Abstract
Diffusion equations are used to describe rotational, translational and internal motions of molecules in uniaxial liquid crystal phases. In addition to exact numerical solutions based on eigenfunction expansions, approximate procedures are also presented to gain direct insight into the relevant aspects of the dynamical problems. Inherent limitations, intrinsic time scale separations and improvements of the model are discussed.
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References
van Kampen, N. G. (1987) Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam.
Pedersen, J. B. (1972) Electron Spin Relaxation in Liquids, L. T. Muus and P. W. Atkins (eds.), Plenum Press, New York, Chap. II.
Nordio, P. L. and Segre, U. (1979) The Molecular Physics of Liquid Crystal, G.R. Luckhurst and G. W. Gray (eds.), Academic Press, Chaps. 16, 18 and 19.
Moro, G., Segre, U. and Nordio, P. L., (1985) Nuclear Magnetic Resonance of Liquid Crystals, J. W. Emsley (ed.),D. Reidel Publishers, Dordrecht, p. 270.
Berne, B. J. (1971) Physical Chemistry VIII B, D. Henderson and W. Jost (eds.), Academic Press, New York.
Hynes, J. T. and Deutch, J. M. (1975) Physical Chemistry XI B, D. Henderson and W. Jost (eds.), Academic Press, New York.
Moro, G. and Nordio, P. L. (1982) Chem. Phys. Letters, 93 429.
Moro, G. and Nordio, P. L. (1984) Molec. Crystals liq. Crystals, 104 361.
Leadbetter, A. J. and Richardson, R. M. (1979) The Molecular Physics of Liquid Crystals, G. R. Luckhurst and G. W. Gray (eds.), Academic Press, Chap. 20.
Moro, G. and Nordio, P. L. (1985) J. phys. Chem., 89 997.
Gorchester, J., Rananavare, S. B. and Freed, J. H. (1989) J. chem. Phys., 90 5764.
Rose, M. E. (1957) Elementary theory of Angular Momentum, J. Wiley and Sons Publishers, New York.
Brink, D. M. and Satchler, G. R. (1968), Angular Momentum, Clarendon Press, Oxford.
EISPACK, Argonne Code Center, Argonne National Laboratory.
Cullum, J. and Willoughby R. A. (1985) Lanczos Algorithm for Large Symmetric Eigenvalue Computations, Birkhauser, Basel.
Moro, G. and Freed, J. H. (1981) J. chem. Phys., 74, 3757.
Moro, G. and Freed, J. H. (1986) Large Scale Eigenvalue Problems, J. Cullum and R. A. Willoughby (eds.), North Holland, Amsterdam.
Moro, G. and Polimeno, A. (1989) Chem. Phys., 131, 281.
Luckhurst, G. R., Zannoni, C., Nordio, P. L. and Segre, U. (1975) Molec. Phys., 30, 1345.
Vold, R. R. (1985) Nuclear Magnetic Resonance in Liquid Crystals, J. W. Emsely (ed.), D. Reidel Publishers, Dordrecht.
Nordio, P. L. and Segre, U. (1977) J. magn. Res., 27, 465.
Vold, R. R. and Vold, L. R. (1988) J. chem. Phys., 88, 1443.
Moro, G. and Nordio, P. L. (1983) Chem. Phys. Letts., 96, 192.
Kramers, H. A. (1940) Physica, 7, 284.
Humphries, R. L. and Luckhurst, G. R. (1978) Molec. Phys., 35, 1201.
Moro, G. and Nordio, P. L. (1985) Molec. Phys., 56, 225.
Moro, G. and Nordio, P. L. (1986) Molec. Phys., 57, 947.
Nordio, P. L., Rigatti, G. and Segre, U. (1973) Molec. Phys., 25 129.
Langer, J. S. (1969) Ann. Phys., 54 258.
Ferrarini, A., Moro, G. and Nordio, P. L. (1988) Molec. Phys., 63, 225. Moro, G. J., Ferrarini, A., Polimeno, A. and Nordio, P. L. (1989) Reactive and Flexible Molecules in Liquids, Th. Dorfmüller (ed.), Kluwer Academic Publishers, Dordrecht.
Moro, G. (1987) Chem. Phys., 118 181.
Emsley, J. W., Luckhurst, G. R. and Stockley, C. P. (1982) Proc. R. Soc. A 381 117.
Ryckaert, J. P. and Bellemans, A. (1975) Chem. Phys. Letts, 30 123.
Flory, P. J. (1969) Statistical Mechanics of Chain Molecules, Interscience, New York.
Counsell, C. R. J., Emsley, J. W., Luckhurst, G. R., Turner, D. L. and Charvolin, J. (1984) Molec. Phys., 52 499.
Ferrarini, A., Nordio, P. L., Moro, G. J., Crepeau, R. H. and Freed, J. H. (1988) J. chem. Phys., 91 5707.
Ferrarini, A., Moro, G., Nordio, P. L. and Polimeno, P. L. (1988) Chem. Phys. Letters, 151 531.
Happel, J. and Brenner, H. (1965) Low Reynolds Number Hydrodynamics, Prentice-Hall, Englewood Cliffs, New Jersey.
Pastor, R. W., Venable, R. M. and Karplus, M. (1988) J. chem. Phys., 89 1112.
Pastor, R. W., Venable, R. M., Karplus, M. and Szabo, A. (1988) J. chem. Phys., 89 1128.
Moro, G. J., Nordio, P. L. and Polimeno, A. (1989) Molec. Phys., 68 1131.
van der Zwan, G. and Hynes, J. T. (1985) J. phys. Chem., 89 4181.
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Ferrarini, A., Nordio, P.L., Moro, G.J. (1994). Diffusion Models for Molecular Motion in Uniaxial Mesophases. In: Luckhurst, G.R., Veracini, C.A. (eds) The Molecular Dynamics of Liquid Crystals. NATO ASI Series, vol 431. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1168-3_3
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DOI: https://doi.org/10.1007/978-94-011-1168-3_3
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