Theory of coupled translational-rotational glassy dynamics in dense fluids of uniaxial particles

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Abstract

The naïve mode coupling theory (NMCT) for ideal kinetic arrest and the nonlinear Langevin equation theory of activated single-particle barrier hopping dynamics are generalized to treat the coupled center-of-mass (CM) translational and rotational motions of uniaxial hard objects in the glassy fluid regime. The key dynamical variables are the time-dependent displacements of the particle center-of-mass and orientational angle. The NMCT predicts a kinetic arrest diagram with three dynamical states: ergodic fluid, plastic glass, and fully nonergodic double glass, the boundaries of which meet at a "triple point" corresponding to a most difficult to vitrify diatomic of aspect ratio ∼1.43. The relative roles of rotation and translation in determining ideal kinetic arrest are explored by examining three limits of the theory corresponding to nonrotating, pure rotation, and rotationally ergodic models. The ideal kinetic arrest boundaries represent a crossover to activated dynamics described by two coupled stochastic nonlinear Langevin equations for translational and rotational motions. The fundamental quantity is a dynamic free-energy surface, which for small aspect ratios in the high-volume fraction regime exhibits two saddle points reflecting a two-step activated dynamics where relatively rapid rotational dynamics coexists with slower CM translational motions. For large-enough aspect ratios, the dynamic free-energy surface has one saddle point which corresponds to a system-specific coordinated translation-rotation motion. The entropic barriers as a function of the relative amount of rotation versus translation are determined.

Original languageEnglish (US)
Article number011502
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume80
Issue number1
DOIs
StatePublished - Aug 6 2009

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Fluid
translational motion
fluids
Barycentre
Kinetics
Aspect Ratio
center of mass
aspect ratio
Mode Coupling Theory
Motion
Langevin Equation
kinetics
saddle points
Saddlepoint
coupled modes
Free Energy
Nonlinear Equations
free energy
Triple Point
glass

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "Theory of coupled translational-rotational glassy dynamics in dense fluids of uniaxial particles",
abstract = "The na{\"i}ve mode coupling theory (NMCT) for ideal kinetic arrest and the nonlinear Langevin equation theory of activated single-particle barrier hopping dynamics are generalized to treat the coupled center-of-mass (CM) translational and rotational motions of uniaxial hard objects in the glassy fluid regime. The key dynamical variables are the time-dependent displacements of the particle center-of-mass and orientational angle. The NMCT predicts a kinetic arrest diagram with three dynamical states: ergodic fluid, plastic glass, and fully nonergodic double glass, the boundaries of which meet at a {"}triple point{"} corresponding to a most difficult to vitrify diatomic of aspect ratio ∼1.43. The relative roles of rotation and translation in determining ideal kinetic arrest are explored by examining three limits of the theory corresponding to nonrotating, pure rotation, and rotationally ergodic models. The ideal kinetic arrest boundaries represent a crossover to activated dynamics described by two coupled stochastic nonlinear Langevin equations for translational and rotational motions. The fundamental quantity is a dynamic free-energy surface, which for small aspect ratios in the high-volume fraction regime exhibits two saddle points reflecting a two-step activated dynamics where relatively rapid rotational dynamics coexists with slower CM translational motions. For large-enough aspect ratios, the dynamic free-energy surface has one saddle point which corresponds to a system-specific coordinated translation-rotation motion. The entropic barriers as a function of the relative amount of rotation versus translation are determined.",
author = "Rui Zhang and Schweizer, {Kenneth S}",
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