1,721,027 research outputs found
Novel approach to numerical measurements of the configurational entropy in supercooled liquids
No full textThe configurational entropy is among the key observables to characterize experimentally the formation of a glass. Physically, it quantifies the multiplicity of metastable states in which an amorphous material can be found at a given temperature, and its temperature dependence provides a major thermodynamic signature of the glass transition, which is experimentally accessible. Measurements of the configurational entropy require, however, some approximations that have often led to ambiguities and contradictory results. Here we implement a novel numerical scheme to measure the configurational entropy Sigma(T) in supercooled liquids, using a direct determination of the free-energy cost to localize the system within a single metastable state at temperature T. For two prototypical glass-forming liquids, we find that Sigma(T) disappears discontinuously above a temperature T-c, which is slightly lower than the usual estimate of the onset temperature for glassy dynamics. This observation is in good agreement with theoretical expectations but contrasts sharply with alternative numerical methods. While the temperature dependence of Sigma(T) correlates with the glass fragility, we show that the validity of the Adam-Gibbs relation (relating configurational entropy to structural relaxation time) established in earlier numerical studies is smaller than previously thought, potentially resolving an important conflict between experiments and simulations
Absence of Marginal Stability in a Structural Glass
No full textMarginally stable solids have peculiar physical properties that were first analyzed in the context of the jamming transition. We theoretically investigate the existence of marginal stability in a prototypical model for structural glass formers, combining analytical calculations in infinite dimensions to computer simulations in three dimensions. While mean-field theory predicts the existence of a Gardner phase transition towards a marginally stable glass phase at low temperatures, simulations show no hint of diverging time scales or length scales, but reveal instead the presence of sparse localized defects. Our results suggest that the Gardner transition is deeply affected by finite dimensional fluctuations, and raise issues about the relevance of marginal stability in structural glasses far away from jamming
Nature of excitations and defects in structural glasses
No full textThe nature of defects in amorphous materials, analogous to vacancies and dislocations in crystals, remains elusive. Here, we explore their nature in a three-dimensional microscopic model glass-former that describes granular, colloidal, atomic and molecular glasses by changing the temperature and density. We find that all glasses evolve in a very rough energy landscape, with a hierarchy of barrier sizes corresponding to both localized and delocalized excitations. Collective excitations dominate in the jamming regime relevant for granular and colloidal glasses. By moving gradually to larger densities describing atomic and molecular glasses, the system crosses over to a regime dominated by localized defects and relatively simpler landscapes. We quantify the energy and temperature scales associated to these defects and their evolution with density. Our results pave the way to a systematic study of low-temperature physics in a broad range of physical conditions and glassy materials
Nonequilibrium critical dynamics of the two-dimensional XY model
No full textThe nonequilibrium critical dynamics of the two-dimensional XY model is investigated numerically through Monte Carlo simulations and analytically in the spin-wave approximation. We focus in particular on the behaviour of the two-time response and correlation functions and show that the ageing dynamics depends on the initial conditions. The presence of critical fluctuations leads to nontrivial violations of the fluctuation-dissipation theorem apparently reminiscent of the three-dimensional Edwards-Anderson spin glass model. We compute for this reason the finite-size overlap probability distribution function and find that it is related to the finite-time fluctuation-dissipation ratio obtained in the out-of-equilibrium dynamics, provided that the temperature is not very low
Can the jamming transition be described using equilibrium statistical mechanics?
No full textWhen materials such as foams or emulsions are compressed, they display solid behaviour above the so-called 'jamming' transition. Because compression is done out of equilibrium in the absence of thermal fluctuations, jamming appears as a new kind of a nonequilibrium phase transition. In this proceedings paper, we suggest that tools from equilibrium statistical mechanics can in fact be used to describe many specific features of the jamming transition. Our strategy is to introduce thermal fluctuations and use statistical mechanics to describe the complex phase behaviour of systems of soft repulsive particles, before sending the temperature to zero at the end of the calculation. We show that currently available implementations of standard tools such as integral equations, mode-coupling theory, or replica calculations all break down at low temperature and large density, but we suggest that new analytical schemes can be developed to provide a fully microscopic, quantitative description of the jamming transition
Structure and dynamics of coupled viscous liquids
No full textWe perform Monte-Carlo simulations to analyse the structure and microscopic dynamics of a viscous Lennard-Jones liquid coupled to a quenched reference configuration of the same liquid. The coupling between the two replicas is introduced via a field E conjugate to the overlap Q between the two particle configurations. This allows us to study the evolution of various static and dynamic correlation functions across the (E, T) equilibrium phase diagram. As the temperature is decreased, we identify increasingly marked precursors of a first-order phase transition between a low-Q and a high-Q phase induced by the field E. We show in particular that both static and dynamic susceptibilities have a maximum at a temperature-dependent value of the coupling field, which defines a Widom line'. We also show that, in the high-overlap regime, diffusion and structural relaxation are strongly decoupled because single-particle motion mostly occurs via discrete hopping on the sites defined by the reference configuration. These results, obtained using conventional numerical tools, provide encouraging signs that an equilibrium phase transition exists in coupled viscous liquids, but also demonstrate that important numerical challenges must be overcome to obtain more conclusive numerical evidence
Microscopic theory of the jamming transition of harmonic spheres
No full textWe develop a microscopic theory to analyze the phase behavior and compute correlation functions of dense assemblies of soft repulsive particles both at finite temperature, as in colloidal materials, and at vanishing temperature, a situation relevant for granular materials and emulsions. We use a mean-field statistical mechanical approach which combines elements of liquid state theory to replica calculations to obtain quantitative predictions for the location of phase boundaries, macroscopic thermodynamic properties, and microstructure of the system. We focus, in particular, on the derivation of scaling properties emerging in the vicinity of the jamming transition occurring at large density and zero temperature. The new predictions we obtain for pair correlation functions near contact are tested using computer simulations. Our work also clarifies the conceptual nature of the jamming transition and its relation to the phenomenon of the glass transition observed in atomic liquids
Microscopic Mean-Field Theory of the Jamming Transition
No full textDense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions by using equilibrium statistical mechanics and develop a fully microscopic, mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain new predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications and whose accuracy we confirm by using computer simulations
Marginally stable phases in mean-field structural glasses
No full textA novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. Using this approach, we provide complete phase diagrams delimiting the location of the marginally stable glass phase for a large variety of pair interactions and physical conditions, extensively exploring physical regimes relevant to granular matter, foams, emulsions, hard and soft colloids, and molecular glasses. We find that all types of glasses may become marginally stable, but the extent of the marginally stable phase highly depends on the preparation protocol. Our results suggest that marginal phases should be observable for colloidal and non-Brownian particles near jamming and for poorly annealed glasses. For well-annealed glasses, two distinct marginal phases are predicted. Our study unifies previous results on marginal stability in mean-field models and will be useful to guide numerical simulations and experiments aimed at detecting marginal stability in finite-dimensional amorphous materials
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