We study the layer-to-layer diffusion in smectic-A liquid crystals of colloidal hard rods with different length-to-diameter ratios using computer simulations. The layered arrangement of the smectic phase yields a hopping-type diffusion due to the presence of permanent barriers and transient cages. Remarkably, we detect stringlike clusters composed of interlayer rods moving cooperatively along the nematic director. Furthermore, we find that the structural relaxation in equilibrium smectic phases shows interesting similarities with that of out-of-equilibrium supercooled liquids, although there the particles are kinetically trapped in transient rather than permanent cages. Additionally, at fixed packing fraction we find that the barrier height increases with increasing particle anisotropy, and hence the dynamics is more heterogeneous and non-Gaussian for longer rods, yielding a lower diffusion coefficient along the nematic director and smaller clusters of interlayer particles that move less cooperatively. At fixed barrier height, the dynamics becomes more non-Gaussian and heterogeneous for longer rods that move more collectively giving rise to a higher diffusion coefficient along the nematic director.
REFERENCES
1.
S.
Chandrasekhar
, Liquid Crystals
(Cambridge University Press
, Cambridge
, 1992
).2.
L.
Onsager
, Ann. N.Y. Acad. Sci.
51
, 627
(1949
).3.
A.
Stroobants
, H. N. W.
Lekkerkerker
, and D.
Frenkel
, Phys. Rev. Lett.
57
, 1452
(1986
).4.
D.
Frenkel
, H. N. W.
Lekkerkerker
, and A.
Stroobants
, Nature (London)
332
, 822
(1988
).5.
P. G.
de Gennes
and J.
Prost
, The Physics of Liquid Crystals
(Clarendon
, Oxford
, 1993
).6.
Z.
Dogic
and S.
Fraden
, Phys. Rev. Lett.
78
, 2417
(1997
).7.
Z.
Dogic
and S.
Fraden
, Philos. Trans. R. Soc. London, Ser. A
359
, 997
(2001
).8.
Z.
Dogic
, Phys. Rev. Lett.
91
, 165701
(2003
).9.
B.
Mulder
, Phys. Rev. A
35
, 3095
(1987
).10.
X.
Wen
and R. B.
Meyer
, Phys. Rev. Lett.
59
, 1325
(1987
).11.
A. M.
Somoza
and P.
Tarazona
, Phys. Rev. A
41
, 965
(1990
).12.
A.
Poniewierski
and R.
Hołyst
, Phys. Rev. Lett.
61
, 2461
(1988
).13.
P.
van der Schoot
, J. Phys. II
6
, 1557
(1996
).14.
P.
Bolhuis
and D.
Frenkel
, J. Chem. Phys.
106
, 666
(1997
).15.
J. A.
Veerman
and D.
Frenkel
, Phys. Rev. A
41
, 3237
(1990
).16.
J. M.
Polson
and D.
Frenkel
, Phys. Rev. E
56
, R6260
(1997
).17.
G. J.
Vroege
and H. N. W.
Lekkerkerker
, J. Phys. Chem.
97
, 3601
(1993
).18.
G.
Cinacchi
, L.
Maderos
, and E.
Velasco
, J. Chem. Phys.
121
, 3854
(2004
).19.
Y.
Martínez-Ratón
, E.
Velasco
, and L.
Maderos
, J. Chem. Phys.
123
, 104906
(2005
).20.
R.
van Roij
and B.
Mulder
, Phys. Rev. E
54
, 6430
(1996
).21.
R.
van Roij
and B.
Mulder
, J. Chem. Phys.
105
, 11237
(1996
).22.
R.
van Roij
, B.
Mulder
, and M.
Dijkstra
, Physica A
261
, 374
(1998
).23.
M.
Dijkstra
and R.
van Roij
, Phys. Rev. E
56
, 5594
(1997
).24.
A.
Galindo
, A. J.
Haslam
, S.
Varga
, G.
Jackson
, A. G.
Vanakaras
, D. J.
Photinos
, and D. A.
Dunmur
, J. Chem. Phys.
119
, 5216
(2003
).25.
R.
van Roij
and B.
Mulder
, J. Phys. II
4
, 1763
(1994
).26.
P. J.
Camp
and M. P.
Allen
, Physica A
229
, 410
(1996
).27.
P. J.
Camp
, M. P.
Allen
, P. G.
Bolhuis
, D.
Frenkel
, J. Chem. Phys.
106
, 9270
(1997
)28.
M.
Adams
and S.
Fraden
, Biophys. J.
74
, 669
(1998
).29.
M.
Adams
, Z.
Dogic
, S. L.
Keller
, and S.
Fraden
, Nature (London)
393
, 99
(1998
).30.
G. A.
Vliegenthart
and H. N. W.
Lekkerkerker
, J. Chem. Phys.
111
, 4153
(1999
).31.
Z.
Dogic
, D.
Frenkel
, and S.
Fraden
, Phys. Rev. E
62
, 3925
(2000
).32.
Z.
Dogic
, K. R.
Purdy
, E.
Grelet
, M.
Adams
, and S.
Fraden
, Phys. Rev. E
69
, 051702
(2004
).33.
P. G.
Bolhuis
, A.
Stroobants
, D.
Frenkel
, and H. N. W.
Lekkerkerker
, J. Chem. Phys.
107
, 1551
(1997
).34.
S. V.
Savenko
and M.
Dijkstra
, J. Chem. Phys.
124
, 234902
(2006
).35.
W.
Helfrich
, Phys. Rev. Lett.
23
, 372
(1969
).36.
I.
Furó
and S. V.
Dvinskikh
, Magn. Reson. Chem.
40
, S3
(2002
).37.
M. P.
Lettinga
and E.
Grelet
, Phys. Rev. Lett.
99
, 197802
(2007
).38.
M.
Bier
, R.
van Roij
, M.
Dijkstra
, and P.
van der Schoot
, Phys. Rev. Lett.
101
, 215901
(2008
).39.
E.
Grelet
, M. P.
Lettinga
, M.
Bier
, R.
van Roij
, and P.
van der Schoot
, J. Phys.: Condens. Matter
20
, 494213
(2008
).40.
M. M.
Hurley
and P.
Harrowell
, J. Chem. Phys.
105
, 10521
(1996
).41.
A. J.
Moreno
and C. N.
Likos
, Phys. Rev. Lett.
99
, 107801
(2007
).42.
P.
Chaudhuri
, L.
Berthier
, and W.
Kob
, Phys. Rev. Lett.
99
, 060604
(2007
).43.
B.
Vorselaars
, A. V.
Lyulin
, K.
Karatasos
, and M. A. J.
Michels
, Phys. Rev. E
75
, 011504
(2007
).44.
R.
Matena
, M.
Dijkstra
, and A.
Patti
, Phys. Rev. E
81
, 021704
(2010
).45.
A.
Patti
, D.
El Masri
, R.
van Roij
, and M.
Dijkstra
, Phys. Rev. Lett.
103
, 248304
(2009
).46.
R.
Richert
, J. Non-Cryst. Solids
172–174
, 209
(1994
).47.
G.
Cinacchi
and L.
De Gaetani
, Phys. Rev. E
79
, 011706
(2009
).48.
C.
Donati
, J. F.
Douglas
, W.
Kob
, S. J.
Plimpton
, P. H.
Poole
, and S. C.
Glotzer
, Phys. Rev. Lett.
80
, 2338
(1998
).49.
A. H.
Marcus
, J.
Schofield
, and S. A.
Rice
, Phys. Rev. E
60
, 5725
(1999
).50.
N.
Giovambattista
, S. V.
Buldyrev
, F. W.
Starr
, and H. E.
Stanley
, Phys. Rev. Lett.
90
, 085506
(2003
).51.
M.
Aichele
, Y.
Gebremichael
, F. W.
Starr
, J.
Baschnagel
, and S. C.
Glotzer
, J. Chem. Phys.
119
, 5290
(2003
).52.
V.
Teboul
, A.
Monteil
, L. C.
Fai
, A.
Kerrache
, and S.
Maabou
, Eur. Phys. J. B
40
, 49
(2004
).53.
R. K.
Darst
, D. R.
Reichman
, and G.
Biroli
, J. Chem. Phys.
132
, 044510
(2010
).54.
L.
Berthier
and W.
Kob
, J. Phys.: Condens. Matter
19
, 205130
(2007
).55.
L.
Pfleiderer
, K.
Milinkovic
, and T.
Schilling
, Europhys. Lett.
84
, 16003
(2008
).56.
57.
58.
A.
Rahman
, Phys. Rev.
136
, A405
(1964
).59.
F.
Volino
, A. J.
Dianoux
, and A.
Heidemann
, J. Phys. (France) Lett.
40
, 583
(1979
).60.
R. M.
Richardson
, A. J.
Leadbetter
, D. H.
Bonsor
, and G. J.
Krüger
, Mol. Phys.
40
, 741
(1980
).61.
J. S.
Van Duijneveldt
and M. P.
Allen
, Mol. Phys.
90
, 243
(1997
).62.
R.
van Roij
, P.
Bolhuis
, B.
Mulder
, and D.
Frenkel
, Phys. Rev. E
52
, R1277
(1995
).63.
R. L.
Blumberg Selinger
, Phys. Rev. E
65
, 051702
(2002
).64.
W.
Kob
, C.
Donati
, S. J.
Plimpton
, P. H.
Poole
, and S. C.
Glotzer
, Phys. Rev. Lett.
79
, 2827
(1997
).65.
M.
Cifelli
, G.
Cinacchi
, and L.
De Gaetani
, J. Chem. Phys.
125
, 164912
(2006
).66.
G.
Brambilla
, D.
El Masri
, M.
Pierno
, L.
Berthier
, L.
Cipelletti
, G.
Petekidis
, and A. B.
Schofield
, Phys. Rev. Lett.
102
, 085703
(2009
).67.
L.
Berthier
, G.
Biroli
, J. -P.
Bouchaud
, L.
Cipelletti
, D.
El Masri
, D.
L’Hôte
, F.
Ladieu
, and M.
Pierno
, Science
310
, 1797
(2005
).68.
C. R.
Nugent
, K. V.
Edmond
, H. N.
Patel
, and E. R.
Weeks
, Phys. Rev. Lett.
99
, 025702
(2007
).69.
E.
Falck
, T.
Róg
, M.
Karttunen
, and I.
Vattulainen
, J. Am. Chem. Soc.
130
, 44
(2008
).70.
A. A.
Gurtovenko
and I.
Vattulainen
, Handbook of Modern Biophysics
, Vol. 2
, edited by T.
Jue
, S. H.
Risbud
, M. L.
Longo
, and R.
Faller
(Humana Press
, 2009
), pp. 121
.71.
S.
Belli
(private communication).© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.
