Recent Work on Random Close Packing

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Recent Work on Random Close Packing
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• 1. Polytetrahedral Nature of the Dense
  Disordered Packings of Hard Spheres
• PRL 98, 235504 (2007)
• A.V. Anikeenko and N. N. Medvedev
• 2. Is Random Close Packing of Spheres Well
  Defined?
• VOLUME 84, NUMBER 10 (2000)
• S. Torquato, T.M. Truskett, P. G. Debenedetti

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The History

• J D Bernal raised the question in 1960 from
  observation
• In the last 48 years, much research was done over
  this, but so far, few satisfactory conclusions
  have been reached

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Why This Is An Important Question

• We can obtain a better insight of phase
  transition
• An EXPERT should be able to show you more its
  importance,
• but sorry, I am just a small potato

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Definition (From Observation)

• The traditional experiments indicated an
  interesting limit 0.636
• One such experiment is done in 1969, limiting
  value 0.637 was obtained simply from experiments.
• Nowadays, 2 ways of simulations are mainly applied

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Can We Have A Theoretical Definition?

• Jammed system means all particles are jammed
• Introducing a parameter that quantifies order
  (difficult one, may be subjective)
• Maximally Random Jammed (MRJ) system is the one
  we desire, and its volume fraction is the RCP
  limit

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Theoretical Definition By Introducing the Concept
ofMaximally random jammed

• A schematic plot of the order parameter
  versus volume fraction for a system of
  identical spheres

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Independent of how we quantify order?

• Can we use simulations to have a feeling for
  the probability distribution for RCP to answer
  the question above?

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How Can We Quantify Order

• In the paper Is Random Close Packing of Spheres
  Well Defined, they didnt come up with an exact
  and simple way to quantify the order
• The paper Polytetrahedral Nature of the Dense
  Disordered Packings of Hard Spheres showed us an
  interesting phenomenon, which inspired me a
  simple way to quantify order

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Quantify Order Using Polytetrahedral Nature

• In a tetrahedron, maximal edge length is emax,
  minimal edge length is 1 (i.e. the diameter of
  the sphere)
• Define a value
• Small values of unambiguously indicate that
  the shape of the simplex is close to regular
  tetrahedron with unit edges.

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Define tetrahedra

• By simply trying, they found that the best value
  may be
• Here, we realize that the choose of the value
  0.225 may be subjective. But, as we go on, we saw
  phenomena independent of 0.225. And, 0.225 may
  just be a most obvious value

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Volume fraction of tetrahedra
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Fraction of spheres involved in tetrahedra
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Polytetrahedral Aggregates

• Definition
• clusters built from three or more face
  adjacent tetrahedra
• Isolated tetrahedra and pairs of tetrahedra
  (bipyramids) are omitted as they are found in the
  fcc and hcp crystalline structures.

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Polytetrahedral Aggregates

• In the general case polytetrahedra have the form
  of branching chains and five-member rings
  combining in various animals MOTIF?

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Volume fraction of polytetrahedra
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Comparison

• Notice the difference between the 2 graphs

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Quantify Order

• This gives me a hint for quantifying order
• I think, we should find the function for volume
  fraction of isolated tetrahedra and bipyramids
  against packing volume fraction, i.e. the
  difference between the 2 graph. We use L to
  denote it.
• From pure observation, we notice that L is
  approximately a constant at low density, but
  after 0.646, L has a sudden increase

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Quantify Order

• We may use K to denote the volume fraction of
  spheres within polytetrahedral aggregates.
• To quantify disorder, we use K/L.
• Thus we use 1/(1K/L) to denote order

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Quantify Order

• But during the process, the value is
  chosen subjectively.

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• But from the left graph, we may expect that
  different choices of
• may lead to the same MRJ result.
• (This is only my naive expectation)

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The Following Work May Be Done

• Obtain the - graph from simulation under
  different choices of
• Is the MRJ is independent of how we quantify
  order?
• Is the limit independent of
• Of course, the most important thing for me is to
  get into the problem

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THANK YOU!