We report on a computer simulation and integral equation study of a simple model of patchy spheres, each of whose surfaces is decorated with two opposite attractive caps, as a function of the fraction χ of covered attractive surface. The simple model explored—the two-patch Kern–Frenkel model—interpolates between a square-well and a hard-sphere potential on changing the coverage χ. We show that integral equation theory provides quantitative predictions in the entire explored region of temperatures and densities from the square-well limit χ=1.0 down to χ0.6. For smaller χ, good numerical convergence of the equations is achieved only at temperatures larger than the gas-liquid critical point, where integral equation theory provides a complete description of the angular dependence. These results are contrasted with those for the one-patch case. We investigate the remaining region of coverage via numerical simulation and show how the gas-liquid critical point moves to smaller densities and temperatures on decreasing χ. Below χ0.3, crystallization prevents the possibility of observing the evolution of the line of critical points, providing the angular analog of the disappearance of the liquid as an equilibrium phase on decreasing the range for spherical potentials. Finally, we show that the stable ordered phase evolves on decreasing χ from a three-dimensional crystal of interconnected planes to a two-dimensional independent-planes structure to a one-dimensional fluid of chains when the one-bond-per-patch limit is eventually reached.

1.
J.
Lyklema
,
Fundamentals of Interface and Colloid Science
(
Academic
,
London
,
1991
), Vol.
I
.
2.
V. N.
Manoharan
,
M. T.
Elsesser
, and
D. J.
Pine
,
Science
301
,
483
(
2003
).
3.
A.
Lomakin
,
N.
Asherie
, and
G. B.
Benedek
,
Proc. Natl. Acad. Sci. U.S.A.
96
,
9465
(
1999
).
4.
J. J.
McManus
,
A.
Lomakin
,
O.
Ogun
,
A.
Pande
,
M.
Basan
,
J.
Pande
, and
G. B.
Benedek
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
16856
(
2007
).
5.
H.
Liu
,
S. K.
Kumar
, and
F.
Sciortino
,
J. Chem. Phys.
127
,
084902
(
2007
).
6.
G. W.
Robinson
,
S.
Singh
,
S. -B.
Zhu
, and
M. W.
Evans
,
Water in Biology, Chemistry and Physics
(
World Scientific
,
Singapore
,
1996
).
7.
G. A.
Jeffrey
,
An Introduction to Hydrogen Bonding
(
Oxford
,
New York
,
1997
).
9.
S. C.
Glotzer
and
M. J.
Solomon
,
Nat. Mater.
6
,
557
(
2007
).
10.
E.
Bianchi
,
J.
Largo
,
P.
Tartaglia
,
E.
Zaccarelli
, and
F.
Sciortino
,
Phys. Rev. Lett.
97
,
168301
(
2006
).
11.
A. W.
Wilber
,
J. P. K.
Doye
, and
A. A.
Louis
,
J. Chem. Phys.
131
,
175101
(
2009
).
12.
A. B.
Pawar
and
I.
Kretzschmar
,
Macromol. Rapid Commun.
31
,
150
(
2010
).
13.
E.
Bianchi
,
P.
Tartaglia
,
E.
La Nave
, and
F.
Sciortino
,
J. Phys. Chem. B
111
,
11765
(
2007
).
14.
W. G.
Chapman
,
G.
Jackson
, and
K. E.
Gubbins
,
Mol. Phys.
65
,
1057
(
1988
).
15.
N.
Kern
and
D.
Frenkel
,
J. Chem. Phys.
118
,
9882
(
2003
).
16.
M. S.
Wertheim
,
J. Stat. Phys.
35
,
19
(
1984
).
17.
R.
Fantoni
,
D.
Gazzillo
,
A.
Giacometti
,
M. A.
Miller
, and
G.
Pastore
,
J. Chem. Phys.
127
,
234507
(
2007
).
18.
G.
Foffi
and
F.
Sciortino
,
J. Phys. Chem. B
111
,
9702
(
2007
).
19.
C.
Gögelein
,
G.
Nägele
,
R.
Tuinier
,
T.
Gibaud
,
A.
Stradner
, and
P.
Schurtenberger
,
J. Chem. Phys.
129
,
085102
(
2008
).
20.
A.
Giacometti
,
F.
Lado
,
J.
Largo
,
G.
Pastore
, and
F.
Sciortino
,
J. Chem. Phys.
131
,
174114
(
2009
).
21.
C. G.
Gray
and
K. E.
Gubbins
,
Theory of Molecular Fluids
(
Clarendon
,
Oxford
,
1984
), Vol.
1
.
22.
J. P.
Hansen
and
I. R.
McDonald
,
Theory of Simple Liquids
(
Academic
,
New York
,
1986
).
25.
F.
Lado
,
Phys. Lett.
89A
,
196
(
1982
).
26.
A.
Walther
and
A. H. E.
Müller
,
Soft Matter
4
,
663
(
2008
).
27.
J.
Russo
,
P.
Tartaglia
, and
F.
Sciortino
,
J. Chem. Phys.
131
,
014504
(
2009
).
28.
F.
Sciortino
,
A.
Giacometti
, and
G.
Pastore
,
Phys. Rev. Lett.
103
,
237801
(
2009
).
29.
F.
Sciortino
,
E.
Bianchi
,
J. F.
Douglas
, and
P.
Tartaglia
,
J. Chem. Phys.
126
,
194903
(
2007
).
30.
L.
Verlet
and
J. J.
Weis
,
Phys. Rev. A
5
,
939
(
1972
).
31.
D.
Henderson
and
E. W.
Grundke
,
J. Chem. Phys.
63
,
601
(
1975
).
32.
A.
Giacometti
,
G.
Pastore
, and
F.
Lado
,
Mol. Phys.
107
,
555
(
2009
).
33.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
(
Academic
,
San Diego
,
2002
).
34.
L.
Vega
,
E.
de Miguel
,
L. F.
Rull
,
G.
Jackson
, and
I. A.
McLure
,
J. Chem. Phys.
96
,
2296
(
1992
).
35.
G.
Orkoulas
and
A. Z.
Panagiotopoulos
,
J. Chem. Phys.
110
,
1581
(
1999
).
36.
N. B.
Wilding
J. Phys: Condens. Matter
9
,
585
(
1997
).
37.
L.
Belloni
,
J. Chem. Phys.
98
,
8080
(
1993
).
38.
E. B.
El Mendoub
,
J. -F.
Wax
,
I.
Charpentier
, and
N.
Jakse
,
Mol. Phys.
106
,
2667
(
2008
).
39.
M.
Ley-Koo
and
M. S.
Green
,
Phys. Rev. A
16
,
2483
(
1977
).
40.
J. M. H.
Levelt Sengers
and
J. V.
Sengers
, in
Perspectives in Statistical Physics
, edited by
H. J.
Raveché
(
North-Holland
,
Amsterdam
,
1981
), Chap. 14.
41.
J. -H.
Chen
,
M. E.
Fisher
, and
B. G.
Nickel
,
Phys. Rev. Lett.
48
,
630
(
1982
).
42.
G. A.
Vliegenthart
and
H. N. W.
Lekkerkerker
,
J. Chem. Phys.
112
,
5364
(
2000
).
43.
D. L.
Pagan
and
J. D.
Gunton
,
J. Chem. Phys.
122
,
184515
(
2005
).
44.
H.
Liu
,
S.
Garde
, and
S.
Kumar
,
J. Chem. Phys.
123
,
174505
(
2005
).
45.
J. J.
Weis
and
D.
Levesque
,
Phys. Rev. E
48
,
3728
(
1993
).
46.
G.
Ganzenmüller
and
P. J.
Camp
,
J. Chem. Phys.
126
,
191104
(
2007
).
47.
F.
Lado
,
E.
Lomba
, and
J. J.
Weis
,
Phys. Rev. E
58
,
3478
(
1998
).
48.
G.
Pastore
,
A.
Giacometti
, and
F.
Sciortino
, “
A numerical study of one-patch colloidal particles: From square-well to Janus
,”
Phys. Chem. Chem. Phys. (submitted).
49.
L.
Hong
,
A.
Cacciuto
,
E.
Luijten
, and
S.
Granick
,
Langmuir
24
,
621
(
2008
).
50.
E.
Zaccarelli
,
S. V.
Buldyrev
,
E.
La Nave
,
A. J.
Moreno
,
I.
Saika-Voivod
,
F.
Sciortino
, and
P.
Tartaglia
,
Phys. Rev. Lett.
94
,
218301
(
2005
).
51.
A.
Giacometti
,
D.
Gazzillo
,
G.
Pastore
, and
T. K.
Das
,
Phys. Rev. E
71
,
031108
(
2005
).
52.
A.
George
and
W. W.
Wilson
,
Acta Crystallogr., Sect. D: Biol. Crystallogr.
50
,
361
(
1994
).
53.
O.
Galkin
,
K.
Chen
,
R. L.
Nagel
,
R. E.
Hirsch
, and
P. G.
Vekilov
,
Proc. Natl. Acad. Sci. U.S.A.
99
,
8479
(
2002
).
54.
W. A.
Eaton
and
J.
Hofrichter
,
Adv. Protein Chem.
40
,
63
(
1990
).
55.
Some authors omit the 4π prefactor in this expansion. For instance, our g(r;l1l2l) are related to the g(l1l2l;r) appearing in Ref. 21 by g(l1l2l;r)=4πg(r;l1l2l).
56.
G.
Stell
,
G. N.
Patey
, and
J. S.
Høye
,
Adv. Chem. Phys.
48
,
183
(
1981
) (See Appendix B.).
You do not currently have access to this content.