Glass is a microscopically disordered, solid form of matter that results when a fluid is cooled or compressed in such a manner that it does not crystallize. Almost all types of materials are capable of glass formation, including polymers, metal alloys and molten salts. Given such diversity, general principles by which different glass-forming materials can be systematically classified are invaluable. One such principle is the classification of glass-formers according to their fragility. Fragility measures the rapidity with which a liquid's properties (such as viscosity) change as the glassy state is approached. Although the relationship between the fragility, configurational entropy and features of the energy landscape (the complicated dependence of energy on configuration) of a glass-former have been analysed previously, a detailed understanding of the origins of fragility is lacking. Here I use simulations to analyse the relationship between fragility and quantitative measures of the energy landscape for a model liquid whose fragility depends on its bulk density. The results reveal that fragility depends on changes in the vibrational properties of individual energy minima in addition to their total number and spread in energy. A thermodynamic expression for fragility is derived, which is in quantitative agreement with kinetic fragilities obtained from the liquid's diffusivity.

Silicon in its liquid and amorphous forms occupies a unique position among amorphous materials. Obviously important in its own right, the amorphous form is structurally close to the group of 4-4, 3-5 and 2-6 amorphous semiconductors that have been found to have interesting pressure-induced semiconductor-to-metal phase transitions. On the other hand, its liquid form has much in common, thermodynamically, with water and other 'tetrahedral network' liquids that show density maxima. Proper study of the 'liquid-amorphous transition', documented for non-crystalline silicon by both experimental and computer simulation studies, may therefore also shed light on phase behaviour in these related materials. Here, we provide detailed and unambiguous simulation evidence that the transition in supercooled liquid silicon, in the Stillinger-Weber potential, is thermodynamically of first order and indeed occurs between two liquid states, as originally predicted by Aptekar. In addition we present evidence to support the relevance of spinodal divergences near such a transition, and the prediction that the transition marks a change in the liquid dynamic character from that of a fragile liquid to that of a strong liquid.

We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming liquids. To this end, we first analyze clusters of highly mobile particles, the string-like collective motion of these mobile particles, and clusters of relative low mobility. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times for the high-and low-mobility particles naturally explains the well-known decoupling of diffusion and structural relaxation time scales. Despite the inherent difference of dynamics between high-and low-mobility particles, we find a high degree of similarity in the geometrical structure of these particle clusters. In particular, we show that the fractal dimensions of these clusters are consistent with those of swollen branched polymers or branched polymers with screened excluded-volume interactions, corresponding to lattice animals and percolation clusters, respectively. In contrast, the fractal dimension of the strings crosses over from that of self-avoiding walks for small strings, to simple random walks for longer, more strongly interacting, strings, corresponding to flexible polymers with screened excluded-volume interactions. We examine the appropriateness of identifying the size scales of either mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the "mosaic" length of the RFOT model relaxes the conventional assumption that the "entropic droplets" are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.

An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this "inherent dynamics" approach we find direct numerical evidence for the long held view that below a crossover temperature, Tx, the liquid's dynamics can be separated into (i) vibrations around inherent structures and (ii) transitions between inherent structures (M. Goldstein, J. Chem. Phys. 51, 3728 (1969)), i.e., the dynamics become "dominated" by the potential energy landscape. In agreement with previous proposals, we find that Tx is within the vicinity of the mode-coupling critical temperature Tc. We further find that at the lowest temperature simulated (close to Tx), transitions between inherent structures involve cooperative, string like rearrangements of groups of particles moving distances substantially smaller than the average interparticle distance.

The glass transition, whereby liquids transform into amorphous solids at low temperatures, is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liquid upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam-Gibbs theory, have sought to relate growing relaxation times to length scales associated with spatial correlations in liquid structure or motion of molecules, the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of molecules leading to structural relaxation, termed ''spatially heterogeneous dynamics,'' provide fresh impetus in this direction. A powerful approach to extract length scales in critical phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale associated with spatially heterogeneous dynamics, which grows as temperature decreases. However, relaxation times that also grow with decreasing temperature do not exhibit standard finite-size scaling with this length. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions.correlation length ͉ dynamic heterogeneity ͉ finite-size scaling ͉ glass transition ͉ relaxation time M ost approaches to understanding the glass transition and slow dynamics in glass formers (1-10) are based on the intuitive picture that the movement of their constituent particles (atoms, molecules, polymers) requires progressively more cooperative rearrangement of groups of particles as temperature decreases (or density increases). Structural relaxation becomes slow because the concerted motion of many particles is infrequent. Intuitively, the size of such ''cooperatively rearranging regions'' (CRR) is expected to increase with decreasing temperature. Thus, the above picture naturally involves the notion of a growing length scale, albeit implicitly in most descriptions. The notion of such a length scale, related to the configurational entropy S c (see Methods), forms the basis of rationalizing (1, 6, 7) the celebrated Adam-Gibbs (AG) relation (1) between the relaxation time and S c .More recently, a number of theoretical approaches have explored the relevance of a growing length scale to dynamical slow down (5,7,9). A specific motivation for some of these approaches arises from the study of heterogeneous dynamics in glass formers (11)(12)(13)(14). In particular, c...

We report computer simulations of oscillatory athermal quasi-static shear deformation of dense amorphous samples of a three dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: for large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g. metallic glasses). The onset of the transition is shown to be related to the onset of energy dissipation. Shear banding is observed for large system sizes, without, however, affecting qualitative aspects of the transition.Understanding the behavior of materials under mechanical deformation is of primary importance for many contexts. While the deformation behavior of crystals is theoretically well understood, no universally accepted framework exists to rationalize the behavior of mechanically driven amorphous systems, although significant progress has been made in recent years in developing a detailed understanding of how an amorphous solid responds to external stresses [1][2][3]. Considerable recent activity has been spurred by an interest in the mechanical behavior of metallic glasses, soft glassy materials, foams and granular packings, and has involved theoretical, computational and experimental investigations [2,[4][5][6][7][8]. Particular interest is understandably focused on the manner in which the response of an amorphous solid changes from nearly elastic response at small applied stress to a state of flow for large applied stress.Many computational investigations have employed the approach of studying the zero temperature behavior of amorphous solids under quasi static conditions (using an Athermal Quasi Static or AQS procedure [9]). In this procedure, systems are kept in local energy minimum configurations, or inherent structures [10,11] while varying the strain. In previous work on model systems of binary Lennard-Jones particles, it has been shown that upon monotonically increasing the applied shear strain, the inherent structures evolve towards energies corresponding to the limit of high temperatures [12]. This and related phenomena are referred to as rejuvenation, in contrast to the well studied process of ageing whereby (typically) a glassy material descends to deeper energy configurations as a function of the waiting time over which it relaxes at a given temperature. In contrast, when a cycle of strain is applied up to a maximum value which is then reversed [13], both ageing and rejuvenation are observed, with small amplitude strains found to reduce the energy of samples ("overage" them), while larger amplitude strains tend more often to increase the energy (thus "rejuvenating" the samples). Initial conditions of the samples in such cases matter: samples with lower initial potential energy are rejuvenated more easily than those with higher energy [13].In a very ...

Amorphous solids are ubiquitous among natural and man-made materials. Often used as structural materials for their attractive mechanical properties, their utility depends critically on their response to applied stresses. Processes underlying such mechanical response, and in particular the yielding behaviour of amorphous solids, are not satisfactorily understood. Although studied extensively, observed yielding behaviour can be gradual and depend significantly on conditions of study, making it difficult to convincingly validate existing theoretical descriptions of a sharp yielding transition. Here we employ oscillatory deformation as a reliable probe of the yielding transition. Through extensive computer simulations for a wide range of system sizes, we demonstrate that cyclically deformed model glasses exhibit a sharply defined yielding transition with characteristics that are independent of preparation history. In contrast to prevailing expectations, the statistics of avalanches reveals no signature of the impending transition, but exhibit dramatic, qualitative, changes in character across the transition.

Using molecular dynamics simulations, we investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a "protein glass transition", occurs at the temperature of dynamic crossover in the diffusivity of hydration water, and also coincides with the maxima of the isobaric specific heat C P and the temperature derivative of the orientational order parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from crossing the Widom line, which is defined as the locus of correlation length maxima emanating from the hypothesized second critical point of water.