31
Views
0
CrossRef citations to date
0
Altmetric
Liquid Crystals

Transient Periodic Dissipative Structures in Nematics Confined between Coaxial Cylinders

Pages 79-122 | Received 01 May 1998, Published online: 24 Sep 2006

References

  • de Gennes , P. G. and Prost , J. 1993 . The Physics of Liquid Crystals , Oxford : Clarendon Press .
  • Chandrasekhar , S. 1992 . Liquid Crystals , Cambridge University Press .
  • Blinov , L. M. and Chigrinov , V. G. 1993 . Electrooptic Effects in Liquid Crystal Materials , Springer Verlag .
  • Pikin , S. A. 1991 . Structural Transformations in Liquid Crystals , Gordon and Breach .
  • Deuling , H. J. 1978 . Solid State Physics Supplement , 14 : 77 this is a review on NPD caused by B and E.
  • Gooden , C. , Mahmood , R. , Brisbin , A. , Baldwin , A. , Johnson , D. L. and Neubert , M. E. 1985 . Phys. Rev. Lett. , 54 : 1035
  • Lonberg , F. and Meyer , R. B. 1985 . Phys. Rev. Lett. , 55 : 718
  • Cognard , J. 1982 . Mol. Cryst. Liquid Cryst. Suppl. , 1 : 1 and
  • Jerome , B. 1991 . Rep. Progr. Phys. , 54 : 391 are reviews on interfacial properties of nematics
  • Pieranski , P. , Brochard , F. and Guyon , E. 1973 . J. Phys. France , 34 : 35
  • Carr , E. F. 1977 . Mol. Cryst. Liquid Cryst. , 34 : 159 (Letters)
  • Srajer , G. , Fraden , S. and Meyer , R. B. 1989 . Phys. Rev. A , 39 : 4828 for reviews see
  • Kini , U. D. 1991 . J. Phys. II. , 1. : 225
  • Guyon , E. , Meyer , R. B. and Salan , J. 1979 . Molec. Cryst. Liquid Cryst. , 54 : 261
  • Ciaponi , S. and Faetti , S. 1990 . Liq. Cryst. , 8 : 473
  • Cladis , P. E. 1991 . Nematics. Mathematical and Physical Aspects , Edited by: Coron , J.-M. , Ghidaglia , J.-M. and Helein , F. 65 London : Kluwer Academic Publishers . see also references therein
  • Dubois-Violette , E. and Manneville , P. 1978 . J. Fluid Mech. , 89 : 273
  • Carrigan , C. R. and Guyon , E. 1975 . J. Phys. France Letters , 36 : 145
  • Leslie , F. M. 1970 . J. Phys. D , 3 : 889
  • Atkin , R. J. and Barratt , P. J. 1973 . Q. J. Mech. Appl. Math. , 26 : 109
  • Kini , U. D. 1988 . J. Phys. France , 49 : 527
  • Palffy-Muhoray , P. , Sparavigna , A. and Strigazzi , A. 1993 . Liq. Cryst. , 14 : 1143
  • Barrat , P. J. and Duffy , B. R. 1995 . Liquid Cryst. , 19 : 57
  • 1996 . Liquid Cryst. J. Phys. D , 29 : 1551
  • Chen , J. , Johnson , D. L. , Bos , P. J. , Sprunt , S. , Lando , J. and Mann , J. A. Jr. 1996 . Appl. Phys. Lett. , 68 : 885
  • Landau , L. D. and Lifshitz , I. M. 1984 . Electrodynamics of Continuous Media , Pergamon Press .
  • While the axial or azimuthal B is experimentally feasible, the radial field is not. When the sample is flat, the axial or the azimuthal B becomes a field in the sample plane; the radial B is the only component normal to the sample walls. In contrast, it seems feasible to generate a radial or an axial E but not the azimuthal one. A radial E would arise by the application of a potential difference between suitably treated cylindrical surfaces. This would have been a good substitute for the radial B. However, E gets modified by director perturbations which makes it necessary to include Maxwell's equations explicitly into the solution so that the modifications of E are connected to the director gradients
  • ηA corresponds to the viscosity with no being normal to the plane of shear. When no is in the shear plane but along (or normal) the flow direction, the viscosity is η B (or η c ). In terms of the viscosities μ k (see ref. 2), γ1 = μ3 - μ2; η A = μ4/2; η B = (μ3+ μ4 + μ6)/2; η c = (μ5 + μ5 - μ2/2. The Parodi relation [2] requires that μ6 = μ2 + μ3 + μ5. The torque viscosities can be written as μ2 = (η B - η C - γ l )/2; μ3 = (η B - η C + γ l )/2
  • Hurd , A. J. , Fraden , S. , Lonberg , F. and Meyer , R. B. 1985 . J. Phys. France , 46 : 905 the extensional viscosity can be expressed in terms of the μ k as v1 = (μ1 + μ4 + μ5 + μ6)2
  • Crawford , G. P. , Ondris-Crawford , R. J. , Doane , J. W. and Zumer , S. 1996 . Phys. Rev. E , 53 : 3647 and references therein. According to the expression of the deformation free energy density in this work, 0 łtm; K 24 ≤ 2 K 1 or 0 ≤ K 24 ≤ 2 K 2, whichever is less. For a calamitic nematic, the latter condition is employed to determine the maximum value of K 24
  • Kini , U. D. 1986 . J. Physique , 47 : 693
  • Pipes , L. A. and Hovanessian , S. A. 1969 . Matrix Computer Methods in Engineering , John Wiley .
  • Bunning , J. D. , Faber , T. E. and Sherrell , P. L. 1981 . J. Phys. France , 42 : 1175
  • Chen , G. P. , Takezoe , H. and Fukuda , A. 1989 . Liq, Cryst. , 5 : 341 and The viscosities are from The elastic constant values are from correspond to μ1 = 0 (assumed), (μ2, μ3, μ4, μ5) = (-0.77, -0.042, 0.716, 0.46) poise; by the Parodi relation, μ6 = -0.352 poise
  • Lonberg , F. , Fraden , S. , Hurd , A. J. and Meyer , R. B. 1984 . Phys. Rev. Lett. , 52
  • Volovik , G. E. 1980 . JETP Letters , 31 : 273
  • Sollich , H. , Baalss , D. and Hess , S. 1989 . Molec. Cryst. Liquid Cryst. , 168 : 189
  • Kuzma , M. R. 1986 . Phys. Rev. Lett. , 57 : 349
  • Fraden , S. and Meyer , R. B. 1986 . Phys. Rev. Lett. , 57 : 3122
  • Warmerdam , T. , Frenkel , D. and Zijlstra , R. J. J. 1987 . J. Physique , 48 ( 3 ) : 19
  • Kini , U. D. 1998 . Liquid Cryst. , 24 : 177 For references to earlier work, see
  • Sagues , F. and San Miguel , M. 1985 . Phys. Rev. A , 32 : 1843

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.