Depression of the nematic-isotropic phase transition temperature at nanopatterned surfaces
Bing Wen,
1
Jong-Hyun Kim,
2
Hiroshi Yokoyama,
2,3
and Charles Rosenblatt
1,
*
1
Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079
2
Yokoyama Nano-structured Liquid Crystal Project, ERATO, Japan Science and Technology Corporation, 5-9-9 Tokodai, Tsukuba, Ibaraki
300-2635, Japan
3
Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
Received 14 February 2002; published 21 October 2002
A spatially varying herringbone pattern with an easy axis alternating in angle between 0 and and having
a period of 200 nm was scribed into a polyimide-coated substrate. The depression of the nematic-isotropic
transition temperature for a nematic layer at the patterned surface relative to its value at a uniformly rubbed
surface was investigated as a function of for 15 88°. It was found that the depression of the transition
temperature increases with , up to 7 mK at =88°. A simple model was developed that includes not only
elasticity, but also anchoring effects at the polyimide. The model, which is used to calculate the thickness of the
nematic layer, indicates that anchoring—rather than elastic—effects play the dominant role in the depression of
the layer’s transition temperature.
DOI: 10.1103/PhysRevE.66.041502 PACS numbers: 61.30.Gd, 64.70.Nd
About 12 years ago Barbero and Durand showed theoreti-
cally 1 that if the nematic liquid crystal director attempts to
follow the topography of a rough surface, the cost of the
associated curvature elastic energy may result in a decrease
of the nematic order parameter S near the surface, or even in
melting into the isotropic phase. This occurs because the
curvature elastic moduli are functions of S: A decrease of the
order parameter results in a decreased elastic energy cost.
Several qualitative and semiquantitative experimental results
for rough surfaces subsequently have been reported 2–7.
Yokoyama, Kobayashi, and Kamei, for example, observed a
depression of the order parameter at the surface, which was
attributed in part to surface roughness 2. Additionally, they
found an anomalous decrease of the anchoring strength near
the nematic-isotropic phase transition due to curvature at the
substrate and the resulting decrease of S 3. Wu and Efron
found that the optical phase retardation is not proportional to
cell thickness when the surface is roughened with a sputtered
SiO
2
layer 4. They interpreted this result in terms of a
reduced order parameter, and therefore a reduced optical bi-
refringence, near the surfaces. Analogous results were ob-
tained by Barberi and Durand 5. Because the elastic melt-
ing model 1 was unable to fully explain their results, they
invoked order electricity 8 in their analysis. More recently
Papanek and Martinot-Lagarde used a surface plasmon tech-
nique to investigate order at a rough SiO
x
surface 6. They
found that the difficult-to-purify liquid crystal methoxyben-
zylidene butylanaline that penetrates the voids has zero order
parameter over the entire bulk nematic range, and that a con-
tinuous transition of the nematic order parameter S from near
zero at the SiO
x
surface to its bulk value in the central part of
the cell occurs over a correlation length of several nanom-
eters. Again, order electricity was invoked to explain the
results. Monkade et al. examined the behavior of the liquid
crystal at a surface covered with needles and columns of SiO
and found that the roughness results in a decrease of the
order parameter 7. A model that minimizes the melting en-
ergy as opposed to the elastic energy and includes order
electricity was needed to explain their full set of results.
With the advent of nanoscopic control of the surface by
atomic force nanolithography 9, it has become possible to
compel the liquid crystal director to adopt a well-defined
profile that varies on very short length scales. This is accom-
plished by the use of the stylus of an atomic force micro-
scope, whereby tiny patterns are scribed into the polymer
that coats the substrate. Pixels as small as tens of nanometers
are possible, with each pixel having a unique easy axis for
director orientation. This technique has been used to create
optical devices 9,10 and to examine the interaction between
the liquid crystal and substrate 11,12. Moreover, because
atomic force nanolithography relies primarily on the inherent
anchoring of a substrate that is patterned for planar align-
ment, it is considerably easier to control than the surface
topography 4–7. In consequence it is now possible to in-
vestigate in great detail the issue of the substrate’s effect on
nematic nucleation and melting.
In this paper we examine how substrate-imposed elastic
deformations affect the nucleation temperature of a nematic
layer at the substrate. We have created nanoscopic herring-
bone patterns in a polyimide-coated substrate, where each
period contains two very long pixels, such that the easy
axes of the two pixels form an angle . The depression T
of the nematic layer’s transition temperature relative to its
value at a uniformly oriented surface was investigated as a
function of , where it was found that the magnitude of T
increases monotonically with up to 7 mK at =88 °. A
model for the surface energy that includes not only elasticity,
but anchoring effects at the polyimide interface, was used in
conjunction with the Kelvin equation and the data for T to
determine the thickness of the nucleated nematic layer 13.
The calculation, which does not include order electricity, in-
dicates that anchoring—rather than elastic—effects play the
dominant role in the depression of the transition temperature.
Two indium-tin-oxide-coated glass substrates were
cleaned sequentually in detergent, acetone, and ethanol. The *Corresponding author. Email address: cxr@po.cwru.edu
PHYSICAL REVIEW E 66, 041502 2002
1063-651X/2002/664/0415027/$20.00 ©2002 The American Physical Society 66 041502-1