Analog simulation of melting in two dimensions

Pouligny, B.; Malzbender, Rainer M.; Ryan, Pat J.; Clark, Noel A.

doi:10.1103/physrevb.42.988

Cited by 34 publications

(16 citation statements)

References 14 publications

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“…3,4,30 Polymeric clusters of mobile particles have also been identified in suspensions of spherical colloid particles at high concentrations [11][12][13][14] and in experiments for shaken granular systems. 31 Collective particle motion has also been inferred in time-of-flight neutron scattering measurements. 32 These observations, taken together, motivate our investigation of whether equilibrium polymerization, in particular, provides an appriopriate model for describing the dynamic heterogeneity of glass-forming liquids.…”

Section: Introductionmentioning

confidence: 99%

Does equilibrium polymerization describe the dynamic heterogeneity of glass-forming liquids?

Douglas

Dudowicz

Freed

2006

The Journal of Chemical Physics

124

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A significant body of evidence indicates that particles with excessively high or low mobility relative to Brownian particles form in dynamic equilibrium in glass-forming liquids. We examine whether these "dynamic heterogeneities" can be identified with a kind of equilibrium polymerization. This correspondence is first checked by demonstrating the presence of a striking resemblance between the temperature dependences of the configurational entropy s(c) in both the theory of equilibrium polymerization and the generalized entropy theory of glass formation in polymer melts. Moreover, the multiple characteristic temperatures of glass formation are also shown to have analogs in the thermodynamics of equilibrium polymerization, supporting the contention that both processes are varieties of rounded thermodynamic transitions. We also find that the average cluster mass (or degree of polymerization) varies in nearly inverse proportionality to s(c). This inverse relation accords with the basic hypothesis of Adam-Gibbs that the number of particles in the cooperatively rearranging regions (CRR) of glass-forming liquids scales inversely to s(c) of the fluid. Our identification of the CRR with equilibrium polymers is further supported by simulations for a variety of glass-forming liquids that verify the existence of stringlike or polymeric clusters exhibiting collective particle motion. Moreover, these dynamical clusters have an exponential length distribution, and the average "string" length grows upon cooling according to the predictions of equilibrium polymerization theory. The observed scale of dynamic heterogeneity in glass-forming liquids is found to be consistent with this type of self-assembly process. Both experiments and simulations have revealed remarkable similarities between the dynamical properties of self-assembling and glass-forming liquids, suggesting that the development of a theory for the dynamics of self-assembling fluids will also enhance our understanding of relaxation in glass-forming liquids.

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Section: Introductionmentioning

confidence: 99%

Does equilibrium polymerization describe the dynamic heterogeneity of glass-forming liquids?

Douglas

Dudowicz

Freed

2006

The Journal of Chemical Physics

124

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“…Here, we try to address this question with a wet granular model system. Granular matter, besides its ubiquity in nature [18,19], has been frequently used as a model system for phase transitions far from thermal equilibrium [20][21][22][23][24][25][26][27][28][29], due to the strongly dissipative particle-particle interactions. Here, we use a mono-layer of wet particles as a model system, because the cohesion arising from the formation of capillary bridges, which mimics molecular bonds, effectively leads to a crystalline structure with a free surface.…”

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confidence: 99%

Analog of surface melting in a macroscopic nonequilibrium system

et al. 2013

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Agitated wet granular matter can be considered as a nonequilibrium model system for phase transitions, where the macroscopic particles replace the molecules and the capillary bridges replace molecular bonds. It is demonstrated experimentally that a two-dimensional wet granular crystal driven far from thermal equilibrium melts from its free surface, preceded by an amorphous state. The transition into the surface melting state, as revealed by the bond orientational order parameters, behaves like a first order phase transition, with a threshold being traceable to the rupture energy of a single capillary bridge. The observation of such a transition in the macroscopic nonequilibrium system triggers the question of the universality of surface melting.

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“…The hexatic phase melts into a liquid with only short-range order. Both transitions are mediated by topological defects, the first by unbinding of dislocation pairs, the second by unbinding of disclination pairs (see [9] for a review).Single layers of identical macroscopic spheres subjected to mechanical vibration undergo transitions that share, at least superficially, many of the characteristics of equilibrium atomic and molecular melting transitions [10,11,12,13]. The external vibration is necessary to keep the macroscopic spheres in motion because of the inevitable loss of energy to friction and inelastic collisions.…”

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Two-Dimensional Melting Far from Equilibrium in a Granular Monolayer

Olafsen

Urbach²

2005

Phys. Rev. Lett.

113

121

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We report an experimental investigation of the transition from a hexagonally ordered solid phase to a disordered liquid in a monolayer of vibrated spheres. The transition occurs as the intensity of the vibration amplitude is increased. Measurements of the density of dislocations and the positional and orientational correlation functions show evidence for a dislocation-mediated continuous transition from a solid phase with long-range order to a liquid with only short-range order. The results show a strong similarity to simulations of melting of hard disks in equilibrium, despite the fact that the granular monolayer is far from equilibrium due to the effects of interparticle dissipation and the vibrational forcing.

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Analog simulation of melting in two dimensions

Cited by 34 publications

References 14 publications

Does equilibrium polymerization describe the dynamic heterogeneity of glass-forming liquids?

Does equilibrium polymerization describe the dynamic heterogeneity of glass-forming liquids?

Analog of surface melting in a macroscopic nonequilibrium system

Two-Dimensional Melting Far from Equilibrium in a Granular Monolayer

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