Memory Effects in Randomly Perturbed Nematic Liquid Crystals
We study the typical domain size and configuration
character of a randomly perturbed system exhibiting continuous
symmetry breaking. As a model system we use rod-like objects
within a cubic lattice interacting via a Lebwohl–Lasher-type
interaction. We describe their local direction with a headless unit
director field. An example of such systems represents nematic LC or
nanotubes. We further introduce impurities of concentration p, which
impose the random anisotropy field-type disorder to directors. We
study the domain-type pattern of molecules as a function of p,
anchoring strength w between a neighboring director and impurity,
temperature, history of samples. In simulations we quenched the
directors either from the random or homogeneous initial
configuration. Our results show that a history of system strongly
influences: i) the average domain coherence length; and ii) the range
of ordering in the system. In the random case the obtained order is
always short ranged (SR). On the contrary, in the homogeneous case,
SR is obtained only for strong enough anchoring and large enough
concentration p. In other cases, the ordering is either of quasi long
range (QLR) or of long range (LR). We further studied memory
effects for the random initial configuration. With increasing external
ordering field B either QLR or LR is realized.
[1] ZurekW.H."Cosmological experiments in superfluid helium?" Nature,
1985, 317, 505.
[2] Bray A.J. "Theory of phase-ordering kinetics" Adv. Phys. 1994,43, 357.
[3] Kibble T.W.B. "Topology of cosmic domains and strings "J. Phys. A:
Math.Gen., 1976, 9, 1387,.
[4] Imry Y.; Ma S. "Random-Field Instability of the Ordered State of
ContinuousSymmetry"Phys. Rev. Lett., 1975,35, 1399.
[5] Feldman D.E. "Quasi-long-range order in nematics confined in random
porous media"Phys. Rev. Lett., 2000,85, 4886.
[6] ChakrabartiJ. Phys. Rev. Lett. 1998, 81, 385.
[7] Cleaver D.J.; Kralj S.; Sluckin T.J.; Allen M P.In Liquid Crystals in
"Complex Geometries Formed by Polymer and Porous Networks"
Crawford G.P. and Zumer S. Eds.; Oxford University Press: London,
1996.
[8] Radzihovsky L. Toner "Anomalous Elasticity of Disordered
Smectics"J.Phys. Rev. Lett., 1997,79, 4214.
[9] Popa-Nita V. " " Statics and Kinetics at the Nematic-Isotropic Interface
in Porous Media"" Eur. Phys. J., 1999, 83, 12.
[10] Popa-Nita V.; Romano S. " Nematic-Smectic A Phase Transition in
Porous Media" Chem. Phys., 2001,91, 264.
[11] De Gennes P.G.; Prost J. "The Physics of LiquidCrystals" Oxford
University Press: Oxford, 1993.
[12] Virga E.G. Variational "Theories for Liquid Crystals" Chapman Hall:
London, 1994.
[13] M.Ambrožic,S.Kral,E.G.Virga"Defect-enhanced nematic surface order
reconstruction" , Phys. Rev. E , 2007,75, 031708 .
[14] M.Ambrožic S. Kralj,T.J.Sluckin, S. Žumer, and D. Sven┼íek
"Annihilation of edge dislocations in smectic-A liquid crystals" Phys.
Rev. E , 2004,70, 051704 .
[15] Lebwohl P.A.; Lasher G. "Nematic-Liquid-Crystal OrderÔÇöA Monte
Carlo Calculation", Phys. Rev. A, 1972, 6, 42.
[16] M.Krasna, M.Cvetko, M. Ambrozic1 "Symmetry breaking and structure
of a mixture of nematic liquid crystals and anisotropic
nanoparticles",Beilstein J. Org. Chem.6, No. 74,2010.
[17] Cruz, C.; Figueirinhas, J. L.; Filip, D.; Feio, G.; Ribeiro, A. C Frère,
Y.;Meyer, T.; Mehl, G. H. "Biaxial nematic order and biaxial order and
phase behavior studies in an organosiloxanetetrapode using
complementary deuterium NMR experiments" Phys. Rev. E,
2008,78,051702.
[18] Popa-Nita, V."Statics and kinetics at the nematic-isotropic interface in
porous media" Eur. Phys. J. B, 1999,12, 83-90.
[19] Popa-Nita, V.; Gerli─ì, I.; Kralj, S. Int. "The Influence of Disorder on
ThermotropicNematic Liquid Crystals Phase Behavior" J. Mol. Sci. ,
10(9), 2009,3971-4008.
[20] Romano, S. Int. J. Mod. Phys. B " Computer simulation study of a
Nematogenic Lattice-Gas model with fourth- rank interactions ",
2002,16,2901-2915.
[1] ZurekW.H."Cosmological experiments in superfluid helium?" Nature,
1985, 317, 505.
[2] Bray A.J. "Theory of phase-ordering kinetics" Adv. Phys. 1994,43, 357.
[3] Kibble T.W.B. "Topology of cosmic domains and strings "J. Phys. A:
Math.Gen., 1976, 9, 1387,.
[4] Imry Y.; Ma S. "Random-Field Instability of the Ordered State of
ContinuousSymmetry"Phys. Rev. Lett., 1975,35, 1399.
[5] Feldman D.E. "Quasi-long-range order in nematics confined in random
porous media"Phys. Rev. Lett., 2000,85, 4886.
[6] ChakrabartiJ. Phys. Rev. Lett. 1998, 81, 385.
[7] Cleaver D.J.; Kralj S.; Sluckin T.J.; Allen M P.In Liquid Crystals in
"Complex Geometries Formed by Polymer and Porous Networks"
Crawford G.P. and Zumer S. Eds.; Oxford University Press: London,
1996.
[8] Radzihovsky L. Toner "Anomalous Elasticity of Disordered
Smectics"J.Phys. Rev. Lett., 1997,79, 4214.
[9] Popa-Nita V. " " Statics and Kinetics at the Nematic-Isotropic Interface
in Porous Media"" Eur. Phys. J., 1999, 83, 12.
[10] Popa-Nita V.; Romano S. " Nematic-Smectic A Phase Transition in
Porous Media" Chem. Phys., 2001,91, 264.
[11] De Gennes P.G.; Prost J. "The Physics of LiquidCrystals" Oxford
University Press: Oxford, 1993.
[12] Virga E.G. Variational "Theories for Liquid Crystals" Chapman Hall:
London, 1994.
[13] M.Ambrožic,S.Kral,E.G.Virga"Defect-enhanced nematic surface order
reconstruction" , Phys. Rev. E , 2007,75, 031708 .
[14] M.Ambrožic S. Kralj,T.J.Sluckin, S. Žumer, and D. Sven┼íek
"Annihilation of edge dislocations in smectic-A liquid crystals" Phys.
Rev. E , 2004,70, 051704 .
[15] Lebwohl P.A.; Lasher G. "Nematic-Liquid-Crystal OrderÔÇöA Monte
Carlo Calculation", Phys. Rev. A, 1972, 6, 42.
[16] M.Krasna, M.Cvetko, M. Ambrozic1 "Symmetry breaking and structure
of a mixture of nematic liquid crystals and anisotropic
nanoparticles",Beilstein J. Org. Chem.6, No. 74,2010.
[17] Cruz, C.; Figueirinhas, J. L.; Filip, D.; Feio, G.; Ribeiro, A. C Frère,
Y.;Meyer, T.; Mehl, G. H. "Biaxial nematic order and biaxial order and
phase behavior studies in an organosiloxanetetrapode using
complementary deuterium NMR experiments" Phys. Rev. E,
2008,78,051702.
[18] Popa-Nita, V."Statics and kinetics at the nematic-isotropic interface in
porous media" Eur. Phys. J. B, 1999,12, 83-90.
[19] Popa-Nita, V.; Gerli─ì, I.; Kralj, S. Int. "The Influence of Disorder on
ThermotropicNematic Liquid Crystals Phase Behavior" J. Mol. Sci. ,
10(9), 2009,3971-4008.
[20] Romano, S. Int. J. Mod. Phys. B " Computer simulation study of a
Nematogenic Lattice-Gas model with fourth- rank interactions ",
2002,16,2901-2915.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57482", author = "Amid Ranjkesh and Milan Ambrožič and Samo Kralj", title = "Memory Effects in Randomly Perturbed Nematic Liquid Crystals", abstract = "We study the typical domain size and configuration
character of a randomly perturbed system exhibiting continuous
symmetry breaking. As a model system we use rod-like objects
within a cubic lattice interacting via a Lebwohl–Lasher-type
interaction. We describe their local direction with a headless unit
director field. An example of such systems represents nematic LC or
nanotubes. We further introduce impurities of concentration p, which
impose the random anisotropy field-type disorder to directors. We
study the domain-type pattern of molecules as a function of p,
anchoring strength w between a neighboring director and impurity,
temperature, history of samples. In simulations we quenched the
directors either from the random or homogeneous initial
configuration. Our results show that a history of system strongly
influences: i) the average domain coherence length; and ii) the range
of ordering in the system. In the random case the obtained order is
always short ranged (SR). On the contrary, in the homogeneous case,
SR is obtained only for strong enough anchoring and large enough
concentration p. In other cases, the ordering is either of quasi long
range (QLR) or of long range (LR). We further studied memory
effects for the random initial configuration. With increasing external
ordering field B either QLR or LR is realized.", keywords = "Lebwohl-Lasher model, liquid crystals, disorder,
memory effect, orientational order.", volume = "7", number = "3", pages = "362-6", }