Aging of surface anchoring and surface viscosity of a nematic liquid crystal on photoaligning poly-(vinyl-cinnamate).

Abstract

Dynamic light scattering was used to measure the azimuthal anchoring energy coefficient W(straight phi) of nematic liquid crystal (5CB) on photoaligning poly-(vinyl-cinnamate) layer. Measurements were repeated several times within two months. The results show that W(straight phi) increases in the first few days after filling the cell with liquid crystal. Then it remains approximately constant at W(straight phi)=5 x 10(-6) J/m(2) for at least two months. Also, presence of very large effective surface viscosity is observed. This phenomenon is of transient nature and attributed to swelling and dissolving of photosensitive polymer into the liquid crystal, which gives rise to an inhomogeneity of viscoelastic properties. Numerical modeling of the fluctuation spectrum shows that an inhomogeneous surface layer can account for the observed effective surface viscosity.

Full text

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Aging of surface anchoring and surface viscosity of a nematic liquid crystal
on photoaligning poly-„vinyl-cinnamate…
Mojca Vilfan,1I. Drevens ˇek Olenik,1,2A. Mertelj,1and M. Cˇopic ˇ1,2
1J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
2Department of Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
?Received 12 February 2001; published 23 May 2001?
Dynamic light scattering was used to measure the azimuthal anchoring energy coefficient W?of nematic
liquid crystal ?5CB? on photoaligning poly-?vinyl-cinnamate? layer. Measurements were repeated several times
within two months. The results show that W?increases in the first few days after filling the cell with liquid
crystal. Then it remains approximately constant at W??5?10?6J/m2for at least two months. Also, presence
of very large effective surface viscosity is observed. This phenomenon is of transient nature and attributed to
swelling and dissolving of photosensitive polymer into the liquid crystal, which gives rise to an inhomogeneity
of viscoelastic properties. Numerical modeling of the fluctuation spectrum shows that an inhomogeneous
surface layer can account for the observed effective surface viscosity.
DOI: 10.1103/PhysRevE.63.061709PACS number?s?: 61.30.Hn, 78.35.?c
I. INTRODUCTION
Surface induced alignment of liquid crystals on polymeric
layers is of great importance for operation of liquid crystal
?LC? display devices. Standard method of preparation of
aligning layers is based on mechanical rubbing of the sub-
strate ?usually polyamide or polyimide?. In 1991, Gibbons
et al. proposed a novel way of aligning by introducing pho-
tosensitive layers ?1?. Illumination of such layers with lin-
early polarized light induces surface anisotropy that is
needed for successful alignment. As recent developments
show, this noncontact method seems to be very promising
for applications in the display industry ?2?.
One of the photopolymers that give good alignment of
nematic liquid crystals is poly-?vinyl-cinnamate? ?PVCi?
?3,4?. Although many experiments were made, the origin of
the aligning ability of PVCi is not yet fully understood
?2,3,5–8?. It was also found that the alignment was unstable
on longer time scales ?5?. In order to find the origin of this
instability we studied aging properties of the PVCi-LC inter-
face.
The main parameter describing the orientational interac-
tion between a substrate and a liquid crystal is the anchoring
energy coefficient ?9,10?. Its magnitude is determined by the
torque needed to turn the average molecular orientation ?di-
rector? at the surface away from the direction of the substrate
easy axes. Two separate cases can be considered: the devia-
tion can be either in the plane of the substrate ?azimuthal
anchoring? or perpendicular to it ?polar anchoring?; the polar
anchoring is usually considerably stronger ?9,11?.
The azimuthal anchoring coefficient W?can be measured
by different methods that usually apply an external torque to
the liquid crystal. The torque can be either mechanic ?11–
13?, electric ?14–16?, or magnetic ?17,18?. A major draw-
back of these methods is that the corresponding distortion
can affect the intrinsic alignment of the liquid crystal. To
avoid this possibility and to observe a liquid crystal in un-
distorted configuration we performed the measurements with
a method based on dynamic light scattering ?DLS? ?19–21?
in which we analyze thermally excited orientational fluctua-
tions in a thin liquid crystal slab and hence no external fields
are needed. It is thus particularly appropriate to test the hy-
pothesis indicated recently by Stoenescu et al. ?22? that the
unwinding of twisted nematic cells is a consequence of glid-
ing of the easy axes due to an external mechanical torque and
not of reduced anchoring. In this paper, we present a proof
that the anchoring energy coefficient indeed remains ap-
proximately constant for over two months.
II. ORIENTATIONAL FLUCTUATIONS IN CONFINED
PLANAR GEOMETRY
To obtain the anchoring energy coefficient from the DLS
measurements we first analyze the orientational fluctuations
?n?of the director in a nematic liquid crystal slab. In bulk
samples, where thermal excitations of director orientation are
overdamped plane waves, the spectrum of the fluctuations is
continuous. The relaxation time ? is related to the fluctuation
wave number q by the well-known equation ?23?
???
K
1
q2,
?1?
where K stands for the Frank elastic constant in one constant
approximation, and ? for effective orientational viscosity.
In confined planar geometry, the sample is limited in the
direction perpendicular to the glass plates (z direction? and
the fluctuation eigenmodes are overdamped sinusoidal stand-
ing waves given by the diffusion equation
K?2?n???
?
?t?n?.
?2?
Fluctuations with wave vector parallel to the plates remain
undistorted. The boundary conditions for Eq. ?2? are deter-
mined as the balance of the torque from the bulk elastic
deformations and the surface torque acting on the liquid
crystal at the boundaries,
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K?
?z?n??W??n??z?0,d?0?,
?3?
where d is the sample thickness. The wave numbers qzof
fluctuations in confined planar geometry are then solutions of
the secular equation ?24?
qztan?qz
d
2??W?
K,
?4?
giving a discrete set of allowed values. The ratio of the elas-
tic constant K and anchoring energy coefficient W?is the
extrapolation length ??K/W?. In the case of extremely
strong ?infinite? anchoring, ? is zero and the eigenvalues are
simple functions of the sample thickness,
qzn??n?1??
d
,
n?0,1,2,3, . . . .
?5?
In the case of finite anchoring, Eq. ?4? can be expanded in
terms of small deviations from qzn. If the anchoring is weak,
i.e., the extrapolation length is larger or comparable to the
sample thickness, series expansion of the secular equation
for the relaxation time of the fundamental mode (n?0), tak-
ing into account Eq. ?1?, yields
?0?
?
2W?d,
?6?
thus giving linear dependence of ?0as a function of d. By
measuring ?0at different thicknesses d, and by knowing the
orientational viscosity ?, the anchoring energy coefficient
W?can be obtained.
So far, the dissipation processes at the boundaries have
been neglected. To take into account these effects, an addi-
tional term has to be added to the boundary conditions ?25?,
?K???
?z?W????z?0,d??????
?t
,
?7?
where ?? is the in-plane component of the director fluctua-
tion, i.e.,
????n?•eˆxy.
?8?
The parameter ? represents the surface viscosity, which is
defined as the ratio of the torque needed to change the ori-
entation of the director at the surface for a certain angle and
the corresponding relaxation velocity ?26,27?. In this case the
secular equation, Eq. ?4?, transforms into
qztan?qz
d
2??W?
K??
K
1
?.
?9?
For weak anchoring, series expansion of Eq. ?9? in conjunc-
tion with Eq. ?1? results in the following relation for the
relaxation time ?0of the fundamental mode:
?0?
?
W??
?
2W?d.
?10?
The linear relation between the sample thickness and relax-
ation time is conserved and the anchoring energy coefficient
can still be determined regardless of the surface viscosity.
The surface viscosity only contributes a term independent of
sample thickness. A similar effect can, however, be obtained
also by a different phenomenon, as will be shown in Sec. IV.
III. EXPERIMENT
The aligning substrate used in our experiment was photo-
active PVCi that changes configuration if illuminated with
UV light. Most probably both photoinduced effects, photoi-
somerization and photocycloaddition are responsible for liq-
uid crystal alignment ?5?. Alignment of the liquid crystal is
planar and the molecules are on average oriented in the di-
rection perpendicular to the polarization of UV light.
To attach the aligning substrate to glass plates, PVCi was
dissolved in chloroform at a concentration of 0.05 wt%.
Cleaned glass plates were dipped into the solution, dried and
put for 1 h in a low pressure chamber at 50°C in order to
evaporate the rest of the solvent. The plates were then illu-
minated with linearly polarized UV light for 50 min using
Hg lamp ?Osram Ultra-Vitalux 300 W?. PVCi coated glass
plates were used to make wedge cells as the DLS measure-
ments have to be performed at different cell thicknesses.
Thicknesses of wedge cells were ranging from approxi-
mately 400 nm to 6 ?m and was very accurately determined
by interferometric method using a Hewlett-Packard 8453
UV-Vis spectrophotometer. Easy axes on both plates were
chosen parallel, giving a homogeneous alignment of the liq-
uid crystal.
The liquid crystal used in our experiment was 4-n-pentyl-
4?-cyanobiphenyl ?5CB? from Sigma-Aldrich, which was
used as received. The cells were filled in the nematic phase
with flow direction parallel to substrate easy axes. The ex-
periment was performed at constant temperature, equal to
32°C.
The dynamic light scattering experiment was performed
with a standard photon correlation setup using a Uniphase
He-Ne laser operating at 632.8 nm. The normalized intensity
autocorrelation function, defined as
g(2)?t??
?I?t??I?t??t??
?I?t??? ?I?t??t??
?11?
was measured using an ALV-5000 correlator, which enables
observation of dynamical processes in the range of 10?8s to
103s. During the experiment, the scattering angle was con-
stant and equal to 3° so that the scattering length was always
larger than the sample thickness. For thicknesses up to ap-
proximately 2 ?m we therefore observe only the fundamen-
tal mode of the orientational fluctuations. For larger thick-
ness the influence of higher modes becomes dominant and
will not be discussed here. The polarization of the incoming
light was parallel to the liquid crystal director and the out-
going polarization was orthogonal, as shown in Fig. 1. In
such a scattering geometry (e-o geometry? only the twist
modes of the director fluctuations are observed and they are
determined by the in-plane anchoring.
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An example of measured g(2)is shown in Fig. 2, where
dots represent measured data. The data can be fitted with a
single exponent decay function and because the measure-
ments were performed in a heterodyne regime, the character-
istic decay time is equal to the fluctuation relaxation time ?0.
The best single exponent fit is plotted as a solid line in Fig. 2.
By translating the sample in the direction perpendicular to
the laser beam and not changing any other parameters, the
autocorrelation function and the relaxation time was mea-
sured as a function of sample thickness.
IV. RESULTS AND DISCUSSION
Figure 3 shows a characteristic dependence of the relax-
ation time ?0on the sample thickness d. In the region below
approximately 2?m the data can be fitted with a straight line
in accordance with Eq. ?10? and the slope of the line yields
?/2W?. The value for ??0.03 Pas for 5CB was taken from
the literature ?28?. The anchoring energy coefficient associ-
ated with the data shown in Fig. 3 is W??3.34 (1?0.11)
?10?6J/m2. The observed nonzero value of ?0for d?0
indicates the presence of a surface viscosity ?. It is conve-
nient to present the viscosity ratio h??/?, having the di-
mension of length. The measurement shown in Fig. 3 gives
h?(107?38) nm.
The DLS experiment was repeated several times during a
2-month period and the corresponding time dependence of
the anchoring energy coefficient is shown in Fig. 4. In the
first few days the anchoring energy coefficient increases.
This increase is probably due to induced ordering of the
polymer by the liquid crystal. PVCi is fairly soft and the
strong liquid crystal order can additionally orient the poly-
mer side chains ?29,30?. This process is saturated after one
week, when W?attains a value of approximately W??5
?10?6J/m2. The anchoring energy coefficient then remains
almost constant for another 60 days. The whole measurement
was repeated with two different cells and in both cases the
anchoring energy showed similar behavior.
With these measurements we support the idea that the
unwinding observed in twisted nematic cells ?22? is a conse-
quence of easy axes gliding and that the anchoring energy
coefficient W?does not change significantly on longer time
scales ?31?.
The effective viscosity ratio h shows much stronger time
variation than W?as can be seen in Fig. 5. A very strong
FIG. 1. Schematic illustration of the experiment. Substrate’s
easy axes are parallel to the director n?and to the polarization of the
incoming light i?, while the polarization of the outgoing beam f?is
orthogonal.
FIG. 2. Measured autocorrelation function of dynamically scat-
tered light on nematic 5CB. The dots represent experimental data,
the solid line is the single-exponent decay fit to the data.
FIG. 3. Fluctuation relaxation time ?0plotted as a function of
sample thickness. Circles represent the experimental data obtained
on the second day after filling the cell with the liquid crystal, the
solid line is linear fit. Anchoring energy coefficient is determined
from the slope of the line and the obtained value for this measure-
ment is W??3.34(1?0.11)?10?6J/m2. The effective surface vis-
cosity is h?(107?38) nm.
FIG. 4. Anchoring energy coefficient W?for 5CB on photoac-
tive PVCi as a function of time.
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increase is observed within the first week, when the mea-
sured value changes from initial h?70 nm?45 nm to over
500 nm?60 nm. The effective viscosity then decreases
slowly until it reaches its initial value after approximately 2
months. Very similar behavior was again observed when the
whole set of measurements was repeated with another cell.
The measured values for surface viscosity are surprisingly
large. If the observed effects were indeed a consequence of
pure dissipation processes on the surface, the expected value
of h would be of the order of molecular length. As seen in
Fig. 5, this is not the case. Studying aging of surface viscos-
ity, we see that apparently two processes contribute to the
behavior shown in Fig. 5. We suggest that the increase in the
first week is due to swelling of the photopolymer, and the
slow relaxation process observed in the following 2 months
is a consequence of slow diffusion of polymer molecules into
the liquid crystal. When equilibrium is finally established,
the sample structure is again homogeneous and the apparent
surface viscosity vanishes. This is consistent with the obser-
vations of Perny et al. ?5?, who also proposed swelling as a
possible explanation for alignment instability.
To prove the presented model, we use numerical calcula-
tions to describe how severely the swelling affects the fluc-
tuation modes of the nematic sample. Since the process of
swelling blurs the LC-PVCi interface, it changes the vis-
coelastic properties of the liquid crystal at the boundaries.
First, the dissolved polymer significantly modifies the orien-
tational viscosity of the liquid crystal ?32,33?. It also reduces
the liquid crystal order parameter in the vicinity of the sub-
strate, which results in reduced Frank elastic constant at the
boundary ?23?. Due to these effects, the viscoelastic param-
eters of the liquid crystal become spatially inhomogeneous.
Taking into account the spatial variation in z direction, the
diffusion equation in one dimension is transformed as
K?z??2?n?
?z2??K
?z
??n?
?z???z??
?t?n?
?12?
while the boundary conditions, Eq. ?3?, remain unchanged.
In our calculation the spatial dependencies of orientational
viscosity and Frank elastic constant were taken as
K?z??K0?1?K1e?z/d0?,
?13?
??z???0?1??1e?z/d1?,
?14?
where K0and ?0are the bulk values and K1and ?1are the
amplitudes of the spatial variations. The thicknesses up to
which the contamination effects have a significant influence
on the constants are denoted as d0and d1, whereas the pa-
rameter z runs from the PVCi-LC interface towards the
middle of the cell symmetrically from both plates. The dif-
ferential equation, Eq. ?12?, was then solved numerically and
the eigenvalue of the fundamental mode was calculated as a
function of the cell thickness. Since the elastic constant can
not be expected to vary more than a factor of 2 even at large
polymer concentrations ?32?, it only slightly affects the cal-
culated values for ?0. It was thus for simplicity considered as
spatially independent, i.e., K1was taken to be zero.
The calculations show that for d?0 a nonzero relaxation
time can be obtained only by increased orientational viscos-
ity at the boundaries. An example of calculated dependence
is presented in Fig. 6. Bulk parameters ? and K for 5CB for
this calculation were taken from the literature ?28?. An inter-
mediate surface layer with d1?150 nm was assumed and
orientational viscosity at the boundaries was chosen to be
five times the bulk value accordingly to previously reported
observations ?32?. The calculated relaxation time ?0shown
in Fig. 6 is obviously in good qualitative as well as quanti-
tative agreement with the measured values ?Fig. 3?.
The observed aging phenomenon of the apparent surface
viscosity can also be explained with our model. The increase
of orientational viscosity at the boundaries in the first days
after the filling of the cell, which results in the increase of the
relaxation time at d?0, is induced by swelling of the sub-
strate. This is a fairly fast process compared to the slow
decrease of the relaxation time at d?0 in the following
weeks. This decrease is modeled by an increase of the thick-
ness d1of the contaminated layer, which might be a conse-
FIG. 5. Surface viscosity parameter h for 5CB on photoactive
PVCi as a function of time.
FIG. 6. Numerical calculations of the fundamental mode relax-
ation time as a function of sample thickness. The nonzero value at
d?0 is obtained by spatial variation of the orientational viscosity.
At the boundaries, the viscosity is taken to have five times the bulk
value, and the thickness of the contaminated layer d1is 150 nm.
The dots are numerically obtained relaxation times and the solid
line is linear fit to the data.
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quence of the slow diffusion of the polymer molecules into
the liquid crystal. If ?1is decreased because of finite amount
of dissolved polymer, the constant term in relaxation time is
reduced. When the sample is homogeneous, the term disap-
pears, which is consistent with the experiments. Our results
thus support the hypothesis that the observed large surface
viscosity is not a consequence of the surface dissipation pro-
cess but can be attributed to the spatial variation of the liquid
crystal viscoelastic parameters.
V. CONCLUSIONS
Dynamic light scattering was used to study aging of azi-
muthal anchoring energy of a nematic liquid crystal on pho-
toaligning poly-?vinyl-cinnamate?. The anchoring energy co-
efficient is found to increase in the first few days after filling
the cell with liquid crystal due to reverse influence of large
orientational order of the liquid crystal on the polymer. The
anchoring energy then saturates and remains almost constant
for another 2 months. This proves that the observed unwind-
ing in twisted nematic cells appears because of gliding of
polymer easy axes and not because of reduced anchoring.
Our measurements show also a large effective surface vis-
cosity. This effect may result from spatial variation of liquid
crystal viscoelastic parameters and not from specific surface
dissipation processes. Hence, the influence of polymer swell-
ing has to be considered in analysis of fluctuations in nem-
atic cells.
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