1. Surface alignment and anchoring transitions in nematic lyotropic chromonic liquid
crystal.
V. G. Nazarenko1
, O. P. Boiko1,2
, H.-S. Park2
, O. M. Brodyn1
, M. M.
Omelchenko2
, L. Tortora2
, Yu. A. Nastishin2,3
, and O. D. Lavrentovich2∗
1
Institute of Physics, prospect Nauky 46, Kiev-39, 03039, Ukraine
2
Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242
3
Institute of Physical Optics, 23 Dragomanov str., Lviv, 79005, Ukraine
(Dated: April 30, 2010)
The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be not only planar
(tangential) but also homeotropic, with the self-assembled aggregates perpendicular to the substrate,
as demonstrated by mapping optical retardation and by three-dimensional imaging of the director
field. With time, the homeotropic nematic undergoes a transition into a tangential state. The
anchoring transitions are discontinuous and can be described by a double-well anchoring potential
with two minima corresponding to tangential and homeotropic orientation.
PACS numbers: 61.30.-v ; 42.65.-k ; 42.70.Df
Spatial bounding of a liquid crystal (LC) lifts the de-
generacy of the molecular orientation specified by the
director n and sets an ”easy axis” n0 at the surface.
Deviation of n from n0 requires some work thus estab-
lishing the phenomenon of ”surface anchoring” that has
been explored extensively for the thermotropic LCs [1–
11]. For lyotropic LCs, such as water solutions of poly-
electrolytes, surfactants, dyes, etc., the studies of anchor-
ing are scarce. The view is that the anchoring of lyotropic
LCs is determined by the excluded volume effect, which
favors the longest dimension of building units to be par-
allel to a substrate [12–15]. We demonstrate that for the
nematic lyotropic chromonic LC (LCLC) [16], n0 can be
both parallel to a substrate (planar or tangential align-
ment, denoted ”P”) and perpendicular (homeotropic, or
H alignment), with discontinuos transitions between the
two, thus suggesting that both entropy and enthalpy con-
trol the surface phenomena.
Reversible chromonic assembly and mesomorphism are
displayed broadly by dyes, drugs and nucleotides [16].
In water, LCLC molecules stack face-to-face, forming
elongated aggregates. The aggregates are not fixed
by covalent bonds, being polidisperse with the aver-
age length l ∝
√
φ ln (E/kBT) that depends on tem-
perature T, volume fraction φ, and the stacking energy
E ∼ (4 − 10) kBT [17]. We study disodium cromogly-
cate (DSCG) [16], C23H14O11Na2 (Spectrum Inc, pu-
rity 98%), dissolved in water at 15 wt % (mixture A)
and 12.5wt% doped with 1.5wt% of Na2SO4 (mixture
B). H alignment was achieved by treating glass plates
with 1% water solution of N,N-dimethyl-N-octadecyl-3-
aminopropyl trimethoxysilyl chloride (DMOAP) [2]. The
two plates are separated by Mylar strips; the cell thick-
ness d was measured by light interference technique. The
cells were filled at TNI + 10 K, sealed with UV-cured
Norland epoxy glue, and cooled down to T = 298 K
with a rate 5 K/ min in the thermal stage HS-1 (In-
stec, Inc.). We used LC PolScope for in-plane mapping
of optical retardation R (x, y) =
d
0
|no − neff | dz, where
neff = n−2
o cos2
θ + n−2
e sin2
θ
−1/2
, θ is the angle be-
tween n and the normal z to the cell, no and ne are the
ordinary and extraordinary refractive indices. At 546
nm and T = 298 K, we determined no = 1.37 ± 0.01
and ∆nA = no − ne = 0.020 ± 0.002 for A and ∆nB =
0.015 ± 0.002 for B [18]. To image n (x, y, z), we used
flurescence confocal polarizing microscopy (FCPM), by
doping the sample with 0.003 wt.% of fluorescent acri-
dine orange (AO, Sigma-Aldrich) and probing it with a
focused laser beam [19]. The fluorescence depends on the
angle between n and polarization P of light, being maxi-
mum for P ⊥ n and minimum for P n, suggesting that
AO intercalates between the DSCG molecules.
The initial unaligned texture coarsens and then shows
dark expanding nuclei of the H state that fill the entire
cell, Fig.1. The H alignment is stable as verified by ap-
plying a strong magnetic field, up to 7 kG, to tilt n. Once
the field is switched off, the H orientation is restored. Af-
ter a certain time τH ≈10-20 hours, the LCLC undergoes
an H-P transition through nucleation and expansion of
birefringent domains, Fig.1c,d. These appear not only at
the periphery but also in the middle of samples, Fig.1c.
Two similar cells, one left under normal conditions and
another one immersed in a mineral oil, demonstrated sim-
FIG. 1: Textural evolution of mixture A in the cell with d =50
µm at T = 298 K, between crossed polarizers. Dark nuclei of
the H state appear at τ ≈10 min after the isotropic-nematic
transition (a), H orientation at τ=25 min (b); appearance,
τ=670 min (c) and expansion, τ=810 min (d) of bright P
regions.

2. 2
FIG. 2: H-P transition viewed as (a) grey scale map of R in
the plane of cell (d =12 µm) and as variation of R along the
lines 1,2, and 3 (inset); b) FCPM vertial cross section of a cell
with tilted boundary.
ilar evolution. Therefore, a possible slow drying is not a
major contributor to the effect, although the dynamics
of aggregate assembly most certainly is. The H-P tran-
sition might be direct, with R abruptly changing from
0 to Rmax = ∆nAd, line 1, or through an intermediate
state with R ≈ ∆nAd/2, lines 2, 3 in Fig.2a. The tilt
βx = ∂R/∂x at the states boundaries vary broadly, from
∼100 nm/µm, to ∼1 nm/µm. FCPM of the vertical
cross sections shows that the boundaries represent sharp
walls that are either vertical (larger βx) or tilted (smaller
βx). For example, Fig.2b shows a tilted (∼ 30o
) bound-
ary separating an H sublayer with n||z and P sublayer
with n⊥z; at either of the two H plates, the transition
from n||z to n⊥z is abrupt.
In thermotropic LCs, H-P transitions are continuous
[4, 10]. Discontinuous transitions were reported for in-
plane realignment at anisotropic crystalline substrates
[1, 8] and for patterned plates with spatially varying easy
axis [11]. To quantify the surface effects further, we use
hybrid aligned wedge cells [5], assembled from two dif-
ferent plates, an H plate with DMOAP and an P plate
with buffed polyimide SE-7511 (Nissan). The dihedral
angle is small, < 0.1o
. The cells show a critical thickness
dc at which R (d) changes abruptly, Fig.3, 4. At d < dc,
if the experiment is performed at the beginning of τH for
mixture A, the stable state is the H state; for the case
B, the stable is the P state. At d > dc, R increases with
with d, featuring a slope α = ∂R/∂d; αA = 0.017±0.002
in A and αB = 0.0067 ± 0.002 in B cells, Fig. 3. The
values of dc vary in the range 5-10 µm from sample to
sample, and within the sample, as does α above dc.
FCPM shows that the transitions in the hybrid wedges
feature boundaries that are either vertical, Fig. 4a, tilted
FIG. 3: R(d) for mixtures A and B in the hybrid aligned
wedges
(similar to the one in Fig.2b), or practically horizontal,
Fig.4c. We compare the cross sections of the thin and
thick parts of the same wedge, Fig.4b,c,d. The thin part
is a uniform H state, with fluorescence equally strong
for any in-plane orientation of P, Fig.4b. In the thick
part, Fig.4c, the top 1/3 is occupied with an H layer,
as evidenced in Fig.4d by an overlap of the fluorescence
profiles. In the bottom 2/3, n is close to planar, as the
fluorescence is weak, Fig.4c,d.
The director in a hybrid cell is determined by the bal-
ance of elastic and anchoring forces. At d → ∞, the
conflicting boundary conditions are satisfied by reorient-
ing n from n0⊥z at the P plate, to n0||z at the H plate.
As d decreases, the elastic torque ∝ (θP − θH) /d, de-
termined by the actual polar angles θP and θH at the
plates, becomes stronger, forcing θP and θH to deviate
from their ”easy” values π/2 and 0. At some thick-
ness, the plate with weaker anchoring might give up,
FIG. 4: Vertical FCPM views of the hybrid aligned wedges
with mixture A; (a) vertical boundary between different di-
rector configurations; (b) homeotropic thin, d = 7 µm and
(c) hybrid thick, d = 16 µm, parts of the same wedge and
comparison of their fluorescent profiles (d).

3. 3
allowing n to be uniform. The details depend on the
anchoring potential fs [5]. As shown by Sluckin and
Poniewierski [7], the simplest potential capable to pre-
dict the first-order transitions in semiinfinite samples is
fs = W2(n · z)2
+ W4(n · z)4
. This form also describes
well reorientation of thermotropic LCs by external fields
[3, 6]. For a hybrid cell, the free energy per unit area
should include both anchoring and elastic terms:
f =
1
2
d
0
K(θ)
dθ
dz
2
dz + W2H sin2
θH + W4H sin4
θH + W2P cos2
θP + W4P cos4
θP , (1)
where K (θ) = K1 sin2
θ + K3 cos2
θ, K1 and K3 are the
splay and bend elastic constants, respectively; the an-
choring coefficients satisfy the inequalities W2H > 0,
W2P > 0, W4H > −W2H and W4P > − W2P , to
guarantee the easy axes n0⊥z at the P plate and n0||z
at the H plate. For analytical treatment, we assume
K1 = K3 = K and keep θ fixed at the plate with a
stronger anchoring, as supported by FCPM, Fig.2b, 4.
For the case A, θH = 0, thus f = fP (θP ) =
Kθ2
P /(2d) + W2P cos2
θP + W4P cos4
θP . The values of
θP that minimize fP are found from the conditions
∂fP /∂θP = 0 and ∂2
fP /∂θ2
P > 0. When d → ∞
and W4P < −W2P /2, fP has an absolute minimum at
θP = π/2 and a local one at θP = 0. The two are sep-
arated by a barrier at θP b = arccos − W2P
2W4P
. For finite
d >> K/W2P , fP with −W2P < W4P < −W2P /2 pre-
serves its double-well features. In particular, θP = 0
is still a local minimum. The coordinate θP,min of the
absolute minimum, however, becomes smaller than π/2,
because of the elastic torque ∝ θP /d. We evaluate
fP near θP ≈ π/2 to find θP,min ≈ π
2 1 − K
2dW2P +K .
The difference ∆fP = fP (θP min) − fP (0) vanishes at
d0P ≈ π2
K
8(W2P +W4P ) . For d < d0P , the uniform H state
θ (z) = 0 is stable, while for d > d0P , the hybrid state
has the lowest energy. The transition is discontinu-
ous, with a big jump ∆θP ≈ π3
8(1+W4P /W2P )+2π2 in the
range 1.31 ≤ ∆θP ≤ 1.57 that corresponds to the lim-
its −W2P < W4P < −W2P /2. Similarly for the case B,
θP = π/2 and f = fH (θH) = K (π/2 − θH)
2
/(2d) +
W2H sin2
θH + W4H sin4
θH. There is a critical thick-
ness d0H ≈ π2
K
8(W2H +W4H ) below which the uniform P state
θ (z) = π/2 is stable and above which the hybrid state
with θH min = π
2
K
2dW2H +K << 1 is stable. The transition
is discontinuous in θH. The qualitative features of this
analytical description remain intact when the full form
of f in Eq.(1) is analyzed numerically.
The thickness d0 should not be confused with the ex-
perimental dc. These two in the first order transitions
are very different, because of the barriers featured by fP
and fH, and because of the surface defect of line ten-
sion ∼ K that separate areas with a different tilt. These
defects are seen as cusps in the R (x) dependencies in
Fig.2a. The nuclei of new alignment should be of a size
exceeding ∼ K/ |∆f| to overcome the nucleation barrier
∼ K2
/ |∆f| and expand. The maximum ∆f is W2 +W4.
To estimate W2 +W4, we first recall that the entropy con-
tribution to the surface energy of a LC formed by long
units is [12] σ ≈ kBT ln l
A , where A ≈5 nm is the distance
between the axes of aggregates [16]. For DSCG, l/A ∼ 10
[20], so that σ is a few units of kBT, the same order of
magnitude as the stacking energy E [17]. Thus W2 + W4
is expected to be on the order of ∼ kBT/A2
∼ 10−4
J/m2
.
This estimate, together with K ∼ 10 pN [21], leads to d0
∼ 0.1 µm, much smaller than dc ∼ 10 µm. The reason is
the large nucleation barrier ∼ K2
/ (W2 + W4) ∼ 10−18
J
>> kBT, which signals that nucleation is heterogeneous
(assisted by inhomogeneities). This feature leads to the
important conclusions that in our system, the metastable
states can be long-lived (an analog of a strongly ”super-
cooled” phase) and that the spurious R, α, and β are
related to factors such as surface roughness. The esti-
mates above are rough and might be altered by factors
such as electrostatic interactions, non-analytical form of
the anchoring potential, etc. However, the main feature,
a strongly discontinuous character of transformations, al-
lows to explain qualitatively the effects such as dc = d0.
The general expression R =
d
0
|no − neff | dz trivially
fits the data in Fig.3 at d < dc, with α=0 in the H
state and α ≈ ∆nB= 0.015 in the P case. For the
deformed states at d > dc, the classical approach is
that the dependencies R (d) are determined by smooth
variations of n with a constant scalar order parameter
S. For the A case, RA (θP ) = dJ(θP , 0)/I(θP , 0), while
for the B case, RB (θH) = dJ(π/2, θH)/I(π/2, θH),
where J (ζ, η) =
η
ζ
K (θ) (no − neff ) dθ,
I (ζ, η) =
η
ζ
K (θ)dθ [5]. For K1 = K3 = K,
RB (d) = d∆nB (π − 2θH + sin 2θH) / (2π − 4θH) and
αB = ∂RB/∂d = ∆nB
2 1 + π2
24
K3
W 3
2H d3 = 0.0075 or
larger at d > dc. The experimental αB = 0.0067 is
by 10% smaller. The difference can be accounted for

4. 4
by the fact that K1 < K3. Numerical evaluation of R
with K1 = K3 shows that αB = 0.0067 corresponds
to K1/K3 ≈ 0.4, a reasonable result [21]. For αA, a
reasonable explanation is much harder to arrive at. The-
oretically, in A case, RA = d∆nA (θP − sin 2θP ) /2θP ,
and αA ≈ ∆nA
2 1 − K2
2W 2
2P d2 0.01. The experimental
value αA ≈ 0.017 is 70% larger. The discrepancy
cannot be explained by K1/K3 = 1. To show this, we
assumed θP = π/2 (to maximize the theoretical αA)
and then evaluated R for K1/K3 = 1. By changing
the ratio K1/K3 in the range 10−5
to 105
, we find αA
changing from 0.0067 to 0.0133, still smaller than the
experimental value. In principle, αA ≈ 0.017 can be
obtained by allowing a nonzero θH ≈ 0.1. However,
with θH ≈ 0.1, one should measure, say R ≈148 nm at
d = 8.7 µm, and the actual result is much smaller, R
≈93 nm, Fig.3. We thus associate the spurious data on
α and R at d > dc with the tilted sharp boundaries such
as the ones shown in Fig.2b and 4c,d, with spatially
varying coordinate zb = zb (x, y). The boundaries
with sharply varying n imply a changing degree of
orientational order S. The latter is expected to happen
through the ”interchanging eigenvalues” of the tensor
order parameter in thin hybrid aligned cells [22] with
d ≈ ξbx, where ξbx is the biaxial correlation length. In
thermotropic nematics, ξbx = (10 − 100) nm, but in
LCLCs, we expect ξbx to be much larger, especially
when the structure reconstructs itself as a result of
anchoring transition and applied elastic or field torque.
In the transient regime, the gradients of the scalar
order parameter can be accommodated by redistribution
of the short and long aggregates in the intrinsically
polydisperse LCLC.
The experiments suggests the following basic features
of anchoring in LCLCs. (1) There are two possible easy
directions n0, a tangential (planar) and a homeotropic
one. In DSCG, the H alignment is stable only within a
finite period of time τH (hours and days). The anchoring
transitions are strongly discontinuous. These features are
described by double-well potentials with the local minima
at θ = 0 and π/2, separated by an energy barrier. (2)
The transient nature of H alignment and its spontaneous
transformation into the P state is the most intriguing
feature. In terms of the surface potential W2H sin2
θH +
W4H sin4
θH, this H-P transition at the DMOAP plate
corresponds to the change from W2H +W4H > 0 to W2H +
W4H < 0. Sluckin and Poniewierski [7] related W2H
and W4H to the temperature dependence S(T) so that
the transitions are temperature-driven. In our case, the
changes in W2H and W4H are of a kinetic nature. Since
the H state is observed after the samples are cooled down
from the isotropic phase, it should be accompanied by the
growth of aggregates, as l ∝
√
φ ln (E/kBT). Short and
long aggregates might align differently at the substrates,
say, normally and tangentially, entropy effect being one
of the reasons. With time, the aggregates grow further,
which might trigger an anchoring transition.
We are grateful to anonymous referee for useful sug-
gestions. The work was supported by NSF Materials
World Network on Lyotropic Chromonic Liquid Crystals
DMR076290, ARRA DMR 0906751, Ohio Research Clus-
ter on Surfaces in Advanced Materials, NAS of Ukraine
Grant #1.4.1B/109, Fundamental Research State Fund
Project UU24/018, and by the Ministry of Education and
Science of Ukraine, Project 0109U001062.
∗
Electronic address: olavrent@kent.edu
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