A novel test-area (TA) technique for the direct simulation of the interfacial tension of systems interacting through arbitrary intermolecular potentials is presented in this paper. The most commonly used method invokes the mechanical relation for the interfacial tension in terms of the tangential and normal components of the pressure tensor relative to the interface (the relation of Kirkwood and Buff [J. Chem. Phys.17, 338 (1949)]). For particles interacting through discontinuous intermolecular potentials (e.g., hard-core fluids) this involves the determination of δ functions which are impractical to evaluate, particularly in the case of nonspherical molecules. By contrast we employ a thermodynamic route to determine the surface tension from a free-energy perturbation due to a test change in the surface area. There are important distinctions between our test-area approach and the computation of a free-energy difference of two (or more) systems with different interfacial areas (the method of Bennett [J. Comput. Phys.22, 245 (1976)]), which can also be used to determine the surface tension. In order to demonstrate the adequacy of the method, the surface tension computed from test-area Monte Carlo (TAMC) simulations are compared with the data obtained with other techniques (e.g., mechanical and free-energy differences) for the vapor-liquid interface of Lennard-Jones and square-well fluids; the latter corresponds to a discontinuous potential which is difficult to treat with standard methods. Our thermodynamic test-area approach offers advantages over existing techniques of computational efficiency, ease of implementation, and generality. The TA method can easily be implemented within either Monte Carlo (TAMC) or molecular-dynamics (TAMD) algorithms for different types of interfaces (vapor-liquid, liquid-liquid, fluid-solid, etc.) of pure systems and mixtures consisting of complex polyatomic molecules.

1.
J. S.
Rowlinson
and
B.
Widom
,
Molecular Theory of Capillarity
(
Clarendon
, Oxford,
1982
).
2.
D.
Henderson
,
Fundamentals of Inhomogeneous Fluids
(
Dekker
, New York,
1992
).
3.
H. T.
Davis
,
Statistical Mechanics of Phases, Interfaces, and Thin Films
(
VCH
, Weinheim,
1996
).
4.
J. D.
van der Waals
,
Z. Phys. Chem.
13
,
657
(
1894
);
English translation,
J. S.
Rowlinson
,
J. Stat. Phys.
20
,
197
(
1979
).
5.
D.
Nicholson
and
N. G.
Parsonage
,
Computer Simulation and the Statistical Mechanics of Adsorption
(
Academic
, London,
1982
).
6.
J. C.
Shelley
and
M. Y.
Shelley
,
Curr. Opin. Colloid Interface Sci.
5
,
101
(
2000
).
7.
D. J.
Tobias
,
K. C.
Tu
, and
M. L.
Klein
,
Curr. Opin. Colloid Interface Sci.
2
,
15
(
1997
).
8.
L.
Saiz
and
M. L.
Klein
,
Acc. Chem. Res.
35
,
482
(
2002
).
9.
E. Martín
del Río
and
E.
de Miguel
,
Phys. Rev. E
55
,
2916
(
1997
).
10.
M.
Bates
and
C.
Zannoni
,
Chem. Phys. Lett.
280
,
40
(
1997
).
11.
S. J.
Mills
,
C. M.
Care
,
M. P.
Neal
, and
D. J.
Cleaver
,
Phys. Rev. E
58
,
3284
(
1998
).
12.
E.
de Miguel
and
E. Martín
del Río
,
Int. J. Mod. Phys. C
10
,
431
(
1999
).
13.
N.
Akino
,
F.
Schmid
, and
M. P.
Allen
,
Phys. Rev. E
63
,
041706
(
2001
).
14.
A.
Galindo
,
A. J.
Haslam
,
S.
Varga
,
G.
Jackson
,
A.
Vanakaras
,
D. J.
Photinos
, and
D. A.
Dunmur
,
J. Chem. Phys.
119
,
5216
(
2003
).
15.
J.
Winkelmann
,
J. Phys.: Condens. Matter
13
,
4739
(
2001
).
16.
G. J.
Gloor
,
G.
Jackson
,
F. J.
Blas
,
E. Martín
del Río
, and
E.
de Miguel
,
J. Chem. Phys.
121
,
12740
(
2004
).
17.
J. G.
Kirkwood
and
F. P.
Buff
,
J. Chem. Phys.
17
,
338
(
1949
).
18.
C. H.
Bennett
,
J. Comput. Phys.
22
,
245
(
1976
).
19.
20.
F. P.
Buff
,
R. A.
Lovett
, and
F. H.
Stillinger
 Jr.
,
Phys. Rev. Lett.
15
,
621
(
1965
).
21.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulation of Liquids
(
Clarendon
, Oxford,
1987
).
22.
C. A.
Croxton
and
R. P.
Ferrier
,
J. Phys. C
4
,
2447
(
1971
).
23.
H. J.
Leamy
,
G. H.
Gilmer
,
K. A.
Jackson
, and
P.
Bennema
,
Phys. Rev. Lett.
30
,
601
(
1973
).
24.
J. K.
Lee
,
J. A.
Barker
, and
G. M.
Pound
,
J. Chem. Phys.
60
,
1976
(
1974
).
25.
K. S.
Liu
,
J. Chem. Phys.
60
,
4226
(
1974
).
26.
J.
Miyazaki
,
J. A.
Barker
, and
G. M.
Pound
,
J. Chem. Phys.
64
,
3364
(
1976
).
27.
A. C.L.
Opitz
,
Phys. Lett. A
47
,
439
(
1974
).
28.
F. F.
Abraham
,
D. E.
Schreiber
, and
J. A.
Barker
,
J. Chem. Phys.
62
,
1958
(
1975
).
29.
G. A.
Chapela
,
G.
Saville
, and
J. S.
Rowlinson
,
Faraday Discuss. Chem. Soc.
59
,
22
(
1975
).
30.
M.
Rao
and
D.
Levesque
,
J. Chem. Phys.
65
,
3233
(
1976
).
31.
G. A.
Chapela
,
G.
Saville
,
S. M.
Thompson
, and
J. S.
Rowlinson
,
J. Chem. Soc., Faraday Trans. 2
73
,
1133
(
1977
).
32.
L.-J.
Chen
,
J. Chem. Phys.
103
,
10214
(
1995
).
33.
C. D.
Holcomb
,
P.
Clancy
, and
J. A.
Zollweg
,
Mol. Phys.
78
,
437
(
1993
).
34.
A.
Trokhymchuk
and
J.
Alejandre
,
J. Chem. Phys.
111
,
8510
(
1999
).
35.
M.
Matsumoto
and
Y.
Kataoka
,
J. Chem. Phys.
88
,
3233
(
1988
).
36.
J.
Alejandre
,
D. J.
Tildesley
, and
G. A.
Chapela
,
J. Chem. Phys.
102
,
4574
(
1995
).
37.
T.-M.
Chang
,
K. A.
Peterson
, and
L. X.
Dang
,
J. Chem. Phys.
103
,
7502
(
1995
).
38.
Y. L.
Yea
,
C.
Zhang
,
H.
Held
,
A. M.
Mebel
,
X.
Wei
,
S. H.
Lin
, and
Y. R.
Shen
,
J. Chem. Phys.
114
,
1837
(
2001
).
39.
F.
Goujon
,
P.
Malfreyt
,
A.
Boutin
, and
A. H.
Fuchs
,
J. Chem. Phys.
116
,
8106
(
2002
).
40.
J. P.
Nicolas
and
B.
Smit
,
Mol. Phys.
100
,
2471
(
2002
).
41.
P.
Smith
,
R. M.
Lynden-Bell
,
J. C.
Earnshaw
, and
W.
Smith
,
Mol. Phys.
96
,
249
(
1999
).
42.
J. G.
Harris
,
J. Phys. Chem.
96
,
5077
(
1992
).
43.
44.
J. R.
Henderson
and
F.
van Swol
,
Mol. Phys.
56
,
1313
(
1985
).
45.
P.
Orea
,
Y.
Duda
, and
J.
Alejandre
,
J. Chem. Phys.
118
,
5635
(
2003
).
46.
P.
Orea
,
Y.
Duda
,
V. C.
Weiss
,
W.
Schröer
, and
J.
Alejandre
,
J. Chem. Phys.
120
,
11754
(
2004
).
47.
J. K.
Singh
,
D. A.
Kofke
, and
J. R.
Errington
,
J. Chem. Phys.
119
,
3405
(
2003
).
48.
J. H.
Irving
and
J. G.
Kirkwood
,
J. Chem. Phys.
18
,
817
(
1950
).
49.
P.
Schofield
and
J. R.
Henderson
,
Proc. R. Soc. London, Ser. A
379
,
231
(
1982
).
50.
J. P.
-
Hansen
and
I. R.
McDonald
,
Theory of Simple Liquids
, 2nd ed. (
Academic
, London,
1986
).
51.
A.
Harasima
,
J. Phys. Soc. Jpn.
8
,
343
(
1953
).
52.
J. P.R.B.
Walton
,
D. J.
Tildesley
,
J. S.
Rowlinson
, and
J. R.
Henderson
,
Mol. Phys.
48
,
1357
(
1983
).
53.
N. N.
Bogoliubov
,
J. Phys. (USSR)
10
,
256
265
(
1946
).
54.
H. S.
Green
,
Proc. R. Soc. London, Ser. A
189
,
103
(
1947
).
55.
F. P.
Buff
,
Z. Elektrochem.
56
,
311
(
1952
).
56.
A. G.
McLellan
,
Proc. R. Soc. London, Ser. A
213
,
274
(
1952
);
A. G.
McLellan
,
Proc. R. Soc. London, Ser. A
217
,
92
(
1953
).
57.
E.
Salomons
and
M.
Mareschal
,
J. Phys.: Condens. Matter
3
,
3645
(
1991
).
58.
D.
Duque
and
L. F.
Vega
,
J. Chem. Phys.
121
,
8611
(
2004
).
59.
D. A.
Kofke
and
P. T.
Cummings
,
Mol. Phys.
92
,
973
(
1997
).
60.
D. A.
Kofke
and
P. T.
Cummings
,
Fluid Phase Equilib.
150
,
41
(
1998
).
61.
M. P.
Moody
and
P.
Attard
,
J. Chem. Phys.
120
,
1892
(
2004
).
62.
K. K.
Mon
and
D.
Jasnow
,
Phys. Rev. A
30
,
670
(
1984
).
63.
K. K.
Mon
and
D.
Jasnow
,
Phys. Rev. A
31
,
4008
(
1985
).
64.
J.
Potvin
and
C.
Rebbi
,
Phys. Rev. Lett.
62
,
3062
(
1989
).
65.
H.
Gausterer
,
J.
Potvin
,
C.
Rebbi
, and
S.
Sanielevici
,
Physica A
192
,
525
(
1993
).
66.
J. E.
Hunter
 III
,
W. P.
Reinhardt
, and
T. F.
Davis
,
J. Chem. Phys.
99
,
6856
(
1993
).
67.
M.
Hasenbusch
,
J. Phys. I (France)
3
,
753
(
1993
).
68.
L. D.
Landau
and
E. M.
Lifshitz
,
Statistical Physics
, 3rd ed. (
Pergamon
, London,
1980
).
69.
R. M.
Lynden-Bell
,
Mol. Phys.
86
,
1353
(
1995
).
70.
B. A.
Berg
and
T.
Neuhaus
,
Phys. Rev. Lett.
68
,
9
(
1992
).
71.
W.
Janke
,
B. A.
Berg
, and
M.
Katoot
,
Nucl. Phys. B
382
,
649
(
1992
).
72.
B. A.
Berg
,
U.
Hansmann
, and
T.
Neuhaus
,
Phys. Rev. B
47
,
497
(
1993
).
73.
B. A.
Berg
,
U.
Hansmann
, and
T.
Neuhaus
,
Z. Phys. B: Condens. Matter
90
,
229
(
1993
).
74.
A.
Billoire
,
T.
Neuhaus
, and
B. A.
Berg
,
Nucl. Phys. B
413
,
795
(
1994
).
75.
T. S.
Jain
and
J. J.
de Pablo
,
J. Chem. Phys.
118
,
4226
(
2003
).
76.
J. S.
van Duijneveldt
and
D.
Frenkel
,
J. Chem. Phys.
96
,
4655
(
1992
).
77.
R. M.
Lynden-Bell
,
J. S.
van Duijneveldt
, and
D.
Frenkel
,
Mol. Phys.
80
,
801
(
1993
).
78.
R.
Allen
,
S.
Melchionna
, and
J.-P.
Hansen
,
Phys. Rev. Lett.
89
,
175502
(
2002
).
79.
R.
Allen
,
S.
Melchionna
, and
J.-P.
Hansen
,
J. Chem. Phys.
119
,
3905
(
2003
).
80.
J. E.
Hunter
 III
and
W. P.
Reinhardt
,
J. Chem. Phys.
103
,
8627
(
1995
).
81.
J. J.
Potoff
and
A. Z.
Panagiotopoulos
,
J. Chem. Phys.
112
,
6411
(
2000
).
82.
J. R.
Errington
,
Phys. Rev. E
67
,
012102
(
2003
).
83.
J. Y.
Lee
and
J. M.
Kosterlitz
,
Phys. Rev. Lett.
65
,
137
(
1990
).
84.
G. M.
Torrie
and
J. P.
-
Valleau
,
Chem. Phys. Lett.
28
,
578
(
1974
).
85.
J. D.
Weeks
,
J. Chem. Phys.
67
,
3106
(
1977
).
86.
D.
Bedeaux
and
J. D.
Weeks
,
J. Chem. Phys.
82
,
972
(
1985
).
87.
M. P.
Gelfand
, and
M. E.
Fisher
,
Physica A
166
,
1
(
1990
).
88.
B.
Widom
,
J. Chem. Phys.
39
,
2808
(
1963
).
89.
H. C.
Longuet-Higgins
,
Proc. R. Soc. London, Ser. A
205
,
247
(
1951
).
90.
J. A.
Barker
,
J. Chem. Phys.
19
,
1430
(
1951
).
91.
J. A.
Barker
,
Proc. R. Soc. London, Ser. A
219
,
367
(
1953
).
92.
J. A.
Pople
,
Proc. R. Soc. London, Ser. A
215
,
67
(
1952
).
93.
J. A.
Pople
,
Proc. R. Soc. London, Ser. A
221
,
498
(
1954
).
94.
R. W.
Zwanzig
,
J. Chem. Phys.
22
,
1420
(
1954
).
95.
J. L.
Jackson
and
L. S.
Klein
,
Phys. Fluids
7
,
228
(
1964
).
96.
E.
Byckling
,
Physica (Amsterdam)
27
,
1030
(
1961
).
97.
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
, 9th ed., edited by
M.
Abramowitz
and
I. A.
Stegun
(
Dover
, New York,
1972
), pp.
877
878
.
98.
E.
de Miguel
and
G.
Jackson
(unpublished).
99.
R.
Eppenga
and
D.
Frenkel
,
Mol. Phys.
52
,
1303
(
1984
).
100.
V. I.
Harismiadis
,
J.
Vorholz
, and
A. Z.
Panagiotopoulos
,
J. Chem. Phys.
105
,
8469
(
1996
).
101.
A.
Provota
,
V. D.
Prassas
, and
D. N.
Theodorou
,
J. Chem. Phys.
107
,
5125
(
1997
).
102.
G. J.
Gloor
, Ph.D. thesis,
Imperial College London
,
2003
.
103.
E. A.
Guggenheim
,
J. Chem. Phys.
13
,
253
(
1945
).
104.
N. B.
Wilding
,
Phys. Rev. E
52
,
602
(
1995
).
105.
J. J.
Potoff
and
A. Z.
Panagiotopoulos
,
J. Chem. Phys.
109
,
10914
(
1998
).
106.
F.
del Río
,
E.
Ávalos
,
R.
Espíndola
,
L. F.
Rull
,
G.
Jackson
, and
S.
Lago
,
Mol. Phys.
100
,
2531
(
2002
).
You do not currently have access to this content.