The possibility of using cholesteric phases for discriminating enantiomers of a chiral solute on the basis of their different transport properties, motivates the investigation of the translational diffusion by taking fully into account the roto-translational coupling. In this article a detailed theoretical analysis is presented for the transport properties evaluated according to the asymptotic limit of the mean-squared displacement. A general relation is derived for the transport coefficients, having as main ingredients the mean-field potential due to the mesophase, and the diffusion tensor with its purely translational and rotational components, and with the blocks describing the roto-translational coupling. The application of the theory to nematic phases shows that the roto-translational coupling generates a dynamical contribution reducing the transport coefficients evaluated by taking into account only the translational diffusion components in the center of diffusion. The theory is also specialized to a cholesteric phase with a given helical pitch for the director arrangement, in a form which is suitable for calculations of model systems of chiral solutes to be presented in a forthcoming paper.

1.
P. G.
de Gennes
and
P. J.
Prost
,
The Physics of Liquid Crystals
, 2nd ed. (
Oxford University Press
, New York,
1993
).
2.
J.
Happel
and
H.
Brenner
,
Low Reynolds Number Hydrodynamics
(
Noordhoff
, Leyden,
1973
).
3.
P. F.
Perrin
,
J. Phys. Radium
5
,
497
(
1934
);
P. F.
Perrin
,
J. Phys. Radium
7
,
1
(
1936
).
4.
G.
Moro
and
P. L.
Nordio
,
J. Phys. Chem.
89
,
997
(
1985
);
D.
Frezzato
and
G. J.
Moro
,
Mol. Cryst. Liq. Cryst.
395
,
253
(
2004
).
5.
A.
Brognara
,
P.
Pasini
, and
C.
Zannoni
,
J. Chem. Phys.
112
,
4836
(
2000
).
7.
Z.
Yaniv
,
G.
Chidichimo
,
N.
Vaz
, and
J. W.
Doane
,
Phys. Lett.
86A
,
297
(
1981
);
G.
Chidichimo
,
Z.
Yaniv
,
N. A. P.
Vaz
, and
J. W.
Doane
,
Phys. Rev. A
25
,
1077
(
1982
).
8.
R.
Blinc
,
B.
Marin
,
J.
Pirs
, and
J. W.
Doane
,
Phys. Rev. Lett.
54
,
438
(
1985
).
10.
G.
Moro
,
P. L.
Nordio
, and
U.
Segre
,
Chem. Phys. Lett.
105
,
440
(
1984
).
11.
C. W.
Gardiner
,
Handbook of Stochastic Methods
(
Springer
, Berlin,
1994
).
12.
D.
Frezzato
,
G. J.
Moro
, and
C.
Zannoni
(unpublished).
13.
A.
Polimeno
,
G. J.
Moro
, and
J. H.
Freed
,
J. Chem. Phys.
104
,
1090
(
1996
).
14.
A.
Ferrarini
,
G. J.
Moro
,
P. L.
Nordio
, and
G. R.
Luckhurst
,
Mol. Phys.
77
,
1
(
1992
);
A.
Ferrarini
,
F.
Janssen
,
G. J.
Moro
, and
P. L.
Nordio
,
Liq. Cryst.
26
,
201
(
1999
).
15.
A.
Ferrarini
and
G. J.
Moro
, in
NMR of Ordered Fluids
, edited by
E. E.
Burnell
and
C. A.
de Lange
(
Kluwer
, Netherlands,
2003
), p.
241
.
16.
D.
Brune
and
S.
Kim
,
Proc. Natl. Acad. Sci. U.S.A.
90
,
3835
(
1993
).
17.
S.
Kim
and
S.
Karrila
,
Microhydrodynamics: Principles and Selected Applications
(
Butterworth-Heinemann
, Boston,
1991
).
18.
M. E.
Rose
,
Elementary Theory of Angular Momentum
(
Wiley
, New York,
1948
).
19.
S. C.
Harvey
and
J.
Garcia de la Torre
,
Macromolecules
13
,
960
(
1980
);
J.
Garcia de la Torre
,
M. C.
Lopez Martinez
, and
J. J.
Garcia Molina
,
Macromolecules
20
,
661
(
1987
).
20.
H.
Brenner
and
D. W.
Condiff
,
J. Colloid Interface Sci.
41
,
228
(
1972
).
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