The anisotropic Lilliput Recent Advances on Nematic Order Reconstruction: Nematic Order Dynamics...
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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 CalabriaCNR-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 IE2,
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=0topological barrier (defects, 2D-wall)biaxial intermediate order inside a calamitic materialbiaxial coherence length B 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 fieldG. 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
Mechanically Induced Biaxial Transition in a Nanoconfined Nematic Liquid Crystalwith a Topological Defect
G. Carbone, G. Lombardo, R. Barberi, I. Musevic, U. Tkalec, Phys. Rev. Lett. 103, 167801 (2009)
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 -cell
ns
ns
n
Planar texture Twisted texture
ns
ns
n
• 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, -Bulk order reconstruction (dynamical G.Virga, EPJ E 13 (2004) 61 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
-cell:distortions in presence of field
The starting splay configuration gives suitable conditions to concentrate all the
distortion in the middle of the-cellunder electric field E
This process depends on the biaxial coherence length B
* of the nematic material *F. Bisi, E. G. Virga, and G. E. Durand, Phys. Rev. E 70, 042701 (2004)
E
bS
LB
The biaxial transition: textures
E<Eth
E>Eth New Topology
E=0
E=0
E
E
S SW
BT
E=0 V E=3.5V E=3.5V
E=3.5V E=0 V E=0 V
SS S
S S S
SW SW
SW
B T T
S → splaySW → splay + biaxial wallB → bendT → twist
Textures slow dynamics
Director in a π-cellTextures in a π-cell
Textures slow dynamics
S SW
BT
S → splaySW → splay + biaxial wallB → bendT → twist
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)
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.
Time/ms
Space (units of )
Numerical model: symmetric caseG. Lombardo, H. Ayeb, R. Barberi, PRE 77, 051708 (2008)
P. S. Salter et al PRL 103, 257803 (2009)
Fluorescence image showing the evolutionof the LC director field with time.
Fluorescence confocal polarising microscopy of a -cell
Time resolved experimentsR.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
th ≤ 80 sec
How fast is Order Reconstruction?
Electric current flowing in a -cell at 40 KHz
The order reconstruction takes place on a timescale of about 10 sec. th ≤ 10 sec
Experiment Numerical Model
(s)
Asymmetric -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)
PI2% PI10% PI20 SiOOblique SiOPlanar
s(degrees) 2.00.2 6.00.4 8.00.4 29.00.6 0.50.4
W 10-4 (J/m2) 1.00.2 2.00.3 2.50.5 1.50.4 1.00.2
[1] I. Dozov, M. Nobili, G. Durand, Appl. Phys. Lett. 70, 1179 (1997)
Experiments with asymmetric cells and strong anchoring
Symmetric cell
Suitable dopants can control the nematic biaxial coherence length in a calamitic nematic
Asymmetric cellDopants are effective also on the surface. And the anchoring breaking?To be published on APL (2010)
F.Ciuchi, H. Ayeb, G. Lombardo, R. Barberi, G. Durand, APL 91, 244104 (2007)
Parallel configuration
Anti-parallel configuration
The cut depends on the texture !
Distortions in presence of field
E
E
bulk effect
surface effect
Bulk or Surface transitions ?
1E-4 1E-3 0,01 0,1 1 100
10
20
30
40
50
60
Tc-8.2 Tc-5.2 Tc-3.2 Tc-1.2 Tc-0.2
Vol
t/m
(msec)
0,1 1 100
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32 5CB in a high-treshold cell
Tc-0.7 Tc-0.6 Tc-0.5 Tc-0.4 Tc-0.3 Tc-0.2
Vo
lt/m
(msec)
Bulk transition Surface transition
5CB and strong anchoring case
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 electro-
optics 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
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 B, is a parameter of the third order term in the Landau-De Gennes Q-model
F. Bisi, E. G. Virga, and G. E. Durand, Phys. Rev. E 70, 042701 (2004)
by varying B, one can favour or inhibit the transient biaxial order of a calamitic nematic
bS
LB
22 3 22
3 2t
b cF a tr Q tr Q tr Q
F.Ciuchi, H. Ayeb, G. Lombardo, R. Barberi, G. Durand, APL 91, 244104 (2007)
Electro-optical experimental set-up
L.C.
glass plate
glass plate
E