Hard-sphere fluids confined between parallel plates at a distance D apart are studied for a wide range of packing fractions including also the onset of crystallization, applying Monte Carlo simulation techniques and density functional theory. The walls repel the hard spheres (of diameter σ) with a Weeks-Chandler-Andersen (WCA) potential VWCA(z) = 4ε[(σw/z)12 − (σw/z)6 + 1/4], with range σw = σ/2. We vary the strength ε over a wide range and the case of simple hard walls is also treated for comparison. By the variation of ε one can change both the surface excess packing fraction and the wall-fluid (γwf) and wall-crystal (γwc) surface free energies. Several different methods to extract γwf and γwc from Monte Carlo (MC) simulations are implemented, and their accuracy and efficiency is comparatively discussed. The density functional theory (DFT) using fundamental measure functionals is found to be quantitatively accurate over a wide range of packing fractions; small deviations between DFT and MC near the fluid to crystal transition need to be studied further. Our results on density profiles near soft walls could be useful to interpret corresponding experiments with suitable colloidal dispersions.

1.
L. Antl. J.
Goodwin
,
R.
Hill
,
R.
Otterwil
, and
J.
Waters
,
Colloids Surf.
17
,
67
(
1986
).
2.
A. van
Blaaderen
and
A.
Vrij
,
Langmuir
8
,
2921
(
1992
).
3.
A.
Yethiraj
and
A. van
Blaaderen
,
Nature (London)
421
,
513
(
2003
).
4.
S. M.
Ilett
,
A.
Orrock
,
W. C. K.
Poon
, and
P. N.
Pusey
,
Phys. Rev. E
51
,
1344
(
1995
).
5.
K. N.
Pham
,
A. M.
Puertas
,
J.
Bergenholtz
,
S. U.
Egelhaaf
,
A.
Moussaïd
,
P. N.
Pusey
,
A. B.
Schofield
,
M. E.
Cates
,
M.
Fuchs
, and
W. C. K.
Poon
,
Science
296
,
104
(
2002
).
6.
A.
Kozina
,
P.
Diaz-Leyva
,
E.
Bartsch
, and
T.
Palberg
, preprint.
7.
U.
Gasser
,
E. R.
Weeks
,
A.
Schofield
,
P. N.
Pusey
, and
D. A.
Weitz
,
Science
292
,
258
(
2001
).
8.
R. P.A.
Dullens
,
D. G. A. L.
Aarts
, and
W. K.
Kegel
,
Phys. Rev. Lett.
97
,
228301
(
2006
).
9.
S.
Egelhaaf
, December
2010
, private communication.
10.
J.
Hernandez-Guzman
and
E. R.
Weeks
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
15198
(
2009
).
11.
B. J.
Alder
and
T. E.
Wainwright
,
J. Chem. Phys.
27
,
1208
(
1957
).
12.
W. W.
Wood
and
J. D.
Jacobsen
,
J. Chem. Phys.
27
,
1207
(
1957
).
13.
W. G.
Hoover
and
F. H.
Ree
,
J. Chem. Phys.
49
,
3609
(
1968
).
14.
W.
Lechner
,
C.
Dellago
and
P. G.
Bolhuis
,
Phys. Rev. Lett.
106
,
085701
(
2011
).
15.
D.
Courtemanche
and
F.
van Swol
,
Phys. Rev. Lett.
69
,
2078
(
1992
).
16.
D.
Courtemanche
and
F.
van Swol
,
Mol. Phys.
80
,
861
(
1993
).
17.
M.
Schmidt
and
H.
Löwen
,
Phys. Rev. Lett.
76
,
4552
(
1996
).
18.
M.
Schmidt
and
H.
Löwen
,
Phys. Rev. E
55
,
7228
(
1997
).
19.
M.
Heni
and
H.
Löwen
,
Phys. Rev. E
60
,
7057
(
1999
).
20.
R.
Zangi
and
S. A.
Rice
,
Phys. Rev. E
61
,
660
, (
2000
).
21.
W.
Kegel
,
J. Chem. Phys.
115
,
6538
(
2001
).
22.
R.
Messina
and
H.
Löwen
,
Phys. Rev. Lett.
91
,
146101
(
2003
).
23.
S.
Auer
and
D.
Frenkel
,
Phys. Rev. Lett.
91
,
015703
(
2003
).
24.
M.
Dijkstra
,
Phys. Rev. Lett.
93
,
108303
(
2004
).
25.
A.
Fortini
and
M.
Dijkstra
,
J. Phys.: Condens. Matter
18
,
L371
(
2006
).
26.
R.
Messina
and
H.
Löwen
,
Phys. Rev. E
73
,
041405
(
2006
).
27.
E.
De Miguel
and
G.
Jackson
,
Mol. Phys.
104
,
3717
(
2006
).
28.
B. B.
Laird
and
R. L.
Davidchack
,
J. Phys. Chem. C
111
,
15952
(
2007
).
29.
R. L.
Davidchack
,
J. R.
Morris
and
B. B.
Laird
,
J. Chem. Phys.
125
,
094710
(
2006
).
30.
B. B.
Laird
and
R. L.
Davidchack
,
J. Chem. Phys.
132
,
204101
(
2010
).
31.
D. H.
Napper
,
Polymeric Stabilization of Colloidal Dispersions
(
Academic
,
London
,
1983
).
32.
Polymer Adsorption and Dispersion Stability, ACS Symp. Ser. 240
, edited by
E.
Goddard
and
B.
Vincent
(
ACS
,
Washington
,
1984
).
33.
J. D.
Weeks
,
D.
Chandler
and
H. C.
Andersen
,
J. Chem. Phys.
54
,
5237
(
1971
).
34.
D. P.
Landau
and
K.
Binder
,
A Guide to Monte Carlo Simulation in Statistical Physics
, 3rd ed. (
Cambridge University Press
,
Cambridge
,
2009
).
35.
J. S.
Rowlinson
and
B.
Widom
,
Molecular Theory of Capillarity
(
Clarendon
,
Oxford
,
1982
).
36.
J. P.
Hansen
and
I. R.
McDonald
,
Theory of Simple Liquids
, 3rd ed. (
Academic
,
New York
,
2006
).
37.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
, 2nd ed. (
Academic
,
San Diego, CA
,
2002
).
38.
F.
Varnik
,
Comput. Phys. Commun.
149
,
61
(
2002
).
39.
S. K.
Das
and
K.
Binder
,
Europhys. Lett.
92
,
26006
(
2010
).
40.
F.
Wang
and
D. P.
Landau
,
Phys. Rev. Lett.
86
,
2050
(
2001
).
41.
F.
Wang
and
D. P.
Landau
,
Phys. Rev. E
64
,
056101
(
2001
).
42.
A.
Winkler
, Dissertation (Johannes Gutenberg-Universität Mainz, unpublished).
43.
T.
Zykova-Timan
,
J.
Horbach
, and
K.
Binder
,
J. Chem. Phys.
133
,
014705
(
2010
).
44.
R. L.
Davidchack
,
J. Chem. Phys.
133
,
234701
(
2010
).
45.
T. M.
Truskett
,
S.
Torquato
,
S.
Sastry
,
P. G.
Debenedetti
, and
F. H.
Stillinger
,
Phys. Rev. E
58
,
3083
(
1998
).
46.
H.
Hansen–Goos
and
R.
Roth
,
J. Phys.: Condens. Matter
18
,
8413
(
2006
).
47.
P.-M.
König
,
R.
Roth
and
K. R.
Mecke
,
Phys. Rev. Lett.
93
,
160601
(
2004
).
48.
P.
Tarazona
,
Phys. Rev. Lett.
84
,
694
(
2000
).
49.
M.
Oettel
,
S.
Görig
,
A.
Härtel
,
H.
Löwen
,
M.
Radu
, and
T.
Schilling
,
Phys. Rev. E
82
,
051404
(
2010
).
50.
V.
Botan
,
F.
Pesth
,
T.
Schilling
, and
M.
Oettel
,
Phys. Rev. E
79
,
061402
(
2009
).
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