The 5th International Symposium on Current Progress in Mathematics and Sciences (ISCPMS 2019), 9-10 July 2019, Depok, Indonesia

1. 9-10 July 2019
Depok, Indonesia
The 5th International Symposium on
Current Progress in Mathematics and
Sciences (ISCPMS 2019)
1
Molecular Dynamics Simulation of
Floating Spheres Forming Two-
Dimensional Hexagonal Close
Packed Structure
Sparisoma Viridi1
, Veinardi Suendo2
1
Department of Physics, Institut Teknologi Bandung, Bandung 40132, Indonesia
2
Department of Chemistry, Institut Teknologi Bandung, Bandung 40132, Indonesia
1
dudung@fi.itb.ac.id, 2
vsuendo@chem.itb.ac.id
20190710_6

2. 9-10 July 2019
Depok, Indonesia
The 5th International Symposium on
Current Progress in Mathematics and
Sciences (ISCPMS 2019)
2
Outline
• Introduction
• Problem
• Simulation
• Results and discussion
• Summaries

3. 9-10 July 2019
Depok, Indonesia
The 5th International Symposium on
Current Progress in Mathematics and
Sciences (ISCPMS 2019)
3
Introduction

4. Hexagonal close packed structure
• Hexagonal close packed structure (HCP) is a
common type of structures in nanoscale sys-
tems, that has been observed in powder con-
sisted of spherical particles of polymethyl-
methacrylate with mean radius about 170 nm
and polydispersity less than about 0.05
9-10 July 2019
Depok, Indonesia
The 5th International Symposium on
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Sciences (ISCPMS 2019)
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P. N. Pusey, W. van Megen, P. Bartlett, B. J. Ackerson, J. G. Rarity, S. M. Underwood, "Structure of crystals of hard
colloidal spheres", Physical Review Letters [Phys. Rev. Lett.], vol. 63, no. 25, pp. 2753-2756, Dec 1989, url
https://doi.org/10.1103/PhysRevLett.63.2753.

5. HCP as template for creating pores
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The 5th International Symposium on
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Andreas Stein, "Sphere templating methods for periodic porous solids", Microporous and Mesoporous Materials [Micro-
porous Mesoporous Mater.], vol. 44-45, no., pp. 227-239, Apr 2001, url https://doi.org/10.1016/S1387-1811(01)00189-
5.

6. Strechable film – H(n)CP
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The 5th International Symposium on
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polydimethylsiloxane
(PDMS)
Xin Yan, Jimin Yao, Guang Lu, Xiao Li,
Junhu Zhang, Kun Han, Bai Yang,
"Fabrication of non-close-packed arrays of
colloidal spheres by soft lithography",
Journal of the American Chemical Society
[J. Am. Chem. Soc.], vol. 127, no. 21, pp.
7688-7689, May 2005, url
https://doi.org/10.1021/ja0428208.

7. HCP structure of 1 mm beads
9-10 July 2019
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The 5th International Symposium on
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Andreea Panaitescu, K. Anki Reddy, Arshad Kudrolli, "Nucleation and crystal growth in sheared granular sphere
packings", Physical Review Letters [Phys. Rev. Lett.], vol. 108, no. 10,, p. 108001, Mar 2012, url
https://doi.org/10.1103/PhysRevLett.108.108001.

8. Multi-domain HCP in ~7 mm beads
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Muhammad Iqbal Rahmadhan Putra, Aufa Rudiawan, Wahyuni Andariwulan, Rubén García Berasategui, Sparisoma
Viridi, "Network analysis of the Brazil nut effect phenomenon with a single intruder", IOP Conference Series: Materials
Science and Engineering [IOP Conf. Ser.: Mater. Sci. Eng.], vol. 546, no. 5, p. 052057, Jun 2019, url
https://doi.org/10.1088/1757-899X/546/5/052057.
Disc thickness 3 mm, beads deameter 6.8 mm and
one particle as intruder with diameter of 2.4 cm

9. 9-10 July 2019
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The 5th International Symposium on
Current Progress in Mathematics and
Sciences (ISCPMS 2019)
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Problem

10. 96 million 'shade balls' at LA
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Mashable, "LA throws 96 million 'shade balls' at its water shortage — and it's mesmerizing | Mashable", YouTube,
13.08.2015, url https://www.youtube.com/watch?v=mEmwJzQjwyw [20190710].

11. Question
• How can these spheres form a HCP structure?
• What is the attractive force between two
spheres?
9-10 July 2019
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The 5th International Symposium on
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12. 9-10 July 2019
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Simulation

13. System
• N spheres with diameter σ and density ρi are
floating on the surface of fluid with density ρf
(gravitational and buoyant forces)
• Spheres will be also under influence of drag
force due to fluid viscosity η
• Between two spheres there will be repulsive
and attractive forces
9-10 July 2019
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The 5th International Symposium on
Current Progress in Mathematics and
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14. Considered forces
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.

15. Gravitational force
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The 5th International Symposium on
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.
gG iii

ρπσ6
1
=

16. Buoyant force
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The 5th International Symposium on
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Sciences (ISCPMS 2019)
16
.
( )gzVB fifi

ρ−=

17. Buoyant force (cont.)
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The 5th International Symposium on
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( )
( )[ ] ( )[ ]{ }













≤+
−≤≤+
+−−+−
−≤
=
.
,0
,
,
,
,
2
1
2
1
2
1
3
8
13
3
1
2
12
4
1
2
1
3
6
1
zz
zzz
zzzz
zz
zV
if
ifif
ififi
if
i
fi
σ
σσ
σσσπ
σ
πσ

18. Drag force
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The 5th International Symposium on
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18
.
( )fiifi vvD

−−= σπη3

19. Normal force
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The 5th International Symposium on
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.
ijijNijijNij vrkN ˆˆ ξγξ 

−=

20. Normal force (cont.)
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The 5th International Symposium on
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20
( )[ ]ijjiij r−+= σσξ 2
1
,0max

21. Attractive force
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.

22. Newton’s second law of motion
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23. Numerical integration
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24. 9-10 July 2019
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Results and discussion

25. Simulation parameters
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26. 9-10 July 2019
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mdfhcp.js

27. t = 0 s
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0.5σ 1.5σ

28. t = 1 s
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0.5σ 1.5σ

29. t = 3 s
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0.5σ 1.5σ

30. t = 4 s
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0.5σ 1.5σ

31. t = 6 s
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0.5σ 1.5σ

32. t = 10 s
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The 5th International Symposium on
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0.5σ 1.5σ

33. Contactopy
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The 5th International Symposium on
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0
50
100
150
200
250
300
0 2 4 6 8 10 12 14 16 18 20
C
t

34. 9-10 July 2019
Depok, Indonesia
The 5th International Symposium on
Current Progress in Mathematics and
Sciences (ISCPMS 2019)
34
Summaries

35. Conclusion
• Simulation of floating spheres forming two-
dimensional hexagonal close packed (HCP)
structure has been performed
• Attractive force must be introduced to the
system in order to get the HCP structure
• Origin of this type of force is unknown
9-10 July 2019
Depok, Indonesia
The 5th International Symposium on
Current Progress in Mathematics and
Sciences (ISCPMS 2019)
35

36. Acknowledgements
• The 5th ISCPMS 2019 Committee and FMIPA
Universitas Indonesia for the invitation in
presenting this work
9-10 July 2019
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The 5th International Symposium on
Current Progress in Mathematics and
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37. 9-10 July 2019
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https://osf.io/a3gjv/

38. 9-10 July 2019
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Thank you