Dynamics of a ±1/2 Defect Pair in a Confined Geometry
Affiliation(s)
1 Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, China. 2 University of Chinese Academy of Sciences, Beijing, China. 3 School of Science, Hebei University of Technology, Tianjin, China.
1 Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, China. 2 University of Chinese Academy of Sciences, Beijing, China. 3 School of Science, Hebei University of Technology, Tianjin, China.
ABSTRACT
This paper investigated the dynamics of a dipole of ±1/2 parallel wedge disclination lines in a confined geometry, based on Landau-de Gennes theory. The behavior of the pair depends on the competition between two kinds of forces: the attractive force between the two defects, aggravating the annihilation process, and the anchoring forces coming from the substrates, inhibiting the annihilation process. There are three states when the system is equilibrium, divided by two critical thicknesses dc1 and dc2 (existing when r0≤15ξ, r0 is the initial distance between the two defects), both changing linearly with r0. When the cell gap d＞dc1, the two defects coalesce and annihilate. The dynamics follows the function of r∝(t0-t)α during the annihilation step when d is sufficiently large, relative to r0, where r is the relative distance between the pair and t0 is the coalescence time. α decreases with the decrease of d or the increase of r0. The annihilation process has delicate structures: when r0≤15ξ and d＞dc2 or r0＞15ξand d＞dc1, the two defects annihilate and the system is uniaxial at equilibrium state; when r0≤15ξ and dc2＞d＞dc1, the two defects coalesce and annihilate, and the system is not uniaxial, but biaxial in the region where the defects collide. When d≤dc1, the defects can be stable existence.
This paper investigated the dynamics of a dipole of ±1/2 parallel wedge disclination lines in a confined geometry, based on Landau-de Gennes theory. The behavior of the pair depends on the competition between two kinds of forces: the attractive force between the two defects, aggravating the annihilation process, and the anchoring forces coming from the substrates, inhibiting the annihilation process. There are three states when the system is equilibrium, divided by two critical thicknesses dc1 and dc2 (existing when r0≤15ξ, r0 is the initial distance between the two defects), both changing linearly with r0. When the cell gap d＞dc1, the two defects coalesce and annihilate. The dynamics follows the function of r∝(t0-t)α during the annihilation step when d is sufficiently large, relative to r0, where r is the relative distance between the pair and t0 is the coalescence time. α decreases with the decrease of d or the increase of r0. The annihilation process has delicate structures: when r0≤15ξ and d＞dc2 or r0＞15ξand d＞dc1, the two defects annihilate and the system is uniaxial at equilibrium state; when r0≤15ξ and dc2＞d＞dc1, the two defects coalesce and annihilate, and the system is not uniaxial, but biaxial in the region where the defects collide. When d≤dc1, the defects can be stable existence.
Cite this paper
Lu, L. , Zhang, Z. (2014) Dynamics of a ±1/2 Defect Pair in a Confined Geometry. Journal of Modern Physics, 5, 2080-2088. doi: 10.4236/jmp.2014.518204.
Lu, L. , Zhang, Z. (2014) Dynamics of a ±1/2 Defect Pair in a Confined Geometry. Journal of Modern Physics, 5, 2080-2088. doi: 10.4236/jmp.2014.518204.
References
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[1] Carbone, G., Lombardo, G., Barberi, R., Musevic, I. and Tkalec, U. (2009) Physical Review Letters, 103, Article ID: 167801. [2] Kurik, M.V. and Lavrentovich, O.D. (1988) Soviet Physics—Uspekhi, 31, 196-224.
http://iopscience.iop.org/0038-5670
http://dx.doi.org/10.1070/PU1988v031n03ABEH005710 [3] Tiribocchi, A., Gonnella, G., Marenduzzo, D. and Orlandini, E. (2010) Applied Physics Letters, 97, Article ID: 143505.
http://dx.doi.org/10.1063/1.3496472 [4] Takuya, O. and Jun-Ichi, F. (2012) Nature Communications, 3, 701-707.
http://dx.doi.org/10.1038/ncomms1709 [5] Takuya, O., Jun-Ichi, F., Kosuke, S. and Yamaguchi, T. (2012) Physical Review E, 86, Article ID: 030701(R). [6] Tkalec, U., Ravnik, M., Copar, S., Zumer, S. and Musevic, I. (2011) Science, 333, 62-65.
http://dx.doi.org/10.1126/science.1205705 [7] Ravnik, M., Alexander, G.P., Yeomans, J.M. and Zumer, S. (2011) Proceedings of the National Academy of Sciences of the United States of America, 108, 5188-5192.
http://dx.doi.org/10.1073/pnas.1015831108 [8] Fleury, J.B., Pires, D. and Galerne, Y. (2009) Physical Review Letters, 103, Article ID: 267801.
http://dx.doi.org/10.1103/PhysRevLett.103.267801 [9] Yoon, D.K., Choi, M.C., Kim, Y.H., Kim, M.W., Lavrentovich, O.D. and Jung, H.T. (2007) Nature Materials, 6, 866-870.
http://dx.doi.org/10.1038/nmat2029 [10] Milette, J., Cowling, S.J., Toader, V., Lavigne, C., Saez, I.M., Lennox, R.B., Goodby, J.W. and Reven, L. (2012) Soft Materials, 8, 173-179.
http://dx.doi.org/10.1039/c1sm06604h [11] Coursault, D., Grand, J., Zappone, B., Ayeb, H., Levi, G., Felidj, N. and Lacaze, E. (2012) Advanced Materials, 24, 1461-1465.
http://dx.doi.org/10.1002/adma.201103791 [12] Gennes, P.G. and Prost, J. (2008) The Physics of Liquid Crystals. 2nd Edition, Science Press, Beijing. [13] Minoura, K., Kimura, Y., Ito, K., Hayakawa, R. and Miura, T. (1998) Physical Review E, 58, 643-649.
http://dx.doi.org/10.1103/PhysRevE.58.643 [14] Bogi, A., Martinot-Lagarde, P., Dozov, I. and Nobili, M. (2002) Physical Review Letters, 89, Article ID: 225501.
http://dx.doi.org/10.1103/PhysRevLett.89.225501 [15] Chuang, I., Turok, N. and Yurke, B. (1991) Physical Review Letters, 66, 2472-2475.
http://dx.doi.org/10.1103/PhysRevLett.66.2472 [16] Pargellis, A., Turok, N. and Yurke, B. (1991) Physical Review Letters, 67, 1570-1573.
http://dx.doi.org/10.1103/PhysRevLett.67.1570 [17] Chuang, I., Yurke, B., Pargellis, A.N. and Turok, N. (1993) Physical Review E, 47, 3343-3356.
http://dx.doi.org/10.1103/PhysRevE.47.3343 [18] Pargellis, A.N., Mendez, J., Srinivasarao, M. and Yurke, B. (1996) Physical Review E, 53, R25-R28.
http://dx.doi.org/10.1103/PhysRevE.53.R25 [19] Minoura, K., Kimura, Y., Ito, K. and Hayakawa, R. (1997) Molecular Crystals and Liquid Crystals Science and Technology. Section A: Molecular Crystals and Liquid Crystals, 302, 345-355.
http://dx.doi.org/10.1080/10587259708041847 [20] Wang, W., Shiwaku, T. and Hashimoto, T. (1998) The Journal of Chemical Physics, 108, 1618-1625.
http://dx.doi.org/10.1063/1.475532 [21] Svensek, D. and Zumer, S. (2002) Physical Review E, 66, Article ID: 021712.
http://dx.doi.org/10.1103/PhysRevE.66.021712 [22] Tóth, G., Denniston, C. and Yeomans, J.M. (2002) Physical Review Letters, 88, Article ID: 105504.
http://dx.doi.org/10.1103/PhysRevLett.88.105504 [23] Bradac, Z., Kralj, S., Svetec, M. and Zumer, S. (2003) Physical Review E, 67, Article ID: 050702. [24] Svetec, M., Kralj, S., Bradac, Z. and Zumer, S. (2006) The European Physical Journal E, 20, 71-79.
http://dx.doi.org/10.1140/epje/i2005-10120-9 [25] Guimaraes, R.R., Mendes, R.S., Fernandes, P.R.G. and Mukai, H. (2013) Journal of Physics: Condensed Matter, 25, Article ID: 404203. [26] Giomi, L., Bowick, M.J., Ma, X. and Marchetti, M.C. (2013) Physical Review Letters, 110, Article ID: 228101.
http://dx.doi.org/10.1103/PhysRevLett.110.228101 [27] Peroli, G.G. and Virga, E.G. (1999) Physical Review E, 59, 3027-3032. http://dx.doi.org/10.1103/PhysRevE.59.3027 [28] Lu, L.X. and Zhang, Z.D. Chinese Physics B, in Press. [29] Bisi, F., Gartland, E.C., Rosso, R. and Virga, E.G. (2003) Physical Review E, 68, Article ID: 021707.
http://dx.doi.org/10.1103/PhysRevE.68.021707 [30] Barberi, R., Ciuchi, F., Durand, G., Iovane, M., Sikharulidze, D., Sonnet, A. and Virga, E. (2004) The European Physical Journal E: Soft Matter, 13, 61-71.
http://dx.doi.org/10.1140/epje/e2004-00040-5 [31] Lombardo, G., Ayeb, H. and Barberi, R. (2008) Physical Review E, 77, Article ID: 051708. [32] Schopohl, N. and Sluckin, T.J. (1987) Physical Review Letters, 59, 2582-2584.
http://dx.doi.org/10.1103/PhysRevLett.59.2582 [33] Lu, L.X., Zhang, Z.D. and Zhou, X. (2013) Acta Physica Sinica, 62, Article ID: 226101. [34] Zhou, X. and Zhang, Z.D. (2013) International Journal of Molecular Sciences, 14, 24135-24153.
http://dx.doi.org/10.3390/ijms141224135 [35] Qian, T.Z. and Sheng, P. (1997) Physical Review E, 55, 7111-7120.
http://dx.doi.org/10.1103/PhysRevE.55.7111