The anisotropic Lilliput
Recent Advances on Nematic Order
Reconstruction: Nematic Order Dynamics
Riccardo Barberi,
Giuseppe Lombardo, Ridha Hamdi, Fabio Cosenza,
Federica Ciuchi, Antonino Amoddeo
Physics Department, University of Calabria
CNR-IPCF- LiCryL – Liquid Crystal Laboratory
Rende, Italy
Nematic Liquid Crystals (NLC)

The Nematic phase is the simplest LC:

elongated molecules

no positional order

only orientational order

high sensitivity to external fields

optical and dielectric anisotropy

flexoelectric materials (abused …)

uniaxial symmetry

NLC have been used for first displays since 1960 and
are currently used for commercial LCDs

Something new for fundamental ideas and/or applications?
Biaxial Coherence Length, Bistable e-book readers (ZBD, HP, Nemoptic +
Seyko, …) …
Textural NLC transitions
Fixed Topology
 Freedericksz transition: slow, non polar IE2,
continuous distortion of the same texture (S is constant, n rotates)
monostable because only one equilibrium state at E=0
Variable Topology
 Anchoring breaking
 Defects creation/annihilation
 Nematic order reconstruction by mechanical constraint
 Nematic order reconstruction under electric field
spatial variation of S without rotation of n
at least 2 equilibrium states with different topology at E=0
topological barrier (defects, 2D-wall)
biaxial intermediate order inside a calamitic material
biaxial coherence length xB to be taken into account
Static Order Reconstruction:
Defect core structure of NLC
N. Schopohl and T. J. Sluckin, PRL 59 (1987) 2582
Biaxiality of a nematic defect
Dynamics of a nematic defect under electric field
G. Lombardo, H. Ayeb, R. Barberi, Phys. Rev. E 77, 051708 (2008)
3D extension
by Kralj,
Rosso, Virga,
Phys. Rev.E
81, 021702
(2010)
Presented this
morning at this
conference
G. Carbone, G.
Lombardo, R. Barberi,
I. Musevic, U. Tkalec,
Phys. Rev. Lett. 103,
167801 (2009)
Mechanically Induced
Biaxial Transition in a
Nanoconfined Nematic
Liquid Crystal
with a Topological Defect
Topographic pattern induced homeotropic alignment of l.c.
Y.Yi, G.Lombardo, N.Ashby, R Barberi, J.E. Maclennan, N.A. Clark, Phys. Rev. E 79, 041701 (2009)
Down to 200 nm
Dynamical Order
Reconstruction: the p-cell
ns
ns
n
ns
n
ns
Planar texture Twisted texture
• L.Komitov, G.Hauck and H.D.Koswig, Phys. Stat. Sol A, 97 (1986) 645
- First experimental observation
• I Dozov, M Nobili and G Durand, Appl. Phys. Lett. 70, 1179 (1997)
-Anchoring Breaking
• Ph.Martinot-Lagarde, H.Dreyfus-Lambez, I. Dozov, PRE 67 (2003)051710 -Bulk biaxial configuration (static model)
• R.Barberi, F.Ciuchi, G.Durand, M.Iovane, D.Sikharulidze, A.M.Sonnet,
G.Virga, EPJ E 13 (2004) 61
-Bulk order reconstruction (dynamical
model)
• R.Barberi, F.Ciuchi, G.Lombardo, R.Bartolino, G.Durand, PRL., 93, (2004) 137801
• S.Joly, I.Dozov, Ph. Martinot-Lagarde, PRL, 96, (2006) 019801
• R.Barberi, F.Ciuchi, H.Ayeb, G.Lombardo, R.Bartolino, G.Durand, PRL., 96, (2006) 019802
p-cell:
distortions in presence of field
The starting splay configuration gives
suitable conditions to concentrate all the
distortion in the middle of the p-cell
under electric field E
x
E
This process depends on the biaxial coherence
length xB* of the nematic material
*F. Bisi, E. G. Virga, and G. E. Durand, Phys. Rev. E 70, 042701 (2004)
xB 
L
bS
The biaxial transition: textures
E<Eth
S
E=0
E
SW
E>Eth
New Topology
T
E=0
B
E
S → splay
SW → splay + biaxial wall
B → bend
T → twist
Textures slow
dynamics
E=3.5V
E=0 V
S
SW
SW
S
E=0 V
T
T
S
SW
E=0 V
E=3.5V
B
S
E=3.5V
S
S
S → splay
SW → splay + biaxial wall
B → bend
T → twist
Textures slow
dynamics
Textures in a π-cell
S
SW
T
B
Director in a π-cell
Fast Dynamics of Biaxial Order
Reconstruction in a Nematic
R.Barberi, F.Ciuchi, G.Durand, M.Iovane, D.Sikharulidze, A.Sonnet, E. Virga, EPJ E 13,61 (2004)
Space
(units of x)
Time/ms
Eigenvalues of Q in the centre of the cell during the transition.
The largest eigenvalue 1 at t =0 corresponds to the eigenvector of Q parallel to the
initial horizontal director: it decreases as time elapses, while the eigenvalue 2
corresponding to the eigenvector of Q in the direction of the field increase.
Numerical model: symmetric case
G. Lombardo, H. Ayeb, R. Barberi, PRE 77, 051708 (2008)
Fluorescence confocal polarising
microscopy of a p-cell
Fluorescence image showing the evolution
of the LC director field with time.
P. S. Salter et al PRL 103, 257803 (2009)
Time resolved experiments
R.Barberi, F.Ciuchi, G.Lombardo, R.Bartolino, G.Durand, PRL, 93 (2004) 137801
S.Joly, I.Dozov, and P.Martinot-Lagarde, Comment, Phys. Rev. Lett. 96 (2006) 019801
R.Barberi, et al., Reply, Phys. Rev. Lett. 96 (2006) 019802
tth ≤ 80 msec
How fast is
Order Reconstruction?
Electric current flowing in a p-cell at 40 KHz
(s)
Experiment
The order reconstruction takes place
on a timescale of about 10 msec.
Numerical Model
tth ≤ 10 msec
Asymmetric p-cells
In asymmetric cells the biaxial wall is created close to a boundary surface
Close to a surface the topology could be changed by anchoring breaking,
which requires weak anchoring
G Barbero and R Barberi, J. Physique 44, 609 (1983)
I Dozov, M Nobili and G Durand, Appl. Phys. Lett. 70, 1179 (1997)
Numerical model:
asymmetric case (strong anchoring)
Experiments with asymmetric
cells and strong anchoring
PI2%
PI10%
PI20
SiOOblique
SiOPlanar
s(degrees)
2.00.2
6.00.4
8.00.4
29.00.6
0.50.4
W 10-4 (J/m2)
1.00.2
2.00.3
2.50.5
1.50.4
1.00.2
[1] I. Dozov, M. Nobili, G. Durand, Appl. Phys. Lett. 70, 1179 (1997)
Suitable dopants can control the
nematic biaxial coherence length in
a calamitic nematic
Symmetric cell
F.Ciuchi, H. Ayeb, G. Lombardo, R. Barberi, G.
Durand, APL 91, 244104 (2007)
Asymmetric cell
Dopants are effective also on the
surface.
And the anchoring breaking?
To be published on APL (2010)
The cut depends on the texture !
Parallel
configuration
Anti-parallel
configuration
Distortions in presence of field
bulk
effect
x
xE
surface
effect
xE
Bulk or Surface transitions ?
5CB and strong anchoring case
Tc-8.2
Tc-5.2
Tc-3.2
Tc-1.2
Tc-0.2
60
32
5CB in a high-treshold cell
30
28
50
Tc-0.7
Tc-0.6
Tc-0.5
Tc-0.4
Tc-0.3
Tc-0.2
26
24
22
20
Volt/mm
Volt/mm
40
30
20
18
16
14
12
10
8
6
10
4
2
0
1E-4
0
1E-3
0,01
0,1
t(msec)
Bulk transition
1
10
0,1
1
t(msec)
Surface transition
10
Conclusions
 Nematic Biaxial Order Reconstruction is a really fast phenomenon





(<=10 msec)
Nematic Biaxial Order Reconstruction must be taken into account
also in the case of surface effects
Anchoring breaking needs a reinterpretation
A tool for a better understanding of confined and highly frustrated
systems
Possibility of novel sub-micro/nano devices for photonics or electrooptics
Note that the Biaxial Order Reconstruction is often present in many
kinds of known nematic bistable devices.
This not only true for Nemoptic-Seyko technology, but even when only defects are
created or destroyed. In the cases, for instance, of “zenithal bistable electro-optical
devices” and “postaligned bistabile nematic displays” whose behavior can therefore
be improved by a suitable control of the biaxial coherence length
Biaxial coherence length
 The biaxial order in a calamitic nematic is mainly governed by the biaxial
coherence length
xB 
L
bS
where L is an elastic constant, b is the thermotropic coefficient of the
Landau expansion and S is the scalar order parameter
 b, and hence xB, is a parameter of the third order term in the Landau-De
Gennes Q-model
2
2b  3  c   2 


Ft  a  tr  Q  
tr  Q    tr  Q  
  3   2   
2
F. Bisi, E. G. Virga, and G. E. Durand, Phys. Rev. E 70, 042701 (2004)
 by varying xB, one can favour or inhibit the transient
biaxial order of a calamitic nematic
F.Ciuchi, H. Ayeb, G. Lombardo, R. Barberi, G. Durand, APL 91, 244104 (2007)
Electro-optical
experimental set-up
glass plate
E
L.C.
glass plate