We present a continuous pseudo-hard-sphere potential based on a cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). Using this potential one can mimic the volumetric, structural, and dynamic properties of the discontinuous hard-sphere potential over the whole fluid range. The continuous pseudo potential has the advantage that it may be incorporated directly into off-the-shelf molecular-dynamics code, allowing the user to capitalise on existing hardware and software advances. Simulation results for the compressibility factor of the fluid and solid phases of our pseudo hard spheres are presented and compared both to the Carnahan-Starling equation of state of the fluid and published data, the differences being indistinguishable within simulation uncertainty. The specific form of the potential is employed to simulate flexible chains formed from these pseudo hard spheres at contact (pearl-necklace model) for mc = 4, 5, 7, 8, 16, 20, 100, 201, and 500 monomer segments. The compressibility factor of the chains per unit of monomer, mc, approaches a limiting value at reasonably small values, mc < 50, as predicted by Wertheim's first order thermodynamic perturbation theory. Simulation results are also presented for highly asymmetric mixtures of pseudo hard spheres, with diameter ratios of 3:1, 5:1, 20:1 over the whole composition range.

1.
G. W.
Wu
and
R. J.
Sadus
,
AIChE J.
51
,
309
313
(
2005
).
2.
A.
Mulero
,
C.
Galan
, and
F.
Cuadros
,
Phys. Chem. Chem. Phys.
3
,
4991
4999
(
2001
).
3.
S. M.
Waziri
and
E. Z.
Hamad
,
Ind. Eng. Chem. Res.
45
,
7251
7255
(
2006
).
4.
J.
Tian
,
H.
Jiang
,
Y.
Gui
, and
A.
Mulero
,
Phys. Chem. Chem. Phys.
11
,
11213
11218
(
2009
).
5.
A.
Mulero
,
Theory and Simulation of Hard Sphere Fluids and Related Systems
(
Springer
,
Berlin
,
2008
).
6.
T. M.
Reed
and
K. E.
Gubbins
,
Applied Statistical Mechanics
(
MacGraw-Hill
,
New York
,
1973
).
7.
J. A.
Barker
and
D.
Henderson
,
J. Chem. Phys.
47
,
4714
(
1967
).
8.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
,
J. Chem. Phys.
54
,
5237
(
1971
).
10.
L.
Verlet
and
J.-J.
Weis
,
Mol. Phys.
24
,
1013
(
1972
).
11.
M. S.
Wertheim
,
J. Chem. Phys.
87
,
7323
7331
(
1987
).
12.
Y. H.
Song
,
S. M.
Lambert
, and
J. M.
Prausnitz
,
Ind. Eng. Chem. Res.
33
,
1047
1057
(
1994
).
13.
G.
Jackson
,
W. G.
Chapman
, and
K. E.
Gubbins
,
Mol. Phys.
65
,
1
31
(
1988
).
14.
W. G.
Chapman
,
G.
Jackson
, and
K. E.
Gubbins
,
Mol. Phys.
65
,
1057
1079
(
1988
).
15.
W. G.
Chapman
,
K. E.
Gubbins
,
G.
Jackson
, and
M.
Radosz
,
Fluid Phase Equilib.
52
,
31
38
(
1989
).
16.
W. G.
Chapman
,
K. E.
Gubbins
,
G.
Jackson
, and
M.
Radosz
,
Ind. Eng. Chem. Res.
29
,
1709
1721
(
1990
).
17.
N. F.
Carnahan
and
K. E.
Starling
,
J. Chem. Phys.
51
,
635
636
(
1969
).
18.
B. J.
Alder
and
T. E.
Wainwright
,
J. Chem. Phys.
33
,
1439
1451
(
1960
).
19.
L. V.
Woodcock
,
J. Chem. Soc., Faraday Trans.
72
,
731
735
(
1976
).
20.
J. J.
Erpenbeck
and
W. W.
Wood
,
J. Stat. Phys.
35
,
321
340
(
1984
).
21.
T.
Boublík
and
I.
Nezbeda
,
Collect. Czech. Chem. Commun.
51
,
2301
2432
(
1986
).
22.
T.
Boublík
,
Mol. Phys.
59
,
371
380
(
1986
).
23.
K. R.
Hall
,
J. Chem. Phys.
57
,
2252
2254
(
1972
).
24.
E. Z.
Hamad
,
Ind. Eng. Chem. Res.
36
,
4385
4390
(
1997
).
25.
R. J.
Speedy
,
J. Chem. Phys.
100
,
6684
6691
(
1994
).
26.
M. N.
Bannerman
,
L.
Lue
, and
L. V.
Woodcock
,
J. Chem. Phys.
132
,
084507
(
2010
).
27.
T.
Biben
and
J.-P.
Hansen
,
Phys. Rev. Lett.
66
,
2215
2218
(
1991
).
28.
T.
Coussaert
and
M.
Baus
,
Phys. Rev. Lett.
79
,
1881
1884
(
1997
).
29.
T.
Coussaert
and
M.
Baus
,
J. Chem. Phys.
109
,
6012
6020
(
1998
).
30.
M.
Dijkstra
,
R.
van Roij
, and
R.
Evans
,
Phys. Rev. Lett.
81
,
2268
2271
(
1998
).
31.
M.
Dijkstra
,
R.
van Roij
, and
R.
Evans
,
Phys. Rev. E
59
,
5744
5771
(
1999
).
32.
C.
Caccamo
,
G.
Pellicane
,
R.
Ricciari
, and
G.
Faggio
,
J. Phys.: Condens. Matter
12
,
2613
2622
(
2000
).
33.
G.
Jackson
,
J. S.
Rowlinson
, and
F.
van Swol
,
J. Phys. Chem.
91
,
4907
4912
(
1987
).
34.
M. L.
de Haro
and
C. F.
Tejero
,
J. Chem. Phys.
121
,
6918
6921
(
2004
).
35.
A.
Santos
,
S. B.
Yuste
,
M. L.
de Haro
,
M.
Alawneh
, and
D.
Henderson
,
Mol. Phys.
107
,
685
691
(
2009
).
36.
A.
Ayadim
and
S.
Amokrane
,
Phys. Rev. E
74
,
021106
(
2006
).
37.
A.
Takhtoukh
and
C.
Regnaut
,
Fluid Phase Equilib.
262
,
149
156
(
2007
).
38.
P.
Paricaud
,
S.
Varga
, and
G.
Jackson
,
J. Chem. Phys.
118
,
8525
8536
(
2003
).
39.
P.
Paricaud
,
S.
Varga
,
P. T.
Cummings
, and
G.
Jackson
,
Chem. Phys. Lett.
398
,
489
494
(
2004
).
40.
P.
Bryk
,
J. Chem. Phys.
122
,
064902
(
2005
).
41.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulation of Liquids
, 1st ed. (
Oxford University Press
,
Oxford
,
1987
).
42.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation
, 2nd ed. (
Academic
,
London
,
2002
).
43.
J. M.
Haile
,
Molecular Dynamics Simulation
, 1st ed. (
Wiley
,
New York
,
1997
).
44.
D. C.
Rapaport
,
The Art of Molecular Dynamics Simulation
, 2nd ed. (
Cambridge University Press
,
Cambridge
,
2005
).
45.
J. A.
McCormick
,
C. K.
Hall
, and
S. A.
Khan
,
J. Chem. Phys.
122
,
114902
(
2005
).
46.
A. J.
Masters
,
J. Phys.: Condens. Matter
20
,
283102
(
2008
).
47.
B.
Hess
,
C.
Kutzner
,
D.
van der Spoel
, and
E.
Lindahl
,
J. Chem. Theory Comput.
8
,
435
447
(
2008
).
48.
49.
W.
Smith
and
T. R.
Forester
,
J. Mol. Graphics
14
,
136
141
(
1996
).
50.
J. C.
Phillips
,
R.
Braun
,
W.
Wang
,
J.
Gumbart
,
E.
Tajkhorshid
,
E.
Villa
,
C.
Chipot
,
R. D.
Skeel
,
L.
Kale
, and
K.
Schulten
,
J. Comput. Chem.
26
,
1781
1802
(
2005
).
51.
J. E.
Stone
,
J. C.
Phillips
,
P. L.
Freddolino
,
D. J.
Hardy
,
L. G.
Trabuco
, and
K.
Schulten
,
J. Comput. Chem.
28
,
2618
2640
(
2007
).
52.
53.
J. E.
Jones
,
Proc. R. Soc. London, Ser. A
106
,
463
477
(
1924
).
54.
J. E.
Lennard-Jones
,
Phys. Soc.
43
,
461
482
(
1931
).
55.
F.
London
,
Z. Phys. A-Hadron. Nucl.
63
,
245
279
(
1930
).
56.
F.
London
,
Trans. Faraday Soc.
33
,
8
26
(
1937
).
57.
J.
Gao
and
J. H.
Weiner
,
Macromolecules
20
,
2525
2531
(
1987
).
58.
B. F.
Abu-Sharkh
and
E. Z.
Hamad
,
Macromolecules
33
,
1345
1350
(
2000
).
59.
B. F.
Abu-Sharkh
,
Macromolecules
33
,
9437
9443
(
2000
).
60.
D. M.
Heyes
and
H.
Okumura
,
Mol. Simul.
32
,
45
50
(
2006
).
61.
D. M.
Heyes
and
H.
Okumura
,
J. Chem. Phys.
124
,
164507
(
2006
).
62.
J. A.
Barker
and
D.
Henderson
,
Mol. Phys.
21
,
187
191
(
1971
).
63.
D.
Adams
,
Mol. Phys.
28
,
1241
1252
(
1974
).
64.
J. K.
Percus
and
G. J.
Yevick
,
Phys. Rev.
110
,
1
(
1958
).
65.
W. R.
Smith
,
D. J.
Henderson
,
P. J.
Leonard
,
J. A.
Barker
, and
E. W.
Grundke
,
Mol. Phys.
106
,
3
7
(
2008
).
66.
R. J.
Speedy
,
Mol. Phys.
62
,
509
515
(
1987
).
67.
S.
Chapman
and
T. G.
Cowling
,
The Mathematical Theory of Non-uniform Gases
, 3rd ed. (
Cambridge Mathematical Library
,
Cambridge
,
1970
).
68.
D. M.
Heyes
,
M. J.
Cass
,
J. G.
Powles
, and
W. A. B.
Evans
,
J. Phys. Chem. B
111
,
1455
1464
(
2007
).
69.
J. I.
Siepmann
,
Mol. Phys.
70
,
1145
1158
(
1990
).
70.
J. J.
de Pablo
,
M.
Laso
, and
U. W.
Suter
,
J. Chem. Phys.
96
,
2395
2403
(
1992
).
71.
E.
Leontidis
,
J. J.
de Pablo
,
M.
Laso
, and
U. W.
Suter
, “
A critical evaluation of novel algorithms for the off-lattice Monte Carlo simulation of condensed polymer phases
,” in
Atomistic Modeling of Physical Properties, Advances in Polymer Science
(
Springer-Verlag
,
Berlin
,
1994
), Vol. 116, pp.
283
318
.
72.
P. V. K.
Pant
and
D. N.
Theodorou
,
Macromolecules
28
,
7224
7234
(
1995
).
73.
V. G.
Mavrantzas
,
T. D.
Boone
,
E.
Zervopoulou
, and
D. N.
Theodorou
,
Macromolecules
32
,
5072
5096
(
1999
).
74.
L. R.
Dodd
,
T. D.
Boone
, and
D. N.
Theodorou
,
Mol. Phys.
78
,
961
996
(
1993
).
75.
J.
Gao
and
J. H.
Weiner
,
J. Chem. Phys.
90
,
6749
6760
(
1989
).
76.
J. P.
Ryckaert
,
G.
Ciccotti
, and
H. J. C.
Berendsen
,
J. Comput. Phys.
23
,
327
341
(
1977
).
77.
A.
Yethiraj
and
C. K.
Hall
,
Mol. Phys.
80
,
469
477
(
1993
).
78.
J. G.
Curro
,
J. Chem. Phys.
64
,
2496
2500
(
1976
).
79.
R.
Dickman
and
C. K.
Hall
,
J. Chem. Phys.
85
,
4108
4115
(
1986
).
80.
R.
Dickman
and
C. K.
Hall
,
J. Chem. Phys.
89
,
3168
3174
(
1988
).
81.
K. G.
Honnell
and
C. K.
Hall
,
J. Chem. Phys.
90
,
1841
1855
(
1989
).
82.
Y. C.
Chiew
,
Mol. Phys.
70
,
129
143
(
1990
).
83.
K. G.
Honnell
and
C. K.
Hall
,
J. Chem. Phys.
95
,
4481
4501
(
1991
).
84.
E. A.
Müller
and
K. E.
Gubbins
,
Mol. Phys.
80
,
91
101
(
1993
).
85.
E. A.
Müller
and
K. E.
Gubbins
,
Mol. Phys.
80
,
957
976
(
1993
).
86.
D.
Ghonasgi
and
W. G.
Chapman
,
J. Chem. Phys.
100
,
6633
6639
(
1994
).
87.
J.
Chang
and
S. I.
Sandler
,
Chem. Eng. Sci.
49
,
2777
2791
(
1994
).
88.
F. A.
Escobedo
and
J. J.
de Pablo
,
J. Chem. Phys.
103
,
1946
1956
(
1995
).
89.
R. J.
Sadus
,
J. Phys. Chem.
99
,
12363
12366
(
1995
).
90.
R. J.
Sadus
,
Macromolecules
29
,
7212
7216
(
1996
).
91.
R. J.
Sadus
,
AIChE J.
45
,
2454
2457
(
1999
).
92.
K.
Nasrifar
and
O.
Bolland
,
Chem. Eng. Commun.
193
,
1277
1293
(
2006
).
93.
J.
Gao
and
J. H.
Weiner
,
J. Chem. Phys.
91
,
3168
3173
(
1989
).
94.
B. J.
Alder
,
J. Chem. Phys.
40
,
2724
(
1963
).
95.
E. B.
Smith
and
K. R.
Lea
,
Trans. Faraday Soc.
59
,
1535
1543
(
1963
).
96.
J. L.
Lebowitz
,
J. Chem. Phys.
41
,
133
(
1964
).
97.
J. L.
Barrat
,
M.
Baus
, and
J. P.
Hansen
,
Phys. Rev. Lett.
56
,
1063
1065
(
1986
).
98.
W. G. T.
Kranendonk
and
D.
Frenkel
,
Mol. Phys.
72
,
679
697
(
1991
).
99.
M.
Dijkstra
,
R.
van Roij
, and
R.
Evans
,
Phys. Rev. Lett.
82
,
117
120
(
1999
).
100.
M. N.
Bannerman
and
L.
Lue
,
J. Chem. Phys.
130
,
164507
(
2009
).
101.
T.
Boublík
,
J. Chem. Phys.
53
,
471
472
(
1970
).
102.
G. A.
Mansoori
,
N. F.
Carnahan
,
K. E.
Starling
, and
T. W.
Leland
,
J. Chem. Phys.
54
,
1523
1525
(
1971
).
103.
A.
Santos
,
S. B.
Yuste
, and
M. L.
De Haro
,
Mol. Phys.
96
,
1
5
(
1999
).
104.
H.
Hansen-Goos
and
R.
Roth
,
J. Chem. Phys.
124
,
154506
(
2006
).
105.
C.
Barrio
and
J. R.
Solana
,
Physica A
351
,
387
403
(
2005
).
106.
A. J.
Haslam
,
G.
Jackson
, and
T. C. B.
McLeish
,
J. Chem. Phys.
111
,
416
428
(
1999
).
107.
A. J.
Haslam
,
G.
Jackson
, and
T. C. B.
McLeish
,
Macromolecules
32
,
7289
7298
(
1999
).
108.
M.
Laso
and
N. C.
Karayiannis
,
J. Chem. Phys.
128
,
174901
(
2008
).
109.
N. C.
Karayiannis
,
K.
Foteinopoulou
, and
M.
Laso
,
J. Chem. Phys.
130
,
164908
(
2009
).
110.
H.
Fynewever
and
A.
Yethiraj
,
J. Chem. Phys.
108
,
1636
1644
(
1998
).
111.
D. C.
Williamson
and
G.
Jackson
,
J. Chem. Phys.
108
,
10294
10302
(
1998
).
112.
T.
van Westen
,
T. J. H.
Vlugt
, and
J.
Gross
,
J. Chem. Phys.
137
,
044906
(
2012
).
113.
D.
Beeman
,
J. Comput. Phys.
20
,
130
139
(
1976
).
114.
W. G.
Hoover
,
Phys. Rev. A
31
,
1695
1697
(
1985
).
115.
S.
Melchionna
,
G.
Ciccotti
, and
B. L.
Holian
,
Mol. Phys.
78
,
533
544
(
1993
).
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