Topologically Induced Glass Transition in Freely Rotating Rods

Obukhov, Sergei; Kobzev, D. E.; Perchak, Dennis; Rubinstein, Michael

doi:10.1051/jp1:1997175

Cited by 13 publications

(37 citation statements)

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“…[192] or b.c.c. [193] lattice, or their endpoints to a cubic or square lattice [194]; in the last case the motion of the needles was assumed to take place in the (three-dimensional) half-space to one side of the lattice plane. In the limit of vanishing needle diameter, assumed throughout, equilibrium properties are again trivial.…”

Section: Needle Modelsmentioning

confidence: 99%

Glassy dynamics of kinetically constrained models

Ritort

Sollich

2003

Advances in Physics

750

1,055

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We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying "equilibrium glass transition". After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and mode-coupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known results for the dynamics of KCMs both in and out of equilibrium, including topics such as relaxation time divergences and dynamical transitions, nonlinear relaxation, aging and effective temperatures, cooperativity and dynamical heterogeneities, and finally non-equilibrium stationary states generated by external driving. We conclude with a discussion of open questions and possibilities for future work.

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Section: Needle Modelsmentioning

confidence: 99%

Glassy dynamics of kinetically constrained models

Ritort

Sollich

2003

Advances in Physics

750

1,055

View full text Add to dashboard Cite

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“…MD- [22] and MC-simulations [23], respectively, have shown the existence of glasslike dynamics. Particularly a critical length l c = L/a (a is the lattice constant) has been determined at which an orientational glass transition occurs [22,23]. However, this transition is not sharp, in close analogy to supercooled liquids.…”

Section: Introductionmentioning

confidence: 97%

“…The molecules were approximated by infinitely thin hard rods with length L which were either fixed with their centers on a fcc-lattice [22] or with their endpoints on a sc-lattice [23]. MD- [22] and MC-simulations [23], respectively, have shown the existence of glasslike dynamics. Particularly a critical length l c = L/a (a is the lattice constant) has been determined at which an orientational glass transition occurs [22,23].…”

Section: Introductionmentioning

confidence: 99%

Microscopic theory of glassy dynamics and glass transition for molecular crystals

Ricker

Schilling

2005

Phys. Rev. E

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We derive a microscopic equation of motion for the dynamical orientational correlators of molecular crystals. Our approach is based upon mode coupling theory. Compared to liquids we find four main differences: (i) the memory kernel contains Umklapp processes if the total momentum of two orientational modes is outside the first Brillouin zone, (ii) besides the static two-molecule orientational correlators one also needs the static one-molecule orientational density as an input, where the latter is nontrivial due to the crystal's anisotropy, (iii) the static orientational current density correlator does contribute an anisotropic, inertia-independent part to the memory kernel, (iv) if the molecules are assumed to be fixed on a rigid lattice, the tensorial orientational correlators and the memory kernel have vanishing l, l ′ = 0 components, due to the absence of translational motion. The resulting mode coupling equations are solved for hard ellipsoids of revolution on a rigid sc-lattice. Using the static orientational correlators from Percus-Yevick theory we find an ideal glass transition generated due to precursors of orientational order which depend on X0 and ϕ, the aspect ratio and packing fraction of the ellipsoids. The glass formation of oblate ellipsoids is enhanced compared to that for prolate ones. For oblate ellipsoids with X0 0.7 and prolate ellipsoids with X0 4, the critical diagonal nonergodicity parameters in reciprocal space exhibit more or less sharp maxima at the zone center with very small values elsewhere, while for prolate ellipsoids with 2 X0 2.5 we have maxima at the zone edge. The off-diagonal nonergodicity parameters are not restricted to positive values and show similar behavior. For 0.7 X0 2, no glass transition is found because of too small static orientational correlators. In the glass phase, the nonergodicity parameters show a much more pronounced q-dependence.

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“…This system of 3D ''crosses'' is a generalization of the hard-needle model that had been developed to study topological effects on rotational and translational diffusion [11]. Earlier papers already implicitly [2] or explicitly [12] suggested that systems consisting of rigidly joined line segments might provide interesting models to study the glass transition. However, to our knowledge, no numerical studies of such ideal 3D glass formers have been reported.…”

mentioning

confidence: 99%

Structural Arrest in an Ideal Gas

2005

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We report a molecular dynamics study of a simple model system that has the static properties of an ideal gas, yet exhibits nontrivial ''glassy'' dynamics behavior at high densities. The constituent molecules of this system are constructs of three infinitely thin hard rods of length L, rigidly joined at their midpoints. The crosses have random but fixed orientation. The static properties of this system are those of an ideal gas, and its collision frequency can be computed analytically. For number densities NL 3 =V 1, the single-particle diffusivity goes to zero. As the system is completely structureless, standard mode-coupling theory cannot describe the observed structural arrest. Nevertheless, the system exhibits many dynamical features that appear to be mode-coupling-like. All high-density incoherent intermediate scattering functions collapse onto master curves that depend only on the wave vector. There probably exist more theories for the glass transition than for any other phenomenon in condensed matter physics except high-T c superconductivity (see, e.g., [1][2][3][4][5][6][7]). Some of these theories assume that the glass transition reflects an underlying (possibly frustrated) thermodynamic phase transition, others describe the glass transition as a purely kinetic phenomenon. One of the most widely used theories of the glass transition is mode-coupling theory (MCT) [3,4,8]. In the standard version of MCT, the glass transition is kinetic in nature but it is caused by the existence of static structural correlations in the system that vitrifies. It is probably fruitless to search for the ''true'' theory of the glass transition, because not all glasses appear to be equivalent [9,10]. However, it is important to disentangle, as much as possible, the roles of structural correlations and purely kinetic effects in the absence of such correlations. In the present Letter, we report simulations of a model system that has the structural properties of an ideal gas. If this system undergoes dynamical arrest, this is a purely kinetic effect. Our aim is to describe the characteristic features of vitrification in this ideal gas.The model system that we use contains particles that consist of three mutually perpendicular line segments of length L, rigidly joined at their midpoints. This system of 3D ''crosses'' is a generalization of the hard-needle model that had been developed to study topological effects on rotational and translational diffusion [11]. Earlier papers already implicitly [2] or explicitly [12] suggested that systems consisting of rigidly joined line segments might provide interesting models to study the glass transition. However, to our knowledge, no numerical studies of such ideal 3D glass formers have been reported. Rather, a lattice-based version of the hard-needle model has been studied by several authors as a model for orientational glass formers [13]. In general, crosses have both translational and rotational motion. However, as we focus on the normal (translational) glass transition, we suppress the ro...

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Topologically Induced Glass Transition in Freely Rotating Rods

Cited by 13 publications

References 1 publication

Glassy dynamics of kinetically constrained models

Glassy dynamics of kinetically constrained models

Microscopic theory of glassy dynamics and glass transition for molecular crystals

Structural Arrest in an Ideal Gas

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