Pablo G. Debenedetti, Frank H. Stillinger, Thomas M. Truskett, and Christopher J. Roberts
Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544
The Journal of Physical Chemistry B
Reprinted from Volume 103, Number 35, Pages 7390-7397
7390 J. Phys. Chem. B 1999, 103, 7390-7397

Pablo G. Debenedetti,*+ Frank H. Stillinger,$% Thomas M. Truskett,+ and Christopher J. Roberts+ Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544,
Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974,
and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544
Received: April 27, 1999; In Final Form: June 28, 1999

FEATURE ARTICLE

Abstract: The topography of the multidimensional potential energy landscape is receiving much attention as a useful object of study for understanding complex behavior in condensed-phase systems. Examples include protein folding, the glass transition, and fracture dynamics in solids. The manner in which a system explores its underlying energy landscape as a function of temperature offers insight into its dynamic behavior. Similarly, sampling in density, in particular the relationship between the pressure of mechanically stable configurations and their bulk density (the equation of state of the energy landscape), provides fresh insights into the mechanical strength of amorphous materials and suggests a previously unexplored connection with the spinodal curve of a superheated liquid. Mean-field calculations show a convergence at low temperature between the superheated liquid spinodal and the pressure-dependent Kauzmann locus, along which the difference in entropy between a supercooled liquid and its stable crystalline form vanishes. This convergence appears to have implications for the glass transition. Application of these ideas to water sheds new light into this substance’s behavior under conditions of low-temperature metastability with respect to its crystalline phases.

I. Introduction
Many of the most striking and provocative phenomena with which physical chemistry and materials science are concerned occur in condensed phases. Examples include the occurrence of metastable states and their destruction by nucleation or spinodal decomposition,¹ shock and detonation wave propagation,^* protein folding from random-coil to native states,³ spontaneous assembly of diverse mesoscopic structures,⁴ and fracture dynamics of solid materials.⁵ A feature common to all of these is the concerted, or cooperative, action of many molecular degrees of freedom subject to the molecular interactions that are present.
A full understanding of collective phenomena exhibited by condensed phases must account for the consequences of each constituent molecule constantly experiencing strong and often competing interactions with many neighbors. This situation has sown the seeds for germination and growth of a general “rugged landscape paradigm” for understanding condensed phase behavior, i.e., a formal representation of many-molecule systems that focuses on the multidimensional potential energy hypersurface. ^6,7
This Feature Article presents some recent results and thoughts that have emanated from this rugged landscape viewpoint. In particular, we concentrate on how the equation of state (including both equilibrium an metastable states) reveals some key aspects of the multidimensional potential energy landscape topography. As will be demonstrated below, this line of investigation goes to the fundamental questions concerning the nature of the liquid state and of the amorphous glasses that can be formed from supercooled liquids. The following section II lays the groundwork for our presentation with the necessary basic definitions and statistical thermodynamic relations to establish the energy landscape representation. Section III considers the information that can be extracted by sampling the system at different temperatures under constant volume conditions; in particular we review and interpret results that have emerged form recent computer simulations on glass-forming binary mixtures.^8-10 Section IV examines the complementary case of sampling in density, which leads to the analysis of spinodal curves and to the issue of the mechanical strength of amorphous solids. Section V illustrates these phenomena with some mean-field calculations of the kind initiated some years ago by Longuet-Higgins and Widom,¹¹ but generalized here, and with implications for the density (or pressure) dependent Kauzmann temperature. Section VI applies these ideas to the case of water, showing connections to the complicated and still-debated properties of this substance’s super-cooled liquid and amorphous solid states at low temperature.^12-14 The final section, section VII, contains our views about the most productive future directions for the rugged landscape approach to open problems in physical chemistry and materials science.

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