Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers
S. Faetti,
1,
*
K. Sakamoto,
2
and K. Usami
3
1
Polylab of INFM and Dipartimento di Fisica, Università di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
2
Nano-Architecture Group, Organic Nanomaterials Center, National Institute for Materials Science, 1-1 Namiki, Tsukuba,
Ibaraki 305-0044, Japan
3
Department of Information Systems Engineering, Osaka Sangyo University, 3-1-1, Nakagaito, Daito-Shi, Osaka 574-8530, Japan
Received 29 January 2007; published 21 May 2007
The azimuthal anchoring energy of the nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl 5CB on a
uv-aligned polyimide substrate with in-plane order parameter S' = 0.2 is measured. The measurements are
performed at temperature T = 24 ° C using simultaneously a high accuracy reflectometric method and a high
accuracy transmitted light method. With both the methods, we observe an apparent surface director rotation
opposite to the orienting torque that would correspond to a negative extrapolation length. It is shown that this
unusual behavior is due to the relatively high birefringence of the uv-aligned polyimide layers. Taking into
account for this birefringence, we find a small but positive extrapolation length. The experimental results are
interpreted in terms of a simple mesoscopic model where the nematic molecules are assumed to be rigidly
attached on the polymer surface and the measured extrapolation length is entirely due to the order parameter
variation in a thin interfacial layer where the nematic order parameter passes from the surface value to the bulk
value within a few nematic correlation lengths. Assuming the surface order parameter is S
0
= 0.37, the corre-
lation length of the nematic liquid crystal is estimated to be
c
' = 2.4 ± 1 nm. The corresponding thermodynamic
extrapolation length is d
e
= 2.8± 1.2 nm that corresponds to a very strong azimuthal anchoring.
DOI: 10.1103/PhysRevE.75.051704 PACS numbers: 61.30.Hn
I. INTRODUCTION
Interfacial phenomena in nematic liquid crystals NLC
are an object of a lot of attention both for their relevance to
basic physics and for the applications in the optoelectronic
industry. The orientation of the director n
s
1 at the interface
is characterized by the zenithal angle
s
with the normal z
axis and the azimuthal angle
s
with a x axis on the surface
plane. In the absence of external torques, the director is
aligned along the easy axis n
e
that minimizes the anchoring
energy Wn
s
1,2. For strong anchoring 1,2 we write
W =
W
a
2
s
-
e
2
, 1
where W
a
is the azimuthal anchoring energy coefficient and
e
is the easy azimuthal angle. If an electric field E much
greater than the Freederickz threshold field is applied in the
surface plane along the x axis, a bulk director twist occurs
with characteristic length = K
2
/
0
a
/ E, where K
2
is the
twist elastic constant,
0
is the vacuum permittivity, and
a
is
the dielectric anisotropy 1. For strong anchoring, the direc-
tor surface rotation is 1,2,
s
=-
K
2
0
a
sin
e
E
W
a
, 2
where
s
=
s
-
e
. Then, W
a
can be obtained from the mea-
surement of
s
. Transmitted light methods 3–11 and re-
flected light methods 12–15 are currently used to measure
the azimuthal anchoring energy. However, only a few of
these methods can provide reliable measurements of strong
azimuthal anchoring energies. Indeed, if there is strong an-
choring, high external fields must be applied to the NLC in
order to induce an appreciable surface director rotation. In
these conditions, a strong director twist is present in the bulk
of the NLC that can greatly affect the optical measurements
especially in the case of transmitted light methods 9. In two
recent papers 16,17 we have shown that the reflectometric
method proposed in 13 and the transmitted light method
proposed in 9 provide accurate measurements of strong azi-
muthal anchoring because they are poorly sensitive to the
bulk director twist. Recently, another high accuracy transmit-
ted light method that is poorly affected by the bulk twist has
been also proposed by Janossy 11.
In this paper, we use simultaneously both the transmitted
light and the reflectometric methods to measure the azi-
muthal anchoring energy at the interface between the NLC 4-
n-pentyl-4'-cyanobiphenyl 5CB and a polyimide layer
aligned by irradiation with polarized uv light 18. This sub-
strate induces a homogeneous planar director orientation
with a zero pretilt angle. The anchoring is determined
switching on an in-plane electric field at 80° with respect to
the easy axis and measuring the consequent surface rotation
of the director. A very small apparent surface director rota-
tion opposite to the surface torque
s
0 in Eq. 2 is
found that would correspond to a negative anchoring coeffi-
cient and to a negative extrapolation length d
e
= K
2
/ W
a
1,2.
This behavior is observed with both the reflectometric and
the transmission light methods. Furthermore, it is also ob-
served if a magnetic field is applied in place of the electric
field. Using a numerical procedure based on the optical Ber-
reman theory of the anisotropic stratified media, we show
that the apparent negative surface rotation is the consequence
of a strong azimuthal anchoring and of a somewhat high
optical anisotropy of the uv-aligned polyimide. By taking
*Author to whom correspondence should be addressed. Electronic
address: faetti@df.unipi.it
PHYSICAL REVIEW E 75, 051704 2007
1539-3755/2007/755/05170412 ©2007 The American Physical Society 051704-1