Systems of two-dimensional hard ellipses of varying aspect ratios and packing fractions are studied by Monte Carlo simulations in the generalised canonical ensemble. From this microscopic model, we extract a coarse-grained macroscopic Landau-de Gennes free energy as a function of packing fraction and orientational order parameter. We separate the free energy into the ideal orientational entropy of non-interacting two-dimensional spins and an excess free energy associated with excluded volume interactions. We further explore the isotropic-nematic phase transition using our empirical expression for the free energy and find that the nature of the phase transition is continuous for the aspect ratios we studied.

1.
P. G.
de Gennes
and
J.
Prost
,
The Physics of Liquid Crystals
, 2nd ed. (
Clarendon Press
,
Oxford
,
1993
).
2.
B.
Madivala
,
J.
Fransaer
, and
J.
Vermant
,
Langmuir
25
,
2718
(
2009
).
3.
B. P.
Binks
and
T. S.
Horozov
,
Colloidal Particles at Liquid Interfaces
(
Cambridge University Press
,
2006
).
4.
J.
Palacci
,
S.
Sacanna
,
A. P.
Steinberg
,
D. J.
Pine
, and
P. M.
Chaikin
,
Science
339
,
936
(
2013
).
5.
L.
Onsager
,
Ann. N. Y. Acad. Sci.
51
,
627
(
1949
).
6.
J. C.
Loudet
,
A. M.
Alsayed
,
J.
Zhang
, and
A. G.
Yodh
,
Phys. Rev. Lett.
94
,
018301
(
2005
).
7.
H. C.
Öttinger
,
Beyond Equilibrium Thermodynamics
(
Wiley-Interscience
,
New Jersey
,
2005
).
8.
A.
Beris
and
B. J.
Edwards
,
Thermodynamics of Flowing Systems: With Internal Microstructure
(
Oxford University Press
,
1994
).
9.
L. M. C.
Sagis
,
Rev. Mod. Phys.
83
,
1367
(
2011
).
10.
J.
Vieillard-Baron
,
J. Chem. Phys.
56
,
4729
(
1972
).
11.
J. A.
Cuesta
and
D.
Frenkel
,
Phys. Rev. A
42
,
2126
(
1990
).
12.
W.-S.
Xu
,
Y.-W.
Li
,
Z.-Y.
Sun
, and
L.-J.
An
,
J. Chem. Phys.
139
,
024501
(
2013
).
13.
J. A.
Cuesta
,
C. F.
Tejero
, and
M.
Baus
,
Phys. Rev. A
39
,
6498
(
1989
).
14.
J. A.
Cuesta
,
C. F.
Tejero
,
H.
Xu
, and
M.
Baus
,
Phys. Rev. A
44
,
5306
(
1991
).
15.
P.
van der Schoot
,
J. Chem. Phys.
106
,
2355
(
1997
).
16.
H.
Schlacken
,
H.-J.
Mögel
, and
P.
Schiller
,
Mol. Phys.
93
,
777
(
1998
).
17.
X.
Xiao
and
P.
Sheng
,
Phys. Rev. E
88
,
062501
(
2013
).
18.
P.
Ilg
,
Phys. Rev. E
85
,
061709
(
2012
).
19.
B.
Gupta
and
P.
Ilg
,
Polymers
5
,
328
(
2013
).
20.
P.
Ilg
,
M.
Hütter
, and
M.
Kröger
,
Phys. Rev. E
83
,
061713
(
2011
).
21.
I. S.
Gradshteyn
and
I. M.
Ryzhik
,
Table of Integrals, Series, and Products
(
Elsevier
,
Amsterdam
,
2007
).
22.
J. W.
Perram
and
M. S.
Wertheim
,
J. Comput. Phys.
58
,
409
(
1985
).
23.
H. H.
Wensink
and
R. L. C.
Vink
,
J. Phys.: Condens. Matter
19
,
466109
(
2007
).
24.
S.
Jordens
,
L.
Isa
,
I.
Usov
, and
R.
Mezzenga
,
Nat. Commun.
4
,
1917
(
2013
).
25.
J. M.
Kosterlitz
and
D. J.
Thouless
,
J. Phys. C
6
,
1181
(
1973
).
26.
L. M. C.
Sagis
and
H. C.
Öttinger
,
Phys. Rev. E
88
,
022149
(
2013
).
27.
L. M. C.
Sagis
,
Phys. Rev. E
88
,
022150
(
2013
).
You do not currently have access to this content.