Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems since very few analytical results exist. In this work, we apply fundamental measure theory, which allows us to derive free energy functionals for hard particles from first principles and with high accuracy, to systems of hard cylinders, cones, and spherotriangles. We provide a general recipe for incorporating biaxial liquid crystal order parameters into fundamental measure theory and use this framework to obtain the phase boundaries for the emergence of orientational order in the considered systems. Our results provide insights into the phase behavior of biaxial nematic liquid crystals and, in particular, into methods for their analytical investigation.
REFERENCES
1.
P.-G.
de Gennes
and J.
Prost
, The Physics of Liquid Crystals
(Oxford University Press
, Oxford, United Kingdom
, 1993
), Vol. 83
.2.
N.
Sebastián
, M.
Čopič
, and A.
Mertelj
, Phys. Rev. E
106
, 021001
(2022
).3.
D. W.
Bruce
, Chem. Rec.
4
, 10
(2004
).4.
X.
Chen
, E.
Korblova
, D.
Dong
, X.
Wei
, R.
Shao
, L.
Radzihovsky
, M. A.
Glaser
, J. E.
Maclennan
, D.
Bedrov
, D. M.
Walba
, and N. A.
Clark
, Proc. Natl. Acad. Sci. U. S. A.
117
, 14021
(2020
).5.
O. D.
Lavrentovich
, Proc. Natl. Acad. Sci. U. S. A.
117
, 14629
(2020
).6.
M. J.
Freiser
, Phys. Rev. Lett.
24
, 1041
(1970
).7.
L. A.
Madsen
, T. J.
Dingemans
, M.
Nakata
, and E. T.
Samulski
, Phys. Rev. Lett.
92
, 145505
(2004
).8.
Biaxial Nematic Liquid Crystals: Theory, Simulation and Experiment
, edited by G. R.
Luckhurst
and T. J.
Sluckin
(Wiley
, Chichester, UK
, 2015
).9.
G. J.
Vroege
and H. N. W.
Lekkerkerker
, Rep. Prog. Phys.
55
, 1241
(1992
).10.
I. I.
Smalyukh
, Annu. Rev. Condens. Matter Phys.
9
, 207
(2018
).11.
S.
Sacanna
, D. J.
Pine
, and G.-R.
Yi
, Soft Matter
9
, 8096
(2013
).12.
T.
Hueckel
, G. M.
Hocky
, and S.
Sacanna
, Nat. Rev. Mater.
6
, 1053
(2021
).13.
L.
Mederos
, E.
Velasco
, and Y.
Martínez-Ratón
, J. Phys.: Condens. Matter
26
, 463101
(2014
).14.
S. C.
McGrother
, D. C.
Williamson
, and G.
Jackson
, J. Chem. Phys.
104
, 6755
(1996
).15.
P.
Bolhuis
and D.
Frenkel
, J. Chem. Phys.
106
, 666
(1997
).16.
H. H.
Wensink
and G. J.
Vroege
, J. Chem. Phys.
119
, 6868
(2003
).17.
P.
Pfleiderer
and T.
Schilling
, Phys. Rev. E
75
, 020402
(2007
).18.
M.
Marechal
, A.
Cuetos
, B.
Martínez-Haya
, and M.
Dijkstra
, J. Chem. Phys.
134
, 094501
(2011
).19.
G.
Odriozola
, J. Chem. Phys.
136
, 134505
(2012
).20.
P.
Kubala
, M.
Cieśla
, and L.
Longa
, Phys. Rev. E
108
, 054701
(2023
).21.
L. J.
Ellison
, D. J.
Michel
, F.
Barmes
, and D. J.
Cleaver
, Phys. Rev. Lett.
97
, 237801
(2006
).22.
P. W. A.
Schönhöfer
, L. J.
Ellison
, M.
Marechal
, D. J.
Cleaver
, and G. E.
Schröder-Turk
, Interface Focus
7
, 20160161
(2017
).23.
P. A.
Monderkamp
, R. S.
Windisch
, R.
Wittmann
, and H.
Löwen
, J. Chem. Phys.
158
, 164505
(2023
).24.
Y.
Martínez-Ratón
and E.
Velasco
, Phys. Rev. E
104
, 054132
(2021
).25.
Y.
Martínez-Ratón
and E.
Velasco
, Phys. Fluids
34
, 037110
(2022
).26.
R.
Alben
, Phys. Rev. Lett.
30
, 778
(1973
).27.
M. P.
Taylor
and J.
Herzfeld
, Phys. Rev. A
44
, 3742
(1991
).28.
A. G.
Vanakaras
, M. A.
Bates
, and D. J.
Photinos
, Phys. Chem. Chem. Phys.
5
, 3700
(2003
).29.
Y.
Martínez-Ratón
, S.
Varga
, and E.
Velasco
, Phys. Chem. Chem. Phys.
13
, 13247
(2011
).30.
S.
Belli
, A.
Patti
, M.
Dijkstra
, and R.
van Roij
, Phys. Rev. Lett.
107
, 148303
(2011
).31.
S.
Belli
, M.
Dijkstra
, and R.
van Roij
, J. Phys.: Condens. Matter
24
, 284128
(2012
).32.
S. D.
Peroukidis
and A. G.
Vanakaras
, Soft Matter
9
, 7419
(2013
).33.
A.
Cuetos
, M.
Dennison
, A.
Masters
, and A.
Patti
, Soft Matter
13
, 4720
(2017
).34.
E.
van den Pol
, A. V.
Petukhov
, D. M. E.
Thies-Weesie
, D. V.
Byelov
, and G. J.
Vroege
, Phys. Rev. Lett.
103
, 258301
(2009
).35.
Y.
Rosenfeld
, Phys. Rev. Lett.
63
, 980
(1989
).36.
R.
Roth
, J. Phys.: Condens. Matter
22
, 063102
(2010
).37.
R.
Roth
, K.
Mecke
, and M.
Oettel
, J. Chem. Phys.
136
, 081101
(2012
).38.
H.
Hansen-Goos
and K.
Mecke
, Phys. Rev. Lett.
102
, 018302
(2009
).39.
H.
Hansen-Goos
and K.
Mecke
, J. Phys.: Condens. Matter
22
, 364107
(2010
).40.
R.
Wittmann
, M.
Marechal
, and K.
Mecke
, J. Chem. Phys.
141
, 064103
(2014
).41.
R.
Wittmann
, M.
Marechal
, and K.
Mecke
, Europhys. Lett.
109
, 26003
(2015
).42.
R.
Wittmann
, “Density functional theory for liquid crystals: Refining fundamental measure theory for anisotropic bodies
,” Ph.D. thesis (FAU University Press
, 2015
), see https://opus4.kobv.de/opus4-fau/frontdoor/index/index/docId/6737.43.
R.
Wittmann
, M.
Marechal
, and K.
Mecke
, J. Phys.: Condens. Matter
28
, 244003
(2016
).44.
M.
Marechal
, S.
Dussi
, and M.
Dijkstra
, J. Chem. Phys.
146
, 124905
(2017
).45.
M.
Marechal
and H.
Löwen
, Phys. Rev. Lett.
110
, 137801
(2013
).46.
R.
Wittmann
and K.
Mecke
, J. Chem. Phys.
140
, 104703
(2014
).47.
R.
Wittmann
, M.
Marechal
, and K.
Mecke
, Phys. Rev. E
91
, 052501
(2015
).48.
P. W. A.
Schönhöfer
, G. E.
Schröder-Turk
, and M.
Marechal
, J. Chem. Phys.
148
, 124104
(2018
).49.
R.
Rosso
, Liq. Cryst.
34
, 737
(2007
).50.
M.
te Vrugt
and R.
Wittkowski
, AIP Adv.
10
, 035106
(2020
).51.
R.
Wittmann
, C. E.
Sitta
, F.
Smallenburg
, and H.
Löwen
, J. Chem. Phys.
147
, 134908
(2017
).52.
C. G.
Gray
and K. E.
Gubbins
, Theory of Molecular Fluids: Fundamentals: I
, 1st ed., International Series of Monographs on Chemistry Vol. 9
(Oxford University Press
, Oxford
, 1984
).53.
P.
Cremer
, M.
Marechal
, and H.
Löwen
, Europhys. Lett.
99
, 38005
(2012
).54.
M.
te Vrugt
and R.
Wittkowski
, Ann. Phys. (Berlin)
532
, 2000266
(2020
).55.
D.
Andrienko
, J. Mol. Liq.
267
, 520
(2018
).56.
D. W.
Allender
and M. A.
Lee
, Mol. Cryst. Liq. Cryst.
110
, 331
(1984
).57.
S. S.
Turzi
, J. Math. Phys.
52
, 053517
(2011
).58.
P.
Hohenberg
and W.
Kohn
, Phys. Rev.
136
, B864
(1964
).59.
R.
Evans
, Adv. Phys.
28
, 143
(1979
).60.
P.
Tarazona
, Phys. Rev. Lett.
84
, 694
(2000
).61.
H.
Hansen-Goos
and R.
Roth
, J. Phys.: Condens. Matter
18
, 8413
(2006
).62.
P.
Tarazona
and Y.
Rosenfeld
, Phys. Rev. E
55
, R4873
(1997
).63.
L.
Onsager
, Ann. N. Y. Acad. Sci.
51
, 627
(1949
).64.
S.
Dussi
, N.
Tasios
, T.
Drwenski
, R.
van Roij
, and M.
Dijkstra
, Phys. Rev. Lett.
120
, 177801
(2018
).65.
A.
Stroobants
and H. N. W.
Lekkerkerker
, J. Phys. Chem.
88
, 3669
(1984
).66.
P. J.
Camp
and M. P.
Allen
, Physica A
229
, 410
(1996
).67.
E.
do Carmo
, D. B.
Liarte
, and S. R.
Salinas
, Phys. Rev. E
81
, 062701
(2010
).68.
A.
Mertelj
, L.
Cmok
, N.
Sebastián
, R. J.
Mandle
, R. R.
Parker
, A. C.
Whitwood
, J. W.
Goodby
, and M.
Čopič
, Phys. Rev. X
8
, 041025
(2018
).69.
N.
Sebastián
, L.
Cmok
, R. J.
Mandle
, M. R.
de la Fuente
, I.
Drevenšek Olenik
, M.
Čopič
, and A.
Mertelj
, Phys. Rev. Lett.
124
, 037801
(2020
).70.
N.
Chaturvedi
and R. D.
Kamien
, Phys. Rev. E
100
, 022704
(2019
).71.
M.
Chiappini
and M.
Dijkstra
, Nat. Commun.
12
, 2157
(2021
).72.
R.
Kotni
, A.
Grau-Carbonell
, M.
Chiappini
, M.
Dijkstra
, and A.
van Blaaderen
, Nat. Commun.
13
, 7264
(2022
).73.
P.
De Gregorio
, E.
Frezza
, C.
Greco
, and A.
Ferrarini
, Soft Matter
12
, 5188
(2016
).74.
M.
Chiappini
, T.
Drwenski
, R.
van Roij
, and M.
Dijkstra
, Phys. Rev. Lett.
123
, 068001
(2019
).75.
U. Marini Bettolo
Marconi
and P.
Tarazona
, J. Chem. Phys.
110
, 8032
(1999
).76.
A. J.
Archer
and R.
Evans
, J. Chem. Phys.
121
, 4246
(2004
).77.
M.
te Vrugt
, H.
Löwen
, and R.
Wittkowski
, Adv. Phys.
69
, 121
(2020
).78.
M.
te Vrugt
and R.
Wittkowski
, J. Phys.: Condens. Matter
35
, 041501
(2022
).79.
H.
Löwen
, Phys. Rev. E
59
, 1989
(1999
).80.
K. R.
Elder
, M.
Katakowski
, M.
Haataja
, and M.
Grant
, Phys. Rev. Lett.
88
, 245701
(2002
).81.
H.
Emmerich
, H.
Löwen
, R.
Wittkowski
, T.
Gruhn
, G. I.
Tóth
, G.
Tegze
, and L.
Gránásy
, Adv. Phys.
61
, 665
(2012
).82.
R.
Wittkowski
, H.
Löwen
, and H. R.
Brand
, Phys. Rev. E
82
, 031708
(2010
).83.
M.
te Vrugt
, M. P.
Holl
, A.
Koch
, R.
Wittkowski
, and U.
Thiele
, Modell. Simul. Mater. Sci. Eng.
30
, 084001
(2022
).84.
M.
te Vrugt
, J.
Jeggle
, and R.
Wittkowski
, New J. Phys.
23
, 063023
(2021
).85.
R.
Wittkowski
and H.
Löwen
, Phys. Rev. E
85
, 021406
(2012
).86.
F.
Kümmel
, B.
ten Hagen
, R.
Wittkowski
, I.
Buttinoni
, R.
Eichhorn
, G.
Volpe
, H.
Löwen
, and C.
Bechinger
, Phys. Rev. Lett.
110
, 198302
(2013
).87.
R.
Wittkowski
and H.
Löwen
, Mol. Phys.
109
, 2935
(2011
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
