As a liquid approaches the glass transition, its properties are dominated by local potential minima in its energy landscape. The liquid experiences localized vibrations in the basins of attraction surrounding the minima, and rearranges via relatively infrequent inter-basin jumps. As a result, the liquid dynamics at low temperature are related to the system's exploration of its own configuration space. The 'thermodynamic approach' to the glass transition considers the reduction in configuration space explored as the system cools, and predicts that the configurational entropy (a measure of the number of local potential energy minima sampled by the liquid) is related to the diffusion constant. Here we report a stringent test of the thermodynamic approach for liquid water (a convenient system to study because of an anomalous pressure dependence in the diffusion constant). We calculate the configurational entropy at points spanning a large region of the temperature-density plane, using a model that reproduces the dynamical anomalies of liquid water. We find that the thermodynamic approach can be used to understand the characteristic dynamic anomalies, and that the diffusive dynamics are governed by the configurational entropy. Our results indicate that the thermodynamic approach might be extended to predict the dynamical behaviour of supercooled liquids in general.

We report a numerical study, covering a wide range of packing fraction Phi and temperature T, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number n(max) of bonded interactions. We show that, when n(max)<6, the liquid-gas coexistence region shrinks, giving access to regions of low Phi where dynamics can be followed down to low T without an intervening phase separation. We characterize these arrested states at low densities (gel states) in terms of structure and dynamical slowing down, pointing out features which are very different from the standard glassy states observed at high Phi values.

We study thermodynamic and dynamic properties of a rigid model of the fragile glass-forming liquid orthoterphenyl. This model, introduced by Lewis and Wahnström in 1993, collapses each phenyl ring to a single interaction site; the intermolecular site-site interactions are described by the Lennard-Jones potential whose parameters have been selected to reproduce some bulk properties of the orthoterphenyl molecule. A system of N=343 molecules is considered in a wide range of densities and temperatures, reaching simulation times up to 1 micros. Such long trajectories allow us to equilibrate the system at temperatures below the mode coupling temperature T(c) at which the diffusion constant reaches values of order 10(-10) cm(2)/s and thereby to sample in a significant way the potential energy landscape in the entire temperature range. Working within the inherent structures thermodynamic formalism, we present results for the temperature and density dependence of the number, depth and shape of the basins of the potential energy surface. We evaluate the total entropy of the system by thermodynamic integration from the ideal-noninteracting-gas state and the vibrational entropy approximating the basin free energy with the free energy of 6N-3 harmonic oscillators. We evaluate the configurational part of the entropy as a difference between these two contributions. We study the connection between thermodynamical and dynamical properties of the system. We confirm that the temperature dependence of the configurational entropy and of the diffusion constant, as well as the inverse of the characteristic structural relaxation time, are strongly connected in supercooled states; we demonstrate that this connection is well represented by the Adam-Gibbs relation, stating a linear relation between logD and the quantity 1/TS(c). This relation is found to hold both above and below the critical temperature T(c)-as previously found in the case of silica-supporting the hypothesis that a connection exists between the number of basins and the connectivity properties of the potential energy surface.

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configurational contributions to pressure are sorted out in a transparent way. Predictions are successfully compared with data from extensive molecular dynamics simulations of a simple model for the fragile liquid orthoterphenyl.PACS numbers: 64.70. Pf, 61.20.Ja, 61.20.Lc Recent years have seen a resurgence in studies devoted to modeling the thermodynamics of supercooled liquids [1,2,3,4,5]. Such studies aim to elucidate the physics of the liquid-glass transition, to develop a thermodynamic description of out of equilibrium systems and to provide keys for a deeper understanding of the dynamics of supercooled states [6]. Numerical studies, boosted by increased computational resources which now allow simulations to track the slowing down of the dynamics over more than 6 decades in time, are providing quantitative estimates for the free energy of simple model systems [7,8,9,10]. The availability of such data provides stringent tests of the theoretical predictions [9,10,11] and helps in the understanding of basic mechanisms associated with the behavior of thermodynamic and dynamic quantities close to the glass transition.Among the thermodynamic formalisms amenable to numerical investigation, a central role is played by the Inherent Structure (IS) formalism introduced by Stillinger and Weber [12]. Properties of the potential energy landscape (PEL), such as depth, number and shape of the basins of the potential energy surface are calculated and used in the evaluation of the liquid free energy [9,10,11,13] In the IS formalism, the system free energy is expressed as a sum of an entropic contribution, accounting for the number of the available basins, and a vibrational contribution, expressing the free energy of the system when constrained in one of the basins [12].Important progress has been made after the discovery that -for models of fragile liquids -the number Ω(e IS ) of distinct basins of depth e IS in a system of N atoms or molecules is well described by a Gaussian distribution [10,14] Ω(e IS ) = e αN eHere the amplitude e αN accounts for the total number of basins. Numerical studies of models for fragile liquids have also shown that the basin free energy can be written as the depth e IS plus a vibrational contribution which, in the harmonic approximation, has the well known formwhere ω i (e IS ) is the i-th normal mode frequency (i = 1...M ) and β = 1/k B T . The M normal mode frequencies define the shape of the basin. If relevant, anharmonic corrections can also be accounted for [11,13]. The quantityln(ω i (e IS )/ω o ) (where ω o is the frequency unit) is found to depend linearly on the basin depth [10], i.e. can be written, in t...

Within the inherent structure (IS) thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)] we address the basic question of the physics of the liquid-liquid transition and of density maxima observed in some complex liquids such as water by identifying, for the first time, the statistical properties of the potential energy landscape (PEL) responsible for these anomalies. We also provide evidence of the connection between density anomalies and the liquid-liquid critical point. Within the simple (and physically transparent) model discussed, density anomalies do imply the existence of a liquid-liquid transition.PACS numbers: 64.70 Pf, 61.20.Ja, 64.20. Lc Water, the most important liquid for life, belongs to a class of liquids for which the isobaric temperature dependence of the density has a maximum. In contrast to ordinary liquids, water expands on cooling below 4C at atmospheric pressure. This density anomaly is associated with other thermodynamic anomalies, such as minima in the compressibility along isobars and an increase of the specific heat on cooling [1]. Recent fascinating studies have attempted to connect these anomalies to the presence of two different liquid structures, separated at low temperature by a line of first order transitions, ending in a second order critical point [2,3,4]. In the case of water, this novel critical point would be located in an experimentally inaccessible region [5]. Despite this unfavorable location, the postulated presence of this critical point provides a framework for interpreting [6] not only features of the liquid state but also the phenomenon of polyamorphism and the first-order like transition between polyamorphs [7]. In this Letter we aim at identifying the statistical properties of the potential energy landscape (PEL) responsible for the density maxima and the connection to the physics of the liquid-liquid transition.The study of the statistical properties of the PELi.e. of the number, shape and depth of the basins composing the potential energy hypersurface -is under tremendous development. Theoretical approaches, based on the seminal work of Stillinger and Weber [8], combined either with calorimetric data [9,10,11] or with analysis of extensive numerical simulations [12,13,14] are starting to provide precise estimates of the statistical properties of the PEL in several materials and models for liquids. A simple model for the statistical properties of the landscape, supported by recent numerical studies [14,15,16], can be built on the basis of the two following hypotheses:1. a gaussian distribution for Ω(e IS )de IS [15,17,18,19,20], the number of distinct basins of energy depth e IS between e IS and e IS + de IS , i.e.Here e αN counts the total number of PEL basins, (N being the number of molecules) E 0 is the characteristic energy scale and σ 2 is the variance of the distribution. A gaussian distribution is suggested by the central limit theorem, since in the absence of diverging correlation, e IS...

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition is a topic of considerable interest. The potential energy surface of model liquids has been increasingly studied, since it provides a connection between the configurational component of the partition function on the one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent interbasin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model have been studied in great detail in recent years. We locate the minima sampled by the liquid by ''quenches'' from equilibrium configurations generated via molecular dynamics simulations, and then calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling.

Self-assembly is the mechanism that controls the formation of well-defined structures from disordered preexisting parts. Despite the importance of self-assembly as a manufacturing method and the increasingly large number of experimental realizations of complex self-assembled nano-aggregates, theoretical predictions are lagging behind. Here, we show that for a nontrivial self-assembly phenomenon, originating branched loopless clusters, it is possible to derive a fully predictive parameter-free theory of equilibrium self-assembly by combining the Wertheim theory for associating liquids with the Flory-Stockmayer approach for chemical gelation.Intermolecular self-assembly is the ability of molecules to form supramolecular assemblies 1 as well as a manufacturing method used to construct aggregate at the nano-or micro-scale, by proper design of the constituent molecules. In the selfassembly bottom-up paradigm, the final (desired) structure is encoded in the shape and properties of the designed building blocks. Realizations of complex self-assembled nano-aggregates [2][3][4] have been guided by intuition and sophisticated experimental techniques. A full comprehension of the self-assembly process requires the ability to predict the structures (and their relative abundance) which will be observed in equilibrium as a function of temperature T and density F, starting from the knowledge of the interparticle interaction potential. Such a request is very much akin to the one that has guided the development of the physics of liquids in the last decades. Differently from the simple liquid case, self-assembly is characterized by a very strong interparticle attraction (significantly larger than the thermal energy k B T) and by the fact that the interaction geometry is far from being spherical. The leading "bonding" interaction may indeed be localized in a specific part of the particle surface (patchy interactions 5 ), it may be active only in the presence of a specific complementary group (lock-and-key interactions, very often encountered in biological self-assembly 6-9 ), or it may be strongly dependent on the particle orientation. 10 The presence of strong and patchy interactions poses significant challenges to a parameter-free description of self-assembly. Only equilibrium chain polymerization, the simplest self-assembly process which takes place when bifunctional particles self-assemble into chains of variable length, can be considered to be sufficiently established. [11][12][13][14][15][16] In this article, we show that for systems with a small average functionality (but larger than two) it is possible to provide a parameter-free full description of the self-assembly process. We study theoretically and numerically one of the simplest but not trivial self-assembly processes, namely, a binary mixture of particles with two and three attractive sites. The presence of three (or more)-functional particles, which act as branching points in the self-assembled clusters, introduces two important phenomena which are missing in equilibr...

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by the mode-coupling theory. We find, surprisingly, that the diffusion constant depends mainly on the fraction of directions in configuration space connecting different local minima, supporting the conjecture that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find an unexpected relation between the number of basins accessed in equilibrium and the connectivity between them.