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  E 2, 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  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 field G. Lombardo, H. Ayeb, R. Barberi, Phys. Rev. E 77, (2008) 3D extension by Kralj, Rosso, Virga, Phys. Rev.E 81, (2010) Presented this morning at this conference

Mechanically Induced Biaxial Transition in a Nanoconfined Nematic Liquid Crystal with a Topological Defect G. Carbone, G. Lombardo, R. Barberi, I. Musevic, U. Tkalec, Phys. Rev. Lett. 103, (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, (2009) Down to 200 nm

Dynamical Order Reconstruction: the  -cell Planar textureTwisted texture L.Komitov, G.Hauck and H.D.Koswig, Phys. Stat. Sol A, 97 (1986) 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) 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) S.Joly, I.Dozov, Ph. Martinot-Lagarde, PRL, 96, (2006) R.Barberi, F.Ciuchi, H.Ayeb, G.Lombardo, R.Bartolino, G.Durand, PRL., 96, (2006)

 -cell: distortions in presence of field The starting splay configuration gives suitable conditions to concentrate all the distortion in the middle of the  -cell under 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, (2004) E

The biaxial transition: textures E<E th E>E th New T opology E=0 E E S SWSW B T

E=0 V E=3.5V E=0 V S S S SS S SWSW SWSW SWSW B T T S → splay S W → splay + biaxial wall B → bend T → twist Textures slow dynamics

Director in a π-cell Textures in a π-cell Textures slow dynamics S SWSW B T S → splay S W → splay + biaxial wall B → bend T → 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 case G. Lombardo, H. Ayeb, R. Barberi, PRE 77, (2008)

P. S. Salter et al PRL 103, (2009) Fluorescence image showing the evolution of the LC director field with time. Fluorescence confocal polarising microscopy of a  -cell

Time resolved experiments R.Barberi, F.Ciuchi, G.Lombardo, R.Bartolino, G.Durand, PRL, 93 (2004) S.Joly, I.Dozov, and P.Martinot-Lagarde, Comment, Phys. Rev. Lett. 96 (2006) R.Barberi, et al., Reply, Phys. Rev. Lett. 96 (2006)  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%PI20SiO Oblique SiO Planar  s (degrees) 2.0      0.4 W (J/m 2 ) 1.0      0.2 [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 cell Dopants 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, (2007)

Parallel configuration Anti-parallel configuration The cut depends on the texture !

Distortions in presence of field bulk effect surface effect

Bulk or Surface transitions ? Bulk transitionSurface 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, (2004)  by varying  B, 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, (2007)

Electro-optical experimental set-up