Within mean field theory, we investigate the bridging transition between a pair of parallel cylindrical colloids immersed in a binary liquid mixture as a solvent that is close to its critical consolute point Tc. We determine the universal scaling functions of the effective potential and of the force between the colloids. For a solvent that is at the critical concentration and close to Tc, we find that the critical Casimir force is the dominant interaction at close separations. This agrees very well with the corresponding Derjaguin approximation for the effective interaction between the two cylinders, while capillary forces originating from the extension of the liquid bridge turn out to be more important at large separations. In addition, we are able to infer from the wetting characteristics of the individual colloids the first-order transition of the liquid bridge connecting two colloidal particles to the ruptured state. While specific to cylindrical colloids, the results presented here also provide an outline for identifying critical Casimir forces acting on bridged colloidal particles as such and for analyzing the bridging transition between them.

1.
H.
Casimir
,
Proc. K. Ned. Akad. Wet.
51
,
793
(
1948
).
2.
R.
Garcia
and
M. H. W.
Chan
,
Phys. Rev. Lett.
83
,
1187
(
1999
).
3.
A.
Ganshin
,
S.
Scheidemantel
,
R.
Garcia
, and
M. H. W.
Chan
,
Phys. Rev. Lett.
97
,
075301
(
2006
).
4.
M.
Fukuto
,
Y. F.
Yano
, and
P. S.
Pershan
,
Phys. Rev. Lett.
94
,
135702
(
2005
).
5.
R.
Garcia
and
M. H. W.
Chan
,
Phys. Rev. Lett.
88
,
086101
(
2002
).
6.
T.
Ueno
,
S.
Balibar
,
T.
Mizusaki
,
F.
Caupin
, and
E.
Rolley
,
Phys. Rev. Lett.
90
,
116102
(
2003
).
7.
M. E.
Fisher
and
P. G.
de Gennes
,
C. R. Acad. Sci. Paris Ser. B
287
,
207
(
1978
).
8.
M.
Krech
and
S.
Dietrich
,
Phys. Rev. Lett.
66
,
345
(
1991
).
9.
M.
Krech
and
S.
Dietrich
,
Phys. Rev. A
46
,
1886
(
1992
);
[PubMed]
M.
Krech
and
S.
Dietrich
,
Phys. Rev. A
46
,
1922
(
1992
).
[PubMed]
10.
C.
Hertlein
,
L.
Helden
,
A.
Gambassi
,
S.
Dietrich
, and
C.
Bechinger
,
Nature
451
,
172
(
2008
).
11.
A.
Gambassi
,
A.
Maciołek
,
C.
Hertlein
,
U.
Nellen
,
L.
Helden
,
C.
Bechinger
, and
S.
Dietrich
,
Phys. Rev. E
80
,
061143
(
2009
).
12.
F.
Soyka
,
O.
Zvyagolskaya
,
C.
Hertlein
,
L.
Helden
, and
C.
Bechinger
,
Phys. Rev. Lett.
101
,
208301
(
2008
).
13.
M.
Tröndle
,
O.
Zvyagolskaya
,
A.
Gambassi
,
D.
Vogt
,
L.
Harnau
,
C.
Bechinger
, and
S.
Dietrich
,
Mol. Phys.
109
,
1169
(
2011
).
14.
U.
Nellen
,
L.
Helden
, and
C.
Bechinger
,
Europhys. Lett.
88
,
26001
(
2009
).
15.
M.
Tröndle
,
S.
Kondrat
,
A.
Gambassi
,
L.
Harnau
, and
S.
Dietrich
,
Europhys. Lett.
88
,
40004
(
2009
).
16.
T. W.
Burkhardt
and
E.
Eisenriegler
,
Phys. Rev. Lett.
74
,
3189
(
1995
);
[PubMed]
T. W.
Burkhardt
and
E.
Eisenriegler
,
Phys. Rev. Lett.
78
,
2867
(
1997
).
17.
E.
Eisenriegler
and
U.
Ritschel
,
Phys. Rev. B
51
,
13717
(
1995
).
18.
A.
Hanke
,
F.
Schlesener
,
E.
Eisenriegler
, and
S.
Dietrich
,
Phys. Rev. Lett.
81
,
1885
(
1998
).
19.
F.
Schlesener
,
A.
Hanke
, and
S.
Dietrich
,
J. Stat. Phys.
110
,
981
(
2003
).
20.
E.
Eisenriegler
,
J. Chem. Phys.
121
,
3299
(
2004
).
21.
S.
Kondrat
,
L.
Harnau
, and
S.
Dietrich
,
J. Chem. Phys.
131
,
204902
(
2009
).
22.
M.
Tröndle
,
S.
Kondrat
,
A.
Gambassi
,
L.
Harnau
, and
S.
Dietrich
,
J. Chem. Phys.
133
,
074702
(
2010
).
23.
T. G.
Mattos
,
L.
Harnau
, and
S.
Dietrich
,
J. Chem. Phys.
138
,
074704
(
2013
).
24.
M.
Hasenbusch
,
Phys. Rev. E
87
,
022130
(
2013
).
25.
R.
Evans
,
U. M. B.
Marconi
, and
P.
Tarazona
,
J. Chem. Soc., Faraday Trans. 2
82
,
1763
(
1986
).
26.
H. K.
Christenson
,
J. Colloid Interface Sci.
104
,
234
(
1985
).
27.
P. A.
Kralchevsky
and
N. D.
Denkov
,
Curr. Opin. Colloid Interface Sci.
6
,
383
(
2001
).
28.
G.
Mason
and
W.
Clark
,
Chem. Eng. Sci.
20
,
859
(
1965
).
29.
D.
Beysens
and
D.
Estève
,
Phys. Rev. Lett.
54
,
2123
(
1985
).
30.
N.
Hijnen
and
P. S.
Clegg
,
Langmuir
30
,
5763
(
2014
).
31.
M.
Hampton
and
A.
Nguyen
,
Adv. Colloid Interface Sci.
154
,
30
(
2010
).
32.
O.
Pitois
,
P.
Moucheront
, and
X.
Chateau
,
J. Colloid Interface Sci.
231
,
26
(
2000
).
33.
D. N.
Mazzone
,
G. I.
Tardos
, and
R.
Pfeffer
,
J. Colloid Interface Sci.
113
,
544
(
1986
).
34.
C. D.
Willett
,
M. J.
Adams
,
S. A.
Johnson
, and
J. P.
Seville
,
Langmuir
16
,
9396
(
2000
).
35.
R. A.
Fisher
,
J. Agric. Sci.
16
,
492
(
1926
).
36.
G.
Lian
,
C.
Thornton
, and
M. J.
Adams
,
J. Colloid Interface Sci.
161
,
138
(
1993
).
37.
T. F.
Mohry
,
A.
Maciołek
, and
S.
Dietrich
,
J. Chem. Phys.
136
,
224902
(
2012
);
[PubMed]
T. F.
Mohry
,
A.
Maciołek
, and
S.
Dietrich
,
J. Chem. Phys.
136
,
224903
(
2012
).
[PubMed]
38.
N.
Vogel
,
M.
Retsch
,
C.
Fustin
,
A.
del Campo
, and
U.
Jonas
,
Chem. Rev.
115
,
6265
(
2015
).
39.
D.
Bonn
,
J.
Otwinowski
,
S.
Sacanna
,
H.
Guo
,
G.
Wegdam
, and
P.
Schall
,
Phys. Rev. Lett.
103
,
156101
(
2009
);
[PubMed]
A.
Gambassi
and
S.
Dietrich
,
Phys. Rev. Lett.
105
,
059601
(
2010
);
[PubMed]
D.
Bonn
,
G.
Wegdam
, and
P.
Schall
,
Phys. Rev. Lett.
105
,
059602
(
2010
).
[PubMed]
40.
V. D.
Nguyen
,
S.
Faber
,
Z.
Hu
,
G. H.
Wegdam
, and
P.
Schall
,
Nat. Commun.
4
,
1584
(
2013
).
41.
Y.
Iwashita
and
Y.
Kimura
,
Soft Matter
9
,
10694
(
2013
).
42.
Y.
Iwashita
and
Y.
Kimura
,
Soft Matter
10
,
7170
(
2014
).
43.
R.
Okamoto
and
A.
Onuki
,
Phys. Rev. E
88
,
022309
(
2013
).
44.
S.
Yabunaka
,
R.
Okamoto
, and
A.
Onuki
,
Soft Matter
11
,
5738
(
2015
).
45.
C.
Bauer
,
T.
Bieker
, and
S.
Dietrich
,
Phys. Rev. E
62
,
5324
(
2000
).
46.
47.
A.
Malijevský
and
A. O.
Parry
,
Phys. Rev. E
92
,
022407
(
2015
).
48.
B.
Chacko
,
R.
Evans
, and
A. J.
Archer
,
J. Chem. Phys.
146
,
124703
(
2017
).
49.
O. A.
Vasilyev
,
Phys. Rev. E
90
,
012138
(
2014
).
50.
O. A.
Vasilyev
,
S.
Dietrich
, and
S.
Kondrat
, “
Nonadditive Interactions and Phase Transitions in Strongly Confined Colloidal Systems
” (unpublished).
51.
A. D.
Law
,
L.
Harnau
,
M.
Tröndle
, and
S.
Dietrich
,
J. Chem. Phys.
141
,
134704
(
2014
).
52.
A.
Pelissetto
and
E.
Vicari
,
Phys. Rep.
368
,
549
(
2002
).
53.
H. B.
Tarko
and
M. E.
Fisher
,
Phys. Rev. Lett.
31
,
926
(
1973
).
54.
H. B.
Tarko
and
M. E.
Fisher
,
Phys. Rev. B
11
,
1217
(
1975
).
55.
K.
Binder
, in
Phase Transitions and Critical Phenomena
, edited by
C.
Domb
and
J.
Lebowitz
(
Academic
,
London
,
1983
), Vol. 8, p.
1
.
56.
H. W.
Diehl
, in
Phase Transitions and Critical Phenomena
, edited by
C.
Domb
and
J.
Lebowitz
(
Academic
,
London
,
1986
), Vol. 10, p.
75
.
57.
T. W.
Burkhardt
and
H. W.
Diehl
,
Phys. Rev. B
50
,
3894
(
1994
).
58.
H. W.
Diehl
and
M.
Smock
,
Phys. Rev. B
47
,
5841
(
1993
).
59.
M.
Krech
,
The Casimir Effect in Critical Systems
(
World Scientific
,
Singapore
,
1994
).
60.
V.
Privman
,
P. C.
Hohenberg
, and
A.
Aharony
, in
Phase Transitions and Critical Phenomena
, edited by
C.
Domb
and
J.
Lebowitz
(
Academic
,
London
,
1991
), Vol. 14, p.
1
.
61.
A.
Hanke
and
S.
Dietrich
,
Phys. Rev. E
59
,
5081
(
1999
).
62.
S.
Kondrat
,
L.
Harnau
, and
S.
Dietrich
,
J. Chem. Phys.
126
,
174902
(
2007
).
63.
S.
Kondrat
, “F3DM library and tools,” available from https://sourceforge.net/projects/f3dm/.
64.
T.
Bieker
and
S.
Dietrich
,
Phys. A
252
,
85
(
1998
).
65.
P. F.
Noble
,
O. J.
Cayre
,
R. G.
Alargova
,
O. D.
Velev
, and
V. N.
Paunov
,
J. Am. Chem. Soc.
126
,
8092
(
2004
).
66.
E. P.
Lewandowski
,
P. C.
Searson
, and
K. J.
Stebe
,
J. Phys. Chem. B
110
,
4283
(
2006
).
67.
E. P.
Lewandowski
,
M.
Cavallaro
,
L.
Botto
,
J. C.
Bernate
,
V.
Garbin
, and
K. J.
Stebe
,
Langmuir
26
,
15142
(
2010
).
68.
C. W.
Shields
 IV
,
S.
Zhu
,
Y.
Yang
,
B.
Bharti
,
J.
Liu
,
B. B.
Yellen
,
O. D.
Velev
, and
G. P.
Lopez
,
Soft Matter
9
,
9219
(
2013
).
69.
70.
D.
Jasnow
,
Rep. Prog. Phys.
47
,
1059
(
1983
).
71.
M.
Labbé-Laurent
,
M.
Tröndle
,
L.
Harnau
, and
S.
Dietrich
,
Soft Matter
10
,
2270
(
2014
).
72.
73.
V.
Privman
and
M. E.
Fisher
,
J. Stat. Phys.
33
,
385
(
1983
).
74.
M. P.
Gelfand
and
R.
Lipowsky
,
Phys. Rev. B
36
,
8725
(
1987
).
75.
D.
Wilms
,
A.
Winkler
,
P.
Virnau
, and
K.
Binder
,
Phys. Rev. Lett.
105
,
045701
(
2010
);
[PubMed]
A.
Winkler
,
D.
Wilms
,
P.
Virnau
, and
K.
Binder
,
J. Chem. Phys.
133
,
164702
(
2010
).
[PubMed]
76.
M. E.
Fisher
,
J. Phys. Soc. Jpn. Suppl.
26
,
87
(
1969
).
77.
P. J.
Upton
,
J. O.
Indekeu
, and
J. M.
Yeomans
,
Phys. Rev. B
40
,
666
(
1989
).
78.
K.
Rejmer
,
S.
Dietrich
, and
M.
Napiórkowski
,
Phys. Rev. E
60
,
4027
(
1999
).
79.
C.
Rascón
and
A. O.
Parry
,
Nature
407
,
986
(
2000
).
80.
A.
Hanke
,
M.
Krech
,
F.
Schlesener
, and
S.
Dietrich
,
Phys. Rev. E
60
,
5163
(
1999
).
81.
G.
Palágyi
and
S.
Dietrich
,
Phys. Rev. E
70
,
046114
(
2004
).
82.
M. E.
Fisher
and
S.-Y.
Zinn
,
J. Phys. A
31
,
L629
(
1998
).
83.
A.
Drzewiński
,
A.
Maciołek
,
A.
Barasiński
, and
S.
Dietrich
,
Phys. Rev. E
79
,
041145
(
2009
).
84.
J.
Israelachvili
,
Intermolecular and Surface Forces
(
Academic
,
London
,
1992
).
85.
O.
Vasilyev
,
A.
Gambassi
,
A.
Maciołek
, and
S.
Dietrich
,
Phys. Rev. E
79
,
041142
(
2009
).
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