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Diffusive transport in two-dimensional nematics
Structure formation in sheared polymer-rod nanocomposites
1. | Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
2. | Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States |
3. | School of Mathematics and LPMC, Nankai University, Tianjin 300071 |
References:
[1] |
R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids, 2nd edition, Wiley-Interscience, 1987. |
[2] |
A. V. Bhave, Kinetic Theory for Dilute and Concentrated Polymer Solutions: Study of Nonhomogeneous Effects, Ph. D. Thesis, MIT, 1992. |
[3] |
W. Brostow, T. S. Dziemianowicz, M. Hess and R. Kosfeld, Blending of Polymer Liquid Crystals with Engineering Polymers: The importance of Phse Diagrams, in Liquid Crystalline Polymers, (eds. R. A. Weiss and C. K. Ober), American Chemical Society, Washington, DC, (1990), 402-415. |
[4] |
G. P. Crawford and S. Zummer, Liquid Crystals in Complex Geometries Formed by Polymer and Porous Networks, Taylor & Francis, London, 1996. |
[5] |
P. G. DeGennes, Dynamics of Fluctuations and Spinodal Decomposition in Polymer Blends, J. Chem. Phys., 72 (1980), 4756-4763.
doi: 10.1063/1.439809. |
[6] |
P. G. DeGennes and J. Prost, The Physics of Liquid Crystals, 2nd edition, Oxford University Press, UK, 1993. |
[7] |
J. K. G. Dhont and W. J. Briels, Stresses in inhomogeneous suspensions, J. Chem. Phys., 117 (2002), 3992-3999.
doi: 10.1063/1.1495842. |
[8] |
J. K. G. Dhont and W. J. Briels, Inhomogeneous suspensions of rigid rods in flow, J. Chem. Phys., 118 (2003), 1466-1478.
doi: 10.1063/1.1528912. |
[9] |
J. K. G. Dhont and W. J. Briels, Viscoelasticity of suspensions of long, rigid rods, Colloids and Surfaces A: Physicochem Eng. Aspects, 213 (2003), 131-156.
doi: 10.1016/S0927-7757(02)00508-3. |
[10] |
J. K. G. Dhont, M. P. G. vanBruggen and W. J. Briels, Long-time self-diffusion of rigid rod at low concentration: A variational approach, Macromolecules, 32 (1999), 3809-3816.
doi: 10.1021/ma981765i. |
[11] |
M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, UK, 1986. |
[12] |
J. J. Feng, G. Sgalari and L. G. Leal, A Theory for Flowing Nematic Polymers with Orientational Distortion, J. Rheol., 44 (2000), 1085-1101.
doi: 10.1122/1.1289278. |
[13] |
Y. Dzenis, MATERIALS SCIENCE: Structural nanocomposites, Science, 319 (2008), 419-420.
doi: 10.1126/science.1151434. |
[14] |
W. E and P. Palffy-Muhoray, Phase Separation in Incompressible e Systems, Phys. Rev. E, 55 (1997), 3844-3846. |
[15] |
H. Eslami, M. Grmela and M. Bousmina, A mesoscopic rheological model of polymer/layered silicate nanocomposites, J. Rhol., 51 (2007), 1189-1222.
doi: 10.1122/1.2790461. |
[16] |
M. G. Forest, Q. Liao and Q. Wang, A 2-D Kinetic Theory for Flows of Monodomain Polymer-Rod Nanocomposites, Commun. Comput. Phys., 7 (2009), 250-282.
doi: 10.4208/cicp.2009.08.204. |
[17] |
M. G. Forest and Q. Wang, Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, Rheol. Acta, 42 (2003), 20-46. |
[18] |
M. G. Forest, R. Zhou and Q. Wang, Chaotic boundaries of nematic polymers in mixed shear and extensional flows, Phys. Rev. Lett., 93 (2004), 088301-088305. |
[19] |
M. G. Forest, Q. Wang and R. Zhou, The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: Finite shear rates, Rheol. Acta, 44 (2004), 80-93.
doi: 10.1007/s00397-004-0380-9. |
[20] |
G. Forest and Q. Wang, Hydrodynamic theories for mixture of polymers and rodlike liquid crystalline polymers, Phys. Rev. E, 72 (2005), 041805.
doi: 10.1103/PhysRevE.72.041805. |
[21] |
A. R. Khokhlov and A. N. Semenov, Liquid-crystalline ordering in solutions of semiflexible macromolecules with rotational-isomeric flexibility, Macromolecules, 17 (1984), 2678-2685.
doi: 10.1021/ma00142a040. |
[22] |
R. G. Larson, Constitutive Equations for Polymer Melts and Solutions, Butterworths, Boston, 1988. |
[23] |
L. C. Polymers, Report of the Committee on Liquid Crystalline Polymers, National Academic Press, 1990. |
[24] |
A. J. Liu and G. H. Fredrickson, Phase separation kinetics of rod/coil mixtures, Macromolecules, 29 (1996), 8000-8009.
doi: 10.1021/ma960796f. |
[25] |
D. Long and D. C. Morse, A rouse-like model of liquid crystalline polymer melts: Director dynamics and linear viscoelasticity, J. Rheol., 46 (2002), 49-92.
doi: 10.1122/1.1423313. |
[26] |
T. C. Lubensky and P. M. Chaikin, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, 1995. |
[27] |
P. A. Mirau, J. L. Serres, D. Jacobs, P. H. Garrett and R. A. Vaia, Structure and dynamics of surfactant interfaces in organically modified clays, J. Phys. Chem. B, 112 (2008), 10544-10551.
doi: 10.1021/jp801479h. |
[28] |
C. Muratov and W. E, Theory of phase separation kinetics in polymer-liquid crystal system, J. Chem. Phys., 116 (2002), 4723-4734.
doi: 10.1063/1.1426411. |
[29] |
M. Rajabian, C. Dubois and M. Grmela, Suspensions of semiflexible fibers in polymeric fluids: Rheology and thermodynamics, Rheol. Acta, 44 (2005), 521-535.
doi: 10.1007/s00397-005-0434-7. |
[30] |
A. V. Richard and H. D. Wagner, Framework for nanocomposites, Materials Today, 7 (2004), 32-37. |
[31] |
R. A. Vaia, Polymer Nanocomposites Open a New Dimension for Plastics and Composites, DTIC Report, 2005. |
[32] |
R. A. Vaia, Nanocomposites: Remote-controlled actuators, Nature Materials, 4 (2005), 429-430.
doi: 10.1038/nmat1400. |
[33] |
H. D. Wagner and R. A. Vaia, Nanocomposites: Issues at the interface, Materials Today, 7 (2004), 38-42.
doi: 10.1016/S1369-7021(04)00507-3. |
[34] |
Q. Wang, A hydrodynamic theory of nematic liquid crystalline polymers of different configurations, J. Chem. Phys., 116 (2002), 9120-9136. |
[35] |
Q. Wang, W. E, C. Liu and P. Zhang, Kinetic theories for flows of nonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecular potential, Phys. Rev. E, 65 (2002), 051504.
doi: 10.1103/PhysRevE.65.051504. |
[36] |
K. I. Winey and R. A. Vaia, Polymer nanocomposites, MRS bulletin, 32 (2007), 314-322.
doi: 10.1557/mrs2007.229. |
[37] |
D. Wu, C. Zhou, Z. Hong, D. Mao and Z. Bian, Study on rheological behaviour of poly(butylene terephthalate)/montmorillonite nanocomposites, Eur. Polym. J., 41 (2005), 2199-2207.
doi: 10.1016/j.eurpolymj.2005.03.005. |
[38] |
J. Zhao, A. B. Morgan and J. D. Harris, Rheological characterization of polystyreneclay nanocomposites to compare the degree of exfoliation and dispersion, Polymer, 46 (2005), 86418660. |
show all references
References:
[1] |
R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids, 2nd edition, Wiley-Interscience, 1987. |
[2] |
A. V. Bhave, Kinetic Theory for Dilute and Concentrated Polymer Solutions: Study of Nonhomogeneous Effects, Ph. D. Thesis, MIT, 1992. |
[3] |
W. Brostow, T. S. Dziemianowicz, M. Hess and R. Kosfeld, Blending of Polymer Liquid Crystals with Engineering Polymers: The importance of Phse Diagrams, in Liquid Crystalline Polymers, (eds. R. A. Weiss and C. K. Ober), American Chemical Society, Washington, DC, (1990), 402-415. |
[4] |
G. P. Crawford and S. Zummer, Liquid Crystals in Complex Geometries Formed by Polymer and Porous Networks, Taylor & Francis, London, 1996. |
[5] |
P. G. DeGennes, Dynamics of Fluctuations and Spinodal Decomposition in Polymer Blends, J. Chem. Phys., 72 (1980), 4756-4763.
doi: 10.1063/1.439809. |
[6] |
P. G. DeGennes and J. Prost, The Physics of Liquid Crystals, 2nd edition, Oxford University Press, UK, 1993. |
[7] |
J. K. G. Dhont and W. J. Briels, Stresses in inhomogeneous suspensions, J. Chem. Phys., 117 (2002), 3992-3999.
doi: 10.1063/1.1495842. |
[8] |
J. K. G. Dhont and W. J. Briels, Inhomogeneous suspensions of rigid rods in flow, J. Chem. Phys., 118 (2003), 1466-1478.
doi: 10.1063/1.1528912. |
[9] |
J. K. G. Dhont and W. J. Briels, Viscoelasticity of suspensions of long, rigid rods, Colloids and Surfaces A: Physicochem Eng. Aspects, 213 (2003), 131-156.
doi: 10.1016/S0927-7757(02)00508-3. |
[10] |
J. K. G. Dhont, M. P. G. vanBruggen and W. J. Briels, Long-time self-diffusion of rigid rod at low concentration: A variational approach, Macromolecules, 32 (1999), 3809-3816.
doi: 10.1021/ma981765i. |
[11] |
M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, UK, 1986. |
[12] |
J. J. Feng, G. Sgalari and L. G. Leal, A Theory for Flowing Nematic Polymers with Orientational Distortion, J. Rheol., 44 (2000), 1085-1101.
doi: 10.1122/1.1289278. |
[13] |
Y. Dzenis, MATERIALS SCIENCE: Structural nanocomposites, Science, 319 (2008), 419-420.
doi: 10.1126/science.1151434. |
[14] |
W. E and P. Palffy-Muhoray, Phase Separation in Incompressible e Systems, Phys. Rev. E, 55 (1997), 3844-3846. |
[15] |
H. Eslami, M. Grmela and M. Bousmina, A mesoscopic rheological model of polymer/layered silicate nanocomposites, J. Rhol., 51 (2007), 1189-1222.
doi: 10.1122/1.2790461. |
[16] |
M. G. Forest, Q. Liao and Q. Wang, A 2-D Kinetic Theory for Flows of Monodomain Polymer-Rod Nanocomposites, Commun. Comput. Phys., 7 (2009), 250-282.
doi: 10.4208/cicp.2009.08.204. |
[17] |
M. G. Forest and Q. Wang, Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, Rheol. Acta, 42 (2003), 20-46. |
[18] |
M. G. Forest, R. Zhou and Q. Wang, Chaotic boundaries of nematic polymers in mixed shear and extensional flows, Phys. Rev. Lett., 93 (2004), 088301-088305. |
[19] |
M. G. Forest, Q. Wang and R. Zhou, The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: Finite shear rates, Rheol. Acta, 44 (2004), 80-93.
doi: 10.1007/s00397-004-0380-9. |
[20] |
G. Forest and Q. Wang, Hydrodynamic theories for mixture of polymers and rodlike liquid crystalline polymers, Phys. Rev. E, 72 (2005), 041805.
doi: 10.1103/PhysRevE.72.041805. |
[21] |
A. R. Khokhlov and A. N. Semenov, Liquid-crystalline ordering in solutions of semiflexible macromolecules with rotational-isomeric flexibility, Macromolecules, 17 (1984), 2678-2685.
doi: 10.1021/ma00142a040. |
[22] |
R. G. Larson, Constitutive Equations for Polymer Melts and Solutions, Butterworths, Boston, 1988. |
[23] |
L. C. Polymers, Report of the Committee on Liquid Crystalline Polymers, National Academic Press, 1990. |
[24] |
A. J. Liu and G. H. Fredrickson, Phase separation kinetics of rod/coil mixtures, Macromolecules, 29 (1996), 8000-8009.
doi: 10.1021/ma960796f. |
[25] |
D. Long and D. C. Morse, A rouse-like model of liquid crystalline polymer melts: Director dynamics and linear viscoelasticity, J. Rheol., 46 (2002), 49-92.
doi: 10.1122/1.1423313. |
[26] |
T. C. Lubensky and P. M. Chaikin, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, 1995. |
[27] |
P. A. Mirau, J. L. Serres, D. Jacobs, P. H. Garrett and R. A. Vaia, Structure and dynamics of surfactant interfaces in organically modified clays, J. Phys. Chem. B, 112 (2008), 10544-10551.
doi: 10.1021/jp801479h. |
[28] |
C. Muratov and W. E, Theory of phase separation kinetics in polymer-liquid crystal system, J. Chem. Phys., 116 (2002), 4723-4734.
doi: 10.1063/1.1426411. |
[29] |
M. Rajabian, C. Dubois and M. Grmela, Suspensions of semiflexible fibers in polymeric fluids: Rheology and thermodynamics, Rheol. Acta, 44 (2005), 521-535.
doi: 10.1007/s00397-005-0434-7. |
[30] |
A. V. Richard and H. D. Wagner, Framework for nanocomposites, Materials Today, 7 (2004), 32-37. |
[31] |
R. A. Vaia, Polymer Nanocomposites Open a New Dimension for Plastics and Composites, DTIC Report, 2005. |
[32] |
R. A. Vaia, Nanocomposites: Remote-controlled actuators, Nature Materials, 4 (2005), 429-430.
doi: 10.1038/nmat1400. |
[33] |
H. D. Wagner and R. A. Vaia, Nanocomposites: Issues at the interface, Materials Today, 7 (2004), 38-42.
doi: 10.1016/S1369-7021(04)00507-3. |
[34] |
Q. Wang, A hydrodynamic theory of nematic liquid crystalline polymers of different configurations, J. Chem. Phys., 116 (2002), 9120-9136. |
[35] |
Q. Wang, W. E, C. Liu and P. Zhang, Kinetic theories for flows of nonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecular potential, Phys. Rev. E, 65 (2002), 051504.
doi: 10.1103/PhysRevE.65.051504. |
[36] |
K. I. Winey and R. A. Vaia, Polymer nanocomposites, MRS bulletin, 32 (2007), 314-322.
doi: 10.1557/mrs2007.229. |
[37] |
D. Wu, C. Zhou, Z. Hong, D. Mao and Z. Bian, Study on rheological behaviour of poly(butylene terephthalate)/montmorillonite nanocomposites, Eur. Polym. J., 41 (2005), 2199-2207.
doi: 10.1016/j.eurpolymj.2005.03.005. |
[38] |
J. Zhao, A. B. Morgan and J. D. Harris, Rheological characterization of polystyreneclay nanocomposites to compare the degree of exfoliation and dispersion, Polymer, 46 (2005), 86418660. |
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