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J. Phys. II France
Volume 6, Numéro 11, November 1996
Page(s) 1557 - 1569
DOI https://doi.org/10.1051/jp2:1996147
References of J. Phys. II France 6 1557-1569
  1. Vroege G.J. and Lekkerkerker H.N.W., Rep. Prog. Phys. 55 (1992) 1241 [CrossRef].
  2. Maeda Y. and Hachisu S., Colloids Surf. 6 (1983) 1 [CrossRef].
  3. Tang J. and Fraden S., Liq. Cryst. 19 (1995) 459 [CrossRef].
  4. Fraden S., in Observation, Prediction and Simulation of Phase Transitions in Complex Fluids, M. Baus, L.F. Rull and J.-P. Ryckaert, Eds. (Kluwer, Dordrecht, 1995).
  5. Durand D., Doucet J. and Livolant F., J. Phys. Ii France 2 (1992) 1769 [EDP Sciences] [CrossRef].
  6. Meyer R.B., in Dynamics and Patterns in Complex Fluids, A. Onuki and K. Kawasaki. Eds. (Springer, Berlin, 1990).
  7. Wen X., Meyer R.B. and Caspar D.L.D., Phys. Rev. Lett. 63 (1989) 2760 [CrossRef] [PubMed].
  8. Onsager L., Ann. N.Y. Acad. Sci. 51 (1949) 627 [CrossRef].
  9. Odijk T., Macromolecules 19 (1986) 2313 [CrossRef].
  10. Frenkel D., Physica 176A (1991) 54.
  11. Khokhlov A.R. and Semenov A.N., Physica 108A (1981) 546; 112A (1982) 605.
  12. Chen Z.Y., Macromolecules 26 (1993) 3419 [CrossRef].
  13. Lifshitz I.M., Grosberg A.Yu. and Khokhlov A.R., Rev. Mod. Phys. 50 (1978) 683 [CrossRef] [MathSciNet].
  14. Hermans J.J. and Ullman R., Physica 18 (1952) 951 [MathSciNet].
  15. Saito N., Takahashi K. and Yunoki Y., J. Phys. Soc. Jpn 22 (1967) 219 [CrossRef].
  16. Simple scaling arguments show that the term in the operator $\mathcal{O}$ involving the positional derivative is smaller than the other term by a factor of order $L/\lambda < 1$, where $\lambda$ denotes the deflection length defined in Section 3.
  17. Here we adopt the zero density reference state, see [18].
  18. Hansen J.P. and McDonald I.R., Theory of Simple Liquids (Academic, London, 1986).
  19. Van Roij R., Bolhuis P., Mulder B. and Frenkel D., Phys. Rev. E 52 (1995) R1277 [CrossRef].
  20. Mulder B., Phys. Rev. A 35 (1987) 3095 [CrossRef] [PubMed].
  21. The order of the transition may depend on both L/D [40] and L/P [41]. For freely rotating rigid rods in the limit $L/D \rightarrow \infty$ the transition is first order, according to the third virial theory of [25]. Simulations on short rods suggest a second order transition [42], although more recent simulation results point at a first order transition [43]. There are strong indications that for tobacco mosaic virus the nematic-smectic transition is second order [39], but the cholesteric-smectic transition in solutions of fd virus is thought to be first order [4].
  22. See Poniewierski [25] for the case L/P = 0. The case L/P > 0 then follows trivially.
  23. This is the first step in a parameterisation expansion, in which both $\rho$ and $\phi$ are expanded in powers of the parameter $\epsilon$.
  24. Van Roij R., to be published.
  25. Poniewierski A., Phys. Rev. A 45 (1992) 5605 [CrossRef] [PubMed].
  26. Tait J.H., Neutron Transport Theory (Longmans, London, 1964).
  27. The operators appearing in equation (17) can be made symmetric by the substitution $\chi \times \psi^{1/2} \rightarrow \chi$.
  28. Odijk T., in Light Scattering, Principles and Development, W. Brown, Ed., in press.
  29. van der Schoot P. and Odijk T., Macromolecules 23 (1990) 4181 [CrossRef].
  30. Odijk T., Liq. Cryst. 1 (1986) 553 [CrossRef].
  31. Parsons J.D., Phys. Rev. A 19 (1979) 1225 [CrossRef].
  32. Lee S.-D., J. Chem. Phys. 87 (1987) 4972 [CrossRef].
  33. Stroobants A., Lekkerkerker H.N.W. and Frenkel D., Phys. Rev. A 36 (1987) 2929 [CrossRef] [PubMed]; Frenkel D., J. Phys. Chem. 91 (1987) 4912 [CrossRef]; Somoza A.M. and Tarazona P., Phys. Rev. A 40 (1989) 4161 [CrossRef] [PubMed]; Somoza A.M. and Tarazona P., J. Chem. Phys. 91 (1989) 517 [CrossRef]; Taylor M.P., Hentschke R. and Herzfeld J., Phys. Rev. Lett. 62 (1989) 800 [CrossRef] [PubMed]; Mori A. and Kimura H., J. Phys. Soc. Jpn 61 (1992) 2703 [CrossRef]; Evans G.T., Mol. Phys. 76 (1992) 1359 [CrossRef].
  34. Veerman J.A.C. and Frenkel D., Phys. Rev. A 41 (1990) 3237 [CrossRef] [PubMed]; 43 (1991) 4334.
  35. In the Lee-Parsons approximation we have for the parameter measuring the width of the orientational distribution $\alpha^{(0)} = \pi^{-1}\phi^{2}(L/D)^{2}(4-3\phi)/(1-\phi)^{2}$. The deflection length is therefore also influenced by the higher order interactions.
  36. Bohle A.M., Holyst R. and Vilgis T., Phys. Rev. Lett. 76 (1996) 1396 [CrossRef] [PubMed].
  37. van der Schoot P. and Odijk T., J. Chem. Phys. 93 (1990) 3580 [CrossRef]; Erratum: 94 (1991) 2377.
  38. Doi M., Shimada T. and Okano K., J. Chem. Phys. 88 (1988) 4070 [CrossRef].
  39. Wang J.H., Lonberg F., Ao X. and Meyer R.B., in Ordering in Macromolecular Systems, A. Teramoto, M. Kobayashi and T. Teramoto, Eds. (Springer, Berlin, 1994).
  40. Somoza A.M. and Tarazona P., Phys. Rev. A 41 (1990) 965 [CrossRef] [PubMed].
  41. Tkachenko A.V., preprint.
  42. Frenkel D., Lekkerkerker H.N.W. and Stroobants A., Nature 332 (1988) 822 [CrossRef].
  43. McGrother S.G., Williamson D.C. and Jackson G., J. Chem. Phys. 104 (1996) 6755 [CrossRef].