ISSN 0030-400X, Optics and Spectroscopy, 2006, Vol. 100, No. 6, pp. 877–880. © Pleiades Publishing, Inc., 2006.
Original Russian Text © L.M. Sabirov, D.I. Semenov, 2006, published in Optika i Spektroskopiya, 2006, Vol. 100, No. 6, pp. 952–955.
877
INTRODUCTION
Molecular light scattering spectroscopy is one of the
most informative methods for studying liquids [1]. At
low intensities of exciting radiation, a sample is mini-
mally affected. For this reason, investigation of the
spectral characteristics of scattered light makes it pos-
sible to obtain valuable information about the behavior
of static and dynamic parameters of liquid crystals
(LCs) near the phase transition from an isotropic liquid
(IL) to an LC. Near this transition, the susceptibility of
the medium is extremely high [2].
Since the IL–LC phase transition is only slightly
first-order, many properties of the isotropic phase
exhibit critical behavior when the temperature
approaches the phase transition temperature T
c
[3]. Pre-
transition phenomena in the LC isotropic phase are due
to the presence of correlations in the orientations of the
long axes of molecules, which arise on small space–
time scales through fluctuations [2]. Within the Lan-
dau–de Gennes theory [4], the temperature behavior of
the correlation radius ξ of fluctuations of the order
parameter can be described as
(1)
where ξ
0
is a value of about the molecule length and T *
is the temperature of the second-order phase transition
(T * < T
c
). At the temperature T *, the size of the ordered
region (the correlation radius) becomes infinitely large.
For most LCs, T
c
– T * ≈ 1 K. When the temperature
approaches T
c
, the correlation radius of fluctuations
increases; however, due to the first-order character of
the transition, it barely reaches 10–12 nm (about 20ξ
0
)
[3].
Since fluctuations of the order parameter on the IL–
LC transition are fluctuations in the spatial distribution
ξ T ( ) ξ
0
T */ T T * – ( ) [ ]
1/2
, =
of the axes of anisotropic molecules, the velocity of
spread of these fluctuations is related to the half-width
of the depolarized component of scattered light (the
Rayleigh line wing) [1]:
(2)
where ∆ν
1/2
is the half-width of the Rayleigh line wing
in inverse centimeters, c is the speed of light, and τ is
the relaxation time of fluctuations of the order para-
meter.
For conventional liquids, the temperature behavior
of the width of the Rayleigh line wing (which is caused
by orientational jumps of molecules by large angles) is
described well by the Debye–Stokes–Einstein hydro-
dynamic equation [1]
(3)
Here, k is the Boltzmann constant, η is the viscosity,
and V
eff
is the effective volume of a molecule. Within
the Landau–de Gennes theory, to describe the tempera-
ture behavior of the Rayleigh line wing in the LC iso-
tropic phase, Eq. (3) is modified to the form [5]
(4)
where γ is the critical index of susceptibility of the iso-
tropic phase and is a quantity having some other
meaning than in (3) [6].
Experimental investigations of the birefringence in
electric [7] and magnetic [8] fields, the optical Kerr
effect [9], the nuclear spin–lattice relaxation [10], and
the temperature behavior of the scattered light intensity
[8] show that γ ≈ 1 in the LC isotropic phase. This fact
∆ν
1/2
1
π c τ
--------, =
∆ν
1/2
kT
π c η V
eff
------------------. =
∆ν
1/2
kT T * – ( )
γ
π c η V
eff
*
--------------------------, =
V
eff
*
CONDENSED-MATTER
SPECTROSCOPY
Depolarized Light Scattering Spectra of the Isotropic Phase
of Nematic Liquid Crystals
L. M. Sabirov and D. I. Semenov
Navoi State University, Samarkand, 703029 Uzbekistan
e-mail: sabirov@uni.uzsci.net
Received June 6, 2005
Abstract—The depolarized light scattering spectra of the isotropic phase of N-(p-methoxybenzylidene)-p-
butylaniline and p-azoxy-anisole nematic liquid crystals were experimentally investigated. The limits of appli-
cability of the mean field approximation of the Landau–de Gennes theory to the description of the temperature
behavior of the depolarized scattering linewidth are determined.
PACS numbers: 78.20.C
DOI: 10.1134/S0030400X06060117