume of the book. On the whole he has provided a comprehensive point of view of an emerging area of research. While libraries are recommended to buy copies, a specialist (whether a theorist or an experimenter) should possess his/her own personal copy.

Mukunda P. Das
Australian & New Zealand Physicist

Once upon a time the metastability of liquids was understood. According to the Gibbs-van der Waals paradigm, isotherms in the pressure-volume diagram have an analytical continuation across the two phase region. The coexistence curve is determined by the continuity of the Helmholtz free energy, leading to the Maxwell equal areas construction. The limits of stability of the liquid and vapor phases are given by the loci of the extrema of the isotherms, the spinodal. Inside the spinodal, the unstable region, the phases separate by the nucleation and growth of smooth-surfaced, spherical droplets.

Such a picture was adequate to explain most experimentally observed phenomena, and to permit the design of, for example, cloud and bubble chambers on the use of which so much of nuclear and particle physics has depended. Unfortunately, in the mid-sixties, this simple and elegant picture was destroyed by Fisher and by Ruelle. They showed that in the thermodynamic limit of statistical mechanics (and how else would one calculate an equation of state?) there was no analytical continuation of the isotherms, spinodals are a figment of the imagination. Furthermore, increasing understanding of critical phenomena at the same period led to the idea, later confirmed by computer simulation, that the droplets formed during phase separation are not spherical and their interfaces are of a dimension grater than two.

The question to be asked, then, in reviewing a new contribution to the literature of the subject is how it approaches the discrepancy between theory and experience and the conceptual problem in understanding metastability. Does the author take a thermodynamical approach, combined with classical nucleation theory, avoiding the conceptual difficulties, does he adopt a rigorous theoretical approach, calling on massive computer simulations to squeeze the last scaling law and fractal dimension out of artificial data or does he attempt a synthesis?

The book under review is rooted firmly in the physical chemistry of the subject. Metastability is understood as the confinement of the system to a restricted part of phase space for a period sufficiently long for quasi-thermodynamic quantities to be meaningful. This is not a theoretical treatise-the index contains one reference to fractals, one to renormalization group, none to scaling or to coarsening. In form the book consists essentially of a set of four independent review articles, each separately (and copiously) indexed with a short 'outlook' and appendices. The four topics are: 'metastable liquids in science and technology', 'thermodynamics', kinetics' and 'supercooled liquids'.

This is an authoritative text which fills a big gap in the literature. In spite of the conceptual difficulty of the subject, it is both readable and comprehensive. It should provide an invaluable handbook both for experimentalists interested in what is known about metastable liquids and for theoreticians who wish to become aware of the great deal which remains to be explained and understood.

P. Schofield
Contemporary Physics

Aside from R.P. Skirpov's book of a quarter of a century ago, this is the only monograph dealing with "metastable liquids". Although Skripov's book was, in its time, an outstanding contribution, much has happened in the intervening years, and Debenedetti's modern presentation of the field is a timely and welcome arrival. In Skripov's time the focus in metastable liquids was mainly on the superheated variety. Since then an enormous interest in supercooled liquids and glasses and the glass transition has developed. Debenedetti's book encompasses both varieties of liquid, and much more.

To me, with my minimal knowledge of the natural and technological importance of metastable liquids, the first chapter of the book constitutes an amazing revelation. One learns that such liquids are fundamental to the survival of many plants and animals. Nature has invented antifreeze proteins that actually inhibit crystallization; that is, they do not merely depress the freezing point. The ascent of sap in a tree forms an example in which the freezing point is actually depressed by the action of "tension". Since tension is an acceptable thermodynamic parameter, the liquid under tension is not strictly metastable, but its structure cannot differ much from its truly metastable counterpart. In one of many technological examples, the plugging of natural gas pipes due to the formation of clathrate hydrates is avoided by developing and using chemical inhibitors that slow the kinetics of clathrate crystallization and act in much the same way as the antifreeze proteins found in fish. Many other examples quickly convince the reader of the importance of the field.

Chapter 2, combined with several appendices, is virtually a course in thermodynamics bearing the author's special insight into the subject, and anyone with a rudimentary knowledge of this subject can experience an extremely useful intermediate to advanced training by reading it carefully. Of special note are the sections on stability and its significance with respect to both metastable and unstable systems.

Chapter 3 deals with kinetics, and deeply with nucleation and spinodal decomposition. These are extremely difficult fields that are presently in a state of great flux, but the author provides an amazingly current and readable account of the subject in both gases and liquids, treating the formation of drops, bubbles, and crystals and replete with an exhaustive bibliography. Indeed, this chapter forms the best review that I know of, and the reader is strongly influenced to try his own hand at unraveling some of the fascinating mysteries that remain unsolved.

Chapter 4 focuses on supercooled liquids, and by an entirely natural sequence of exposition quickly moves into glasses and the glass transition. Again, the discussion and the bibliography are exhaustive but eminently readable. Both thermodynamics and kinetic aspects of the glass transition are dealt with, and there is a special treatment of "glassy water", a subject of ubiquitous importance. There is still no consensus on whether the glass transition is a truly thermodynamic or dynamic transition (or no transition at all-but merely a slowing down of kinetics). So here we are again at the frontier and there are fascinating problems to be solved. Among the tools that are discussed, again at readable level, is the mode coupling theory.

The entire book is distinguished by the timeliness and exhaustiveness of its bibliography, which in itself represents a major contribution. Professor Debenedetti has provided a panoramic picture of the field while not compromising the details. The book should be extremely useful to researchers and students alike. It can serve as both a textbook and an up-to-date window on the state of the art in the field of metastable fluids.

I give this book a grade of "excellent" and I recommend it strongly.

Howard Reiss
Journal of Chemical Education

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