We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin - a quasi-spherical protein.

1.
A.
Patti
and
M.
Dijkstra
,
Phys. Rev. Lett.
102
,
128301
(
2009
).
2.
J.
Israelachvili
,
Intermolecular and Surface Forces
(
Academic
,
San Diego, CA
,
1992
).
3.
Z.
Tang
,
Z.
Zhang
,
Y.
Wang
,
S. C.
Glotzer
, and
N.
Kotov
,
Science
314
,
274
(
2006
).
4.
T.
Liu
 et al.,
J. Am. Chem. Soc.
128
,
15914
(
2006
).
5.
S.-T.
Yau
and
P. G.
Vekilov
,
Nature (London)
406
,
494
(
2000
).
7.
Z.
Zhang
and
S. C.
Glotzer
,
Nano Lett.
4
,
1407
(
2004
).
10.
P. D.
Hempstead
 et al.,
J. Mol. Biol.
268
,
424
(
1997
).
11.
Analysis of the crystallographic data of POM {Mo72×30; X = Fe3+} (from Cambridge Crystallographic Data Centre No – 132027) reveals that the distance between the oxygen atoms of the water molecules bound to the linker molecules between two neighbouring POMs lies in the range of 2.7 – 2.9 A, which implies hydrogen bonding interactions.
12.
E. G.
Noya
,
C.
Vega
,
J. P. K.
Doye
, and
A. A.
Louis
,
J. Chem. Phys.
127
,
054501
(
2007
).
13.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulation of Liquids
(
Oxford University Press
,
New York
,
1987
).
14.
E.
Mani
,
E.
Sanz
,
P. G.
Bolhuis
, and
W. K.
Kegel
,
J. Phys. Chem. C
114
,
7780
(
2010
).
15.
S. J.
Veen
 et al., (To be submitted).
16.
A. A.
Verhoeff
 et al.,
Phys. Rev. Lett.
99
,
066104
(
2007
).
17.
See supplementary material at http://dx.doi.org/10.1063/1.3702203 for the phase diagrams of patchy particles (SM Figs. 1 and 2).

Supplementary Material

You do not currently have access to this content.