8 Fréedericksz-Like Positional Transition Triggered by An External Electric Field
351
8.5 Conclusion
In summary, using the Green’s function method, the total energy for a microparticle
suspended in an NLC cell in the presence of an external electric field is calculated.
It is found that with the application of the external electric field, it is possible to
create an anisotropic bubble around the microparticle with a vertical fast “lane” for
the microparticle to move from the midplane to a new equilibrium position. Such a
new equilibrium position is decided via a competition between the buoyant force and
the effective force built upon the microparticle inside the “lane”. The threshold value
of external field, which triggers positional transition under appropriate conditions
of surface anchoring feature, field direction and molecular dielectric anisotropy,
depends on thickness L and Frank elastic constant K and slightly on the microparticle
size and density, in a Fréedericksz-like manner as coined by the authors before, but
by a factor. For an NLC cell with planar surface alignment, a bistable equilibrium
structure for the transition is found when the direction of the applied electric field
is (a) perpendicular to the cell wall with positive molecular dielectric anisotropy,
and (b) parallel to the undeformed director field n 0 of the NLC cell with negative
molecular dielectric anisotropy. When the electric field applied is parallel to the two
plates and perpendicular to the anchoring direction, the microparticle suspended in
NLC will be trapped in the midplane, regardless of the sign of the molecular dielectric
anisotropy. Explicit formulae proposed for the critical electric field agrees extremely
well with the numerical calculation.
References
1. de Gennes, P.G., Prost, J.: The Physics of Liquid Crystals, 2nd edn. Clarendon Press, Oxford,
UK (1993)
2. Jákli, A., Lavrentovich, O.D., Selinger, J.V.: Physics of liquid crystals of bent-shaped
molecules. Rev. Mod. Phys. 90, 045004 (2018)
3. Daniel, J.C., Audebert, R.: Small Volumes and Large Surfaces: The World of Colloids in Soft
Matter Physics edited by M. Williams (Springer-Verlag, Berlin Heidelberg, Daoud and C.E
(1999)
4. Chaikin, P.M., Lubensky, T.C.: Principles of Condensed Matter Physics, Cambridge University
Press, CambridgeCambridgeCambridge, UK (2000)
5. Comiskey, B., Albert, J., Yoshizawa, H., Jacobson, J.: Nature 394, 253 (1998)
6. Wang, Z., Zhe, J.: Chip 11, 1280 (2011)
7. Araki, T., Buscaglia, M., Bellini, T., Tanaka, H.: Nat. Mater. 10, 303 (2011)
8. Smalyukh, I.I.: Annu. Rev. Condens. Matter Phys. 9, 207 (2018)
9. Kim, Y.-K., Wang, X., Mondkar, P., Bukusoglu, E., Abbott, N.: Nature 557, 539 (2018)
10. Nance, E.A., Woodworth, G.F., Sailor, K.A., Shih, T.-Y., Xu, Q., Swaminathan, G., Xiang, D.,
Eberhart, C., Hanes, J.: Sci. Transl. Med. 4, 149ra119 (2012)
11. Woltman, S.J., Jay, G.D., Crawford, G.P.: Nat. Mater. 6, 929 (2007)
12. Poulin, P., Cabuil, V., Weitz, D.A.: Phys. Rev. Lett. 79, 4862 (1997)
13. Vilfan, M., Osterman, N., ˇ
Copiˇ c, M., Ravnik, M., Žumer, S., Kotar, J., Babiˇ c, D., Poberaj, I.:
Phys. Rev. Lett. 101, 237801 (2008)
14. Ognysta, U., Nych, A., Nazarenko, V., Muševiˇ c, I., Škarabot, M., Ravnik, M., Žumer, S.,
Poberaj, I., Babiˇ c, D.: Phys. Rev. Lett. 100, 217803 (2008)
351
8.5 Conclusion
In summary, using the Green’s function method, the total energy for a microparticle
suspended in an NLC cell in the presence of an external electric field is calculated.
It is found that with the application of the external electric field, it is possible to
create an anisotropic bubble around the microparticle with a vertical fast “lane” for
the microparticle to move from the midplane to a new equilibrium position. Such a
new equilibrium position is decided via a competition between the buoyant force and
the effective force built upon the microparticle inside the “lane”. The threshold value
of external field, which triggers positional transition under appropriate conditions
of surface anchoring feature, field direction and molecular dielectric anisotropy,
depends on thickness L and Frank elastic constant K and slightly on the microparticle
size and density, in a Fréedericksz-like manner as coined by the authors before, but
by a factor. For an NLC cell with planar surface alignment, a bistable equilibrium
structure for the transition is found when the direction of the applied electric field
is (a) perpendicular to the cell wall with positive molecular dielectric anisotropy,
and (b) parallel to the undeformed director field n 0 of the NLC cell with negative
molecular dielectric anisotropy. When the electric field applied is parallel to the two
plates and perpendicular to the anchoring direction, the microparticle suspended in
NLC will be trapped in the midplane, regardless of the sign of the molecular dielectric
anisotropy. Explicit formulae proposed for the critical electric field agrees extremely
well with the numerical calculation.
References
1. de Gennes, P.G., Prost, J.: The Physics of Liquid Crystals, 2nd edn. Clarendon Press, Oxford,
UK (1993)
2. Jákli, A., Lavrentovich, O.D., Selinger, J.V.: Physics of liquid crystals of bent-shaped
molecules. Rev. Mod. Phys. 90, 045004 (2018)
3. Daniel, J.C., Audebert, R.: Small Volumes and Large Surfaces: The World of Colloids in Soft
Matter Physics edited by M. Williams (Springer-Verlag, Berlin Heidelberg, Daoud and C.E
(1999)
4. Chaikin, P.M., Lubensky, T.C.: Principles of Condensed Matter Physics, Cambridge University
Press, CambridgeCambridgeCambridge, UK (2000)
5. Comiskey, B., Albert, J., Yoshizawa, H., Jacobson, J.: Nature 394, 253 (1998)
6. Wang, Z., Zhe, J.: Chip 11, 1280 (2011)
7. Araki, T., Buscaglia, M., Bellini, T., Tanaka, H.: Nat. Mater. 10, 303 (2011)
8. Smalyukh, I.I.: Annu. Rev. Condens. Matter Phys. 9, 207 (2018)
9. Kim, Y.-K., Wang, X., Mondkar, P., Bukusoglu, E., Abbott, N.: Nature 557, 539 (2018)
10. Nance, E.A., Woodworth, G.F., Sailor, K.A., Shih, T.-Y., Xu, Q., Swaminathan, G., Xiang, D.,
Eberhart, C., Hanes, J.: Sci. Transl. Med. 4, 149ra119 (2012)
11. Woltman, S.J., Jay, G.D., Crawford, G.P.: Nat. Mater. 6, 929 (2007)
12. Poulin, P., Cabuil, V., Weitz, D.A.: Phys. Rev. Lett. 79, 4862 (1997)
13. Vilfan, M., Osterman, N., ˇ
Copiˇ c, M., Ravnik, M., Žumer, S., Kotar, J., Babiˇ c, D., Poberaj, I.:
Phys. Rev. Lett. 101, 237801 (2008)
14. Ognysta, U., Nych, A., Nazarenko, V., Muševiˇ c, I., Škarabot, M., Ravnik, M., Žumer, S.,
Poberaj, I., Babiˇ c, D.: Phys. Rev. Lett. 100, 217803 (2008)