Large polar pretilt for the liquid crystal homologous series
alkylcyanobiphenyl
Zhibin Huang and Charles Rosenblatt
Department of Physics, Case Western Reserve University, Cleveland,
Ohio 44106
(August 17, 2004)
Abstract
Sufficiently strong rubbing of the polyimide alignment layer SE-1211 (Nissan Chemical Industries, Ltd.) results in a large pretilt of the liquid crystal
director from the homeotropic orientation. The threshold rubbing strength
required to induce nonzero pretilt is found to be a monotonic function of
the number of methylene units in the homologous liquid crystal series alkylcyanobiphenyl. The results are discussed in terms of the dual easy axis model
for alignment.
Typeset using REVTEX
1
For vertically-aligned (hometropic) liquid crystal cells, it often is desirable to have a
b from the substrate normal, especially if the azimuthal
“pretilt” θ0 of the nematic director n
orientation can be regulated. In fact, for some applications in which the optical retardation
must be controlled passively, i.e., by the surface rather than by an electric field, a large
pretilt angle may be needed. Various methods have been attempted to obtain high pretilt
from the homeotropic direction, although only a few techniques have achieved the desired
results. Lee and Seo [1], for example, dipped a homeotropically-aligning polyimide in a
solvent for thirty minutes, obtaining a pretilt angle of ∼ 35◦ from the substrate normal for
a positive dielectric anisotropy liquid crystal. Scharf, et al [2] devised a method in which a
homeotropic alignment agent (silane) is printed in a grating pattern onto a planar aligning
substrate (SiOx ). The coverage ratio and the period and direction of the grating determine
the polar and azimuthal liquid crystal orientations, with the full range 0◦ ≤ θ0 ≤ 90◦
of pretilt being achieved.
Another technique involves rubbing a polyimide that has a
relatively rigid backbone but is designed for homeotropic alignment [3—5]. Although Ref.
[3] counterintuitively found that the pretilt angle decreases with increasing rubbing strength
nf , our group determined [5] that a controllable and temporally robust large pretilt angle
θ0 > 40◦ can be achieved above a threshold rubbing strength using the polyamic acid SE1211 (Nissan Chemical Industries, Ltd.) and the liquid crystal pentylcyanobiphenyl (5CB).
Hatoh, et al suggested that such a pretilt of n
b is caused by a rubbing-induced tilt of the
polyimide’s alkyl side chains [6]. We have inferred, however, that our preparation process of
baking at an especially high temperature and rubbing results in two concommitant easy axes
for orientation: One easy axis is approximately — but not necessarily exactly — perpendicular
to the substrate and the other easy axis is approximately parallel to the substrate [7,8]. The
concept of dual easy axes also has been suggested by Andrienko, et al [9,10] from their work
using polarized ultraviolet light to obtain polar pretilt of the director.
In this paper we
examine the pretilt angle vs. rubbing strength at substrates coated with a homeotropicallyaligning polyimide for the homologous series of liquid crystals alkylcyanobiphenyl “nCB”
2
(5 ≤ n ≤ 8). Our central result is that the threshold rubbing strength nth
f for the onset of
nonzero pretilt θ0 increases with an increase in the number of methylene units in the liquid
crystal tail, which is consistent with the dual easy axis model [7] and the characteristic
behavior of liquid crystals at a surfactant-coated substrate.
We used the polyamic acid SE1211, approximately 4% by weight, dissolved in solvent.
The mixture was spin coated onto indium tin oxide (ITO)-coated glass slides (3.2 × 0.8 cm)
at 1800 rpm for 9 s. The slides were prebaked at 80◦ C for 30 min, and then were fully
baked at 200◦ C for 50 min. This baking temperature is warmer than that prescribed by
the manufacturer, who suggests 180◦ C. The slides then were rubbed with a cotton cloth
(Yoshikawa Chemical Co., YA-25-C) using a rubbing machine that has a roller radius of
r = 4 cm. In order to examine multiple rubbing strengths, the slides were “gradiently”
rubbed, such that one side of the slide was elevated by an angle of 1.58◦ on the bed of the
rubbing machine. The height of the bed then was raised until the cotton fibers osculated
the lower edge of the slide with no deformation of the fiber pile; this defined the nf = 0
position. The fiber pile at the upper edge of the slide was deformed by approximately δ
= 0.088 cm. The slide was translated with velocity s = 0.42 cm s−1 beneath the rubbing
cylinder a total of N = 6 times, with the roller rotating at a rate ν = 8.33 rotations per
second. The “rubbing strength” nf is defined as the number of fibers passing a position of
1
unit width [11], and is given by nf ≈ (2rδ) 2 2πNνrσf /s. nf was varied continuously across
the slide due to changes in the deformation δ of the cotton fiber with position. A liquid
crystal cell was created by placing mylar spacers between two slides — one slide unrubbed
and the other slide gradiently rubbed — and adjusting for maximum parallelism. The cell
thickness was determined to be ` = (15.5 ± 0.9) µm using interferometric scheme [12]. Each
of the four cells was filled with the liquid crystal nCB in the isotropic phase, and then cooled
into the nematic phase.
The apparent pretilt angle θ0 for each cell was obtained by measuring the optical retardation through the cell. Light from a He-Ne laser passed consecutively through a light
chopper at frequency f = 237 Hz, a polarizer oriented at 45◦ with respect to the rubbing
3
direction of the sample, a Babinet-Soleil compensator, a cylindrical lens of focal length 150
mm, the sample, an analyzer, a second lens that recollimated the beam, and into a photodetector. The detector output, proportional to the total light intensity I, was fed into a lock-in
amplifier referenced to the frequency of the light chopper. The cylindrical lens created an
approximately rectangular beam profile at the sample, 0.15 × 1 mm in size, with the smaller
dimension being parallel to the rubbing direction. The shape of the beam served two purposes: The narrow dimension limited the range of rubbing strengths ∆nf probed by the
beam, and the wide dimension allowed us to average over a large area for a given nf . This
averaging process was useful because, even though local variations in the rubbing strength
(for a given nominal value nf ) are small, the induced tilt angle θ0 can be a strong function
of nf ; θ0 could vary by up to ±2◦ . The cell was mounted on a horizontal translation stage
and was translated along the rubbing direction in order to measure the retardation as a
function of rubbing strength. For each position, and therefore for each value of nf in the
cell, the compensator was adjusted to minimize the signal into the lock-in amplifier, and the
measured value of the optical retardation from the compensator was taken to be equal in
magnitude to the sample retardation α.
The pretilt angle was determined from the measured retardation as follows. First, sufficiently rigid anchoring conditions were assumed, which was verified previously for θ0 & 15◦
[5]. It turns out that the dual easy axis picture [7,8] necessitates that the effective polar
anchoring strength coefficient become vanishingly small in the region near the threshold
rubbing strength nth
f .
Our preliminary data suggest that this is, indeed, the case; the
results will be published elsewhere [13].
Returning to the experiment at hand, for very
small θ0 (θ0 ¿ 15◦ ) the weakened anchoring strength coupled with elastic torque gives rise
to an artificially larger measured tilt at the rubbed SE-1211 substrate, i.e., the measured
value of θ0 is larger than the pretilt angle of an isolated substrate.
In consequence, the
actual retardation vs. nf should be slightly more rounded in the vicinity of nth
f . This was
not deemed a significant issue for this work, which focuses on nth
f vs. homolog number.
We then calculated the director profiles across the cell by minimizing the free energy of
4
deformation Fel = 12 [K11 sin2 θ(z) + K33 cos2 θ(z)] (∂θ(z)/∂z)2 , where K11 is the splay elastic
constant and K33 is the bend elastic constant. Values of the parameters K11 and K33 for
the calculation were taken from Ref. [14]. The calculated values of the retardation αcalc
were matched numerically to the measured values of α by assuming a particular value of the
R
f
pretilt angle θ0 in the relation αcalc = (2π/λ)[nef
e (z) − no ]dz, where λ is the wavelength of
f
light, no is the ordinary refractive index, and nef
e (z) is the effective extraordinary refractive
f
index at the position z along the normal from the surface of the cell. nef
e (z) was obtained
£ 2
¤
2
f
2
2 −1/2
, where values for no and ne for
from the relation nef
e (z) = cos θ(z)/no + sin θ(z)/ne
each homolog at the appropriate temperature(s) were obtained from Ref. [15], and θ(z) is
the calculated polar angle of the director at position z. Finally, θ0 was adjusted so that αcalc
was equal to the measured value of α. A plot of θ0 vs. nf is shown in Fig. 1. Earlier we
had shown that these values are temporally robust for the liquid crystal 5CB [5].
6
−1
The pretilt angles at low rubbing strengths (up to nth
f ∼ 2 × 10 cm ) are close to
zero. For rubbing strengths nf larger than a liquid crystal-dependent threshold value nth
f ,
the retardation increases continuously to a high value, corresponding to a rise in the pretilt
angle from almost zero to approximately 35◦ .
We remark that 35◦ is not an asymptotic
value for the pretilt, and considerably larger pretilts may be obtained with stronger rubbing
or more intense baking conditions for the polyamic acid (hotter and/or longer in duration).
The existence of a threshold rubbing strength nth
f below which the pretilt is small or zero
is due to a convergence of several phenomena. As discussed in Ref. [7], threshold behavior
is a consequence of the existence of two orthogonal easy axes, at least for bidirectional
rubbing. Nevertheless, on examining the surface-induced director tilt in the smectic-A phase
above the smectic-C phase transition for a unidirectionally-rubbed substrate, we concluded
that the two easy axes need not be mutually orthogonal [8].
This raises a question: If
the easy axes are not orthogonal, why is there a threshold rubbing strength to achieve a
nonzero pretilt θ0 (rather than a continuous variation of pretilt) in the nematic phase for
unidirectional rubbing? We believe the key to this problem is the demonstrated existence
5
[16—18] of a minimum rubbing strength nYf required for disentanglement and reorientation of
the polymide backbone, an effect similar to the yield stress associated with a Bingham fluid.
The polyimide’s response is weak for nf < nYf , and θ0 remains close to zero. For nf > nYf the
polymer reorients, facilitating a torque on the director if the easy axes are not orthogonal.
This would result in a small pretilt angle, increasing with increasing rubbing strength [8].
For sufficiently large nf a rubbing strength is reached above which the tilt grows rapidly with
Y
rubbing strength [7]; this corresponds to nth
f (which must be larger than nf ). In principle a
well-defined threshold nth
f exists only when the easy axes are perfectly orthogonal, although
if the easy axes are nearly orthogonal an approximate threshold rubbing strength nth
f may
be indentified and θ0 vs. nf will be slightly rounded in this region.
The significant new feature in this work is the dependence of nth
f on homolog number:
nth
f increases with increasing alkyl chain length. A single but tilted easy axis is not likely
to engender this behavior, although a pair of (nearly) orthogonal easy axes will. It is well
known that surface monolayers consisting of molecules with longer aliphatic tails enhance the
homeotropic ordering of liquid crystals, both from the standpoint of more complete wetting
of a nematic layer in the isotropic phase and polar anchoring strength within the nematic
phase [19—24]. Perhaps more relevant is the observation that for glass coated with the
silane surfactant dimethyloctadecylaminopropyl trimehtoxysily chloride (DMOAP), Chen,
et al observed more complete wetting of longer chain homologs of nCB as compared to the
shorter homologs [25], indicating the importance of the liquid crystal’s alkyl chain length in
promoting homeotropic order. Now consider our alignment layer SE-1211, which consists
of long alkyl side chains that promote homeotropic order and a polyimide backbone that,
when aligned, tends to promote planar order. Overbaking the polyamic acid has two effects:
It further imidizes the backbone, thereby promoting nearly planar alignment, and cleaves
away a fraction of the side chains, thereby weakening the homeotropic alignment. For strong
rubbing the backbone becomes sufficiently aligned, allowing the liquid crystal to overcome
the homeotropic alignment tendency due to the side chains [7]. In the orthogonal dual easy
axis model for which there is a surface free energy Fsurf = A sin2 θ0 + B cos2 θ0 + C sin4 θ0
6
[7], a nonzero tilt θ0 = sin−1 [(B − A) /2C]1/2 obtains when B > A. Here A is the quadratic
rubbing strength-dependent anchoring strength coefficient for homeotropic alignment [26],
B is the quadratic coefficient for planar alignment [26], and C is the quartic coefficient
required for stability [27]. But the propensity for homeotropic order, and thus A, is related
to the length of the liquid crystal tail [25], and thus for longer homologs the rubbing must be
stronger to overcome the enhanced homeotropic tendency, i.e., stronger rubbing is required
for B to become larger than A. Thus, nth
f increases with increasing liquid crystal tail length.
We comment on two additional points. First, the shapes of the θ0 vs. nf curves appear
to be similar, although we must excerise caution.
As noted above, the response of the
polymide is highly nonlinear with rubbing strength, and therefore it is not obvious that θ0
th
should be proportional to the quantity nf − nth
f , where nf is a depends on homolog number.
Second, in Ref. [7] we observed that for a given rubbing strength and for a liquid crystal
possessing a smectic-A to nematic phase transition, a tilt transition from θ0 6= 0 to θ0 = 0
occurs in the nematic phase on cooling, and that the temperature at which this occurs is
lower (closer to TNA ) for stronger rubbing.
The origin of this effect is surface-induced
smectic ordering, which favors the homeotropic orientation. Thus, a more strongly rubbed
substrate would need to be closer to TNA , where the homeotropic tendency is greater, for
this tilt transition to occur.
Our results for 8CB qualitatively are consistent with this
behavior, although perhaps not as convincing as the results in Ref. [7]. This is due to the
larger surface roughness in the present samples — we found topographical features of 18 nm
over distances of 0.8 µm — which tends to suppress surface-induced smectic order [28].
Acknowledgments:
We wish to thank Dr. Ichiro Kobayashi of Nissan Chemical In-
dustries, Ltd. for useful conversations and a supply of the polyamic acid SE1211.
This
work was supported by the Department of Energy’s Office of Basic Energy Sciences under
grant DE-FG02-01ER45934 and by the National Science Foundation’s Solid State Chemistry program under grant DMR-0345109. Acknowledgment also is made to the Donors of
the Petroleum Research Fund, administered by the American Chemical Society, for partial
7
support of this research under grant 37736-AC7.
8
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10
FIGURES
FIG. 1. θ0 vs. nf . Circles correspond to 5CB [Open circles at 25 ◦ C and solid circles at 32 ◦ C],
stars to 6CB, squares to 7CB, and triangles to 8CB [upward triangles at 33.75 ◦ C (about 0.25◦ C
above TNA ), rightward triangles at 34 ◦ C, leftward triangles at 36 ◦ C, and downward triangles
at 38 ◦ C]. Typical horizontal error bars are shown, and are due primarily to the uncertainty in
locating nf = 0. Uncertainty in θ0 ∼ ±2◦ , primarily from the spread in θ0 due to small variations
in rubbing strength.
11
40
Pretilt Angle (Degrees)
35
30
25
20
15
10
5
0
0
1
2
3
-1
Rubbing Strength (cm )
4
6
5 x 10