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