Abstract
We extend the theory for surface modes at the nematic-isotropic interface1,2,3,4 to study comparatively two systems: nematic-non-nematic and polymer nematic mixtures. We employ the dynamical generalization of the Landau de Gennes model for the orientational (non-conserved) order parameter, coupled with the Cahn Hilliard equation for concentration (conserved parameter), and include hydrodynamic degrees of freedom. The densities to include the coupling between the concentration of the nonnematogen and polymer fluids and the orientational order parameter. Two representative phase diagrams are shown. The method of matched asymptotic expansions is used to obtain a generalized dispersion relation. Further analysis is made in particular cases. Orientational order parameter relaxation dominates in the short wavelength limit, while in the long wavelength limit, the viscous damping processes become important. There is an intermediate region (depending on the temperature) in which the interaction between conserved parameter dynamics and hydrodynamics is important.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Popa-Nita, V. and Sluckin, T. J. (2002) Phys. Rev. E 66, 041703.
Popa-Nita, V. and Oswald, P. (2003) Phys. Rev. E 68, 061707.
Popa-Nita, V., Sluckin, T. J., and Kralj, S. (2005) Phys. Rev. E 71, 061716.
Popa-Nita, V., Oswald, P., and Sluckin, T. J. 2005 Mol. Cryst. Liq. Cryst. 435, 215-875.
Liquid Crystals in Complex Geometries, edited by G. P. Crawford, S. Zumer (Taylor Francis, London, 1996).
Cahn, J. W. and Hilliard, J. E. (1959); (1958) J. Chem. Phys. 28, 258; 31, 688.
Matsuyama, A., Evans, R. M. L., and Cates, M. E. (2000) Phys. Rev. E 61, 2977; Eur. Phys. J. E 9, 79 (2002), 89 (2002).
de Gennes, P. G. and Prost, J. (1993) The Physics of Liquid Crystals (second edition, Oxford University Press).
Flory, P. J. (1953) Principles of Polymer Chemistry (Cornell University Press, Ithaca).
Doi, M. and Edwards, S. F. (1989) The Theory of Polymer Dynamics (Clarendon, Oxford).
Hess, S. (1976) Z. Naturforsch. 31a, 1507.
Olmsted, P. D. and Goldbart, P. (1992) Phys. Rev. A 41, 4578 (1990); A46, 4966.
Qian, T. and Sheng, P. (1998) Phys. Rev. E 58, 7475.
Holmes, M. H. (1995) Introduction to Perturbation Methods (Springler-Verlag).
Landau, L. D. and Lifshitz, E. M. (1959) Fluid Mechanics (Pergamon Press, Oxford).
Levich, V. G. (1962) Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, N.J.).
Langer, J. S. (1967) Ann. of Phys. 41, 108; Zittartz, J. (1967) Phys. Rev. 154, 529; Bray, A. J. (1998) Phys. Rev. E 58, 1508; W. van Saarloos, (1998) Phys. Rep. 301, 9.
Shinozaki, A. and Oono, Y. (1993) Phys. Rev. E 47, 804; Bray, A. J. (1998) Phys. Rev. E 58, 1508.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Popa-Nita, V., Sluckin, T.J. (2007). Waves at the nematic-isotropic interface: nematic-non-nematic and polymer-nematic mixtures. In: Rzoska, S.J., Mazur, V.A. (eds) Soft Matter under Exogenic Impacts. NATO Science Series II: Mathematics, Physics and Chemistry, vol 242. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5872-1_17
Download citation
DOI: https://doi.org/10.1007/978-1-4020-5872-1_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5871-4
Online ISBN: 978-1-4020-5872-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)