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Shearing the I-N phase transition of liquid crystalline polymers: Long-time memory of defect initial data
One order parameter tensor mean field theory for biaxial liquid crystals
1. | Department of Mathematical Sciences, Kent State University, Kent, OH 44242, United States |
2. | Liquid Crystal Institute, Kent State University, Kent, Oh 44242, United States |
References:
[1] |
B. R. Acharya, A. Primak and S. Kumar, Biaxial nematic phase in bent-core thermotropic mesogens, Phys. Rev. Lett., 92 (2004), 145506.
doi: 10.1103/PhysRevLett.92.145506. |
[2] |
R. Alben, Phase transitions in a fluid of biaxial particles, Phys. Rev. Lett., 30 (1973), 778-781.
doi: 10.1103/PhysRevLett.30.778. |
[3] |
D. W. Allender and M. A. Lee, Landau theory of biaxial nematic liquid crystals, Mol. Cryst. Liq. Cryst., 110 (1984), 331-339.
doi: 10.1080/00268948408074514. |
[4] |
D. Allender and L. Longa, Landau-de Gennes theory for biaxial nematics reexamined, Phy. Rev. E, 78 (2008), 011704.
doi: 10.1103/PhysRevE.78.011704. |
[5] | |
[6] |
M. A. Bates, Influence of flexibility on the biaxial nematic phase of bent core liquid crystals: A Monte Carlo simulation study, Phys. Rev. E, 74 (2006), 061702.
doi: 10.1103/PhysRevE.74.061702. |
[7] |
R. Berardi and C. Zannoni, Do thermotropic biaxial nematics exist? A Monte Carlo study of biaxial Gay-Berne particles, J. Chem. Phys., 113 (2000), 5971-5979.
doi: 10.1063/1.1290474. |
[8] |
B. Bergersen, P. Palffy-Muhoray and D. A. Dunmur, Uniaxial nematic phase in fluids of biaxial particles, Liq. Cryst., 3 (1988), 347-352.
doi: 10.1080/02678298808086380. |
[9] |
P. Biscari, M. C. Calderer and E. M. Terentjev, Landau-de Gennes theory of isotropic-nematic-smectic liquid crystal transitions, Phys. Rev. E, 75 (2007), 051707.
doi: 10.1103/PhysRevE.75.051707. |
[10] |
F. Biscarini, C. Chiccoli, P. Pasini, F. Semeria and C. Zannoni, Phase diagram and orientational order in a biaxial lattice model: A Monte Carlo study, Phy. Rev. Lett., 75 (1995), 1803-1806.
doi: 10.1103/PhysRevLett.75.1803. |
[11] |
F. Bisi, E. G. Virga, E. C. Garland, Jr., G. De Matteis, A. M. Sonnet and G. E. Durand, Universal mean-field phase diagram for biaxial nematics obtained from a minmax priniciple, Phys. Rev. E, 73 (2006), 051709.
doi: 10.1103/PhysRevE.73.051709. |
[12] |
C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comput., 19 (1965), 577-593.
doi: 10.1090/S0025-5718-1965-0198670-6. |
[13] |
P. J. Camp and M. P. Allen, Phase diagram of the hard biaxial ellipsoid fluid, J. Chem. Phys., 106 (1997), 6681-6688.
doi: 10.1063/1.473665. |
[14] |
C. Chiccoli, P. Pasini, F. Semeria and C. Zannoni, A detailed Monte Carlo investigation of the tricritical region of a biaxial liquid crystal system, Int. J. Mod. Phys. C, 10 (1999), 469-476.
doi: 10.1142/S0129183199000358. |
[15] |
P. G. de Gennes, "The Physics of Liquid Crystals," Clarendon Press, Oxford, 1974. |
[16] |
G. De Matties, S. Romano and E. G. Virga, Bifurcation analysis and computer simulation of biaxial liquid crystals, Phys. Rev. E, 72 (2005), 041706.
doi: 10.1103/PhysRevE.72.041706. |
[17] |
G. De Matties, A. M. Sonnet and E. G. Virga, Landau theory for biaxial nematic liquid crystals with two order parameter tensors, Continuum Mech. Thermodyn., 20 (2008), 347-374.
doi: 10.1007/s00161-008-0086-9. |
[18] |
R. Ennis, "Pattern Formation in Liquid Crystals: The Saffman-Taylor Instability and the Dynamics of Phase Separation," Ph.D. dissetation, Chemical Physics, Kent State University, 2004. |
[19] |
M. J. Freiser, Ordered states of a nematic liquid, Phys. Rev. Lett., 24 (1970), 1041-1043.
doi: 10.1103/PhysRevLett.24.1041. |
[20] |
M. J. Freiser, Successive transitions in a nematic liquid, Mol. Cryst. Liq. Cryst., 14 (1971), 165-182. |
[21] |
W. M. Gelbart and B. A. Baron, Generalized van der Waals theory of the isotropic-nematic phase transition, J. Chem. Phys., 66 (1977), 207-214.
doi: 10.1063/1.433665. |
[22] |
J. Israelachvili, "Intermolecular & Surface Forces," Academic Press, London, 1992. |
[23] |
L. Longa and G. Pajak, Luckhurst-Romano model of thermotropic biaxial nematic phase, Liq. Cryst., 32 (2005), 1409-1417.
doi: 10.1080/02678290500167873. |
[24] |
L. Longa, P. Grzybowski, S. Romano and E. Virga, Minimal coupling model of the biaxial nematic phase, Phys. Rev. E, 71 (2005), 051714.
doi: 10.1103/PhysRevE.71.051714. |
[25] |
G. R. Luckhurst and S. Romano, Computer simulation studies of anisotropic systems II. Uniaxial and biaxial nematics formed by non-cylindrically symmetric molecules, Mol. Phys., 40 (1980), 129-139.
doi: 10.1080/00268978000101341. |
[26] |
L. A. Madsen, T. J. Dingemans, M. Nakata and E. T. Samulski, Thermotropic biaxial nematic liquid crystals, Phys. Rev. Lett., 92 (2004), 145505.
doi: 10.1103/PhysRevLett.92.145505. |
[27] |
W. Maier and A. Saupe, A simple molecular theory of the namatic liquid-crystalline state, Zeischrift Naturforschung, 13 (1958), 564-566. |
[28] |
K. Merkel, A. Kocot, J. K. Vij, R. Korlacki, G. H. Mehl and T. Meyer, Thermotropic biaxial nematic phase in liquid crystalline organo-siloxane tetrapodes, Phys. Rev. Lett., 93 (2004), 237801.
doi: 10.1103/PhysRevLett.93.237801. |
[29] |
P. K. Mukherjee, Improved analysis of the Landau theory of the uniaxail-biaxial nematic phase transition, Liq. Cryst., 24 (1998), 519-523.
doi: 10.1080/026782998206966. |
[30] |
B. M. Mulder, Solution of the excluded volume problem for biaxial particles, Liq. Cryst., 1 (1986), 539-551.
doi: 10.1080/02678298608086278. |
[31] |
P. Palffy-Muhoray, The single particle potential in mean-field theory, Am. J. Phys., 70 (2002), 433-437.
doi: 10.1119/1.1446860. |
[32] |
P. Palffy-Muhoray and B. Bergersen, van der Waals theory for nematic liquid crystals, Phys. Rev. A, 35 (1987), 2704 -2708.
doi: 10.1103/PhysRevA.35.2704. |
[33] |
S. Sarman, Molecular dynamics of biaxial nematic liquid crystals, J. Chem. Phys., 104 (1996), 342-350.
doi: 10.1063/1.470833. |
[34] |
C. S. Shih and R. Alben, Lattice model for biaxial liquid crystals, J. Chem. Phys., 57 (1972), 3055-3061.
doi: 10.1063/1.1678719. |
[35] |
S. Sircar and Q. Wang, Shear-induced mesostructures in biaxial liquid crystals, Phy. Rev. E, 78 (2008), 061702.
doi: 10.1103/PhysRevE.78.061702. |
[36] |
S. Sircar and Q. Wang, Dynamics and rheology of biaxial liquid crystal polymers in shear flows, J. Rheol., 53 (2009), 819-858.
doi: 10.1122/1.3143788. |
[37] |
A. M. Sonnet, E. G. Virga and G. E. Durand, Dielectric shape dispersion and biaxial transitions in nematic liquid crystals, Phys. Rev. E, 67 (2003), 061701.
doi: 10.1103/PhysRevE.67.061701. |
[38] |
A. M. Sonnet and E. G. Virga, Steric effects in dispersion forces interactions, Phys. Rev. E, 77 (2008), 031704.
doi: 10.1103/PhysRevE.77.031704. |
[39] |
J. P. Straley, Ordered phases of a liquid of biaxial particles, Phy. Rev. A, 10 (1974), 1881-1887.
doi: 10.1103/PhysRevA.10.1881. |
[40] |
M. C. J. M. Vissenberg, S. Stallinga and G. Vertogen, Generalized Landau-de Gennes theory of uniaxial and biaxial nematic liquid crystals, Phy. Rev. E, 55 (1997), 4367-4377.
doi: 10.1103/PhysRevE.55.4367. |
[41] |
L. J. Yu and A. Saupe, Observation of a biaxial nematic Phase in potassium Laurate-1-Decanol-Water mixtures, Phys. Rev. Lett., 45 (1980), 1000-1003.
doi: 10.1103/PhysRevLett.45.1000. |
show all references
References:
[1] |
B. R. Acharya, A. Primak and S. Kumar, Biaxial nematic phase in bent-core thermotropic mesogens, Phys. Rev. Lett., 92 (2004), 145506.
doi: 10.1103/PhysRevLett.92.145506. |
[2] |
R. Alben, Phase transitions in a fluid of biaxial particles, Phys. Rev. Lett., 30 (1973), 778-781.
doi: 10.1103/PhysRevLett.30.778. |
[3] |
D. W. Allender and M. A. Lee, Landau theory of biaxial nematic liquid crystals, Mol. Cryst. Liq. Cryst., 110 (1984), 331-339.
doi: 10.1080/00268948408074514. |
[4] |
D. Allender and L. Longa, Landau-de Gennes theory for biaxial nematics reexamined, Phy. Rev. E, 78 (2008), 011704.
doi: 10.1103/PhysRevE.78.011704. |
[5] | |
[6] |
M. A. Bates, Influence of flexibility on the biaxial nematic phase of bent core liquid crystals: A Monte Carlo simulation study, Phys. Rev. E, 74 (2006), 061702.
doi: 10.1103/PhysRevE.74.061702. |
[7] |
R. Berardi and C. Zannoni, Do thermotropic biaxial nematics exist? A Monte Carlo study of biaxial Gay-Berne particles, J. Chem. Phys., 113 (2000), 5971-5979.
doi: 10.1063/1.1290474. |
[8] |
B. Bergersen, P. Palffy-Muhoray and D. A. Dunmur, Uniaxial nematic phase in fluids of biaxial particles, Liq. Cryst., 3 (1988), 347-352.
doi: 10.1080/02678298808086380. |
[9] |
P. Biscari, M. C. Calderer and E. M. Terentjev, Landau-de Gennes theory of isotropic-nematic-smectic liquid crystal transitions, Phys. Rev. E, 75 (2007), 051707.
doi: 10.1103/PhysRevE.75.051707. |
[10] |
F. Biscarini, C. Chiccoli, P. Pasini, F. Semeria and C. Zannoni, Phase diagram and orientational order in a biaxial lattice model: A Monte Carlo study, Phy. Rev. Lett., 75 (1995), 1803-1806.
doi: 10.1103/PhysRevLett.75.1803. |
[11] |
F. Bisi, E. G. Virga, E. C. Garland, Jr., G. De Matteis, A. M. Sonnet and G. E. Durand, Universal mean-field phase diagram for biaxial nematics obtained from a minmax priniciple, Phys. Rev. E, 73 (2006), 051709.
doi: 10.1103/PhysRevE.73.051709. |
[12] |
C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comput., 19 (1965), 577-593.
doi: 10.1090/S0025-5718-1965-0198670-6. |
[13] |
P. J. Camp and M. P. Allen, Phase diagram of the hard biaxial ellipsoid fluid, J. Chem. Phys., 106 (1997), 6681-6688.
doi: 10.1063/1.473665. |
[14] |
C. Chiccoli, P. Pasini, F. Semeria and C. Zannoni, A detailed Monte Carlo investigation of the tricritical region of a biaxial liquid crystal system, Int. J. Mod. Phys. C, 10 (1999), 469-476.
doi: 10.1142/S0129183199000358. |
[15] |
P. G. de Gennes, "The Physics of Liquid Crystals," Clarendon Press, Oxford, 1974. |
[16] |
G. De Matties, S. Romano and E. G. Virga, Bifurcation analysis and computer simulation of biaxial liquid crystals, Phys. Rev. E, 72 (2005), 041706.
doi: 10.1103/PhysRevE.72.041706. |
[17] |
G. De Matties, A. M. Sonnet and E. G. Virga, Landau theory for biaxial nematic liquid crystals with two order parameter tensors, Continuum Mech. Thermodyn., 20 (2008), 347-374.
doi: 10.1007/s00161-008-0086-9. |
[18] |
R. Ennis, "Pattern Formation in Liquid Crystals: The Saffman-Taylor Instability and the Dynamics of Phase Separation," Ph.D. dissetation, Chemical Physics, Kent State University, 2004. |
[19] |
M. J. Freiser, Ordered states of a nematic liquid, Phys. Rev. Lett., 24 (1970), 1041-1043.
doi: 10.1103/PhysRevLett.24.1041. |
[20] |
M. J. Freiser, Successive transitions in a nematic liquid, Mol. Cryst. Liq. Cryst., 14 (1971), 165-182. |
[21] |
W. M. Gelbart and B. A. Baron, Generalized van der Waals theory of the isotropic-nematic phase transition, J. Chem. Phys., 66 (1977), 207-214.
doi: 10.1063/1.433665. |
[22] |
J. Israelachvili, "Intermolecular & Surface Forces," Academic Press, London, 1992. |
[23] |
L. Longa and G. Pajak, Luckhurst-Romano model of thermotropic biaxial nematic phase, Liq. Cryst., 32 (2005), 1409-1417.
doi: 10.1080/02678290500167873. |
[24] |
L. Longa, P. Grzybowski, S. Romano and E. Virga, Minimal coupling model of the biaxial nematic phase, Phys. Rev. E, 71 (2005), 051714.
doi: 10.1103/PhysRevE.71.051714. |
[25] |
G. R. Luckhurst and S. Romano, Computer simulation studies of anisotropic systems II. Uniaxial and biaxial nematics formed by non-cylindrically symmetric molecules, Mol. Phys., 40 (1980), 129-139.
doi: 10.1080/00268978000101341. |
[26] |
L. A. Madsen, T. J. Dingemans, M. Nakata and E. T. Samulski, Thermotropic biaxial nematic liquid crystals, Phys. Rev. Lett., 92 (2004), 145505.
doi: 10.1103/PhysRevLett.92.145505. |
[27] |
W. Maier and A. Saupe, A simple molecular theory of the namatic liquid-crystalline state, Zeischrift Naturforschung, 13 (1958), 564-566. |
[28] |
K. Merkel, A. Kocot, J. K. Vij, R. Korlacki, G. H. Mehl and T. Meyer, Thermotropic biaxial nematic phase in liquid crystalline organo-siloxane tetrapodes, Phys. Rev. Lett., 93 (2004), 237801.
doi: 10.1103/PhysRevLett.93.237801. |
[29] |
P. K. Mukherjee, Improved analysis of the Landau theory of the uniaxail-biaxial nematic phase transition, Liq. Cryst., 24 (1998), 519-523.
doi: 10.1080/026782998206966. |
[30] |
B. M. Mulder, Solution of the excluded volume problem for biaxial particles, Liq. Cryst., 1 (1986), 539-551.
doi: 10.1080/02678298608086278. |
[31] |
P. Palffy-Muhoray, The single particle potential in mean-field theory, Am. J. Phys., 70 (2002), 433-437.
doi: 10.1119/1.1446860. |
[32] |
P. Palffy-Muhoray and B. Bergersen, van der Waals theory for nematic liquid crystals, Phys. Rev. A, 35 (1987), 2704 -2708.
doi: 10.1103/PhysRevA.35.2704. |
[33] |
S. Sarman, Molecular dynamics of biaxial nematic liquid crystals, J. Chem. Phys., 104 (1996), 342-350.
doi: 10.1063/1.470833. |
[34] |
C. S. Shih and R. Alben, Lattice model for biaxial liquid crystals, J. Chem. Phys., 57 (1972), 3055-3061.
doi: 10.1063/1.1678719. |
[35] |
S. Sircar and Q. Wang, Shear-induced mesostructures in biaxial liquid crystals, Phy. Rev. E, 78 (2008), 061702.
doi: 10.1103/PhysRevE.78.061702. |
[36] |
S. Sircar and Q. Wang, Dynamics and rheology of biaxial liquid crystal polymers in shear flows, J. Rheol., 53 (2009), 819-858.
doi: 10.1122/1.3143788. |
[37] |
A. M. Sonnet, E. G. Virga and G. E. Durand, Dielectric shape dispersion and biaxial transitions in nematic liquid crystals, Phys. Rev. E, 67 (2003), 061701.
doi: 10.1103/PhysRevE.67.061701. |
[38] |
A. M. Sonnet and E. G. Virga, Steric effects in dispersion forces interactions, Phys. Rev. E, 77 (2008), 031704.
doi: 10.1103/PhysRevE.77.031704. |
[39] |
J. P. Straley, Ordered phases of a liquid of biaxial particles, Phy. Rev. A, 10 (1974), 1881-1887.
doi: 10.1103/PhysRevA.10.1881. |
[40] |
M. C. J. M. Vissenberg, S. Stallinga and G. Vertogen, Generalized Landau-de Gennes theory of uniaxial and biaxial nematic liquid crystals, Phy. Rev. E, 55 (1997), 4367-4377.
doi: 10.1103/PhysRevE.55.4367. |
[41] |
L. J. Yu and A. Saupe, Observation of a biaxial nematic Phase in potassium Laurate-1-Decanol-Water mixtures, Phys. Rev. Lett., 45 (1980), 1000-1003.
doi: 10.1103/PhysRevLett.45.1000. |
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