Anisotropic diffusion of light in polymer dispersed liquid crystals
Alenka Mertelj
1
and Martin Čopič
1,2
1
J. Stefan Institute, Jamova 39, SI-1001 Ljubljana, Slovenia
2
Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
Received 6 October 2006; published 18 January 2007
Anisotropic diffusion of light was experimentally first observed in bulk nematic liquid crystals. The origin of
anisotropy in such a system is due to the optical anisotropy of nematic liquid crystal and to anisotropic
scattering of light from nematic orientational fluctuations. In polymer dispersed liquid crystals PDLCs an-
isotropic scatterers—i.e., nematic droplets—are embedded in an optically isotropic polymer. The anisotropy of
diffusion of light in this system therefore depends only on the anisotropic scattering from a single nematic
droplet and on the average orientation of the droplets in PDLCs. In the absence of an external field droplets in
PDLCs are randomly oriented and diffusion of light is isotropic. In an external field the droplets are on average
oriented in the direction of the external field and the diffusion of light becomes anisotropic. We calculated the
diffusion tensor and expected anisotropy of the diffusion of light as a function of an external field, kR, and
volume fraction using the theory developed for bulk nematic liquid crystals. Our calculations show that the
anisotropy of diffusion tensor can have both the signs and that the magnitude of diffusion constants increase
with increasing external field.
DOI: 10.1103/PhysRevE.75.011705 PACS numbers: 42.70.Df, 61.30.Pq, 03.65.Nk
I. INTRODUCTION
Polymer dispersed liquid crystals PDLCs are interesting
for applications as well as for fundamental research of light
scattering in turbid systems. Particular attention is given to
the switching behavior of PDLC films for their applicability
as light shutters or in electro-optical displays 1. Although
first produced decades ago 2, PDLCs are still of interest for
many new applications in photonic devices 3 and in ran-
dom lasers 4,5. The transmittance of the PDLC films de-
pends on the applied electric field that switches the films
from an opaque, multiple-scattering state to a clear, transpar-
ent state. The theoretically calculated single-scattering pic-
ture gives a good description of the film transmittance 6–8,
but is insufficient to explain the angular dependence of the
scattered intensity of light where multiple-scattering effects
are important 9,10. Multiple light scattering can be a hin-
drance in the production of PDLCs 11 as well as useful
when PDLC’s are used as random amplifying media 4 or
switchable screens. Understanding of multiple scattering in
PDLCs is important for it is a switchable key property in any
application.
Multiple light scattering in bulk nematic liquid crystals
has been studied both theoretically 12,13 and experimen-
tally 14,15, and it has been shown that the diffusion of light
in such system is anisotropic. The origin of this anisotropy is
due to the optical anisotropy of nematic liquid crystals and to
anisotropic scattering of light from nematic orientational
fluctuations. In PDLCs the situation is different: anisotropic
scatterers—i.e., nematic droplets—are embedded in an opti-
cally isotropic polymer. The anisotropy of the diffusion of
light in this system therefore depends on the anisotropic scat-
tering from a single nematic droplet and on the average ori-
entation of the droplets in PDLCs.
In this paper we address the problem of the anisotropy of
the diffusion of light in PDLCs and its dependence on the
ordering of the droplets, on the configuration of the director
field within the droplets, on the radius, and on the volume
fraction of the droplets in the PDLC film. We calculated the
diffusion tensor and light diffusion anisotropy using the
theory developed for bulk nematic liquid crystals 12,13.
The discrete dipole approximation DDA17 was used to
calculate the scattering cross section of a single nematic
droplet. Our results show that the sign and the size of the
anisotropy in the PDLC system is not a trivial function of the
relevant parameters. While previous studies of multiple scat-
tering have mostly focused on transmittance of a PDLC film,
we calculate a complete diffusion tensor, so multiple scatter-
ing in diffusive regime can be calculated for any direction
and sample shape.
II. THEORY AND RESULTS
Polymer dispersed liquid crystal materials consist of ran-
domly distributed nematic liquid crystal droplets embedded
in an isotropic solid polymer matrix. The refractive index of
the polymer is usually chosen so that it is close to the ordi-
nary index of refraction of the liquid crystal. Actual values of
the indices of refraction of a polymer and liquid crystal in
PDLCs differ from the values in the bulk, since both the
liquid crystal and solid polymer matrix are contaminated by
each other. The configuration of the nematic director the
direction of the optical axis in the droplet in PDLCs is usu-
ally bipolar in the absence of a field and close to uniform in
a strong field Fig. 1. So in both cases in the interior of a
droplet the director points predominantly along one direction
n. In the absence of an external electric or magnetic field the
average orientations of different droplets are random and the
system is optically isotropic. In an external field the droplets
partially orient along the direction of the field and the scat-
tering properties, and consequently propagation of light
through such a system becomes anisotropic.
The scattering properties of PDLCs depend on the con-
figuration of the director field within a single droplet, the size
PHYSICAL REVIEW E 75, 011705 2007
1539-3755/2007/751/0117056 ©2007 The American Physical Society 011705-1