Browsing by Author "Charbonneau, P"
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Item Open Access ADVANCES IN THE MOLECULAR SIMULATION OF MICROPHASE FORMERS(2022-01-01) Charbonneau, P; Zhang, KThis chapter details the different experimental microphase formers and provides a minimal theoretical framework to present the simulation challenges associated with studying model microphase formers. Block copolymers are by far the most studied microphase formers. The chapter focuses on the phenomenological field theory description of the universality of the microphase formation and of the nature of the order-disorder transition. The chapter describes molecular simulation methods that have been specifically designed to achieve equilibrium in the periodic microphase regime. It details the thermodynamic framework and a free energy integration simulation method, followed by a concrete introduction to the ghost particle/cluster switching method. The chapter discusses several classical Monte Carlo algorithms to enhance the efficiency of simulating disordered microphases. It presents three models for which quantitative results have been obtained: a one-dimensional, a lattice, and an off-lattice microphase former. Fine-tuning colloidal suspensions to allow the formation of periodic microphases thus remains an open experimental problem.Item Open Access Comment on "kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system"(Physical Review Research, 2021-09-01) Hu, Y; Charbonneau, PHuerta [Phys. Rev. Research 2, 033351 (2020)2643-156410.1103/PhysRevResearch.2.033351] report a power-law decay of positional order in numerical simulations of hard disks confined within hard parallel walls, which they interpret as a Kosterlitz-Thouless (KT)-type caging-uncaging transition. The proposed existence of such a transition in a quasi-one-dimensional system, however, contradicts long-held physical expectations. To clarify if the proposed ordering persists in the thermodynamic limit, we introduce an exact transfer matrix approach to expeditiously generate configurations of very large subsystems that are typical of equilibrium thermodynamic (infinite-size) systems. The power-law decay of positional order is found to extend only over finite distances. We conclude that the numerical simulation results reported are associated with a crossover unrelated to KT-type physics, and not with a proper thermodynamic phase transition.Item Open Access Correlation lengths in quasi-one-dimensional systems via transfer matrices(Molecular Physics, 2018-06) Hu, Y; Fu, L; Charbonneau, P© 2018 Informa UK Limited, trading as Taylor & Francis Group. Using transfer matrices up to next-nearest-neighbour interactions, we examine the structural correlations of quasi-one-dimensional systems of hard disks confined by two parallel lines and hard spheres confined in cylinders. Simulations have shown that the non-monotonic and non-smooth growth of the correlation length in these systems accompanies structural crossovers [Fu et al., Soft Matter 13, 3296 (2017)]. Here, we identify the theoretical basis for these behaviours. In particular, we associate kinks in the growth of correlation lengths with eigenvalue crossing and splitting. Understanding the origin of such structural crossovers answers questions raised by earlier studies, and thus bridges the gap between theory and simulations for these reference models.Item Open Access Dynamical heterogeneity and nonlinear susceptibility in supercooled liquids with short-range attraction(Physical Review Letters, 2007-09-24) Charbonneau, P; Reichman, DRRecent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here we study in detail the behavior of nonlinear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard nonlinear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids. © 2007 The American Physical Society.Item Open Access Erratum: [N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4(Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2012-12-05) Zhang, K; Charbonneau, PItem Open Access Erratum: Emergence of limit-periodic order in tiling models (Physical Review E - Statistical, Nonlinear, and Soft Matter Physics (2014) 90 (012136))(Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2016-02-29) Marcoux, C; Byington, TW; Qian, Z; Charbonneau, P; Socolar, JESItem Open Access Exact theory of dense amorphous hard spheres in high dimension. III. the full replica symmetry breaking solution(Journal of Statistical Mechanics: Theory and Experiment, 2014-10-01) Charbonneau, P; Kurchan, J; Parisi, G; Urbani, P; Zamponi, F© 2014 IOP Publishing Ltd. In the first part of this paper, we derive the general replica equations that describe infinite-dimensional hard spheres at any level of replica symmetry breaking (RSB) and in particular in the fullRSB scheme. We show that these equations are formally very similar to the ones that have been derived for spin glass models, thus showing that the analogy between spin glasses and structural glasses conjectured by Kirkpatrick, Thirumalai and Wolynes is realized in a strong sense in the mean-field limit. We also suggest how the computation could be generalized in an approximate way to finite-dimensional hard spheres. In the second part of the paper, we discuss the solution of these equations and we derive from it a number of physical predictions. We show that, below the Gardner transition where the 1RSB solution becomes unstable, a fullRSB phase exists and we locate the boundary of the fullRSB phase. Most importantly, we show that the fullRSB solution predicts correctly that jammed packings are isostatic, and allows one to compute analytically the critical exponents associated with the jamming transition, which are missed by the 1RSB solution. We show that these predictions compare very well with numerical results.Item Open Access Gas-solid coexistence of adhesive spheres(Journal of Chemical Physics, 2007-05-28) Charbonneau, P; Frenkel, DIn this note, the authors investigate whether the gas-liquid critical point can remain stable with respect to solidification for narrow attractive interactions down to the Baxter limit. Using a crude cell theory, the authors estimate the necessary conditions for this to be true. Possible realizations are briefly discussed. © 2007 American Institute of Physics.Item Open Access Geometrical frustration: a study of four-dimensional hard spheres.(Phys Rev E Stat Nonlin Soft Matter Phys, 2009-03) van Meel, JA; Frenkel, D; Charbonneau, PThe smallest maximum-kissing-number Voronoi polyhedron of three-dimensional (3D) Euclidean spheres is the icosahedron, and the tetrahedron is the smallest volume that can show up in Delaunay tessellation. No periodic lattice is consistent with either, and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms "icosahedral" and "polytetrahedral" packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4D Euclidean hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in four dimensions is less facile than in three dimensions, which is consistent with earlier observations [M. Skoge, Phys. Rev. E 74, 041127 (2006)]. We conclude that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.Item Open Access Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions(2017-04-01) Charbonneau, P; Kurchan, J; Parisi, G; Urbani, P; Zamponi, FDespite decades of work, gaining a first-principle understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution in the mean-field limit of infinite spatial dimension, and numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the description and uncover its more sensitive features. We conclude with a brief overview of ongoing research.Item Restricted Hard-sphere crystallization gets rarer with increasing dimension.(Phys Rev E Stat Nonlin Soft Matter Phys, 2009-12) van Meel, JA; Charbonneau, B; Fortini, A; Charbonneau, PWe recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free-energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J. A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and to compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature (London) 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys. (to be published)].Item Open Access Linking dynamical heterogeneity to static amorphous order(Journal of Statistical Mechanics: Theory and Experiment, 2016-07-01) Charbonneau, P; Dyer, E; Lee, J; Yaida, S© 2016 IOP Publishing Ltd and SISSA Medialab srl. Glass-forming liquids grow dramatically sluggish upon cooling. This slowdown has long been thought to be accompanied by a growing correlation length. Characteristic dynamical and static length scales, however, have been observed to grow at different rates, which perplexes the relationship between the two and with the slowdown. Here, we show the existence of a direct link between dynamical sluggishness and static point-to-set correlations, holding at the local level as we probe different environments within a liquid. This link, which is stronger and more general than that observed with locally preferred structures, suggests the existence of an intimate relationship between structure and dynamics in a broader range of glass-forming liquids than previously thought.Item Open Access Mode-coupling theory(Journal of Statistical Mechanics: Theory and Experiment, 2005-05-01) Reichman, DR; Charbonneau, PIn this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori-Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory. © IOP Publishing Ltd.Item Open Access Monte Carlo approach for studying microphases applied to the axial next-nearest-neighbor Ising and the Ising-Coulomb models(Physical Review B - Condensed Matter and Materials Physics, 2011-06-09) Zhang, K; Charbonneau, PThe equilibrium phase behavior of microphase-forming systems is notoriously difficult to obtain because of the extended metastability of their modulated phases. In this paper we present a systematic simulation methodology for studying layered microphases and apply the approach to two prototypical lattice-based systems: the three-dimensional axial next-nearest-neighbor Ising (ANNNI) and Ising-Coulomb (IC) models. The method involves thermodynamically integrating along a reversible path established between a reference system of free spins under an ordering field and the system of interest. The resulting free-energy calculations unambiguously locate the phase boundaries. Simple phases are not found to play a particularly significant role in the devil's flowers and interfacial roughening plays at most a small role in the ANNNI layered regime. With the help of generalized order parameters, the paramagnetic-modulated critical transition of the ANNNI model is also studied. We confirm the XY universality of the paramagnetic-modulated transition and its isotropic nature. © 2011 American Physical Society.Item Restricted Numerical and theoretical study of a monodisperse hard-sphere glass former.(Phys Rev E Stat Nonlin Soft Matter Phys, 2010-04) Charbonneau, P; Ikeda, A; van Meel, JA; Miyazaki, KThere exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a deeply supersaturated monodisperse four-dimensional (4D) hard-sphere fluid, which has no such complexity, but whose strong intrinsic geometrical frustration inhibits crystallization, even when deeply supersaturated. As an application, we compare its behavior to the mode-coupling theory (MCT) of glass formation. We find MCT to describe this system better than any other structural glass formers in lower dimensions. The reduction in dynamical heterogeneity in 4D suggested by a milder violation of the Stokes-Einstein relation could explain the agreement. These results are consistent with a mean-field scenario of the glass transition.Item Open Access Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices(Physical Review B, 2021-10-01) Hu, Y; Charbonneau, PIsing models with frustrated next-nearest-neighbor interactions present a rich array of modulated phases. These phases, however, assemble and relax slowly, which hinders their computational study. In two dimensions, strong fluctuations further hamper determining their equilibrium phase behavior from theoretical approximations. The exact numerical transfer matrix (TM) method, which bypasses both difficulties, can serve as a benchmark method once its own numerical challenges are surmounted. Building on our recent study [Hu and Charbonneau, Phys. Rev. B 103, 094441 (2021)2469-995010.1103/PhysRevB.103.094441], in which we evaluated the two-dimensional axial next-nearest-neighbor Ising model with transfer matrices, we here extend the effective usage of the TM method to Ising models with biaxial, diagonal, and third-nearest-neighbor frustration models. The high-accuracy TM numerics help resolve various physical ambiguities about these reference models, thus providing a clearer overview of modulated phase formation in two dimensions.Item Open Access Out-of-equilibrium dynamical fluctuations in glassy systems(Journal of Chemical Physics, 2004-11-22) Chamon, C; Charbonneau, P; Cugliandolo, LF; Reichman, DR; Sellitto, MIn this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a criticallike dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving "extreme value" distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective σ model approach. © 2004 American Institute of Physics.Item Open Access Phase behavior and far-from-equilibrium gelation in charged attractive colloids(Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2007-05-03) Charbonneau, P; Reichman, DRIn this Rapid Communication we demonstrate the applicability of an augmented Gibbs ensemble Monte Carlo approach for the phase behavior determination of model colloidal systems with short-ranged depletion attraction and long-ranged repulsion. This technique allows for a quantitative determination of the phase boundaries and ground states in such systems. We demonstrate that gelation may occur in systems of this type as the result of arrested microphase separation, even when the equilibrium state of the system is characterized by compact microphase structures. © 2007 The American Physical Society.Item Open Access Postponing the dynamical transition density using competing interactions(Granular Matter, 2020-08-01) Charbonneau, P; Kundu, JSystems of dense spheres interacting through very short-ranged attraction are known from theory, simulations and colloidal experiments to exhibit dynamical reentrance. Their liquid state can thus be fluidized at higher densities than possible in systems with pure repulsion or with long-ranged attraction. A recent mean-field, infinite-dimensional calculation predicts that the dynamical arrest of the fluid can be further delayed by adding a longer-ranged repulsive contribution to the short-ranged attraction. We examine this proposal by performing extensive numerical simulations in a three-dimensional system. We first find the short-ranged attraction parameters necessary to achieve the densest liquid state, and then explore the parameter space for an additional longer-ranged repulsion that could further enhance reentrance. In the family of systems studied, no significant (within numerical accuracy) delay of the dynamical arrest is observed beyond what is already achieved by the short-ranged attraction. Possible explanations are discussed.Item Open Access Resolving the two-dimensional axial next-nearest-neighbor Ising model using transfer matrices(Physical Review B, 2021-03-25) Hu, Y; Charbonneau, PSome features of the phase diagram of the two-dimensional axial next-nearest-neighbor Ising model have long been debated. The extended structural correlations and long relaxation times associated with its Kosterlitz-Thouless phase indeed result in analytical and numerical treatments making contradictory predictions. Here, we introduce a numerical transfer matrix approach that bypasses these problems and thus clears up various ambiguities. In particular, we confirm the transition temperatures and the order of the transition to the floating incommensurate phase. Our approach motivates considering transfer matrices for solving long-standing problems in related models.