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Jamming at High Densities

marginally jammed. Jamming at High Densities. Ning Xu Department of Physics & CAS Key Laboratory of Soft Matter Chemistry University of Science and Technology of China Hefei, Anhui 230026, P. R. China http://staff.ustc.edu.cn/~ningxu. Point J (  c ). unjammed. jammed. Volume fraction

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Jamming at High Densities

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  1. marginally jammed Jamming at High Densities Ning Xu Department of Physics & CAS Key Laboratory of Soft Matter Chemistry University of Science and Technology of China Hefei, Anhui 230026, P. R. China http://staff.ustc.edu.cn/~ningxu Point J (c) unjammed jammed Volume fraction  pressure, shear modulus = 0 pressure, shear modulus > 0 Will well-known properties of marginally jammed solids hold at high densities?

  2. Simulation Model • Cubic box with periodic boundary conditions • N/2 big andN/2 small frictionlessspheres with mass m • L/ S= 1.4  avoid crystallization • Purely repulsive interactions Harmonic: =2; Hertzian: =5/2 • L-BFGS energy minimization (T = 0); constant pressure ensemble • Molecular dynamics simulation at constant NPT (T > 0)

  3. Low volume fraction High volume fraction potential increases Potential Field Interaction field on a slice of 3D packings of spheres At high volume fractions, interactions merge largely and inhomogeneously Would it cause any new physics?

  4. d Critical Scalings A crossover divides jamming into two regimes C. Zhao, K. Tian, and N. Xu, Phys. Rev. Lett. 106, 125503 (2011).

  5. Potential Pressure Bulk modulus Shear modulus Coordination number Marginally Jammed zC=2d, isostatic value d Critical Scalings Marginal jamming Scalings rely on potential C. S. O’Hern et al., Phys. Rev. Lett. 88, 075507 (2002); Phys. Rev. E 68, 011306 (2003). C. Zhao, K. Tian, and N. Xu, Phys. Rev. Lett. 106, 125503 (2011).

  6. Potential Pressure Bulk modulus Shear modulus Coordination number Marginally Jammed Deeply Jammed d Critical Scalings Deep jamming Scalings do not rely on potential C. Zhao, K. Tian, and N. Xu, Phys. Rev. Lett. 106, 125503 (2011).

  7. g1max g1max  - c Structure  Pair Distribution Function g(r) What we have known for marginally jammed solids? • First peak of g(r) diverges at Point J • Second peak splits • g(r) discontinuous at r = L, g(L+) < g(L) L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E 73, 041304 (2006).

  8. d Structure  Pair Distribution Function g(r) What are new for deeply jammed solids? • Second peak emerges below r = L • First peak stops decay with increasing volume fraction • g(L+) reaches minimum approximately at d C. Zhao, K. Tian, and N. Xu, Phys. Rev. Lett. 106, 125503 (2011).

  9. marginal  increases deep D() ~ 2 d Vibrational Properties  Density of States • Plateau in density of states (DOS) for marginally jammed solids • No Debye behavior, D() ~  d1, at low frequency • If fitting low frequency part of DOS by D() ~ ,  reaches maximumat d • Double peak structure in DOS for deeply jammed solids • Maximum frequency increases with volume fraction for deeply jammed • solids (harmonic interaction)  change of effective interaction L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett. 95, 098301 (2005). C. Zhao, K. Tian, and N. Xu, Phys. Rev. Lett. 106, 125503 (2011).

  10. d Participation ratio Define Vibrational Properties  Quasi-localization • Low frequency modes are quasi-localized • Localization at low frequency is the least at d • High frequency modes are less localized for deeply jammed solids C. Zhao, K. Tian, and N. Xu, Phys. Rev. Lett. 106, 125503 (2011). N. Xu, V. Vitelli, A. J. Liu, and S. R. Nagel, Europhys. Lett. 90, 56001 (2010).

  11. What we learned from jamming at T = 0? • A crossover at dseparates deep jamming from marginal jamming • Many changes concur at d • States at d have least localized low frequency modes • Implication: States at dare most stable, i.e. low frequency modes there have • highest energy barrier Vmax Glass transition temperature may be maximal at d? N. Xu, V. Vitelli, A. J. Liu, and S. R. Nagel, Europhys. Lett. 90, 56001 (2010).

  12. Vogel-Fulcher d d Glass Transition and Glass Fragility Glass transition temperature and glass fragility index both reach maximum at d L. Berthier, A. J. Moreno, and G. Szamel, Phys. Rev. E 82, 060501(R) (2010). L. Wang and N. Xu, to be submitted (2011).

  13. 1 < 2 < d a d < 3 < 4 t Dynamical Heterogeneity At constant temperature above glass transition, dynamical heterogeneity reaches maximum at d  Deep jamming at high density weakens dynamical heterogeneity L. Wang and N. Xu, to be submitted (2011).

  14. Conclusions • Critical scalings, structure, vibrational properties, and dynamics undergo • apparent changes at a crossover volume fraction d which thus separates • marginal jamming from deep jamming • Is the crossover critical? • Experimental realizations: charged colloids, star polymers Acknowledgement Cang Zhao USTC Lijin Wang USTC Kaiwen Tian will be at UPenn Brought to you by National Natural Science Foundation of China No. 91027001

  15. Thanks for your attention & Welcome to visit USTC

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